Okay so let us continue with our discussion which is whose aim is to define what a regular function at a point is okay. So let me again go back to this definition, the definition says that you know you have function f with values in k the base field and it is defined in an open set containing the point small x of course that open set could be that open set is being considered as an open set in the affine variety or quasi affine variety in which x exists okay and we say the function f is regular at that point if it is if it can be written as a quotient of polynomials okay that is there are two polynomials whose quotient will define a function a quotient of polynomials will define a function into the field the base field scalar value function wherever the denominator polynomial does not vanish that is actually so this a function of the form g mod h where g and h are polynomials will always define a function on dh on this basic open set dh which you know in its own right is actually an affine variety and the fact is that you will you will just have to find a point a h such that dh intersection x capital X contains small x and which is possible because it is basically because any open set is a finite union of such dh's okay for various h's right which is a fact that we have already seen. In fact any open set here is the complement of a closed set and that closed set is given by the 0 set of an ideal and that ideal is finitely generated and therefore the that closed set is given by the intersection of the 0 sets of the generators of the ideal and therefore its complement is given by the corresponding union of basic open sets namely the loci the open sets where the corresponding generators of the ideal does not vanish individual it is union of that okay that is how every open set is a finite union of basic open sets and therefore this is my definition and this definition seems to be correct for if you look at a basic open set a good function on this is of that form okay but the point is that whenever you make a point wise definition what you are actually doing is you are gluing okay and the problem with gluing is that it can produce new objects if you glue objects of a certain type it can produce a completely new object okay. So if you glue functions locally you might get something which is very different from what an ordinary function is for example if you glue topological spaces in a funny way you might get a topological space that looks very different from the ones that you started with okay we are going to see later that if you glue affine spaces finitely many affine spaces you can get a projective space okay. So for example if I take two copies of the you know if I take for example the usual topology and take two copies of the unit disk on the real plane and you know if I make them look like two open two hemispheres of a sphere and then glue them like this I will get a sphere okay and the point is that the new topological space I have got which is a sphere is very very special because it is compact which is not a property that is shared by either of the two open disks I started out to glue it. So the problem is that gluing of objects in mathematics can produce new objects which have properties are completely different okay the same thing happens also when you try to glue functions and what I am saying is that whenever you make a definition point wise you are actually doing some gluing and then for all you know you might ask the following thing can happen if I look at all the functions on affine space itself which are regular at every point they could be very well different from polynomials what is the guarantee that they could not they are no different from polynomials but the answer is that you are not going to get anything new okay and that is what that is a surprise and it is a pleasant surprise and that is what we are going to prove okay. So let me try to explain that so just to stress this gluing business let me write out so let me make a few you know let me make few notational conventions so what I am going to do is X in An, K and affine variety or a quasi-affine variety so let me do the following thing let me let me do it one by one let X in An be an affine variety I define O of X to be the regular functions set of regular functions on X okay and so you see this is a new notation I am using this is a calligraphic O okay for regular functions because as yet I do not know anything about a global regular function except that is locally a quotient of polynomials okay and certainly I do not expect it to be anything I cannot expect it to be anything unless I prove something about it okay. So and similarly you know if U inside X inside An so this is irreducible closed and then U is an open inside this irreducible closed and U is a quasi-affine variety so a quasi-affine variety is supposed to be just an open subset of an affine variety then again O of U is defined to be regular functions on U okay and this is these are global definitions okay and how do these global definitions come they come from local definitions point wise definitions okay and so let me so let me write down what is what is the definition of so for example if you right suppose I write Phi belongs to O U means what means okay Phi is a map from U to K is a map that is regular at each small x in U okay and of course I am writing this for U but you know I can as well write it for the same thing will also work for X where X is actually an affine variety okay but I am taking a quasi-affine variety right. So what is a regular function on a quasi-affine variety it is a function which is values in the field which is just a map but with the property that it is regular at every point that