of experience managing obstetrics and gynecology journal. It is one of the most respected and consulted journals in the industry. Could you please tell us a bit more about your roles and responsibilities as well as about the journal? Yes, I happy to. So obstetrics and gynecology is a monthly peer-review journal. It's owned by the American College of Obstetricians and gynecologist and published by Walters-Clure Health. We have over 46,000 subscribers who are the fellows of the American College of OBGYNs. So they are practicing physicians and mostly in the United States but also many international as well. So our journal is focused on clinical medicine. Our journal receives over 2,200 submissions per year and we accept probably between 18 and 20 percent of those. Most articles go through peer-review, although we have started editorially rejecting a select group before peer-review. Peer-review consists of three, mostly usually three people. One person is a member of our editorial board and the other two people are experts in that field. Our editorial board really serves as sort of the eye of the general reader out in practice. We have three editors, an editor-in-chief, associate editor in gynecology and associate editor in obstetrics, and they are all practicing clinicians at this time. They are remote to our office so we don't see them in person every day but we do talk with them by phone once per week, which is fantastic because that's actually where all of our editors discuss the manuscripts that are to be rejected or sent out for revision or accepted. So it's a great opportunity for those of the three editors and our statistical editor to consult on all of the manuscripts that come through our office. And I hopefully it's reassuring for authors too because it's not as if one, only one person has a sole final say on something. It's really a collaborative effort and we have a great team. That's fantastic. And a little bit more about your particular role as senior director and managing editor for the journal and the society. So could you throw some more light on that? Absolutely. So there are five people who work for the journal full-time. Myself, the managing editor, we have a manuscript editor, production editor, an editorial administrator and editorial assistant. So our editorial assistant and editorial administrator work very closely with their editors to manage the peer review process. So my role is to oversee that process and by that I mean to keep an eye on what's new and important out in the field to stay up to date with materials coming out of the committee of publication ethics, the council of science editors, any of those professional publishing organizations to ensure that our journal is following best practices and acting ethically. And there's also the day-to-day housekeeping types of things and making sure that we are we are treating our reviewers well and our authors well. Part of that is timing. So that's something that we keep a close eye on and we monitor frequently. So every week we're actually looking at statistics about what kind of manuscripts we have and where they are in the process. So how many are out for revision? How many are under peer review? How many have been accepted and are with the publisher for the next issue? So we're always monitoring that entire workflow from beginning to end to make sure that we're processing things in a timely manner and that we're not building up a backlog but that we're also not having too few so they were sort of in a jam when we're at the end of the cycle. So that's a large part of that. So keeping track of statistics. We also look at monthly statistics and that's looking at how long it took a paper to get through the process from submission to publication. And we look at different intervals along the way. How long does a manuscript take to get through peer review? How long does the editor take to make a decision? How long does it take to be revised? How long does that second editor's decision take and then how long does it stay in our office before it's transmitted to the publisher? So that's an example of some statistics that we track that I track quite regularly. So we also have staff meetings. We try to do that twice per month and that's an opportunity for all of my team to talk about what projects we're working on and also if there's something that's come up to address that and to fix it if we need to. So a lot of my job also entails emailing and communicating with many different people. So our journal is published by a commercial publisher so I coordinate activities and communicate quite frequently with our publisher, with our production editor, with even with ad sales, all of those groups of people, marketing, any of those people at our publisher because it takes a big team to publish a journal. And so part of my job is just you know just communicating with that group. Along those same lines another job of mine is to communicate with our society, the American College of Obstetricians and Gynecologists. So there are many different colleagues that I have within the college and they do a range of things. We have a publications department, there's a resource center, there's communications marketing. So sometimes it's just meeting with them to see you know where we are in certain projects to help support them. Although we don't, although our journal is editorially independent from the college, we are of course part of the college. So it's just managing those relationships and being open and available to my colleagues. And of course the budget is an important component of my job, keeping track of that, making sure that we're on track. So just being responsible financially is a big component of my job as well. From the editorial side one of my jobs is also to to monitor what we're publishing and make sure that there's a quality that we're producing a quality product. And so although I don't copy edit manuscripts anymore, I certainly look at page proofs and I can advise on style matters, work, I help our production editor work on art. So there's that editorial component of my job as well. And then finally there is a web component of my job and it requires you know knowledge of the digital world. And so that's everything from a web platform to social media. So our journal is hosted on Walter's Clure's platform. And every month when our issue goes live, we do some things behind the scenes to make sure it looks good and add some extra content there that we hope will be useful for our readers. But then we also have social media platform. We are on Facebook and Twitter and LinkedIn actually. And so and social media requires engagement on the part of the editorial office. So I work with my staff to think about what we're going to post that week and then monitor what we've posted to see if there's conversations out there that we need to address and respond to in a timely manner.


Russian officers are dissatisfied with Gerasimov and Shoygu. United Kingdom Defence Intelligence reacted to the dismissal of Major-General Ivan Popov, the commander of the 58th Combined Arms Army in Russia, who allegedly reported to the command after the difficult situation in Zaporizhia oblast. The intelligence noted that the Russian Federation had regularly dismissed commanders since the beginning of the invasion of Ukraine, but the situation with Popov drew attention because he was dismissed for raising concerns, not for allegedly poor military results. In a leaked video intended for his subordinates, Popov sharply criticised the leadership of the Ministry of Defence of the Russian Federation saying that it is hitting us from the rear, viciously beheading the army at the most difficult and intense moment. Popov's comments highlight the serious dissatisfaction that many officers are likely to have with the military's senior leadership, the intelligence said. The intelligence adds that his complaints largely echo those made by Wagner Group owner Yevgeny Prigozhin prior to his June 2023 mutiny. Direct criticism from subordinates is likely to become an increasing problem for Defence Minister Sergei Shoygu and Chief of the General Staff General Gerasimov, the intelligence said. Earlier, Russian Major General Ivan Popov, who goes under the name of Spartak, told his subordinate soldiers that he had been fired after releasing a report on the current problems in Russia's armed forces.


So what about the second chair you mentioned? This is about a chair originally designed by Marcel Breuer, who was a teacher at the Bauhaus at that time. Let me tell you about the Bauhaus. It was the first modern design school in Germany and its influence continues till today in the way design is taught and practiced around the world. It's an interesting story about Breuer. When he was a faculty at Bauhaus, he used to drive a bicycle back and forth and would observe the handle bar of the bicycle every day. He realized that this bent metal pipe has not been used in furniture so far and that inspired him to develop this range of furniture. This chair became extremely popular in India after Godridge started manufacturing it. But what about the patent of the chair? Godridge started manufacturing it after the patent had expired. They even designed a metal table to go with it. And this became the iconic table and chair set that we see in government offices and banks all over the country. So this chair is popularly called the cantilever chair and I want to show you why this design has remained timeless and hasn't changed for five decades. People don't realize what a fantastic chair this is. So it consists of one S bent metal pipe which is a single continuous piece and that provides comfort while sitting but also it gives you springiness while you sit. Then this cane weave, it adds to the comfort but also it provides ventilation and that's absolutely great for hot and humid climates. Additionally, the seat and the back have a wooden frame and these are separately assembled which makes the manufacturing process really easy because the metal part is done separately and then these frames are added on separately.  It is important for the designer to have a good understanding of possibilities and limitations of materials and manufacturing. I was thinking that classic designs like the chairs you just showed stay forever but in the modern context products are evolving constantly. Yes, this is due to constant advancement in technologies manufacturing and materials also change as do people's aspirations.


