فشرف بالاشتغالي بالعلم ولا تبغي به ما عشت يا بدا بدا وياله من شراف عظيمي الآخر شيء is ويعتقد كمال أهلية ورجحانه على قبقة you also need to know that your teacher is more capable than all his peers that's what you need to believe as a teacher that my teacher is far greater than his peers that's what I believe that's what a student of knowledge should believe regardless of his teacher he shouldn't say oh teacher so and so I think he's better than you he should not say that but he should believe that the teacher he's taking from is greater than the rest the reason why because that's the closest from you to benefit from him if you believe in your heart there's somebody out there like I know he's better than my teacher are you going to benefit fully from your teacher no you're not but once you believe that your teacher is the one who knows it all he knows it better than his peers you're going to fully benefit from him and take what he has to offer all of this is for your own self it's for you to actually trust your teacher open up to your teacher some of those who came before us would offer something in charity on their way to their teachers look at the Salaf they used to go out before they come to the حلقة they would go on their way they would give charity on their way on behalf of their teacher and they would make this دعاء تصدق بشيء he would give something in charity before he comes to the gathering before he comes to gain knowledge from his teacher all the way to the class the student what he would do is he would pay he would give صدق on the way and he would say this دعاء what would he say and they would stop the page saying oh well do not disclose their shortcomings to me and do not take away the lessons of their knowledge from me this is what they would say لا بستر عيبا معاليبي عني ولا تذهب بركة علمه مني oh well cover from me veil from me the shortcomings and the mistakes of my teacher do not show that to me ولا تذهب بركة علمه مني and oh well do not take away from me the blessings of his knowledge that which he has do not take it away from me imagine the one who is going out of his way he is looking for his teacher's mistakes he is actually looking for his teacher's mistakes really let's verify that did he say that okay let's verify that everything that the teacher says you go out of your way you want to verify it about him about him so you can what so you can have something against him سالفوا هذي أمه they would ask Allah not to show him they would ask Allah to protect him from it they would turn a blind eye towards their teacher even if they saw something they would say I did not see it they did not want to know any of that imagine a lady in your own winch and goes out and even posts and tweets and comments the shortcomings of his teacher what do you imagine what do you imagine as I said before to you the one who is teaching you the person you are taking knowledge from is a person who is inherited whose position the prophet's position and this is the way you deal with a person who is inherited the prophet's the prophet's knowledge is this how you deal with a person who is sitting in the position of the message and I said this before to you that the scholar and the person of knowledge the thing that they inherit is not just knowledge they also inherit the respect that the prophet are given they inherit part of that the scholars and the people of knowledge and your teachers what they inherit as well is the respect that you would give to the prophet you give it to them as well تعظيم and I they gain that as well now ربيع the companion of here is الربيع ابن السليمان المرادي الربيع ابن السليمان المرادي هو الصاحب الشافعي يتمد الشافعي he was a student of the one who inherited the kitab of the Umm فمن مم الشافعي رحمهم الله تعالى he said الربيع ابن السليمان المرادي يتمد الشافعي he said the following may Allah have mercy on both of them one said I never had the courage to drink even a sip of water in the presence of Imam Shafi'a in veneration of him الله أكبر some narrations they mention ما تصفحت ورق I never turned over a page some other narrations mentioned that I never turned a page over in the presence of an Imam Shafi'a I never did that in veneration respect glorify honoring him رحمه الله تعالى I never and here he said I never drank a water in front of Imam Shafi'a ever then imagine a student that comes in front of his teacher kisses his teacher talks back at his teacher says to his teacher وعا really forget that questions his teacher's statements questions his teacher what's the validity of this خابة وخسر خابة وخسر that person has become destroyed في الدنيا ولااخرة he has و لذلك قد نقل it was transmitted it was transmitted from ألمام عليم بنبي طالب رضي الله عنه that he said من علمني حرفاً سرت له عبد and then he would reach a letter letter I will be enslaved for them meaning I will be enslaved to that person they will kind of own me now respect and honor نقل some scholars have done اعتراد of that statement they didn't accept it a slave here doesn't mean the slavery of Allah it means slave as in like the way you master tells his slave what to do my point here is that the status of the person who teaches you is something that has become very little in the eyes of students of knowledge they learn after their teacher and they genuinely think and a lot of the time if you look at them they still don't know more than their own teacher they still don't الله I was recently told one of the Mashayikh in Somalia some of his students graduated from Medina University they went and they graduated from Medina University and their teacher is one of the most most knowledgeable scholars in the country they went they came back and they resided in the same places of course and now what they're saying is that he doesn't know we know because they're graduates from the university of Medina so they open an institute right next to his one and they're teaching but الله الله I say by Allah's name he's still more knowledgeable than them even though they're still graduating that just shows you what our English can seat be full of yourself like these people are going to be the home of knowledge knowledge is going to be protected from it and I've seen genuinely speaking it was all honesty and when I say this this is not a consistent blame at everybody but generally speaking people who graduate from prestigious universities are the ones who are filled with arrogance صلاحة and if you look at a lot of them they have the least knowledge they have the least knowledge the ones who graduate from universities they have and they genuinely do have less knowledge then the ones who've what who studied the most the classic way they start with the بشايف and the علماء and took knowledge from them so humbleness is needed the person who taught you is always somebody you honor and you respect even if you differ with them or a مسألة you always respect them you always respect them the leader of the faithful Ili Ibn Ali Terbid may Allah be pleased with him said among the rights of the squalor above you the students is that upon coming to a lesson you should you should greet him everyone else in general you should sit in front of him and never point with your hand in this presence the author here now mentions Ili Ibn Ali the things that he said that the right of the scholar is here he means teacher of course is and to send him that the rest of the people you say generally but the teacher you don't do that he's not like the rest of the people you come and give them that's him okay وان تجلس أمامه as for the teacher you sit in front of him that's another one وَلَا تُشِيرَنْ عِنْدَكَ بِيَدِكَ don't point at him you don't do that yeah you must not wink at anyone or make similar gestures nor tell your teacher that such and such person has said something contrary to the teacher don't in the teacher's gathering وَلَا تَعْزَمِ زَنَّبِ عِنَيكِ and you don't wink like that in front of your teacher sometimes some people what we take that statement as well is laughing in front of your teacher he says something you find conferences that you go to the Mashaikh they make a joke and what do you find when the Mashaikh make a joke some people are laughing it's all Adam why are you laughing for it's bad manners it's truly bad manners when the Sheikh is talking when the Mashaikh come winking in front of the Sheikh he will think you're talking about him they think it's something that you said something he said you're laughing about you see it's not good don't say to your teacher someone so sick different to what you said you come to your teacher and you say oh you said that well another Sheikh I went to or another person I know said different to what you said don't say that to him don't oppose your teacher don't say Fulan opposes you in this don't say Alan opposes you in this don't say that to him now do you not backbite anyone in front of him don't backbite anyone in front of him don't say oh it's Fulan is this that's disrespecting him now don't consult with anyone else in this presence don't speak to other students and and you consult them and you take their advice on board when he's there no you don't do you do when you have water but the teacher is the water and the students are the when the teacher is absent within yourselves you can consult one another if the teacher is there then you take it from him why are you going to go to the students disrespecting him again do you not grab his garment when he stands up appealing for him to wait some people they grab the teacher can I talk to you or disrespectfully put their hand on your shoulder grabbing you from the shoulder you don't touch the teacher you never ever touch you never place a finger on the teacher who gave you the rights to touch your teacher you touch him put his hand on you grab you by the shoulder put his hand on your your head to the teacher all of those are one brother told me one time شعب درشيل علي سوفي came and one of the kids what he did was he wanted to do a picture with the sheikh and what he did was he grabbed him by the shoulder like a friend just like a friend he put his hand over the sheikh and he said sheikh come close let's take the picture هؤلاء يضرب بالجريد والنعب those people should get beaten with yeah they should get laughed سوء الأدبلي who gave you the rights to put your hand on the sheikh all of these are bad manners that you see manifest in many of us we don't tend to see the seriousness of it you see don't grab his garment you should you should insist that he teaches if he becomes tired you see the teacher sleeping he's tired he's finished he's taught you as much as he could don't persist on him after you saw his tired this is disrespecting him again if he does اعدار and says I can't do it like that don't push him to it if he says I don't want to do that what about this what about this it's annoying don't do that if he becomes lazy and tired from doing something do not do إلحاح إلحاح means you persistently go on to him too much down and do you not allow yourself to grow tired or bored of his continued don't say to a teacher I can't hang around with him I can't be bothered I don't want to لا do not give up on that ولا تعلن never tell away from from your teacher من طول صحبتي the lengthy companionship of his لذلك it's one of the reasons no chef he mentions أخي لان تلال العلم إلا بسيتة سأوم بك عن تفصيلها ببياني my brother you're not going to attain knowledge unless you take six steps and from them is صحبة أستاذ وطول زمان صحبة أستاذ for the companionship of a teacher so he never gets tired of that إلا تشبع never get tired of it and say oh I saw him yesterday I don't want to say today no worries I'm not going to meet him don't never get tired of his companionship all of these are respect of the student towards the teacher No A student should indeed strive to adorn himself with the qualities pointed out by عادي عبeee أنا شعوره may Allah be pleased with him he should defend his teacher upon hearing others و لو كان يستطيع أن يكون ذلك ، يجب أن يكون لتواجه في مكان التنظيم يجب أن يأتي إلى شخصه ، و يبقى كل أعلى قواته و as well as the qualities referred to with regards to the teacher in the previous segment يجب أن يكون في سطة ربشوالة تحديد من المستوى و يجب أن يكون لديه حالة بكل ما يرامله هل الوثى رحم الله يمكّذ و يبقى أن يتقدم بهذه الشصال التي أرشدها؟ أرشد إليها عليهم كل من هؤلاء المشاهدات التي نتكلم عنها وعالي ستبقى مجموعة من العلم يجب أن يأتي مع هذه الستابعات من عالي من أبيع طالق يجب أن يدعوه معه يجب أن يأتي مع هذه المشاهدات مجموعة أخرى هو أن يرد غيبة الشيخين قدر وإذا كانت تساعدتك في مجموعة مجموعة يجب أن تدفعه ويدفع المشاهدات التي أقوم بها هذا حقه لك هذا هو الحق الذي يجب عليك إذا كان يجب أن يتكلم عنه إذا كان يتكلم عنه always dare to defend him never will I take that from you No, my teacher is not that I don't accept that وعي رد غيبة الشيخين قدر نعم وردارك اللي براسة السلامي يقول من دبه عم عربي أخي anyone who defects the honor of his brother or sister الله will defend your honor the day of judgment your honor will be defended and it will be protected the day of judgment That's just a normal Muslim person فمبالك would you then think the person who has Minnah on you after your parents when did your parents give you brothers and sisters the scholars they say that the teacher is of the manzilla of your parents you know why the reason is because your parents gave you the worldly life and this one gave you the hereafter life you're living in this world because of your parents bringing you to this world you live you breathe because of them but the revelation is a soul it's a life he gave you the other life so he has a Minnah that you don't ever forget a rights that he has on you that you consistently remember so whenever you're in a gathering a person who favored you a person who honored you how dare does somebody back by you back by him in front of you and you're silent about it or even you're in consent with it or even you propagate it or even you bring it out خاب وخسر if you're not able to speak to these people because they're ignorant so much and they're stubborn and they're stubborn and they're arrogant and hard headed then just what did he say فار قداني كلمجرس say I'm not going to say he's gathering anymore you guys are backbiting my teacher I'm going to leave the gathering I'm not going to as they say I'm not going to entertain in any way for more shape this kind of gathering I am not okay it's hypocrisy that yesterday you were backbiting your teacher and then tomorrow you want to come to his gathering you want to take knowledge from him that is what? hypocrisy and remember what you do is what you will get them in this world صح الجزاء من جنس العمل this same person who's got the audacity to talk to you about your teacher remember they are doing the same about you not very far when they do that they will be doing the same very soon to you as well so you're only benefitting yourself in this regard then the اوطرحمة الله he talks about اداب the etiquettes of entering into the gathering of knowledge he said when you come to your teacher in his gatherings you come to him in that gathering with complete characteristics متنظيفا كما ذكرنا في المعلم just like we mentioned for the teacher you come clean pure no dirty socks smelling socks the whole mosque is what is this اعوذ بالله you don't come to the حلقة or the circle with your breath smelling kicking use call game aquafresh macleeds there's different varieties use them tic tac do something smell nice when you come to the gathering don't your clothing when the teacher comes to you you smell nice so when he comes close to you you ask him a question sometimes some students they'll come up to you and their breath is not smelling nice it's very and he says I have four questions they're like no I just have one just ask one question even that one question he wanted it to be so fast if he asks you you say quickly it's not permissible you can't that is harmful for the teacher it's disrespectful to the teacher because that same person if he was going to go to a wedding what would he have done you see so that's all disrespect your teacher you're not giving him the right that he deserves if you were going to an amazing place if you were going to a you dress up trust me everybody has one a moment where they dress up this is something that they need to do when they come to the teacher's gathering مططحيرا مستعمل للسواك use your سواك here toothbrush is enough سواك is a سنة though فاردن قلب من الأمور الشغلة cleanse your heart just like for the T-Shake also the student when you come into the gathering get clothes of everything else come to the gathering open minded you're not going to engage in anything else وَأَلَّا يَتْخُلَ بِغَيْسْتِ إِدَانِنْ don't just come walking into the teacher's room knock the door so you can come in that's what he says وَأَلَّا يُسَلَّمْ عَلَا الْحَاضِينَ إِذَا دَقَلَ وَيَخُوْصَّهُ also when you do come in you don't give salam to everybody disrespect you come in you give salam to everyone hey you're late sit down some people come in and when they come in they want to be know that they walked in they just have that persona where they want people to realize their entrance you're late there's nothing to show off by this when you come in you specify the salam with the teacher when you sit down when he leaves the gathering what do you do you give salams to the teacher specifically and the rest of the people you say سلام عليكم and you walk away he should also give salam for leaving the gathering and this is referred to in the Hadith the first salam is none the more worthy of being given than the last so the person when he leaves the gathering he should also do the leaving one because the Hadith of Prophet ﷺ which is that the first salams are not for your second salams in other words both of them are as important as each other he says سلام عليكم when you come in and he says سلام عليكم when you leave he should not walk over others in order to sit at the front instead he should sit at the last row or house circle unless the sheikh tells him to come forward or if he knows that the students normally give him preference over themselves if the student comes late then he has no rights break the people's necks walks in and he wants to take the first spot like he's that shouldn't be the case rather he sits where he finds the space that's where he sits except though if the teacher says to him come forward إلا أي أقدر if the teacher says to come next to me you specifically come sit here because the teacher for some reason wants him to be here but if he knows that the student always leave a spot for him and that's always the case then that's not an issue he can now he should not ask anyone to give up his place for him and if someone wants to give him preference over himself in this regard he should not accept that as this was was the example set by إله إي الله بيز with him also the author who he mentions is he shouldn't tell somebody to get up for me I really want you to get up for me from this particular place that you're at no don't okay he comes and says oh yesterday I was sitting here so please can you get up he can't if this person sees you and then some half feels like I'll get up for you then he shouldn't accept it he said this is in accordance to and this was an example which he set and this example is found in تير ميدين أحمد it is Muslim based on the hadith of the prophet عليه السلام where he said لا يقيموا أحاديكم أخاهم في المجلسة تما يجلس فيه that one of you should not make your brother or your sister stand up for you in a seat get up for me this is my way get up he should not do that and then when he pushes takes him away he sits in that spot he should not do that then سالي مولا بن عمر and he said فكان الرجل يقوموا لبن عمر فلا يجلس فيه عبد الله بن عمر sometimes he used to come and people would see him because this is بن عمر will not tell them to get up for him they would just see him from far and they would get up for him عبد الله بن عمر will not sit and he will not take it and he will walk away from it however if there is benefit to this or if the teacher orders this then this is acceptable that a seizure give up this place to someone else إلا أن يقول في تقدمه مصلحة للحاضرين the author here now talks about if this particular individual if this particular individual him coming forward there is a great benefit in it أو أمره الشيخ بذلك or if the teacher commands him to do so ولا يجلس وصط الحلقة إلا لضروة he should never sit in the middle of this gathering unless there is a necessity for that he should not sit in the midst of a circle unless this is necessary and should not sit between two companions without their permission if however they make room for him he should sit down between them and fold his legs as to not take up too much space now if you come you see two people that are together don't sit in the middle of them ولا يجلس بيلة صاحبين إلا بإذنهما you should never sit in between two individuals except with their permission فإن فسح لحو if they choose to give you space قعد that you can sit وضم انفسه and then even then you tuck yourself in you let yourself out and just relax and you spread yourself out you keep yourself old keep yourself old yourself yourself together that being known that two people are together when you do cause that to them it causes enmity and hate in the gathering okay so you don't want to have that in the gathering he should behave well with his peers as well as others attending the assembling as this is considering respect for the teacher and concerning order in his class he should sit before the sheikh in the class he should sit before the sheikh in the manner of the student and not that and not that of the teacher and speak in a lower voice unless it is necessary that he raises voice he should not fidget with his hands or anything else and he should not look around without due reason rather he should turn himself towards the sheikh with full attention the author here تكسب في أدام الطالب العلم معرفقائه when it comes to your friends and your colleagues the author here says و ينبغ أيضر يتأدب معرفقته يجب أن تكون جيدا مع your colleagues and those who are present in the gathering of the sheikh because having good manners with your colleagues and having good manners with those you're sitting in the gathering with is actually good manners with your teacher and it's respecting his gathering و يقعد بين يدي الشيخ قعدة المتعلمين and the student sits in front of the teacher the sit of a student of knowledge and he doesn't sit like a teacher you don't sit as a teacher in the sense where you are the individual who sits the highest and you و ذلك ألمام النسائي his teacher أحمد بل صالح I read he kicked him ألمام النسائي out of the gathering I kicked him out أحمد بل صالح kicked him out and misily the reason why he kicked him out was because the sai was a man who used to love to dress and used to dress very well and used to look very profound in his gathering so I told him get out of my gathering and never want to see you here again and school something must have triggered that off the teacher told him leave so النسائي was kicked out of that gathering so he used to go behind the wall and used to learn from there he never stopped learning but ألمام النسائي because of something that was in his heart towards أحمد بل صالح any reason he could find the critique he wanted to but then he found something on another أحمد بل صالح who was not أحمد بل صالح his teacher it was another one because something was in his heart he didn't verify which of the two it was so he jumped the gun and he criticized and critiqued أحمد بل صالح this is something that entered النسائي's heart towards his teacher the point here though is that the student sits in the gathering with humility, humbleness dresses and acts like a student if his sheikh for example wears a bisht those things that Saudi wear Saudi that thing that they wear you see that big thing over the شباق you guys know it right that big thing that they wear on top of the thob that is genuinely war by the scholars and the leaders of the country that students of knowledge don't wear that so for a student of knowledge to wear that in the حلق of the sheikh is something bad that's worn by the sheikh by a load he wears that so within the custom if there's something like that within the custom we don't have something like that do we something that's unique for the teacher do we a chair a chair okay that's good chair on the table is the teacher generally students should all sit on the floor then but is there something wary that we think that's only for the sheikh no one else wears it some places in the imam some places in the imam the imam the imam so صح the imam and the shemaq things like that in the Arabic language the word imam they use it as a turban a turban is the imam of them this is called the shemaq the one that you like the shemaq and the bish that they wear on top of it that thing they wear on it that is genuinely for the scholars that's generally for who the scholars so when you see somebody wearing that in Saudi Arabia in the Kaaba I remember what it was in my life I got it from a shop so I just wanted to check it out so I went to the Haram with it just checking it out if I look all good in it and then they kept coming up to me they asked me questions in the Kaaba people started coming up to me asking me questions you know I did this in the Haram what do you think is the jair is it I followed that up quick everything I put it in my because they come up to you thinking you're a scholar and they start asking you questions it was good though like in that when I wore that they thought I was the guard of the Kaaba you see so I could go into places where