means what so for every so for every X in U there exist polynomials GX HX in K of X1 etc Xn where of course your U is being considered in U is being considered inside X which is being considered in some in An okay your U is an open subset of X capital X it is a quasi-affine variety and it is being considered in some affine space it is an irreducible closed subset of some affine space and there are polynomials such that D of HX contains X and Phi is the same as GX by HX on DHX this is the you see this is the definition on DHX or rather I should say DHX may not be all of on an open neighbourhood of small X contained in D of HX this is what it means for give me a point X I can the function Phi in an open neighbourhood of that small point small X is the same function that I would get if I evaluate a quotient of polynomials which that with the denominator polynomial lot vanishing and the polynomials being taken in the property number of variables in which dimensional affine space you are considering U and X okay so you see see this definition is you see this is a problem with this definition the problem with this definition is it is so arbitrary in a certain sense see I could have you know the same space the same affine variety X could sit in so many affine spaces see if I if X for example is a two plane then X could be A2 or X could be two plane in A3 may be the X Y plane or it could be the two plane in some AN it could be anywhere and depending on where it is I have to take polynomials in as many variables and then I have to take a quotient so you see it is a there is so much arbitrary in this definition there is so much arbitrary in this definition and that sometimes is a little scary okay but the point is that you have this for every point X so now you see note that the DHX where X is in X where X is in U is an open covering of capital X right because I said for every point small X I am getting this HX says that the affine open set DHX contains X okay and this affine open set basic affine open set DHX is considered in this affine space that affine space of that dimension in which is that number of variables in which number of variables you have taken the polynomial HX okay and of course since I say this such a HX X is for every X in U it means that all these DHXs they cover U okay but then what do we know about the Zariski temple we know that it is quasi-compact therefore what it will tell you is that out of this out of this collection of DHX I can just be content with having only finitely many okay so by the quasi-compactness by the quasi-compactness of U okay U is after all a subset of X which is internal subset of AN and then you know when you take subsets and take the induced topology the noetherianness goes down it is hereditary so U becomes a noetherian topological space and you know a noetherian topological space is quasi-compact as we saw in the last lecture. So U is quasi-compact and that means every open cover has a finite sub cover so what it means is that there exist X1 etc Xm in U such that U is DHX1 intersection sorry union U is contained in the union of all these DHXI HXM and well of course Phi restricted to Phi is GXI by HXI in a neighbourhood of XI contained in DHD of HXI for every I this is what it means. So you see what it means so what it means is when you say that you are having a regular function what it means is that you are actually taking quotients of polynomials and finitely many such quotients such that these quotients they agree on the intersections you see if you take the intersection of DHXI with DHXJ then in that intersection Phi will locally be both GXI by HXI and it will also be equal to GXJ by HXJ so what you are saying is you are saying that a general regular function is simply gotten by taking finitely many quotients of polynomials with the property that these quotients of polynomials agree the functions that they define upon evaluation agree on these intersections okay and this is exactly what gluing is gluing is you take functions locally and then so many functions with certain property glue to give a bigger function if they all give on the intersections the functions should agree. So what you are saying is just take finitely many quotients of polynomials such that the locus of the non vanishing of the denominator polynomials covers your space that is U in this case and such that these quotients wherever the loci where the denominator polynomials do not vanish intersect the quotients evaluate to the same function okay such this is what a regular function on U is okay it is got by locally so what you are so a global regular function a regular function on an open set is actually gotten by gluing finitely many quotients of polynomials so it is a gluing process and now so this is how it is for U it is the same definition instead of U I can put capital X also the same definition works for any subset in fact if you want of affine space but particular in fact instead of U I could have put any subset of affine space okay and I could have said regular functions on that set but we are interested only in regular functions on either open sets or on closed sets either they should be regular functions on irreducible open sets they are open subsets that is either they should be we are interested in functions on either irreducible closed subsets that is functions on affine sub varieties or we are introduced we are interested in functions on open subsets of such affine sub varieties okay so U is an open subset of X and of course whenever I am considering a subset I am certainly not looking at the empty set so U is a non-empty open subset and mind you a non-empty open subset is both irreducible and dense okay because capital X is