Hello, my name is Dr. John Scott. I'm a product manager on the Blackboard Ally Accessibility Solution, and I've spent the last several years visiting dozens of colleges and universities around the world, analyzing over a billion digital content items for accessibility. And through this investigation, I've learned a few things about challenges institutions face in delivering accessible, inclusive digital learning experiences. First, what we're starting to see is a culture shift around how we think about accessibility. Accessibility is no longer exclusively associated with people with disabilities. We're not just thinking about access for people who use screen readers. We're also thinking about the access issues faced by students who rely on a mobile device to access their content, or students who are second language learners, students with dyslexia and other kinds of processing challenges, students who just need more flexible ways to engage with their content. We've also learned a lot in neuroscience about how engaging content through different sensory modalities, through different forms of engagement, can empower learners and improve cognitive processes. And we enable that through more accessible content. The more accessible the content is, the more easily it can be transformed into these different media. And so what we start to realize when we prioritize accessibility, when we make inclusion part of the core mission of our teaching and learning processes, we're not just benefiting those students with disclosed disabilities. We're providing more equitable, more accessible learning experiences for all of our students. And this is going to impact the mission of education, specifically as we transform into fully online and digital learning environments. Accessibility will be a key pillar in that transformation.


Advances in the extraction, purification and characterization of keratin proteins from hair and wool fibers over the past century have led to the development of a keratin-based biomaterials platform. Like many naturally derived biomolecules, keratins have intrinsic biological activity and biocompatibility. In addition, extracted keratins are capable of forming self-assembled structures that regulate cellular recognition and behavior. These qualities have led to the development of keratin biomaterials with applications in wound healing, drug delivery, tissue engineering, trauma and medical devices. This review discusses the history of keratin research and the advancement of keratin biomaterials for biomedical applications. This article was authored by Mark E. Van Dyke and Jillian G. Rouse.


The learner centric MOOC model that is the LCM model consists of the elements learning dialogues, learning by doing activities, learning experience interactions and learning extension trajectories. Here let us focus on what learners do that is the learning by doing activities. A learning by doing or an LBD is a formative assessment activity designed by an instructor. For students to self check their level of concept attainment or for them to immediately apply the concepts that they have seen and learnt in the LED or for integration of various concepts and various parts of the module in the MOOC. LBDs can be in the form of multiple choice questions or they can require longer responses in the form of a text box or so on. The main goal of an LBD is formative assessment. To see how that is achieved let us examine the dynamics of learning by doing. Learners perform an LBD activity right after which they receive rapid specific and constructive feedback that guides them on improving their learning. This feedback can be designed by the instructor and provided by the platform such as feedback for various options of a multiple choice question LBD. For such a question the learner can go through the various options reason through them and click on the option of their choice. Once they click the MOOC platform the system provides them feedback. You will see that this feedback goes beyond correct or wrong. It is specific and constructive in the sense the feedback here is telling the learner what they can do, what are the resources they can access, what they should revise and so on so that they can get their reasoning and their response correct. Each option has its own specific constructive feedback that helps the learner figure out exactly what went wrong and how to fix it. Now some of our MOOC instructors want to go beyond multiple choice questions. We may want to assign questions requiring longer answers or some design question or maybe even a problem solving activity. What can be done in such a case? For such goals LBDs can be designed and the LBD can contain the statement of the problem or statement of the longer question that the learner has to work on. The learner can provide their responses even if they are long in a text box and finally feedback can be provided to learners via rubrics that can be used in a self-assessment or a pure assessment process. We will now go to a reflection spot. You will see a screen containing a question. This reflection spot is about the differences between learning by doing activity and a regular multiple choice quiz. What are some differences? These list two differences. Now that you have thought about the question and written your responses, let us see what some of your responses could have been. In fact some of you may have listed more than two differences and this is because there are many differences between LBD and regular multiple choice quizzes. One of the main differences is in the goal of such an activity or such a quiz. While learning by doing activities can be considered as assessment, they are formative assessment activities. That means their primary goal is not to grade the learner but to provide feedback to the learners so that they can improve their learning. Another difference is that some typical multiple choice questions give feedback in terms of correct or wrong answers. As we had mentioned earlier the feedback designed in a learning by doing multiple choice activity goes beyond it. Each option in a multiple choice learning by doing activity tells the learner not only if they were correct or wrong and even goes beyond telling them why they were wrong. In fact it guides the learner on what she or he could do to improve their understanding. And LBD provides an immediate application of concepts seen, LBDs appear right after the content LEDs not only at the end of the module. LBDs or learning by doing can be in the format of multiple choice questions but they can even go beyond. As we saw they can be longer assignments or problems. The feedback in such LBDs is provided via peer review so learning by doing activities are learner centric in the sense they exploit the power of peer learning. The process of peer review helps both the giver of the feedback and the receiver of the feedback. As MOOC instructors the main takeaways for us is that we should follow up each learning dialogue with corresponding learning by doing activities. And we should ensure customized constructive feedback for each learning by doing activity.


What are the red flags that you need to not touch a stock? For me, if a stock is easy to borrow, red flag. If a stock has SSR, red flag. If a stock is day one, red flag. If a stock is low float, red flag, guys. Red flag, does all this stuff make sense, okay? So because Mbot had all these red flags, I was not allowed to touch it.