other people I don't turn got got that way I was relaxing with the that in the Haram not with them but I could I could do things I could get away with things that normal people could so just giving you guys a tip if you guys want to do that on board so the author here sorry I never finished the point he says don't raise your voice in front of your teacher ever shout loud say something loud never don't ever do that okay don't laugh in your teacher's gathering ولا يضحك ولا يكثروا كلام من غير حاجة don't even increase in speech okay without no need so if he says something for example you want to ask a question some people love to go in with their question just ask the question with the most summarized speech some people say okay then I'll start from the beginning I'll start from the beginning basic what it was is on the 12th 19 and they go in and they run you for a background check the teacher does not care of all of that just ask the question that but because the teacher was told before have been tied to a student don't cut them off so he's just going to have to listen 20 minutes okay so he's just going to listen to all of that in reality that's incorrect the student fast so basically my question is what is the rule regarding CFS and the teacher he answers the question so the student doesn't go off topic and speak too much he also doesn't play with his fingers and he doesn't play with any of that also when you're starting with your teacher this thing that people keep doing this all the time looking right left turning away your vision from the teacher is also bad manners consistently look at him when you're noting something down look at him right and left you only look at at times of necessity only times of necessity when he then he was narrated from Heisham Ibn Ammar he came to Imam Malik رحمه الله he came to Imam Malik and in the city of Medina an elephant came you know the Arabs have never seen elephants Indians you guys have seen it right yeah you guys got elephants some people have never ever in their life seen an elephant have I ever seen an elephant yeah when I was a kid I went to the London Zoo they've got it there yeah that's what I'm sorry yeah I was going to cry so in the Arab world there's no such thing as an elephant the animals never been seen before of course Abraha came to destroy the Kaaba with it but majority of them don't know how elephant looks like so in Imam Malik's time an elephant came so they all ran to it they wanted to see this animal they arrived and then they ran Heisham Ibn Ammar stayed with Imam Malik he didn't even look back he just stayed consistent look at Imam Malik and seen with him Imam Malik said to him why don't you go people are running he said I didn't leave my family because of that I never left my land to see elephants came to take knowledge from you he preferred looking at Imam Malik and looking at Imam Malik the way he carries himself and the way Imam Malik is then to see an animal he's never seen what will that do to a teacher when he sees that from you that nabaah he's going to open knowledge up for you he's going to be how serious you are and he's going to give you a lot صحيخ he will ولا يلتفت يبيني ولا شي مانين يغاني حاجة بل يكونوا متوجيحة للشيخ مصغيان إلى كلامي even if your teacher tells you something you've already heard of sometimes the teacher might repeat the same point again and again okay he might tell you the same story he might even crack the same joke صح you laugh like it was the first time okay you know your parents sometimes they tell you the same joke all the time and they tell you the same story all the time well you pretend like it was the first time really 112 who goes through that sees their parents telling the same story all the time yeah who feels that that happens sometimes to them yeah you guys don't you feel ربائي محمد محمد محمس who else we generally all go the manners of the son is that he pretends that this is the first time that he's heard the story he goes that's it like it's fascinated with the story even if you feel bored صح you listen all the time that's the same with the teacher when he tells you something you've heard of before you just listen to it as though it's the first time it's the first time ناني أوتكوز انت شعبتا في اختيار أخضى الأوقات الشيخ وفي الصبر على العلم ومن ما يتأكد لعتناء به أن لا يقرع على الشيخ في حال شغل قلب الشيخ وملله وستيفازه وغمه وفرحه وجوعه وعطشه ونعاسه وقلقه ونحو ذلك من ما يشق عليه أو يمنعه من كمال حضور القلب ومنشاط وأي يغتلم أوقاتا أوقات نشاط الشيخ ومن آداب أن يحت من جفوة الشيخ وسوء خلقه وأن لا يصده ذلك عملازمته وعتقادي كمال ويتأول ليفعله وقواله التي ظاهر والفساد طويلات صحيحة فما يعجز فما يعجز عن ذلك إلا قليل التوفيق أو عديمه وإذا جف الشيخ ابتداه وبلاعتدالغ إلى الشيخ واضحر أن ما الذنبله والعتب عليه فذا لكااااااااااااااان فاعله في الأخرى والدنياا وأنقال قلبي شيخه Rohh وقد قالوا من لم يصبل عل validل للتعلّم ببقي عمّراه في عباياه في عباياه ومصبر عليه按 أمره إلى عز الآخرة والدنيا ومنه الأثر المشهور عن ابن عباس رضي الله عنهما ذللت طالبا فعززت مطلوبا


What is going on guys, today I am back with another Destiny 2 video and today I have more information about Destiny 2 for you including what we will get in a beta, new exotic weapons and also pre-order exclusive bonuses and a few tad things more but before we go any further I am giving away this resurrectionist emblem, to end testing please drop a like on this video and leave a comment, Winnet will be picked and announced on a Sunday but more details are on screen now, ok so I've been asleep for the past 5 hours and damn I needed it, I've woken up to more info surrounding Destiny 2 so let's get into it, ok so more info about the beta has arised and what exactly we will be able to play during this beta, so we will be able to play the first story mission, homecoming, which is the mission where you fight off the cabal attacking the tower, small spoiler though people actually failed, like you didn't know that already, we will also be able to play the inverted spider strike which is pretty cool and if you guys want to see more on that strike I do have a complete gameplay of me playing it which we will find linked in the video description, there will also be pvp for us to play, not sure exactly on the game mode yet though, there will be 3 new subclasses for us to try out that being the dawn blade which belongs to the warlock, the arc strider which is of course the hunter's super and the sentinel, they're captain america style titan super, there will also be 3 other subclasses we can use during this beta, at the moment though we don't know for sure what these are but if I had to guess I'd say the hunter's gunslinger, the titan striker and the warlock's void walker, now we're covered all beta info regarding release dates in the video I posted yesterday, which if you guys do want to check out you'll find it linked in the video description, so that's it and what we will get from the beta, pretty damn cool, now we all know Sony and Playstation have exclusive rights to the game, these rights bring them some exclusive content which includes a new strike called the lake of shadows where we dive deep into the european dead zone and cause mayhem, they get exclusive armor, they get an exclusive ship called the city apex, a pvp map called retribution, an exotic sniper rifle called the borealis and that's about it, so what's new here, well we have found out a little more information about this exotic sniper rifle the borealis, this sniper rifle indeed offers all three burn types arc, solar and void, which you can switch between at any time, seems a little old p2me pve wise but hey details are scarce and it could just be a fad, we will just wait and see, so moving on, now this is kind of big news, people the ward of dawn is returning, well kind of, in an interview with pcgamer luke smith smolkov how the titan's new subclass has the option to cast a bubble, this is what he said, one of the sentinel trees actually has the option to when you cast your super you can press and hold that super activation button and you'll place a ward of dawn instead, so the titan bubble is returning, so all you bubble lovers out there i suppose this is good news for you, more details on this super though to come, okay so moving on, now if you're a pc gamer and you pre-order the digital deluxe edition on battle.net you will receive exclusive loot, that being a legendary sword, a legendary player emote and a cabal themed emblem, so loot for days for pre-ordering on pc, it's just a shame about that release date, 24th of october damn and people that's all i have for you at the moment, no doubt there are more info will come so stay tuned, if you're new around here and enjoy daily destiny videos make sure you subscribe, leave a like it's also much much appreciated, thanks as always though for stopping by and i'll see you on that next one


So my name is Abad Ishtaya. My background is in conflict studies. Today I work for an organization called ZIMAM. Our focus is on building the infrastructure and the pipelines for young people to be more actively engaged in politics in general, but also more specifically in local government. This comes from a clear kind of need for young people to be more engaged in politics in the face of an aging leadership in Palestine. I'm here at USIP today discussing political orientation research which I led in Palestine back home. So how this project started is that we're in the business of organizing. And if you want to organize, you've got to know the lay of the land, like who's out there, who you should organize and where they live and so on. And we realized quickly after we started is that we don't really understand that kind of stuff in Palestine. Current research, I would say, provides an overall picture of who supports which political party. So let's say the percentage of people who support Fatah versus percentage of support Hamas and so on. But there are a lot of assumptions there because there hasn't been elections for so long, so you can't really measure that support. You can't validate it. And also there's an assumption that Hamas is different from Fatah. We had a different theory kind of that they're not that different anymore. So we needed to understand more and that's where the idea of the political orientation research project that is a lot more rigorous and a lot more actionable came from. I would say two things here. The first one is that Palestinians don't seem to be too busy thinking about the shape of the outcome. Of course the Palestinians want the conflict to end and want there to be peace. But they don't think too much about one state or two states. And I think that is because they seem to think that they can't really control that outcome. At the same time, there seem to be high opposition to the one state solution in particular. 62% of the population strongly opposed a one state solution versus 42% opposing a two state solution. And it looks like the opposition comes from two places. If a conflict ends today or before it ends it's really hard for people to imagine living with the enemy or the occupier. But the other part seems to be cultural because the more you're opposed to the one state solution, the more socially conservative on the moral foundations one tends to be. So that gives us a bit of nuance as to where the opposition to the one state solution comes from. I think there's a pretty clear conclusion where we saw 40% of Palestinians nearly, 39% of Palestinians, who opposed all political parties and they are actually very politically active at the same time. So they don't believe in traditional political parties but they are further left to the Palestinian average. They are young, 70% of them are under 30 years old. They are pragmatic, so they support a pragmatic solution. And they're also more likely to be peaceful in how to deal with Israel. They supported peaceful, popular resistance as opposed to armed resistance. So this is a big conclusion. But in order for us to kind of operationalize that conclusion, we need to think of peace building and the peace building community through a wider lens, a lens that also includes development. Because maybe I would argue that if you ask people, are you a peace activist? You're going to get a very small percentage saying yes. But then if you actually look at the 40%, they are naturally supporting peace. So you want to tackle the things that they want to engage in. Maybe you want to tackle state building and nation building, which is essential for peace building. Maybe it's economic development and political development, which again is essential for peace building. So if we look at it this way and we look at the research with a complex lens, there are serious conclusions and consequential conclusions that can be drawn for the peace building community and peace building in general.