both irreducible and dense I mean because capital X is irreducible okay. So you see what we have defined as regular functions is something that is very strange it is these are gotten by gluing finitely many quotients of polynomials so now I can ask what will I get if I put O of if I apply this O to An itself what will I get if I apply O to DH what will I get if I apply O to X what will I get if I apply O to DH intersect X what will I get the answer is very beautiful the answer is you will get exactly what you go what you will get if you apply A okay that is the beautiful thing okay and the fact is that is the sophisticated way of saying that is that that describes that is why all the four are actually affine varieties okay. So in more general algebraic geometry you can define A the A for objects which are affine objects okay and then you can define the O for any general object and then the theorem is that a general object is an affine object if and only if the O is the same as the A okay and that is exactly what is happening here alright. So I mean that is saying it in very loose terms okay to understand the exact import of that statement you should study a scheme theory which is which should be a second course in algebraic geometry okay but nevertheless does not do any harm in my stating it here. So if at all you go ahead to study scheme theory you can come back and try to remember this statement okay so let me so let me make that statement let me make let me make this remarkable statement so here is theorem O of An is equal to A of isomorphic I should say okay let me put isomorphic. So here is the theorem the theorem is that what you define as regular functions are going to give back exactly these functions which are given for which are given when you apply A to these objects either affine space or affine varieties or basic open subsets of affine space or basic open subsets of affine varieties okay this is the statement right. So the technique of proof is literally the same it is basically it is a technique in commutative algebra. So what I will do is I will let me first prove the first one and in fact you can see that you can deduce the remaining if you are a little careful and just apply the same philosophy as the proof of the first okay. So what I will do is let me prove let us prove O of An is isomorphic to A of An let us prove this alright let us prove this so how does one do this. So what I will do is I will do the following thing. So I will define a map define a map A of An to O of An by very very simple map take the A of An is just the polynomial ring in n variables okay and simply send it send a polynomial G to the function G from An to K so it is a very very simple map. So what you do is take up take an element here what is it it is a polynomial in n variables over K and a polynomial in n variables over K is a function it is a function from An to K by evaluation you can evaluate the polynomial at every point and that is in that is in certainly a regular function because a regular function is something that is locally given by quotients of polynomials and this is globally given by single polynomial and the single polynomial G can be written as G by 1 if you want you can think of this G as G by 1 and the locus where 1 does not vanish is everything okay and therefore it is also a regular function so all I am just trying to say is that every polynomial is certainly a regular function there is no doubt about it a regular function is something that locally looks like a quotient of polynomials but something that is globally a polynomial is also a regular function because it is a polynomial divided by 1 if you want and 1 is a constant polynomial which always makes sense okay. Now the fact is that you see just like all the polynomial form a ring you can add two polynomials you can multiply them and then they form a vector space over K and then so the ring of polynomials is a K algebra okay it is a finitely generated K algebra. In fact it is a free polynomial algebra in so many variables the same way the ring of regular functions is also the set of regular functions is also a ring that is the first thing you have to realize because you see you take sum of two regular functions okay the sum will also be regular because if you take a regular function is locally given by a quotient of two polynomials and if you take two such regular functions and add in a suitable neighbourhood the corresponding quotients of polynomials the sum of quotients of two polynomials is again a quotient of two polynomials okay in the correct neighbourhood where the denominator does not vanish and the product of two quotients of polynomials is again a quotient of polynomials right. So the moral of the story is that when I define this O of something whatever it is the regular functions on that thing that is a ring in fact that is a K algebra it is it has addition it has multiplication it is a vector space over K you can easily see that if you take a regular function multiplied by a scalar the result is again a regular function because locally you are just multiplying the numerator polynomial by that scalar okay in the in the expression locally as a quotient of polynomials for that function okay and it is also clear that that is a K algebra and so on. So these isomorphisms that I have written here they are not just isomorphisms of rings they are isomorphisms of K algebra okay they are isomorphisms they are ring isomorphisms they are isomorphisms of vector spaces also okay that means scalars go to scalars lambda a scalar lambda in K thought of as a constant polynomial lambda goes to the same constant function lambda thought of as a regular function okay. So these are all K algebra homomorphisms okay. So this map this map that I have written here is actually it is very easy to see that it is obvious to see that it is a ring homomorphism because g you know f g1 plus g2 what g goes to and what I mean this association will preserve addition multiplication it is K linear and all that.  