Now, this past paper asks you to read the following extract from Act 1 scene 2 and answer the question that follows. At this point in the play, the Scottish army, led by Macbeth and Banquo, are fighting a Norwegian invasion and a rebel army led by Macdonald, sergeant. Doubtful as it stood, as two spent swimmers that do cling together and check their art, the merciless Macdonald worthy to be a rebel for through that, the multiplying villainies of nature do swarm upon him, from the western isles of cairns and gather glasses and fortune on his damned quarrel smiling showed like a rebel's whore, but all's too weak for brave Macbeth, while he deserves that name.  Duncan So, starting with this extract, how does Shakespeare present Macbeth as a powerful character? And of course, the key words in this question, so what you need to focus your attention on when answering this question is of course the extract, but you're starting with it. And then, how Shakespeare's presented, presenting Macbeth, in other words, what literary techniques are used? And of course, the main character to focus on is Macbeth and how powerful he's presented. And of course, in this extract, as we've mentioned when we're looking at it, when reading through the play, this is when the sergeant is reporting back to Duncan of how Macbeth early on is so loyal, very brave, and he's basically won the rebellion for King Duncan.  Now, let's look at how to answer. So, of course, as I mentioned, when you're writing an essay, you always have to begin with an introduction. It doesn't have to be too detailed. However, you do need to tie your introduction to the key words and to show what you're going to be talking about. So, let's look at the introduction. Shakespeare presents Macbeth as a powerful character through depicting him as incredibly brave and valiant in the face of seemingly insurmountable odds. Indeed, in the passage of the extract, we learned that Macbeth was incredibly fearless in spite of being outnumbered by Macdonald. Shakespeare does this to illustrate to us just how noble and brave Macbeth is. Hence, his downfall within the play is all the more tragic to us as the audience, as we learn that he was brave and loyal when fighting this country. Now, of course, as I mentioned, here you have to talk about, from the outset of your essay, the key words, powerful character. And then what we've done is gone on to talk about how the extract is presenting Macbeth as powerful and brave. But then the second part of this introduction talks about elsewhere in the play. We learn about and we talk about the downfall. And, of course, this is what makes it more tragic for us because he seems, from this extract at least, to be really, really powerful. Now, what this introduction does is it summarizes a nutshell what you're going to talk about. So now let's look at the different examples. Firstly, Macbeth is portrayed in the extract as a powerful character through the vivid and violent description of how he managed to kill Macdonald. We learned that he unseemed him from the nape of his chaps. And this presents a fairly gruesome and vivid image of Macbeth's skills when fighting at war. The violent verb, unseemed, portrays Macbeth as incredibly violent. However, contextually, this is used to reveal just how skillful Macbeth is as a warrior. Hence, he's conveyed in this extract as incredibly powerful as he was skilled and ruthless in dealing with the enemies of his king and protecting the state. So now, as you can see here, this is taking a quote from here, so that he unseemed him from the nape to the chaps. And of course, again, this, as I mentioned, is taken a direct example. However, in addition to taking this direct example, we then focus in on the technique. And in this case, of course, it's the violent verb describing how Macbeth bloodily killed his opponent. What we've then done is added some context. This shows how skillful Macbeth is as a warrior and of course, contextually, he was a knight and he protected his king. And of course, this therefore shows him as really powerful because he was ruthless in dealing with the enemies of king and protecting his state, which was the most important thing to do as a knight and a nobleman at the time during the Elizabethan era. Secondly, Macbeth is portrayed in this extract as being incredibly brave and valiant, as he's unstoppable in his focus on winning the war for King Duncan. The sergeant depicts him in Banquo as two spent swimmers who despite being exhausted, bravely fought against the vastly stronger army of Macdonald and one. This metaphor is powerful as it reveals that despite being outnumbered and exhausted, Macbeth still fought for King Duncan, hence this depicts Macbeth as an incredibly powerful and admirable character. And again, I've taken a quote from the passage delved into it, talked about the technique that Shakespeare is using. And of course, the technique here is metaphor and explained and linked it back to how we can see Macbeth as being powerful. Thirdly, Macbeth is portrayed as highly impressive as King Duncan appears to be incredibly peace in his determination to win the war. This is shown when King Duncan exclaims, O valiant cousin worthy gentlemen, these are planetary sentences coupled with positive adjectives, valiant and worthy, illustrate that Macbeth is really admirable and accomplishes aurea. This establishes Macbeth in our eyes as a highly decorated soldier who's very focused on protecting the state for the king, conveying him as a powerful character. So this is now my third example from the extract. So as I've mentioned, what you want to do is select three examples from the extract before you go elsewhere in the play. Now this third example again, actually, even if it's a question relating to how Macbeth is powerful, you can talk about how other characters perceive him as powerful. And of course, in this case, I've talked about how King Duncan, the king himself perceives them as powerful by using his exclamation marks. And of course, these exclamatory sentences show his enthusiasm. And I've then talked about another way that Shakespeare uses this in terms of techniques. And these are the positive adjectives, valiant and worthy. And of course, what this does, therefore, is establishes Macbeth in our eyes as a really powerful character. Now you then need to move on to the second half of the question which is to do with elsewhere in the play. Now one way to consider how to introduce this is using terms such as that being said. However, this is to show maybe perhaps an opposing perspective, or in addition, moreover, to show other agreeing perspectives, but taking from elsewhere in the play. That being said, we later find that Macbeth is easily led into committing registered by his wife, Lady Macbeth, which is a stark contrast with a brave and promising depiction of him at the outset of the play. When Lady Macbeth goes to him by questioning his masculinity, he defends himself. I dare do all that may become a man. This is a striking contrast, the previous depiction of Macbeth as we find that Lady Macbeth is able to take advantage of his insecurities and control with him into killing King Duncan. Indeed, we find the seeds of ambition which were initially planted by the witches take firm hold as we learn that Macbeth will ultimately kill the king and become ruler of Scotland. However, this hamsha presents his weakness as we learn that his inability to refuse his wife's orders as well as his growing ambition mean that his power and stature in our eyes begin to diminish. Now, when we look at this paragraph, and this is from elsewhere in the play, actually, what I have selected is quotation that show how Macbeth is not powerful as a character because we're looking now at what we call his hamsha, his fate or flaw. In other words, what makes him not powerful is the fact that he is able to be manipulated by his wife. His wife questions his masculinity and this is what causes him to stop being loyal to the king because he wants to show that he's a man. So he says I dare do all that may become a man, which of course is a striking contrast to the previous discussion of Macbeth by the sergeant. What I then mention is the notion of regicide. This is of course killing a king, which was seen as the worst sin one could possibly commit contextually in a spheath in England. And of course, the other thing that causes him to have a fatal flaw is ambition.  Later on in the play, Macbeth is easily led into killing the people he loves because of the power which is going to his head and his ambition is to become king and stay as king. This could show that he as a man is powerful, but he's mentally unstable and easily persuaded into doing things such as organizing the murder of his best friend, Banquo. This is seen when Macbeth tells Lady Macbeth, there shall be done a deed of dreadful note. The use of the literation of D is effective as it creates the effect of Macbeth putting emphasis on the D words to symbolize the stabbing of his best friend. This is a contrast Macbeth would see in earlier stages of the play as Macbeth would protect his friend and not let him die. This establishes Macbeth as a man of many emotions, but also as a man that's unstable. Now again, as I mentioned, what I'm doing is showing how and why Macbeth might not be completely powerful as an individual because not only does he kill his best friend because he now, once he is king, all he's focused on is just protecting his power, but this worry is encapsulated in the quote when he says a deed of dreadful note.  However, Macbeth could be presented as a weak character when he fights a major threat. This is when Macbeth is fighting Macduff and he says, I'll not fight with thee. This should show Macbeth is weak and scared as he knows he will lose. The use of the juxtaposition knot and fight reveals Macbeth's change of character from being strong and fearless to scared and weak. This is effective as it shows even the most dangerous tyrants can lose power and become scared. Macbeth has finally lost all that is close to him and therefore the audience can infer that Macbeth gets his sum of his power from this close to him. Now what this paragraph illustrates is towards the end of the play when he finally comes up against Macduff and he learns that Macduff was not born of woman, so according to the prophecies in Act 4 Scene 1 where he learns that the only person that can kill him is someone who's not born through woman but through a caesarean and then he just gives up, he says I'll not fight with thee and of course this shows him as very powerless because it shows that he will not, that he knows that he will lose. He has lost in the fight for the supernatural. Now let's conclude. Overall Macbeth is initially presented as a powerful character as we find that his fierce loyalty to King Duncan coupled with the bravery in war makes him an admirable character. Nevertheless as he becomes consumed with ambition and greed he descends from being an admirable character to someone who's detestable and he ultimately loses his life as a result. This essay is examined in-depth how Macbeth is powerful but to an extent and again this conclusion ties it back to the question how Macbeth is presented. It then similarly to the introduction talks about how to an extent and the essay discusses Macbeth is powerful from the beginning, however he loses this power because he becomes consumed by ambition and greed therefore the argument that's made in this essay is that Macbeth ultimately is seen as powerful but to an extent once ambition and greed take hold he then becomes less and less powerful and this is of course being illustrated through the essay.