Hi everyone, Joe for Jasper. He's doing a recap video for our Sunday Funday Football Mixer Random Team of rig number one on a Sunday, the 10th of September. Big thanks everybody who got in. It was a box of elite football, a box of 2022 Panini 1 football, and a fanatics under wraps mini helmet. Big thanks everybody who got into this. Here's the stuff from the elite box, a lot of numbered cards, a lot of fun stuff here, including that one of one Aaron Rodgers for the Jets. That was pretty nice. Got the Luke Keekley also from elite and then the hit from Panini 1 was the Christian Accoye to 49. The mini helmet went to Eric Jennings and let's show you what he got. He got a Sean Clifford autographed mini helmet. There's the auto right there. Also numbered. You can kind of see it right there and it's a little dark shadow right there. But that's a 25. Maybe there you go. You can catch it in the light right there. So pretty cool stuff. Thanks everyone. I'll see you next time for the next one.


OK, so in fact, I was listed as organizer of this conference. Actually, my role is just to humanitarian one to help Anton to find a nice building which available three days. Sure, of course. Yeah, and also Anton asked me to talk about samsikic. It's not actually my active memory, this subject now. But I'll just give a very short review of what is going on in string theory and how one can understand and generalize the structures. But first of all, I just want to say that there is a following simple question. One can calculate volume of unitary group with a natural with respect to a measure related associated with natural Romanian metric. My trace of square is killing metric. So it's some number. You can calculate it's actually a double gamma function. It's a product of volume of spheres. It's very easy to see. But then I can expand it as maybe a log of volume, get a volume. And now I can see the volume to power inverse, take a logarithm, and try to expand as n goes to infinity. Yeah, so it's simple exercise with sterling formula. But it's not a gamma function. It's a double gamma function. And you get something like some minus n square of log n minus square root of 2 pi log n. And then I write, I hope so. And then you get series with g greater than 2, earlier characteristic of modulus space of curves without markpoints to power n to power 2 minus 2g. Yeah, that's one knows from a horror in Zegir. It's Bernoulli number divided by something by 2g minus 2. This is also one can calculate. So it's one can really easy check. This is really not a big deal. But the question, can we make intrinsic proof of it? And at the moment, it's not the case. So I think it will be a really good goal to find an intrinsic explanation. So it's actually part of general patterns that have considered integral of space by n matrices take logarithm and expand to get some high genus expansion, which we know in some class of kind of integral situations. But in general, there should be some inner explanation. So I will speak about the following thing. There is a model, will be b model, and a categorical language. So what is a model? Suppose we get a compact, for a moment, simple electric manifold. And then there are a group of between invariants, which are virtual fundamental classes of model space of stable maps, which are in commulges of certain degree x to power n times mj n bar, regression coefficients. d here is a degree of a curve, which I interpreted as just a integral homologic class. And this dimension is calculated through some formula. It's half of real dimension of x minus 3 times genus of my curve minus 1, 1 minus genus, plus number of mark points, and plus integral first gen class of tangent bundle over homologic class d. So there are such classes. And it's well known that the whole thing can be organized to co-homological field theory. So you have vector space h equal to just commulge of x. And you get a map from h to power n to commulge of mj n bar. You take the sum of all the things with weight with powers q to power d. It's kind of depending on formal parameters, qi where i ranks from 1 to r, which is rank of second homology. You calculate, you can see the kind of qi to powers integral over corresponding basis of the representative of this commulge classes over divisor d. It takes some of all possible degrees. So you get a commulge field theory depending on some parameters. And now there is a description of what goes into Bay model if it exists. And Bay model's story is not so obvious what was originally the story if genus is equal to 0. All this reduced to a story about variation of host structures. Sorry, I left exponential host structures, at least part of this gen zero invariance. Namely, if mere object exists, it should be a complex algebraic variety of the same dimension as x with holomorphic algebraic volume element. And a potential, we just map to, which is again, polynomial map, a double should be proper map. And then again, this will be object dual to x in symplectic formats also will depend on r parameter where r is. And one can identify parameters. One with another, such that logarithm of qi, i equal to 1 to r, will be ratio of two integrals. You integrate exponent of w times volume over certain cycles and divide by integral of exponent of w of volume of gamma 0, gamma 1, gamma r, are some integer chains. Not necessarily close, such chains that can integrate exponent of potentials. They go to infinity at the direction of an exponent decay. Maybe I should put 2 by square root of minus 1 here. Yeah, so this coordinates will be kind of transcendental coordinates on model space of these varieties, these potentials. And one, if you call it different integrals, one can translate to structure about gen zero part of invariance. But for hygienists, it's kind of extremely painful. So it goes from hygienists. How to describe in terms of these B models? Not really clear at all. Let's consider some kind of most central case in the whole story. You just look on this equation, kind of central case and dimension of x is 6 or 3, or complex dimension 3. And first chain class is 0. Then in this case, what you get essentially for each of, then it means that curves of any degree of any genus without mark point should form 0 dimensional model space. And so it should count again, you just get these numbers. And all the equations that we get, homological field theory became completely vacuous in this case. The whole story is defined by just all information will be some series FG, where G greater than 0 will be functions in R variables, which are expanded to some form of power series and for small genus with the logarithm corrections. So F0, it's kind of understood through variational whole structure. But for hygienists, there was a model proposed by physicists, kind of Feynman integral, proposed by Bershatsky-Chikotya-Guryev-Affa. It's called Cadiro-Spencer theory. What is Cadiro-Spencer theory? One can make a very general class of Feynman integrals with full form. Suppose you get a differential gradedly algebra in degree, which sits in degrees 0, 1, 2, and 3. And that's for degrees. And you have a differential of degree plus 1. And also, suppose you get a pairing, which is kind of non-degenerate. Why I put comparatives is because larger will be infinite dimensional and compatible with a bracket. So A, B, C, maybe no causal rule signs. It's OK. And compatible with differential. Then one can write Chern-Siemann's functional on kind of G1, say. You integrate a gamma with d gamma over 2n plus gamma gamma gamma over 6i. You can see the Chern-Siemann's of gamma is this pairing. And then you can try to integrate exponent of Chern-Siemann's functional modulo gauge transformation by degree 0. So Cadiro-Spencer theory is a particular example for some Lie algebra. And what is Lie algebra? It is the following. You can see the d bar forms on collabial three-fold, which is will be merudul. Y potential will be 0, in this case. You can see the d bar form with values in divergence-free holomorphic vector fields. So locally, you can see the tensor product of functions forms in Z bar, depending on Z bar, and holomorphic vector fields in Z with 0 divergence. This slight problem with the pairing. Because if you have two forms, let's say A and B, there are two forms, which A belongs, let's say, 0i form.  And B belongs to 0, 3, minus i form. Uncontrollably multiply, because the product will be 0, 3 forms. And then it should do something with holomorphic vector fields. But because it's divergence-free, it should be one can substitute to form. It says it's d bar closed to form, to comma anything form. Holomorphic vector fields, you contract this holomorphic column element to get two form in holomorphic direction. Because d bar closed, you can write d minus 1 of this. You get one form in holomorphic direction. So what you do is essentially integrate your place by forms. And the pairing A, B will be integral of B inverse of A with B. Because we say if it's closed, it should be total derivative of something. There is some slight problem along some finite dimensional space with the definition. But you get some field theory. And this guy's Bishorovsky's category of opposite. If you start to calculate exponent of Chairman Simon's action for this theory divided by h bar and take logarithm expansion, you should get h to power 2 minus 2g minus 2 times fg. Yeah, unfortunately, I think it's a very ill-defined, this all Feynman integrals diverge. But also there's really no way to canonically regularize it. So it's extremely bad shape. But it gives some idea about a holomorphic anomaly equation. A holomorphic anomaly equation, it's kind of very close relative to what Maxim Kazaryan explained just before. Essentially, it says that he didn't actually explain what is a holomorphic anomaly equation. He said that you get some infinite dimensional space. You get some decomposition to Lagrangian subspace and functions. So it gives a Lagrangian submanifold. And then you try to quantize this Lagrangian submanifold to get a vector and a value representation. And this holomorphic anomaly equation means that if you kind of change parameters of your series, this vector stays the same. So it's more of the same as these equations which he explained. So now what are these categories? In a sense, it's a way to regularize this BCOV and improve that genetic series which come from symplectic geometry coincide with series coming from complex geometry. So this was a project which was started more than 10 years ago. And this was a project which is not yet completely satisfactory shape, which says the following. So how we encode this Gromov fitting invariance through some algebraic data? So for simply, the algebraic data will be the following. It will be finite collection of complex numbers, which can be thought here as a critical values of w in this example. It could be, in principle, this potential should be 0. It should be just 1 number 0. Then for each number, you get some algebraic gadget which is called a smooth compact infinity category with collaborative structure. And so the category CI, in this example, this potential is that, actually, let me explain, it's a critical values of w or it's the same as eigenvalues of operator of quantum product by first-gen class. So this one can make comparison between A and B model. And so you get this infinity category. The category will be the following. It will be, if I try to define Foucaille category for manifold, it consists of Lagrange manifold. Lagrange manifolds will be some kind of abstraction to existence of this object in the category. And one can shift by identity template by some eigenvalue, get something non-empty. So there are not one Foucaille category, but several Foucaille categories corresponding to eigenvalues. And here are the things called the category of matrix factorizations. And so it's some algebraic gadgets, smooth compact infinity category.  