Then how do you show it is injective it is injective why is it injective well if you take two polynomials g1 and g2 which has functions are different it means that there is a point in an where the values of g1 and g2 are different that means the difference polynomial g1 minus g2 does not vanish at that point okay and that should tell you that g1 and g2 cannot be the same okay. So it is very clear that it is injective the injectivity is just very severe okay in other words you know I am another way to say it is that I am saying that if you take a polynomial and if I evaluate it as a function and suppose as a function it is a 0 map as a function then the polynomial has to be the 0 polynomial okay. So this is something that is obvious probably it just requires the fact that the field K is infinite okay which is true because the field is an algebraically closed field and algebraically closed field is infinite okay. Of course the problem is over finite fields you can always find polynomials which are non-zero polynomials but which evaluated as functions end up being 0 function okay that can happen for finite fields but small K is not a finite field it is an algebraically closed field and an algebraically closed field is always infinite and for an infinite field if you have polynomial which if it is upon evaluation it is the 0 map then the polynomial has to be the 0 polynomial okay that is the statement that it is injective okay but what is really crucial is the fact that it is so injective so that requires a little bit of proof so let me do that. So that is where a little bit of commutative algebra will come in and you will recognize what is going on if you have done a course in earlier course in commutative algebra and where you have proved that you know the you have proved the quasi compactness of the Zariski topology when you take the prime spectrum offering okay. So let me do this it is surjective so what I will do is I will start with so let phi be a regular function okay take a regular function right so phi is a map from An to K and by definition of what a regular function is there exists finitely many points okay and such that the union is the whole affine space and such that phi is quotient of polynomials in this sense okay. So let me write that down there exist points same such that An is d h1 h sub x1 d sub hxm okay where hx1 through hxm are polynomials in invariables and phi is equal to gxi by hxi on dhxi for every i and of course gx1 through gxm they are also polynomials in invariables okay this is from the definition of what a regular function is okay. Now you see see the first thing is that this has a meaning in terms of commutative algebra the meaning that it has in terms of commutative algebra is that the ideal generated by the hxi is the unit ideal okay so this means commutative algebraically so you know it is a translation of all these geometric facts into commutative algebra okay and you extract some information from commutative algebra so the fact that A is union of all this means that the ideal generated by hx1 etc hxm is one is ideal generated by one namely it is a whole polynomial this is the first thing that needs to be noted and why is this true why this is true is because well if this ideal is not the unit ideal then it is a proper ideal and then we know that every proper ideal is contained in a maximal ideal okay and you know the maximal ideal is a that corresponds to a point okay so what will happen is that if you that point will have some coordinates okay but that point will be here it is a point of A n so it has to be in one of these so that means that at least one of the hxis does not vanish at that point but that will contradict the fact that this is contained in the ideal of that point okay so this is exactly what I am going to prove if not if not hx1 ideal generated by hx1 etc hxm is contained in a maximal ideal which is of the form say x1 x1-lambda1 etc xn-lambdan okay this will tell you that you see it will tell you that so you know if I apply if I apply the Z right you know if I1 is contained in I2 then Z of I1 contains Z of I2 where Z is the operation that associates to an ideal it is 0 set. So this will tell you that Z of hx1 etc hxm contains Z of this maximal ideal which is actually the point which is actually simply the point singleton point lambda1 through lambdan okay alright that means what this tells you is that this point is you know it tells you that this point is a common this point is a common 0 of all these hx okay and if this point is a common 0 of all these hx that contradicts this statement because this point is here okay and by definition every point here has to be contained in some locus where a certain h does not vanish but then you are saying that I have but I have been able to find the point which is not in any of these okay it is a contradiction the contradiction to an is equal to dh1 dhx1 union dhxn xn okay right. So the moral of the story is that indeed the idea this condition the fact that the affine space is a finite union of certain basic open affine open sets means that the equations corresponding to those basic affine open sets those polynomials actually generate the unit ideal okay. So what all this will tell you is that this generate the unit ideal so what will tell you is that there exists there exists you know let me give some other names okay so let me use ff's so there are f1 