From DailyDoseOfWeirdNews.com, I'm Darren Marlar and this is your Daily Dose of Weird News. The 60-year-old leader of a polygamous community in Canada has been found guilty of having 25 wives. ***I'd say time has already been served, though. He has obviously been punished enough. Justin Bieber has cancelled the remaining 15 shows of his Purpose World Tour due to unforeseen circumstances. The decision is on purpose, but we don't know the purpose. According to the book American Bedtime Routines, 18% of Americans allow their pets to sleep in bed with them. I wonder how many of those were horse owners. A Michigan woman accused of stealing flowers from local cemeteries to decorate her own home has found out what it's going to cost her. A judge in Flint sentenced Lisa Corcoran of Vienna Township on Monday to nine months in jail with credit for 36 days already served. She pleaded guilty in June to attempted larceny of items valued at between $1,000 and $20,000. The 44-year-old Corcoran also will serve three years of probation and perform community service.  I think the entire nine months of jail time and her community service should be spent caring for that cemetery. The man in China who claimed he was abducted for two months was eventually released by his captors because he ate too much. Perhaps that's why I've never been kidnapped. One look at me and the criminals would have to know they couldn't afford the food budget. President Trump told a crowd Tuesday night in Youngstown, Ohio that other than Lincoln he is our most presidential of presidents and believes he could one day be on Mount Rushmore. According to a survey, the five U.S. states with the fittest residents are Oregon, New Mexico, Wyoming, Vermont and Connecticut. Mississippi is ranked as one of the most unhealthy states, possibly due to the toxic waste trucked in from Oregon, New Mexico, Wyoming, Vermont and Connecticut. We could all get stressed and even freak out a little bit from time to time, but the last person you want to find out is having a full-blown nervous breakdown is your pilot. Fortunately, the United Airlines jet hadn't taken off yet. In Austin, Texas, a pilot began addressing passengers via the intercom about her divorce and the presidential election she called both candidates liars before breaking into tears. The plane was still parked on the runway, as she spoke, and about half the passengers got up and left. In a since-deleted video posted by a passenger, the pilot could be heard saying, Don't worry, I'm going to let my co-pilot fly. Although, after this mental breakdown, I would be wondering if her co-pilot was just a figment of her imagination. Microsoft says that MS Paint will live on and that Sunday's announcement was all a big misunderstanding. In response to the attention, the potential removal of Paint received, the company clarified that the popular feature will live on in the Windows store for all three people who still use it. There is a sunken Nazi ship off the coast of Iceland, possibly carrying $130 million worth of gold. But there is some question as to who gets the gold. I vote me. $12.9 billion, you'd think an aircraft carrier would have pretty much everything you can think of. And the brand new Gerald R. Ford does. Well, except for one thing, urinals. It's a surprising first for the Navy, which came about following the decision to make every head gender-neutral. That will reportedly make it easier for the Navy to pivot and change the corresponding birthing area to housing female sailors vs. male and vice-versa as the makeup of deployments change. Those are the pros. The cons, according to design experts, are that toilets eat up more space than urinals and are much less sanitary. As one such expert explains, man are more likely to miss their mark in a toilet. Nevertheless, President Trump commissioned the warship on Saturday in Norfolk, Virginia. Don't look for this baby on the high seas anytime soon, though. A battery of at-sea tests and work-ups are required first, which could take up to four years to complete. People who are blessed to have solid networks of good friends and caring neighbors boost their chances of survival by 50% according to research from Brigham Young University in Provo, Utah. The team analyzed nearly 150 international studies with 300,000 people from four continents that examined the association between survival odds and social networks. People who had the strongest social networks were nearly twice as likely to be alive at any given age than those who were lonely. And the opposite is also true, having just a few friends is as damaging to survival as smoking 15 cigarettes a day or being an alcoholic. Heck, I've got over 3,000 friends on Facebook, so I'm like immortal, right? There's a 38% chance you'll catch the flu if someone in your household is infected.  A Florida family was jolted awake one recent morning, startled to find that 15 pounds of frozen meat had crashed onto their roof. Travis Adair says, It was like thunder and it awakened me out of sleep. When family members went outside to investigate, they found two packages of frozen Italian pork sausage in their yard and three more on the roof. Adair adds that the meat sacks must have fallen from above since they were too heavy to have been thrown onto the roof from the ground. Is why if Jenny speculated the meat fell from a plane and may have related to a drug deal? Yes, because underground black market drug transactions are also done using stuff you can get from any grocery store deli counter. San Francisco Bay Area McDonald's is testing out crab sandwiches. It gets really soggy though when you dip it into the melted butter. While going through his storage, Alice Cooper discovered some art that could be worth millions. You know, it's nice to know that an aging rock star put something away for his future, but even if he forgot he put it away. Ex-White House spokesman Sean Spicer needed a mini-fridge when he started with the Trump administration, so he allegedly took one from an office of junior staffers. The Wall Street Journal reports that about a month into his short run on the national stage, Spicer lacked a fridge to keep his lunch and beverages chilled, so he sent one of his aides to the office in a building near the White House. The young staffers told the Spicer aide that they would not give up their mini-fridge, so Spicer waited until they left, sneaked into their office and carried the fridge up the White House driveway around 8pm one night. Wow! Stealing from the less powerful below you, right from the first day, that's gotta be a record. Cat Zodia in Malaysia is the world's first five-star hotel for cats. The hotel swimming pool is almost never crowded. The 2018 Ford Mustang GT will be the fastest ever 0-60 mph, although Ford is not saying precisely how fast, thanks to a new 10-speed automatic transmission, electronic drag mode and upgraded 5.0-liter V8 engine. Exactly what you need for that stop-and-go rush-hour traffic. Never miss a single episode of the show. You can download the free Marlar House mobile app. In the app, you can find links to my Facebook, Twitter and Instagram. Watch my videos, listen to my podcasts, sign up for the Marlar Sheet newsletter to automatically be registered for giveaways, buy T-shirts or mugs, download audiobooks I've narrated, see my latest blog posts and more. The Marlar House mobile app is free for iOS and Android users. Download it now by clicking the mobile app tab at DarrenMarlar.com or search for Marlar House in your phone app store. Please support my channel by sharing the daily dose of weird news on Facebook, Twitter, Reddit and other social networks. If you liked this video, please give it a thumbs up and be sure to subscribe if you want to see more. And click that little bell icon next to the subscribe button to be notified when I post new videos. Find even more weird news that I didn't have time for at DailyDoseOfWeirdNews.com. I'm Darren Marlar and I'll see you next time, weirdoes!