But modular gadget equivalents, you get finite number of parameters. So this thing is kind of algebraic number of parameters. So in principle, one should have again some kind of mathematical programs working effectively with this stuff. Like in Maxim Kazarin's talk, but it's completely different calculus. The Calabria structure, it's also one can formulate in this way. Calabria structure is the following gadget. For each category, we can associate something called negative cyclic homology. And this is actually a module over Taylor series in one variable, which in this subject is variable denoted by letter u. It's come from kind of non-commutative geometry and con operator and so on. And the whole thing seems to work when this model is actually free of finite rank. So you get vector bundle. And this Calabria structure is a section of line bundle with vanish at 0. And derivative should be invertible element more since the same sense as Maxim explained here. So it will be some invertibility property. It will be Calabria structure. And then one can make. But this thing, the category of Calabria structure gives not much. Each individual category gives a factor from its homology, or there are some Ho Chi homology of hn at u equal to 0 to power n, maps to, for each category, ci with fiber, it maps to homology of model space of curves, but without bar. Without bar and with arrow. With arrow it means I can see the stable curves with tangent direction at each point. This is pure algebraic game and how it roughly constructed. One can encode this infinity category seeking some cyclic tensors. And the cyclic tensors you put make from the invariance according to ribbon graphs. And it will be co-chains in the ribbon graphs. So that's basically, so it's pure algebraic construction. And the plan to prove this whole thing was that this pure algebraic construction, one can specify for Foucaille category identify with grammar between invariance, or specify with complex manifold in cities some kind of regularization of this Cadare Spencer theory. So there's a problem. There's an arrow and there's no bar. And to go from to replace mjn head by mjn bar, one need to make an additional choice. Choice is the following. Actually, I forgot to say they get a vector bundle with flat connection and with regular singularity for each category. And the choice is the following. You can see the direct sum of hn of this category C i multiplied by kind of one-dimensional bundle this connection which I denote by exponent of w i divided by u. So you can see the connection whose in one-dimensional function whose solution is exponent. You take direct sum. You get a bundle of this flat connection with second-order pole on a formal disk. And identify these things as formal neighborhood at infinity at 0 of a connection of the following type. This will be du du, kind of trivial bundle. And connection consists of given by two matrices. By hn you denote how should change or how should complex. What is hn? Nectarically homologin. Hn? Oh, negative hn. OK. And the other in the C i? C i of category. OK. Ah, OK. Thank you. Yeah. So you take direct sum, get some formal guy, and now you just want to make some gauge transformation to get just two matrices a and b. There will be, again, finally many parameters how to do it. And if you do it, then you extend your theory to mj and bar. If you do it differently, extend in different way. And these different choices are related by this given telegroup. So it was very nice. And there was some kind of account of this story by Kevin Costolo. But somehow we also communicate with him a lot. And there was some kind of final problem. We cannot really make it to the closed formula. And the reason is completely idiotic. This is a pure combinatorial equation how we go through, make more less space. This stabilization should give some tool to go to mj and bar. And eventually we construct some cell complex which homotopic will into mj and bar. And for example, we want to calculate the integral of fundamental class, like fg. And the problem is this complex is of infinite, it's infinite dimensionals, homotopic will into mj and bar. It's infinite dimensional. And I don't know any good, nice representative of the fundamental class. It will be represented, it will be closed formula, and then we can kind of state the physicists that the problem is solved. Yeah, what is, yeah, yeah, eventually, yeah.  But that's why it's not really yet kind of formal, official kind of picture of the story. Yeah, yeah, so that was a picture about closed gromo-fitting invariants. Now I want to say a few words about, just before going on, just I want to mention some important thing. This was my proposal by Sergey Baranikov. And it's slightly different linear algebra. So instead of having a infinity algebra and all this data, he has a vector space, which is also infinity algebra, and a dimensional vector space. And a lot of elements in symmetric powers over cyclic powers of my vector space. Satisfying some, you get tensors in such things. Satisfying some, again, more carton equation. And then gives the classes homology of mg and bar. Now I should put prime. And prime is, it's a contraction of mg and bar. Namely, if you have on your stable curve, you get components which are free, which don't have marked points, you ignore the complex structure on such guys. Yeah, that's actually was a space which somehow appeared intermediate in my proof of this area function of written conjecture, some intermediate space. And the classes are here, not on mg and bar. So it's not terribly perfect story one should really remove this prime. And it's not clear how these parameters are related to these parameters. It is not to me. Why not to pull them back? You can just take it. Why not to pull them back to the... No, no, no, maybe we get... Because it's the elements in homology. And co-gonology to also. Also, okay, good, okay. But this will satisfy the hegematics. It's probably not, I'm afraid. Yeah, okay, so it was about close invariant. And now there's a pretty interesting story about open invariant, open closed gv invariant. And let's me concentrate on the case of Calabi-Yau III falls. Yeah, so you see that it's kind of case which is completely kind of perpendicular to this semi-simple case which makes an expense of... The freedom is huge. You get plenty of functions and no equation of... Can I make one there? Oh, just before going on, I want to say that it's really kind of color from all this picture. For Calabi-Yau III falls, one can... This gauge choices, one can make it's pretty explicit in geometric situation. If you get Y Calabi-Yau III falls and you have a choice of volume element. It's a variety, but I should choose volume element. And also, I choose a subspace. This was denote some sort of orthogonal space, a value of VF, I've forgotten you. Which you... Complimentary space, L, yeah. And you choose L in H3, YC, DRAM. Complimentary to terms of Hodge filtration, to H3-0 plus H2-1, which is actually called F2 of H3 is Hodge filtration. Then if you get such things, then the whole story, all this gauge choices will be automatically made. And then we get number FG for energy. And... Maybe at least two. And this number satisfies some question if you rotate L. But in particular, what you can see is that this FG are functions on some algebraic variety. Because so it's a G, it's kind of algebraic function on model spaces of this Y, volume, and L. This is algebraic variety. And it's correspond to really kind of algebraic parameters for categories, coherence shifts. And for example, if Y is mirror dual to quintics, then Y depends on one parameter, volume depends on one parameter, and this Lagrangian space in four-dimensional space depends on three parameters. You get five-dimensional algebraic variety. And FG will be thinking of this. And FG, which you can see in actual ground-fitting invariance, is obtained by restriction to some transcendental sub-manifold here. But so we see that it's algebraically dependent. So if you consider series coming from genetic function, there will be polynomials in first five series. And Yaw and Company checked it. And, yeah, so, yeah, so, but up to now, and also Albert Kliem calculated maybe first 50 polynomials. But because this technology is still not available, so he used some kind of boundary data. But for very large genes, they are not sufficient. You get some freedom. Gamow of canonical equation does really determine two things completely. So, so, so theoretical is answer exist, but in practical terms, it's not yet here. What is the, is there a definition of these FGs, except? Yeah. No, that's, it's only definition, yeah. Yeah, essentially, yeah, Castello has some paper when he have a definition of G without going to constructing logical field theory at all, yes, but it's very hard to extract any number. Now it's about open close ground between invariants.  Then one can try to count the following guys. One can count make a genetic series FGH, or number FGH, it's the sum of degrees, Q to power degree, and here I get a number of curves of genus G in H-holes and boundary belongs to this three-dimensional sphere. Yes, strictly speaking, it's not really well-defined problem in normative geometry, let's get boundary, model space with real boundary. But then there was suggestion by Vito Yakovina how to regularize a problem. One considers each curve and also draw something like roughly gradient lines on underlying sphere connecting points. Yes, so roughly speaking, one can consider maybe degenerate surfaces which consist of several components, and there will be some gradient, it's a bit long story, some gradient line connecting point on one circle to another circle in the three. And then the whole guy will have no boundary, so it's really well-defined numbers for homological spheres. Yes, so you get a parameter, it looks like you get new variable to raise to power H. Yes, and what is this new variable? And then there was a picture by thesis of a conifold transition. If you get a sphere in Kalevius three-fold, then I can construct a new family, one parameter family and one parameter will be responsible for this H of symplectic manifolds. Namely, do the following. You consider neighborhood of a sphere, neighborhood looks like a cotangent bundle to a sphere. And you can also identify this complex quadric in CT-C4. Then this complex quadric you can degenerate. You get kind of singular complex variety, so it means a contract S3 to a point. But now we can smooth in the complex geometry, make a kind of blow-up, but only get a kind of small blow-up. You glue inside CP1 instead. If it's a full blow-up, you glue CP1 cross CP1, but you just contract one. So you glue CP1. So in topological, you contract and reform, you get S2. And what you get? You get total space of two-dimensional bundle over CP1. Yeah, so you replace three-dimensional sphere by two-dimensional sphere. And now in this symplectic manifold, it has extra new homologic class, homologic class of the sphere. And then it means that it has more parameters as a symplectic manifold. You can change a symplectic structuring parameter corresponding to the sink. And the claim is that closed Gromok-Wittern invariance for kind of x, maybe tilde, for x tilde equal to open-closed for original for x and this dimensional sphere. And more or less, it's kind of clear, because if you consider this curve, then after this procedure, you get a curve and have some copies of CP1 added to this curve. Yeah. Yes. So before you get curve plus three-dimensional sphere, which is not really anything reasonable, but after this transition, you get a curve and copies of CP1. Yeah, the same one can do with several S-Series and these joint spheres. Then you get more parameters and get things depending on more parameters. Yeah. I want to say what is corresponding to B-model in the category language model. In B-model, it's actually opposite situation.  