etc fm polynomials in n variables such that sigma fi hxi is equal to 1 I get this okay in other words the one is in ideal generated by the hx so one should be generated by a ring linear combination of the hx and that is what I have written here these ff's are ring elements the coefficients from the ring okay so of course I is equal to 1 to n okay. Now you see now the point is that I will have to show that let us go back to what I started with and what I want to show I started with a regular function on an okay and I am just trying to prove subjectivity of this map so I have started with something here a regular function an and I am trying to find that come show that it comes from here so I have to cook up a polynomial which is equal to that function okay so I will have to use this information to cook up a polynomial g such that if I consider g as a map I get this phi that is what I will have to do okay and that is pretty easy to see so the trick is you multiply both sides by phi okay multiply both sides by phi okay and what I will so let me do that so sigma i equal to 1 to m fi hxi into phi is equal to phi okay I get this just by multiplying both sides by phi and then I use the fact that you know you see phi is gxi by hxi on dhxi but if I cross multiply I will get phi times hxi equal to gxi not only on dxi I will get it everywhere okay so I am using the following fact if two polynomials are equal on an open set if two polynomials treated as functions they coincide on a non-empty open set if the two functions defined by two polynomials if they coincide as a function on a non-empty open set then the polynomials are equal okay so what this equation tells me is that on this non-empty open set dhxi the function phi times hxi and gxi they are the same okay and I want to say from that that they are the same phi times hxi and gxi are the same if you want as regular functions on the whole space so I am using so in fact let me restate it more correctly I am saying that if you have two regular functions which coincide on an open set then they have to coincide on the whole space if two regular functions coincide on a non-empty open set then they coincide on the whole space the reason is the reason is topological the reason is because regular functions are continuous and open subsets are dense it is very simple the reason is topological okay. So all I am saying is that if I have two regular functions okay and if they the fact that they coincide on an open set on an open set means that the difference regular function is 0 on an open set okay but the set of points where a function is 0 is a closed subset because a function is continuous therefore this open subset is contained in a closed set but the open subset is dense which will tell you that the open subset that it will tell you that these two regular functions are the same everywhere okay.  So psi inverse of a closed subset of here is a closed subset of K and is a closed subset of U this is what I will have to show alright but then what is a closed you know the Zariski topology on K which is A1 the Zariski topology is just the compliment finite topology namely the only closed sets of finitely many points so to so psi inverse of a closed set is just a sin inverse of finitely many points and to show that that is and psi inverse behaves well with respect to unions psi inverse of a union of sets is the union of psi inverse of those sets psi inverse behaves well with respect to the operation of taking unions. So to show that psi inverse of a finite set of points is closed it is enough to show that psi inverse of a single point is closed okay so enough to show psi inverse of a point lambda in K is a closed set a closed subset of U this is what I will have to show okay. So but you see but then given X in U there exists GX HX with X belonging to D of HX and psi is equal to GX by HX okay so what this will tell you is that you know it will tell you that so in a neighbourhood of X containing contained in D HX this is what this is the definition local definition alright but then but psi inverse of a lambda intersection this neighbourhood is just GX mod HX inverse lambda in intersection this neighbourhood and this is just equal to Z of so GX mod HX has to be lambda so GX has to be lambda HX so GX minus lambda HX has to be 0 so it transits to Z of GX minus lambda HX intersection this neighbourhood which is of course closed closed in this neighbourhood and you have done because you know to check that a subset of a topological space is closed it is enough to check it on an open cover okay. So what I have done is I have for every neighbourhood every point I have shown that psi inverse lambda intersection that neighbourhood is a closed subset in that neighbourhood okay and if I vary X I get an open cover and now for each of the sets in the open cover I have verified that the inverse image intersected with that set of the open cover is a closed subset okay so this proves the lemma now let me prove another lemma which is the lemma that I want to apply there. So of course you know I am here I am looking at regular function either on an affine variety or a quasi affine variety fine okay so here is lemma 2 in fact if two regular functions agree on a non-empty open subset then they are equal if you have two regular functions they are equal on non-empty open subset then they are equal everywhere proof is two lines proof is trivial two functions agree on a non-empty open subset means the difference function is 0 on a non-empty open subset but any non-empty open subset is dense okay for the Zariski topology. So you have a function that is you have a continuous function that is 0 on a dense open subset so it has to be 0 everywhere so it