I don't know what I would have done. Let me know what you guys would have done in the comments. So the item is damaged and missing parts and it still sold for $100. This one's pretty interesting. Hey, Bolo Buddies, thanks for watching. Amazing, right? All right, let's get started. Hey, Bolo Buddies, thanks for watching. All right, in this video, we are gonna talk about June 2023 bolos. These bolos were shared from members of my Bolo Buddies Facebook group, which looks like this. And this is the post that I popped up. And basically, everybody in the group is invited to share their Bolo. What they have to do is tell me where they got it, what they paid for it, and what it sold for. And they can tell me if they took a best offer, what that best offer was, if it sold on auction, which platform it sold on. All platforms are welcome and everybody is welcome to share. So join the Facebook group and come share a Bolo. These are just, I love these videos because I learn so much every single video. So thank you all for being here. Thank you for watching. Be sure to subscribe if you have not already. And let's get started with the first Bolo. This one's pretty interesting. Four 20 ounce bottles of Sierra Mist Discontinued. We had so much fun sourcing these after Pepsi announced they were no longer manufacturing Sierra Mist and that Starry was not the same flavor, just rebranded. We took the kids out one afternoon to our local gas stations and grocery stores buying up what was left on the shelves. We would make predictions at each stop on how many we would find. The buyer was all in at $44 for a set of four 20 ounce bottles after shipping. We had $4.77 in them after tax. Carbonation tax? What's carbonation tax? We have sold numerous two liters, 20 ounces and even many cans so far. Definitely a Bolo and actually very easy to ship. Just package tightly and slap a fragile liquid sticker on top and send it. This is what it looks like. It says Sierra Mist 20 ounce bottles, bundle of four, new sealed same day shipping, $27.99 plus the buyer paid shipping. So shipping is a little high. So it looks like they were all in for $44 for four bottles of Sierra Discontinued Mist. What do you guys think about that? Would you do that? Worth it? Not worth it? Sold this African tribal mask for $80 on Poshmark today. Bought a box of eight masks for $20 at a local auction. African tribal mask, wooden hand carved African mask multicolored. That is absolutely beautiful. So it is hand carved. So somebody probably really took some time and effort into making that and it is incredible. Okay, let's look at the next one here. Starting out June's curbside deals strong. Walking around the block last night with my wife, we passed the house that has been getting work done on it, including putting in central heat and air. There are two air conditioning window units on the curb that look to be in very nice shape. I picked them up and within 10 minutes sold one for 70 to my next door neighbor. The other one was listed on Facebook Marketplace and sold within 24 hours for $60. That gold is out there people. Can anybody guess who this came from? Who is our curbside picker? Jerry, Jersey Shore thrifter. He found another Bolo sitting on the side of the road. The man is a genius. All right, I always hit the, I should give his wife credit too because it sounds like they were sourcing those together. I always hit the books at estate sales. I find other buyers usually pass by them and the dealers are only too happy to get rid of them. Such was the case here. I got two boxes of books for under $10. Two sales and I'm already deep into profit sold for $129. This is what it looks like. Built to grind 25 years of hardcore skateboarding independent trunk, truck, first edition. Oh boy, bought for 99 cents. At the Goodwill sold in five minutes on Mercari. Listed for 300 sold for 275. Manhattan Toy Company, Blue Trinosaurus Rex Vintage 1984 Rare. And I featured this guy in my Manhattan Toy Bolo category video, so definitely go check that out. I found this figure at a yard sale. I paid 50 cents. The figure is from a Columbia Pictures movie Sinbad. It is missing the swords. Every hand is supposed to hold a sword and is also broken off its platform. I found it this way and sold it for $100 plus shipping. So the item is damaged and missing parts and it still sold for $100. Columbia Pictures Industries, Cali, The Golden Voyage of Sinbad, 11 inch action figure. This one was sold by Flippin' It Good. This is his YouTube channel. Definitely go and sub him up. He is a Bolo buddies member which means he has joined memberships for perks. There is more information about that in the description of the video. If you would like a shout out of your pop-up, of your YouTube channel or eBay store and a link down in the description, you can join perks at level two. This one also comes from Flippin' It Good. And he said, I found this DVD set at a yard sale for $5. It sold after two days of being listed. I sent offer to Watchers and was accepted. It sold for $100 plus shipping. Clint Eastwood 20 film collection, Blu-ray 2013 set with book, 22 disc tested. Does that mean he watched the whole thing? Did he watch the whole thing? 22 discs, that would be a long, long video. I found these at my local IFA country store. They were running sales on Western boots. I paid 50 and have a few scratches from people trying the boots. I used leather conditioner to get rid of the scuff. They sold for 200 plus shipping. So, Flippin' It Good does a lot of retail arbitrage. A lot of times he goes to like Burlington Coat Factory, Marshalls, TJ Maxx, all of those different places. He's also bought Los Cargo palettes. You can check out more about that on his YouTube channel. These are Tony Lama Western boots, size eight and a half. And this is what they look like. We bought these soup bowls for $6 at an estate sale. They sold for full asking price in a few days. They are Fishes, Eddie, Pantone, Universe, various colors, band, six rim soup bowls, Cy, Cy, Cy, Syracuse. Hey, I got it guys, I got it. Syracuse and it says China. I think that's Syracuse. Am I saying that right? I don't even know. Anyway, that's what it looks like. Bolo, all right. This one is, oh, this one was bought from my whatnot. Yay, so I have a whatnot. I don't know, it's not a channel. I'm on the whatnot app and I sell live. I have live shows over on whatnot. There we go. And I've been doing a lot of jewelry lately and I really, really am enjoying it because I don't know a lot about jewelry and I'm really bad with titles. So if I can't Google Lensit and do sell similar, I really, really struggle with keywords. So this one I probably could have come up with a good title, but what I've decided is that I really wanna bring my awesome jewelry over to whatnot for you guys to buy. So that's what I did with this piece. It is a Joan Rivers watch and bracelet set. In the case, it was stunning and I knew Joan Rivers is typically a Bolo. So if you guys find anything Joan Rivers, definitely look it up. I started this, I believe at $5. She said, I purchased it for $34.89, shipping and fee included. Sold for auction on eBay at $196.18. After fees and shipping was 167.12. After all said and done, she made $132.23. She said, this was my first eBay auction experience. I don't know if she meant eBay auction or whatnot auction, but either way, thank you so much for coming over and hanging out at my whatnot show. Thank you for supporting the channel and just thank you, thank you for sharing. I appreciate it so much. Anybody that has bought anything from me on whatnot and if it has been a Bolo for you, I would love for you guys to share it under the June post or I also have a post that looks like this that says share your best whatnot Bolo. So something you bought on whatnot and flipped for a profit. It doesn't have to be from me. So both of those posts are up right now. So go and share a Bolo. And again, thank you for sharing. I appreciate it. And it doesn't have to be a Bolo for me. It can be from anybody on whatnot, you guys. And if you're not on whatnot, there is a link down below. You can join and get $15 to shop. That is free money. So just try it. You're gonna love it. It's super, super fun. Come watch me. You don't have to buy anything. Just come hang out. And if you wanna sell on whatnot, I have a link down below. It's also a referral link. And when you use that, it will tell whatnot that I referred you and you may be more likely to get accepted quicker. Whatnot does have a marketplace also so you can sell things in a buy it now section. And I just think that that's gonna be expanding so much in the near future. But I'm loving the online auction portion of it because I'm live and I can chit chat with you guys. So come on over and see me. And again, thank you to everybody that has come over because there have been so many of you that have come. I am just overwhelmed with the support and I just can't even thank you enough. So thank you. It was definitely a shock at how supportive everyone was. I just, I can't believe it. So thank you. I know I'm saying thank you a lot, but really it just means a lot to me. All right. This one comes from She Picker. She is two sister pickers on eBay. She is also a Bolo Buddies member. She said, I purchased this