The typical rational curve should be this minus one, minus one. If you get this curve, you can contract, then you get a one-parameter family of new Calabi-Yau three-folds of Calabi-Yau, Y tilde, and how it's obtained, you contract a curve to a point and then try to smoothen it. So it's exactly this procedure, but in a sense, it goes opposite way. You don't blow up now. You contract a point, you get things, but now try to smoothen it. So go from singular guy to quadratic singularity. It's absolutely a parameter for deformation. So that's the story, and also in categories, it's also very nice, namely, you can see the category of coherent shifts on my Calabi-Yau right here, that's abstract category, which could be Foucaille category, and then this curve C, O of C is its object of this category and curve C, and it's a spherical object. So it means that X group from this object to itself, arc homology of three-dimensional sphere, then this contracting to curve to a point makes singular variety, and perfect plexus on a singular variety, it's a quotient category. Oh, it's not a quotient category, sorry, it's semi orthogonal complement to O. It's E such X from E of the spherical object is zero. Actually, it's perfect plexus on this category, it's a kind of full subcategory, it's kind of singular variety, and you can deform it using, as a category, a triangulated category, and you get this new family. This thing's actually not really yet done, so one can guess it's, the whole thing, behave nicely, so you get any three-dimensional Calabi-Yau category, you get spherical object, and you get new one-parent family. And now, and also this thing should be kind of a theorem, that this open-closed invariance are closed and don't fit invariance, so one should find some kind of formulation and watch as open-closed group invariance in two different frameworks, kind of, in B-model in more abstract categorical model. So meaning of open-closed invariance in B-model is the following, in B-model is integral of exponent of chance simons divided by h-bar of a watt, over, for the algebra, will be another, the algebra will be d-bar forms, actually, as well as there. In general, one get, this open-closed invariance will be defined for B-model and plus any, let's say, coherent shifts or coherent shifts or galmorphic bundle, which is spherical object, could be rigid galmorphic bundle, yeah, so consider d-bar forms, as well as endomorphisms of this bundle, and then this Calabi, that will be another quantum field theory, of halomorphic chance simons, yeah, there is actually much better situation here, this halomorphic chance simons, you also get some Feynman diagrams or expansion, and the whole thing is divergent as for Kaderi-Spencer theory, but there is canonical organization of all Feynman diagrams, so the whole thing is well defined, and in pure categoricals, I think it should be used to matrix integral, that's it, and categorically, you calculate the matrix integral, yeah, and here there's a really interesting point here, the whole thing exists, there's also kind of this additional choice, which I made, this gauging, this gauge choice, should kind of affect this matrix integral as well, because it's how we define what are stable curves, and so the, again, think which is not yet really done, so one can make a guess, to define the chance simons integral in algebraic situation, algebraic model, one needs a measure on space of objects, in the category of my bundles, yeah, and I need a way to define measure, and it's not clear at all, because this Calabi structure gives what's called shifted, minus one shifted, symplectic structure on model space of object, what does it mean that you've considered deformation of any, roughly, you've considered deformation of any holomorphic bundle, or any particular category, on the standard space will be x group shifted by one, and get this Calabi pairing gives you symplectic structure of degree minus one, on the super space, and then in this situation one get a, also chance simons function will be some function whose commentator is itself equal to zero, but for this odd symplectic structure there's no canonical volume element, unlike even case, and it's additional data, so we have a kind of classical master equation that things commit to the server, but there's no way to write what is Laplacian, makes, doesn't make sense without volume element, and volume element is something not one for free, and I think it's really coming from this additional trivialization of negative cyclic homology, which appear for, and this is not yet, from identification, negative cyclic homology should be, Hohschild homology is seriously new, and it should realize this line vector bundle. Yeah, that's actually interesting algebraic gadget to translate everything to algebra, and then we can see that we can translate infinite dimensional integrals as finite things to some game with tensors. Yeah, so that's what's going on, yeah, and in fact, if you have, you see I write it, if it's, if it'll be homomorphic bundle, get kind of six dimensional field theory, but if it's coherent shift supported on some in the curve, it looks really two dimensional theory, because this curve could be contracted to point it in zero dimensional series, so it should be reduced to matrix integrals on the nose stuff. Yeah, so in fact, this holomorphic chain of simons theory, depending on dimension of support of your shift, will be quantum field series in different dimensions, zero, two, four, and six. Yeah, so you get this holomorphic chain of simons, this kind of quantum field theory in dimensions zero, two, four, and six. Actually, I want to say that this one important thing, in this open closed things, I have two indices, genus and whole, and here I should get also two parameters, I get h bar, but also consider n copies of my wave vector bundle, yeah, so I should, so there are parameters h bar and n, and genus and h, they correspond to each, there are two parameters, can there, some kind of Laplace transform going here. Can we say QFT mean two dimensional topological point of field? No, no, no, quantum field, not topological, yeah. No, there will be some super symmetry here, so there are tools to calculate stuff, but it's not topological. Yeah, in principle, in some special cases, one can write things in a model. There was one point here, essentially, yeah, all this nice story, I have to say, but up to now, there's really no example of compact Calabria 340, we even know these numbers, yeah, so it's all, because of all things, it's not fully done in this algebraic transition, yeah, so it's, at least not in the sense that it can show numbers to physicists, yeah, so this, and almost all things which do physicists explicitly, it's some kind of limit case, say, you consider non-compact symplectic manifolds, so consider non-compact symplectic manifold, which can be, say, the formula, it's xv, it sits in some compact symplectic manifold, when we have divisive infinity should be semi-ample, so it means that intersection with any curve would be non-negative. Then, so, symplectic manifolds, from which the whole story can work, usually realizes complement to divisor, and then consider gv invariance for x bar with omega n plus, add some parameter, kind of one over epsilon times the class of divisor infinity, it should be positive, non-negative class, so it makes sense, and when epsilon goes to zero, you can go to the limit, and only curves which do not intersect the divisor infinity, so in a sense, open manifolds are kind of limits of close, guys from which there is a good picture, unfortunately I don't know good algebraic translation what is non-compact manifold, yeah, so it's things which is still missing, but here we have plenty of calculation, we've done, and in particular one can apply to the case when x is a cotangent bundle to some three-dimensional manifold times three, which is on a situation, and then this open grammar fitting invariance in the story, it means that you calculate channel Simon's theory, real channel Simon's theory, but for un bundles, the n goes to infinity, and it's spent in n, divided by h bar, so you got two parameters in h bar, and in particular this question which I think about the volume, it should be some kind of limiting case for a case of three-dimensional sphere, yeah, so this explanation should go through this thing, yeah, so one can get also three-dimensional theory in, is one of degenerate cases, yeah, okay, and finally we want to see what is the role of topological recursion from this perspective, yeah, and topological recursion when you make generating series, it will be serious in infinitely many variables, yeah, in principle the whole stuff also work in very general situation, I get gravitational descendants, but how what will be geometric meaning series in infinitely many variables, in variables like t1, t2, maybe p1, p2, infinitely many variables, and how are you going to try to see these variables, the picture is that Lagrangian manifold which you consider now is not one connected, but it has first homology, suppose it's Lagrangian manifolds across R2, so it's some kind of thing like this, and then if you get now you count your manifolds with boundary, each boundary components will wrap some number of times, and one can see that its number of times will be, if it's, and some situations could be kind of always positive, so this number of times will be a, a, a, i times wrap is supposed to weight Pi to this thing, yeah, so it's a way how to introduce infinitely many variables, and, and, and what does it mean, this infinitely many variables, yeah, so this, another way to arrange the whole thing was to have symmetric functions in, you can have functions, something like t, j, n of n, of n variables for each n, symmetric in these variables, and when you expand, you get some Taylor coefficients which will be wrapping, I think, and, so the way to do the following, this variable z1, zn can be sort as parameters of objects in 4k category, because when you have this s1 cross R2, one can put on this, it's like a manifold, but also it can be if I put rank one local system, which depends on one parameter, and my guess is it's, these functions which appear in functions of many, many variables which appear, this is the i runs through some algebraic varieties, some kind of algebraic curves, this algebraic curves parameterize objects in even 4k category, and that's, again, should be kind of translated to some pure algebraic game, but in principle one can see, one can go to more examples, for example one can see the things, these two generators of first homology, and it will be, instead of curves, we get surfaces and so on, yes, and pre-abstructly, of course, in real life, in principle, we can get Lagrange manifolds with arbitrary rank of h1, so we get a huge family of objects of categories, and my guess is it's, again, chance, so we get some object depending on zi, and my guess is it's what you calculate here, to calculate chance-samus, exponent of interval of chance-samus, oops, near easy one plus, plus easy n, yes, that's, that's maybe how one can really see this stuff, okay, thank you. For fukai category, there are no poles. Sorry? You're in for objects of fukai category, there are no poles. Poles? Yes, because the functions which we are studying, they have poles and diagonals. But homes, no, but here there's something singular, because homes between, if you have objects, depending on parameter, then homes really jump on diagonal, identity morphism disappears. Yes, homes are between different objects. No, no, but you can see the, if you can see the, under morphisms of this guy, this dimension of homology jumps when points start to coincide. No, just, yeah, that's it. Yeah. On that point, so if you take a carburetor, so called as a tangent boundary, and so your chance-samus is there, chance-samus, right? Yeah. My question is, what happens if you take a similar direction? No, no, if you make a general Calabius refold, and yeah, I've considered a general Lagrangian manifold sitting in Calabius refold, x6, say, yeah, then the channel-samus will be, in a sense, one can write formal stuff. This Lagrangian manifold will contain infinitely many loops, which will be boundaries of holomorphic disks, or maybe collection of loops with boundaries, of course. It will be isolated plenty of loops, and you kind of modify chance-samus section by adding, consider connection, which are not flat, but have some defect, and yeah, so it's pretty complicated story. Yeah, so it's going to be set, it's kind of local functional. It's, it has some information coming from ambient manifold here. One can write some action on this way.