Amish handmade stickly sofa for 120 at an estate sale. It was the last couple of hours and it was an everything has to go sale. By the end, the estate company was practically giving things away. The value of the sofa is between 2,500 and 3,000. I had it listed on Facebook marketplace for about four months. Put it on sale for 1,800 and it sold within a week. The buyer lives in California and arranged for a moving company to come pick it up. Wow. It's a stickly handmade wood sofa couch, Amish made from 1998. Original fabric. How awesome is that? And She Picker is pretty new. Her and her sister do this together. So that is awesome. She is She Picker across all platforms except eBay. She's two sister pickers there. And I will link her down in the description. She is also gonna be on what not. So follow her over there. It's She underscore Picker. She hasn't had a show yet, but she is planning to do one soon. So I bought these teachers manuals at a Goodwill for $1.69 each. They are building Block 3D science books. I listed them for 100 each. I bought a total of 14 of them. I listed each for $100. Sold three to the same buyers for 75 each. Wow. She is kicking booty. Kicking booty? Kicking booty. I guess she's kicking booty. Anyway, that one comes from She Picker also. I can't believe I just said kicking booty. What? What am I talking about? Hi Courtney. I sold a Walt Disney World Figment light switch cover for a best offer of $63. Figment is the character on it. The light switch cover is from 1982 and hard to find. I found it at the Goodwill bin. So I had about 25 cents into it, super lightweight. Had it listed for about four months. It did not take up a lot of room. So I just sat on it and waited for the right buyer. Thank you so much for all you do and all the information shared. Big high fives to everyone on their finds. And this is what it looks like and it looks like it's sold on Poshmark. All right. This one comes from Black Dog Vintage and this is her YouTube channel. She said, I actually sold miniature Lamoge tea sets and two miniature vases signed GF and two separate auctions. One went for 159.06 and 108.56. The buyer was in Canada and I could not combine shipping for him. So I canceled the auctions and did a buy it now for him and he purchased them this way. Yes, I've had to do that also. She said, I bought a lot of miniature tea sets and porcelain items in an auction for a final bit of $9. The items that the person won was only part of the lot that I won. Dollhouse miniatures can be quite collectible. Don't pass them by. This is what it looks like. So 264.62 miniature tea sets. Yes, awesome. Dollhouse in the title. This one comes from Bolo Buddy's member, Nina's Jules and that is YouTube and eBay for her. She said, we bought this from our neighbor's garage sale for $15. Sold for full asking price of $89.99. We always pick up fuel, T-H-U-L-E items. They flip fast. It is a rooftop cargo bag carrier and this is what it looks like. First time sharing, this is one of two.  Comps were showing anywhere between 20 to 45 on the brand. I listed at 50 and it sold in less than three hours on Poshmark. Wow, that's awesome. And this is what it looks like. So she listed it high. You know, sometimes you can get more on Poshmark. This is my second. The day I found and listed the eight pound book at the bins, one sold for 149.99. I always send offers so I tried listing higher. At first I sold offers at 140. Oh, sent offers at 140. No one was buying, but I did get a lot of likes. So I started sending offers for 120. My goal was obviously to flip it as fast as possible. Within three weeks, I got an offer of 85. I was scared to counter because I didn't wanna lose the sale. I decided I wouldn't take less than 100. The buyer paid immediately. So it looks like she sold it for 100. It is a vintage black slaw dictionary revised fourth edition 1968 hardcover. And it's an eight pound book. So whatever it is for weight at her Goodwill Benz. My son found this, he's my thrifting partner, paid 3.99 at the Goodwill, started it at auction at 300. Had a few offers. I accepted an offer of 500 plus shipping within two hours. Would you guys have let the auction ride or would you have accepted the $500 offer? Eek, I don't know what I would have done. That's so hard because she had it up for auction at 300. Within two hours had an offer of 500. So she could have declined the 500 and let the auction ride. At this point, she had no bids or she could accept it and she accepted it. I don't know what I would have done. Let me know what you guys would have done in the comments. This one comes from Bolo Buddies member childhood finds.  I have about 10 cents into this lot. I made for the buyer and it sold for $200. So she must have had maybe single listings and somebody asked her to create a bundle. This is what it looks like. It's Lake Tahoe, 13 antique postcards sold for $200. And again, this comes from childhood finds and I just not too long ago featured her eBay store in a featured Bolo video of just her sold items. You guys can check that out. This is what the video looks like and I will link it down below. She is a Bolo finder. She is a wealth of knowledge. Go and subscribe to her. We're trying to get her to 1,000 subscribers. And thank you guys so much for being here. Thank you for watching. Let me know in the comments which Bolo was your favorite and there's gonna be more videos like this coming soon. This is the first one of June. Go check out all of the May and all of the months before. This is a series. There is an entire playlist of these and you learn so much. And I would love for you guys to come over to the Facebook group and share your best Bolo of the month. Thank you guys so much for being here. Thank you for watching. Be sure to like, comment, subscribe and share and thanks for watching.


This lecture is part of Berkeley Math 115, an introductory undergraduate course on number theory, and will be about the chronicle symbol. So we've previously discussed the Legendre symbol, and which is written AB, and if you remember this tells you whether or not A is a quadratic residue of B, where B is a prime and is greater than zero. And we saw it was a bit inconvenient to have B restricted to being a prime, so we extended this to the Jacobi symbol, where B is now odd and positive. And we saw that it was very convenient to have this defined for non-prime values of B and made it much easier to evaluate, for example. And you can obviously ask the question, can you actually extend it to all integer values of B? And you can sort of do this using something called the chronicle symbol AB, which is defined for all, well maybe all A and B, although actually there are rather good reasons for slightly restricting the values of A and B that you define it for. And we can define the chronicle symbol as follows. If A and B is non-zero, we can define it by saying AB is equal to the Legendre symbol for B prime and greater than zero, and then we have to define A2, and we define A2 to be this funny thing that's plus one for A congruent to plus or minus one, mod seven, minus one for A congruent to plus or minus three, so mod eight, mod eight, and zero for A congruent to zero, mod two. And then we define A minus one, B plus one if A is greater than zero and minus one if A is less than zero, actually greater than or equal to zero there. And then we define it in general by saying AB1B2 is equal to AB1 times AB2, so this defines it for all B. And this B is zero, if B is zero, then it's a bit messy. In fact, what you do is you just sort of define one zero to be equal to minus one zero to be equal to zero one to be equal to zero minus one to be one and not B is equal to A naught to be equal to zero otherwise. And however, this does give problems as we will see a little bit later. So what properties does this have? Well, first of all, just like the Jacobian and the Legendre symbol, AB is plus or minus one if A and B co-prime and not if and not co-prime. Secondly, we get some sort of periodicity properties. If A is congruent to zero or one, mod four, then it's periodic in the denominator, so A of B plus NA is equal to AB. If A is two mod four, then we get period four A. And if A is congruent to three mod four, what we get is a mess. For this reason, the classical chronicle symbol was sometimes only defined when A is congruent to zero or one mod four and B is greater than zero. And this avoids a few of the minor complications we're going to see later. And the chronicle symbol is also multiplicative, so A1, A2, B is equal to A1, B, A2, B and AB1, B2 is equal to AB1 times AB2, except unfortunately, this isn't quite true. This only holds for A and B being none zero. If A and B are zero, it actually breaks down a little bit because you've got zero minus one times minus one minus one is not equal to minus one zero times minus one because this is plus one and this is minus one and this is plus one. And there doesn't seem to be any really good way to fix this. You might say you could make this equal to plus one, but that would cause other things to go wrong. Basically, there's a strong case for just restriction of the chronicle symbol to at least, at least B being positive. As we'll see later, there's no actual reason for taking B to be negative. Then we have a sort of version of quadratic reciprocity. This says that AB is equal to plus or minus BA where this sign is given as follows. First of all, we take minus one, the A prime minus one over two times B prime minus one over two, just as for the Legendre symbol, except here A prime and B prime are the odd parts of A and B. And we also have to multiply by minus one if A and B are both less than zero. So as you see from this, the quadratic reciprocity formula for the chronicle symbol is actually a bit of a mess. And the best thing to do is to use only for A and B odd and positive. And then it just becomes the usual Legendre quadratic reciprocity rule where you get this is times minus one to the A minus one over two times B minus one over two. This means that we can in fact evaluate the chronicle symbol just as fast as the Jacobi symbol. And to do that, you just turn the chronicle similar into the Jacobi symbol. What you do is you take out the factors of two and minus one from the numeration denominator, so you can reduce the case when A and B are odd and positive. And then it's just a Jacobi symbol. So we can just evaluate it in the usual way. Next, we can give a little table of the chronicle symbol and also the Jacobi symbol and the Legendre symbol. So what I'm going to do is I'm just going to take these to be the zero values of X and Y. So on this row, we have X zero, which is just a load of zeros. That's it. We have to remember to have a couple of ones there. And X one just is even more boring because it's just one's absolutely everywhere. And then an X two is this funny thing that is one, if something is plus or minus one mod eight and so on. So we get it goes back like this and then it goes back the other way. And then X three is easy because this just as period three, it just goes zero, one, minus one, zero, one, minus one, zero, one, minus one, and so on. Now this row here does not have period two. It only has period eight. So let's mark in blue the rows that have nice periodicity. So this is period one. That's nice. That's nice. This doesn't have nice periodicity. It only has period eight, but that is period three. And then X four is actually even easier. This is period two. It just goes one minus one everywhere. So it oscillates one and zero. So this also has nice periodicity. And X five is period five. And it goes one, minus one, minus one, one, naught, one, and so on. And I'm not going to do any more because this is getting a little bit uninteresting. But what I can do is we can mark which of these are values of the Legendre symbol and which are values of the Jacobi symbol and which are values of the chronicle symbol. So the Legendre symbol only works if the denominators are prime. So we get these ones here. And we get these ones here. And then we get the ones seven and so on. So here this is Legendre symbol. And then the Jacobi symbol, we get some extra ones. So we would also get these ones here. So we'd get all odd numbers. So here we would have Jacobi symbol and we would also have ones for nine. So the Jacobi symbol are these ones and also the ones we get for the Legendre symbol. The classical chronicle symbol cover the values given in purple. They're the ones that are zero or one mod four. So we get these ones here and so on. So this purple is classical chronicle rather than the full chronicle symbol. And now let's take a quick look at what happens down here. So x minus one has a lot of minus ones and then a one and then a lot of ones. And at this point we should point out that two of these values are kind of rather dubious. So these values here are definitely somewhat icky and you shouldn't really use them because they cause things to be non multiplicative and so on. Anyway we can get x minus two just by we have to take x two and multiply the this bit by minus one and this bit by plus one. So we get minus one zero one zero one zero minus one zero here and this one we just multiply by one so we get one zero minus one zero minus one zero one and so on. And for x minus three again we take this one we multiply it by minus one so we get one minus one zero one minus one zero one minus one and so on. And so we should continue marking in some rows and columns with nice periodicity. So this one also has nice periodicity. If we look at which columns of nice periodicity we see that they have nice periodicity but for the classical chronicle symbol and otherwise they tend not to in fact if you look at this one this column here for example it's really rather a mess. So blue is the one sort of period periodicity we expect so the nth column should have period n and so on except sometimes it doesn't. And let's just remind ourselves that here we get minus one zero times minus one minus one is not equal to minus one zero so that's really bad. So what can you actually use this extended chronicle symbol for? Well one of the things it's used for is the Dirichlet L series of an imaginary quadratic field. So a typical imaginary quadratic field would be z with the integers i adjoined where i squared is equal to minus one so this would be all numbers of the form m plus n i and an imaginary quadratic field has an invariant called it's discriminant which i'm not going to define now. I just say it's denoted by d and the discriminant for the ring of Gaussian integers turns out to be minus four and then the the chronicle symbol d p where d is congruent to zero or one mod four so the discriminant is always congruent to zero or one mod four this is where the condition being zero or one mod four in the definition of the chronicle symbol originally came from. Here for p and odd prime so this tells you how the prime decomposes in this imaginary quadratic field so this is the plus one if p splits as a product of two distinct primes in the imaginary quadratic field for example five is equal to two plus i times two minus i so it's equal to minus one if p does not split so if we take the prime three you can't factor it any more in the Gaussian integers and we get naught if p becomes the square of something so so here we have two squared is equal to two is equal to one plus i squared times the unit minus i so the chronicle symbol tells you how primes decompose in imaginary quadratic fields as I said for this you only need the denominator to be positive and you only need the numerator to be zero or minus one mod four and if you stick to this case it gets rid of much of the rather unpleasant behavior of the chronicle symbol. We can also use this to define the directly L series of an imaginary quadratic field and this is defined to be sum over n of dn times one over n to the s and I think what I'll do is I'll just give an example for the Gaussian integers so here we're going to take d equals minus four and we're going to take the Gaussian integers n plus n i and try and figure out what this is well here dn goes one zero minus one zero one zero minus one and so on so our L series is equal to one over one to the s minus one over three to the s plus one over five to the s minus one over seven to the s and so on and now you can see this L series actually factorizes so it's one over one plus three to the minus s times one over one minus five to the minus s times one over one plus seven to the minus s times one over one plus eleven to the minus s and so on so this is a product overall primes of one over one minus i of p times p to minus s where pi of p is just this chronicle symbol dp which in our case is just minus four p so this is rather like the factorization of the Riemann zeta function except we've got this sort of extra sign in and I'll just give an application of this and we'll be seeing more of this quite a lot more of this later if we take L of s times zeta of s this is actually gives us something called the zeta function of the imaginary quadratic field if we multiply these two together um then um this is can be written as um well well here this L series is one over one plus three to minus s one over one minus five to minus s and so on and the zeta function is one over one minus three to minus s one over one minus five to the minus s and so on so if you multiply them together we get a factor one over one minus two to minus s times one over one minus three minus two s times one over one minus five to minus s squared times one over one minus seven two s times one over one minus eleven to minus two s and so on and this is what happens when p is common to three mod four and this is what happens when p is common to one mod four and this is that the left over case when p is even well what can we do with this well um what we do is we notice that zeta of s becomes infinite at s equals one as we remember on the other hand L of s um at s equals one is equal to one minus a third plus a fifth minus a seventh and so on so this is actually finite and none zero in fact if you remember livenits is four minutes actually equal to pi over four although we we don't need that anyway what this means is that this product is infinite at um s equals one because that's that that's none zero and this is infinite so what this means is that this product um must be infinite and if we look at some of the terms product of all these terms um is finite and um none zero so a fairly easy estimate and this is obviously finite and none zero so that means the product of all the remaining terms um so the product over p is common to one mod four of one over one minus p minus s squared is infinite so the number of primes p common to one mod four must be infinite so um using this funny l series constructed from the chronicle um symbol um can actually be used to show the number of primes that are common to one mod four is infinite um this is the basic idea underlying Dirichlet the proof of Dirichlet's theorem Dirichlet's theorem about primes in arithmetic progression that we will be um giving later on in a few lectures time um okay so um next lecture we'll be um taking a look at at binary quadratic forms