In the previous class we have seen the different adsorption based materials where the hydrogen it gets adsorbed onto the surface of sorbent and the bond formed was weak Vendables bond. Now in this class we will look at another class of materials which are absorption based materials wherein the bond formed is a stronger bond compared to the materials we have seen earlier. Now this is just a repetition to mention that different among the different hydrogen storage materials that we have we will be looking at we have already seen where we can store hydrogen as a molecule without dissociating it into hydrogen atoms and that can be done on the surface of high surface area materials or the porous materials with high porosity and pore volume this we have already studied. Now in this class we will start with the other category of materials used for solid state hydrogen storage which are wherein the hydrogen molecule it disintegrates or dissociates to form hydrogen atom and that hydrogen atom that forms a bond with the material. So the class of materials that we will look in today's class is metal hydrates. Now we have already seen that the different solid state storage methods wherein these could be either physics option based or adsorption based where the molecule of hydrogen that sits onto the surface of these materials and it forms a weak bond that we have already studied. Now today we are going to look at the absorption based material and here in the molecule it disintegrate it dissociates into hydrogen atom gets into the interstitial sites and this is a bulk phenomena compared to the adsorption based phenomena which was a surface phenomena and here the bond formed comparatively is a stronger bond. A paper which is reported in nature and this is a very good comparison which shows that if we have to store hydrogen in different ways like whether it is liquid state or solid state or gaseous state, how the volume of the tank, how the size of the tank will vary. Now let us say if we want to store 4 kg of hydrogen for a vehicle which has to be driven for a 400 kilometers and then we can store hydrogen either in a compressed form then the tank size at when it is storing at 200 bar will look like something this. If however we liquefy hydrogen then this will be the tank size however if we store in the form of metal hydride that will even reduce. So on a volume basis this is reduced further if we store in one of the metal hydride form that we are going to learn which is LA Ni5 or it can further reduce depending upon what is the capacity of these materials, metal hydrides which we are using. Let us say if we use MG2 Ni then the size further reduces. So this is a very good pictorial representation of how the size of the tank it reduces as we move from compressed to liquid to solid state storage. Thus like if we have for example compared to gasoline which is having an energy density 47.3 mega joule per kg and an energy density 35.5 mega joule per liter here with solid state storage if we compare this is volumetric energy density is about 12.63 mega joule per liter. So this is how the comparison goes. Now if we plot together the volumetric and gravimetric storage capacity for different ways of storing hydrogen we can see that the capacities for a pressurized container at a metal tank or type 1 tank this is lower. If it is pressurized with a composite tank then the capacity of storage it increases but compared to the method of either liquid state storage here in this shows 70.8 is the typical volumetric capacity of hydrogen being stored in the liquid form. So all the materials based storage or the solid state storage they have a higher capacity that is volumetric capacity. But then we will also see that they have some of the materials they have good gravimetric capacity also. But at the same time the materials which we are going to learn like the metal hydrides they have good volumetric capacity but their own weight because of their own weight the gravimetric capacity is relatively lower. So the solid state materials we can see definitely they have a advantage when it comes to volumetric hydrogen storage capacity but then depending on what materials we are using their gravimetric capacity is definitely vary over a wider range. Now hydrogen in the very first class we have seen that it has one electron and that one electron in the 1s orbital that is reactive and can react with many elements so almost all elements of the periodic table. Now depending upon what sort of bond it is forming these can be the hydrides which are formed they can be classified. Like for example the elements highlighted in red form ionic hydride, elements highlighted in pink they form covalent hydride, those in blue they form metallic hydride, in teal they form covalent polymeric hydride and those which are in yellow they form metastable hydride. So depending upon what is the interaction, what is the metal to hydrogen or the element to hydrogen interaction the bond formed we can classify these hydrides into different classes. Like the ionic hydrides these are formed by hydrogen being reacting with the alkali or alkaline earth metals. These are usually formed when the electronegativities of the two atoms these are very much different. The hydrogen in ionic hydrides it is found usually found as negatively charged ion and these materials the ionic hydrides where the element to the hydrogen bond or the bonding is ionic in nature they have high conductivities either below or at the melting point. Now typical examples the binary hydrides with which are the ionic hydrides are sodium hydride or calcium hydride or there can be complex hydrides like lithium aluminium hydride or sodium aluminium hydride. Now the other class of such hydrides is the covalent hydride. These hydrides are formed when the electronegativities are almost similar. So in that case the sharing of electron takes place and then the formation of hydride occurs. So usually these hydrides are formed with non-metals and the interaction is involved is a weak van der Waals force as like these covalent hydrides are usually not usable for hydrogen storage. The reason being most of these hydrides these are having low melting point these are low melting point solids or low boiling point liquids or these are gases and they have toxicity they can have even like low thermal stability. So as such they are usually not used for hydrogen storage purpose. Some of the typical well known examples like ammonia water or H2S. The next category of such hydrides is the metallic hydride and this metallic hydrides are formed when hydrogen reacts with either transition metals or rare earth metals or lanthanide actinide series. So the bond formed based on the nature of the bond formed these are known as metallic hydrides. So the bond formed is metallic and because of the very easy uptake and good reversible capacity of these materials the taking up of hydrogen release of hydrogen is relatively easier as such these are most widely used for hydrogen storage application. Some of the examples like vanadium hydride or titanium hydride or titanium iron hydride of this class of hydrides. Now the important category of absorption based materials is the metal hydrides and they are specifically of interest because of their reversible capacities. These are simple in the sense they can combine chemically directly with hydrogen when these materials are exposed to hydrogen at certain pressure temperature conditions they form hydrides. So the uptake as well as release of hydrogen is simple with these metal hydrides. So it is a simple method subjected to temperature and pressure changes we can have hydrogen being stored and released from these metal hydrides. They also have good storage capacity and that is high on the volume basis for such metal hydrides. In fact this is higher than the liquid state hydrogen storage. This is about 60% higher than the liquid storage in case of metal hydrides. At the same time with these metal hydrides we can store hydrogen for any amount of time. So for long durations we can store and that too at ordinary temperature and pressure conditions. By ordinary temperature and pressure conditions we mean we have a variety of metal hydrides they can even store we have some of the metal hydrides which can even store at room temperature or ambient pressure conditions. Now this becomes important when we compare this method of storage as against the compressed state storage where we have seen that the storage of hydrogen occurs at very high pressure 700 bar. However in metal hydrides we do not require very high temperatures at the same time the pressure the temperature required are also close to room temperature or it could be higher depending upon which metal hydride we are selecting. But unlike the liquid state storage when the storage was carried out at 20 Kelvin here the temperatures involved are not that low. At the same time the metal hydrides are very much stable they can be stored for longer much longer durations and they are quite stable below their dissociation temperature. Important thing here is that until the temperature is raised or let us say if there has been a leak in a metal hydride based storage system the reaction of release of hydrogen is endothermic. Because of that a self cooling effect may arise and that will further reduce the temperature of the metal hydride because of the endothermicity of the reaction and that will stall the reaction or the release of hydrogen. So it is very safe to handle and store hydrogen and since we are not using very high pressures or very low temperatures for storing hydrogen as such that tank design are not that sophisticated as we have used in case of compressed hydrogen tank where the pressure requires were high requirement was very high or like the liquid hydrogen tanks where super insulations were required so as to reduce the heat flow. But since the temperatures of operation and the pressure of operations are moderate here we do not require such sophisticated tank design. Now let us look at the mechanism of hydrogen uptake in these this class of material which is metal hydrides. Now the first figure it shows hydrogen molecule far away from the surface and as it approaches the near to the metal surface. In that case in the second figure this metal these hydrogen molecule it interacts with the surface atoms and initially that interaction is by means of weak van der Waals forces there after the hydrogen molecule it dissociates dissociates into hydrogen atoms and these hydrogen atoms get chemisorbed after dissociation in the third step. Remember that hydrogen enters into the matrix of the material it sits into the it occupies the subsurface sites further it diffuses deep into the bulk and then it occupies the bulk lattice sites. So this is how the hydrogen uptake in these metal hydrides take place. Now if we see the mechanism of hydrogenation or dehydrogenation in these type of materials a simple reaction can be written the metal. Now this M is either a metal or it could be it could form the metal it could be a metal hydride it could be a solid solution or it could be inter metallic compounds that can be used. So metal on reacting with hydrogen molecule like this is x by 2 H2 forward reaction forming metal hydride plus certain amount of heat is being released. Now since the metal hydride which is being formed that has a lower energy compared to the metal and the hydrogen molecules so a heat is released in the forward reaction. So the formation of metal hydride from metal and hydrogen is a exothermic reaction heat is released however the reverse of it that is getting the hydrogen or release of hydrogen from these metal hydrides is an endothermic reaction. That means we have to supply the heat to the metal hydrides in order to get this hydrogen back. So the discharging process of the reverse reaction is a endothermic reaction. Now the conditions of absorption and desorption or the uptake of hydrogen is absorption