Welcome back to another day here in beautiful South Africa everybody I hope you're ready for outdoor greatness, so we're just hanging out here at the lodge to stay breakfast And we're getting ready to go after an Impala, a Gemsbuck, and maybe some other species that are out here Some of these planes game that have been roaming around yesterday. I was out filming with Rob We had a successful hunt. He got a blue wildebeest It was an awesome hunt and we saw so many different animals So I am so jacked for today. So Rob's gonna get on the camera.  So basically we're gonna get in the truck We're gonna look for animals We're gonna get out and then we're gonna try to make a proper stock on them The bow is gonna be extremely challenging here at this place Just because of the wind and the thick thick cover that is here So even if you get fairly close which would be extremely hard because the ground is harder here There's a lot of crunchy things. It's gonna be very hard with the wind swirling plus the actual movement of the arrow With the wind so I'm decided to go with the rifle and I'm gonna be using The same caliber rifle almost the exact same As what I used in New Zealand. Hope y'all are ready to see some more Africa. We got a big safari day going down So let's get to it So lucky it came in. I'm gonna see if we hit him good. I think I hit him How lucky was that? That was awesome. How lucky was that? We were just about to go side in the seven millimeter that Rob used yesterday. It was a little off and This red Lashway was up on the hill with some other Impalas and some female Lashways and We just switched guns to a 243. So I think I made a good shot of them right on the shoulder Excellent shot. Beautiful. Beautiful majestic animal. I didn't get a waterbuck at the last place And this is kind of like a waterbuck's cousin One of the things with these African animals that's different with our North American animals is their vials are a little Father up in their chest sometimes have to hit them right in the shoulder. So you need a little bit bigger caliber Or just make a good shot and his leg is totally broken So that just put him down Hannah got vitals. So Great shot. Great shot. All right y'all we just got this beautiful red Lashway here and still got tons of time in the day What's the history on the red Lashway Patrick? He came from Zimbabwe or Zambia? Quite a few years ago. We There was quite a lot of people that just love this trophy and as you can see it's such a beautiful horns so we thought we'd try them out in South Africa and bring them down from Zambia and They really are animals that enjoy wet areas and you see the swampy areas and that We've got a couple of places even though it doesn't look like that. Yeah, but they do very well here so about 40 50 years ago we brought them in and We've really they've really done extremely well. So another example of Conservation yep hunting actually creates more animals. I know that sounds crazy, but It works. There's a big population of them now in South Africa, which never was never was there and in Zambia So we've increased the numbers. Awesome. Well, this is gonna make a beautiful trophy, but I think we got extremely lucky there Yeah, he did on the way to the shooting range. Yeah, there was a nice impala there too and that was on the list And I think it was a pretty easy choice to go after the luckily we had the 243. Yeah, yeah, exactly So hopefully that rifle is on what we'll have to go set it in now But awesome man. Well, let's load this and then we'll go and look for some more animals. Yeah, okay That's how you do it in South Africa. We roll if this has been with us all week Skinning our animals. He is brilliant with a knife. This is where the skinning is done and the refrigeration So I actually have Got a few animals from previous hunts in here. There's also salt in here like you've seen in the other places Look at this y'all So Cephas They'll clean them right here They're on this track Goes around into the refrigeration room. It's ready to go It's an operation. Wow This room right here is the meat processing Facility, this is very very very nice very well done All stainless steel. This is like a nice kitchen. So we've just run over to the range quickly to side in the seven millimeter yesterday Rob made a shot that was kind of close I'll let you see it on his channel, but it was off. I shot the 243 this morning made a great heart heart shot on That red Lashway. I'll probably use that gun on an Impala But something bigger like a Gems buck which we're also doing after you got to have something with some more punch So Patrick's gonna get our get our target ready and we're gonna go side in make sure this thing's on I'm actually gonna let the the expert do this He's definitely got the most experience you had a blue wildebeest three times twice why it was full gallop at 200 yards Which is very very impressive. So it was on it that distance Kind of kind of still probably a little high. It was high right high and right so we're gonna see what's going on right here Never seen you miss Like if it was me, I would probably be like well, I guess I forget miss I ain't here Yeah, so it's that that's significant difference and this one's the same. I know I'm there was right here when I shot When I pulled the trigger I knew where my My your triangle. I knew what my triangle was so how many inches do we need to we want it over there to 100? Yeah, so you're calling You are three inches right and three inches down is what you need to do So if it's a minute you need to go three minutes left three minutes down, okay? Well, our fears were confirmed The rifle shooting high and right Makes sense with what happened yesterday if you'll watch Rod's video Rob's the best shooter we got here He's gonna dial it in and then we'll be ready for the the bigger Animals that are out here. So we just heard on the radio.  It's ridiculous there's a black Impala on the property and Ryan and his pH they found it and they shot it, but they're having a hard time tracking it So we might have to go help them until we go out and hunt again So we're just gonna spread out and try to walk. There's a little creek bed here and Patrick and David they think that the black Impala maybe just bedded down somewhere in there This is so much like Texas y'all instead of mesquites. They have what is called? Acacia Acacia trees they look just like mesquites. There's short scrubby trees with really Tall thorns. Yeah, we're gonna walk in the line. Just watch the guy next to you So I don't know how Cephas tells the direction of the animals by like dry dirt card dirt But he can literally look at it and see like when the animals are struggling and Track their direction. It's insane What did I just say that coming in? Wow This is good. We've got a bit of blood now. We just picked up Patrick's on the trail again Seems like Cephas is really tracking good now blood is dry, so it's harder to see on this Desert-style dirt one thing to look for is just the easiest path, you know So what would you do if you were shot? You'd run in the easiest path things that aren't gonna get in your way as much so that's one way You can often tell But there's lots of different pathways out here in the brush So he was standing right here and see a large Cool of blood where he slowed down Way different way of hunting than what we do in America like this is safari style they're used to Hunting bigger game and stuff too where you have to have other people and Like if someone misses you you could die, you know, normally like if it was just me and Rob humming We'd probably just we'd sit there for 30 minutes and just kind of quietly whispered but With the style hunting, you know, they're like they won't they really want you to get the animal down Make sure that they're gonna get down. Obviously they have animals to get away We've just had like four or five shots here. So hopefully Some Paula's down, but we're pretty much chasing it. This is really odd for me and Rob just chasing an animal like this Okay, it looks like we got something down here So black and Paula Fantastic news. We got the Impala The only black Impala on the property. We got it done they tracked it down thanks to Cephas and the other guys and We're able to put another shot in it and got it down. So that's a spectacular Animal to get here. I'm super glad for Ryan. Then we got that animal recovered. I know how it is To a wounded animal and then you know not find it for a while So luckily we got it back quick. Now we're gonna get in the truck and go see if we can find some more animals Gimsbok on the hill Oh, yeah, that's when you know