here and the release of hydrogen is desorption. So the conditions are like for absorption when the supply pressure it is higher than the equilibrium pressure now what is this equilibrium pressure we will see little later. So provided that the supply pressure it gets it is higher than the equilibrium pressure absorption of hydrogen into such metal hydrides take place and this process as I mentioned it is an exothermic process however this equilibrium pressure that also changes if there is a change in the temperature. So this equilibrium pressure also depends upon temperature. Similarly the desorption is a endothermic process wherein heat has to be supplied for releasing these hydrogen being stored from the matrix to get hydrogen molecules. So whenever the equilibrium pressure, equilibrium pressure is higher than the pressure outlet pressure we can get the desired hydrogen and this process since we know that it is an endothermic process and all at the same time the equilibrium pressure we know that it is also temperature dependent. Now the changing both the pressure and temperature that will changing the pressure and temperature will result in to either absorption or desorption of hydrogen in these materials. Now let us look at the formation of metal hydrides in little more detail how the process takes place. Now this can be represented on a potential energy diagram. Now this is how the distance is increasing from the metal. Now far away from the metal surface where there is hydrogen molecule now if we see the potential energy difference between the hydrogen molecule and when it dissociates into 2 hydrogen atoms this is 435.99 kilojoule per mole that is the dissociation energy for hydrogen. Now the first attractive interaction that the hydrogen molecule when it approaches on to the metal surface that it observes is the weak van der Waals interaction. So that is the weak van der Waals force it observes and it gets physics of onto the surface. Now the first step is physics option that occurs on to the surface of the metal and at that time like the distance is about 1 hydrogen molecule distance and the heat of absorption for this physics option is about 10 kilojoule per mole. Now there is a difference or there is an activation barrier between the hydrogen molecule and its dissociation into hydrogen atoms. Also there is a barrier towards hydrogen being chemisobbed onto the surface of the metal. So chemisoption of the hydrogen. So now these potential energy activation energy barriers these needs to be overcome and that then the process occurs. So that requires sufficient energy to be supplied for the for overcoming this activation energy barrier.  So this dissociation and chemisoption occurs at the surface and usually this energy involved is about 50 kilojoule per mole in the process this is roughly around 50 kilojoule per mole. Now these hydrogen atoms which gets chemisobbed onto the surface these have high surface mobility and they interact with the other surface atoms they form different phases and thus that gives rise to a very high surface coverage. Now after they get chemisobbed they enter into the subsurface they penetrate inside the metal surface and they enter into the matrix or the interstitial positions that we have seen in the previous slide. They enter into the metal matrix so they penetrate into the metal surface and they start to form hydride phase by means of diffusion. And finally they further diffuse into the undergoes bulk diffusion and then occurs the nucleation and growth of the hydride phase. So this is how the entire process of formation of metal hydride is. So starting from physisoption onto the surface of the metal atom it enters it undergoes dissociation, chemisoption, penetration into the metal surface finally forming a hydride phase and that hydride phase or the hydrogen diffuses inside forming hydride phase and further the nucleation and growth of the hydride phase occurs. Now this hydrogen which enters into the metal matrix or the material and sits into the interstitial position that goes into the different voids of the different lattice. Like they can go into either tetrahedral or octahedral voids of the different structures like BCC or HCP or FCC type of lattice. Now when it enters into the lattice then like when the hydrogen when the concentration of hydrogen is lower into the metal matrix it exothermically it enters into the lattice and that leads to expansion that entering into the lattice that leads to expansion of the lattice. That also leads to reduction in the symmetry like typically that expansion which is considered is like 2 to 3 angstrom cube per hydrogen atom. Now thereafter the problem is that the stability of these hydrides that also depends upon the size of these interstitials. Now in the BCC lattice like tetrahedral and octahedral voids they got distorted largely and in FCC hydrogen concentration in the octahedral sites is comparatively lower. So in alpha phase where it forms a sort of solid solution it starts to form hydride that it enters into the tetrahedral sites these are half filled here in another phase these are fully foiled voids and that leads to significant distortion of the lattice. Now if we want to know how much amount of hydrogen has been taken up by a material then there are different ways of finding that. So there are different measurement techniques which exist. Now these measurement techniques are like can be divided into either volumetric technique or gravimetric technique or temperature programmed desorption. Now we usually draw like the in these measurement techniques like the two volumetric and the gravimetric technique we draw isotherms. Now these isotherms they are plotted showing the hydrogen uptake for different pressures at constant temperature. Now in the first method which is the volumetric technique usually what we do is we have a we introduce known aliquots of hydrogen into a known calibrated volume and after that the hydrogen absorption that will cause a decrease in the pressure. So because we know the pressure all the volumes in the systems they are calibrated and we introduce hydrogen at a certain pressure and that reduction in the pressure because of absorption or taking up of the hydrogen by the material will result into a drop in pressure and that change in pressure is measured at a known volume and then we can use the different state equations to find out how much amount of hydrogen has been taken in. Similarly, we can do for desorption. So there was a decrease in pressure during absorption where when we supply the required heat so that the hydrogen comes out in the reverse process that is desorption the increase in the pressure can be measured and then we can find out the hydrogen released amount. So this is in the volumetric technique. Now the another method is the gravimetric method wherein instead of recording the change in pressure we see the change in mass. So a very well calibrated micro balance and a sensitive micro balance is used for measuring the change in mass subjected to different hydrogen like gas pressures and then the major problem lies is that of buoyancy. And the third method is instead of keeping here the samples at constant temperature here we can change we can see the desorption of the material subjected to different temperatures. So these are the different methods in which using which we can measure how much is the hydrogen uptake. Now when we measure how much is the hydrogen uptake what we do is we plot like the isotherms which are like this is one of the isotherm and ideal isotherm shown here as a function of concentration of hydrogen. So the amount of hydrogen being taken up by the material H by M hydrogen by metal ratio and as a function of pressure. Now what happens is when we have low amount of hydrogen in the beginning when the we have smaller amount of hydrogen to metal ratio for say less than 0.1 the hydrogen it gets dissolved into the metal and this is a sort of exothermic process and then it forms a solid solution which is known as the alpha phase. In this process the metal expands as I mentioned like the expansion is about 2 to 3 angstrom cube per hydrogen atom however what happens is when the hydrogen concentration it increases it goes beyond say 0.1. So the strong hydrogen-hydrogen interaction occurs hydride phase starts forming that starts to nucleate that starts to grow and that leads to distortion in the metal distortion in the metal matrix. Now usually the hydrogen concentration in the hydride phase usually is considered as H by M equal to 1. Now it is observed that when this higher concentration the volume expansion is in the of the lattice is significant and that is approximately even 10 to 20 percent of the metal lattice which introduces variety large number of large amount of stresses on to the phase boundaries and because of these stresses the decrepitation of the material can result and the material can become brittle and so particle size can also reduce. Now if we see the typical and ideal pressure temperature isotherm then there are 3 regions we can see the first region which is here shown as alpha phase, second where the hydrogen is formed as a this is a solid solution phase. The second region where both the alpha and beta phase are coexisting beta is the hydride phase. So alpha and beta phase both coexist and the third phase where it is only the beta phase. Now if we apply the Gibbs phase rule which is the number of degrees of freedom that is equal to the number of components here the components are 2 there are 2 components the metal and the hydrogen so C is equal to 2 in this case. Now if we apply the Gibbs phase rule for the first region which is the alpha region. Now here the here if we see then this Gibbs phase rule if we apply there are 2 phases there is hydrogen and alpha. So for the region 1 for the region 1 we have 2 components and then we have 2 phases. If we put in this equation F is equal to C plus 2 minus P then we get the number of degrees of freedom equal to 2 that means our concentration varies with the pressure this is in the first region. Now if we see the second region where the 2 phases are coexisting region 2 again the number of components is same but the number of phases are 3. So there is hydrogen and alpha phase and a beta phase. So as such the number of degrees of freedom for region 2 is 1 and that is why we get a plattue. So the concentration changes here at a constant pressure and this we will see we will define in the next class that equilibrium pressure is given by this plattue pressure. So in the second region the number of degrees of freedom is only 1 however if we now look at the third region again in the region third we have 2 components and 2 phases hydrogen and beta phase. So as such the number of degrees of freedom is again 2 and thus there is a rise in the pressure as the hydrogen gas pressure rises and here is also a change in the concentration. So this is a typical and ideal isotherm now there are irreversibilities involved there are several changes are involved in these isotherms that we will see in the next class. To summarize what we have learned in this class we have seen the metal hydrides special class of material which can store hydrogen reversibly and that is the biggest advantage of these materials. They show a high storage capacity on the volume basis and hydrogen can absorb on these metal hydrides and we have also learned what are the different steps involved in absorption of hydrogen in these materials. We have seen that there are different ways in which we can measure the uptake of hydrogen like the volumetric method or the gravimetric method or it could be TPD and thereafter we can get the different PCT curves. So the series of PCT curves we will see in the next class these PCT isotherms or curves these are used to study the behavior of hydrogen absorption and desorption and what more information we can get from these PCT that we will see in the next class. Thank you.