is obvious so proof is any non-empty open subset is dense and it is just and a function which is 0 on a dense a continuous function which is 0 on a dense open subset has to be 0 everywhere simple topology. So if you apply these two lemma I mean I need this lemma now you look at now you look at this equation that I have written here in this equation you know if I calculate if I look at the product Hxi times phi the product Hxi times phi is Gxi and Dhxi okay but Hxi times phi is also a regular function it is a product of two regular functions and Gxi is also a regular function because you have already seen every problem is regular function so you are saying the regular function phi times Hxi is equal to the regular function Gxi on the non-empty open subset Dhxi therefore by this lemma it is the same everywhere therefore for Hxi times phi I can put Gxi okay. So what I will get is I will get sigma i equal to 1 to m fi Gxi equal to phi and that tells you that phi is actually that polynomial given on that given by the left side that is the polynomial that I wanted okay so now I let me continue so let me rewrite that sigma i equal to 1 to m fi Hxi phi is equal to phi this is equality as regular functions okay but Hxi times phi is the same as Gxi because Hxi times phi is equal to Gxi on Dhxi and therefore on whole affine space because of this lemma therefore I can replace Hxi times phi as Gxi everywhere so what this will tell you is that it will tell you that phi is actually sigma i equal to 1 to m Hfi Gxi and that is the end of the proof I have proved that the regular function is actually the function that you get by evaluating a polynomial what is that polynomial here is a polynomial okay that is the proof. So you see there is a tricky bit of commutative algebra coming inside the proof okay so the moral of the story is there is no difference between the ring of regular functions on affine space and polynomials on affine space okay so every regular function on affine space which is defined locally by gluing polynomials by gluing quotients of polynomials if you take a regular function on the whole affine space which you have gotten locally by gluing quotients of polynomials the resulting regular function is actually a polynomial in other what that means to what that means to say is that it is the function that is gotten by evaluation of single polynomial and that this is the this is that fact written in the form of an equation okay so you do not get anything new okay. Now you can use the same technique of proof to prove the other statements okay all the time you will use this fact that whenever the corresponding space is a union is contained in a union of finitely many basic open affines then the corresponding equations polynomials that occur in those that define those basic opens the ideal generated by that is the unit that is the key and then from that by applying this lemma you can get this you can get the proof for all the other cases okay. So in the case of so in all these cases your regular functions agree with the ring of functions that we defined the coordinate ring of functions that we defined okay so I will stop here.


Hi, I'm Sheila Allen. I'm chair of the board at Explorer Science Center. We're located on Fifth Street in Davis. We've been there for over 20 years. We're a community resource for our new scientists that are coming up and through. So we have a gallery that people can come and visit. And we also have summer camps. And but we are not just in Davis. We have a traveling program that goes to 18 counties all around California, to the north, to the south, to the ocean, and up to the mountains. So we bring science to the classroom. And so we are very excited to be here for the big day of giving. A great thing that we have this summer is for the first time we have an astronomy class for teenagers. And so they are going to be learning about what's going on out in space. So things about like exoplanets, planets, and other solar systems, about the talk about maybe going back to the moon again, and learn how to use telescopes, and learn about data that comes in to see how we can find out about exploration in other worlds. So that's just an example of one of the things that we're looking at this summer.


QuickBooks Desktop 2023 Budgeting Overview Let's do it within 2-its QuickBooks Desktop 2023 Support Accounting Instruction by clicking the link below giving you a free month membership to all of the content on our website broken out by category, further broken out by course. Each course then organized in a logical, reasonable fashion, making it much more easy to find what you need then can be done on a YouTube page. We also include added resources such as Excel practice problems, PDF files and more like QuickBooks backup files when applicable. So once again click the link below for a free month membership to our website and all the content on it. Here we are in QuickBooks Desktop, get great guitars practice file going through the setup process. We're going to do every time Maximize on the homepage to the gray area and the view drop down. Noting we got the hide icon bar open windows list checked off open windows open on the left hand side. We're going to open up the major financial statement reports that being the balance sheet and income statement reports drop down company and financial. Let's take a look at the profit and loss the P and L. I'm going to change the range here for the two months that have activity in it. That being 010123 to 022823 in our practice problem. I'm going to change it from the total here to a month by month comparison. So we'll break this down month by month. So we've got January February and then the total for those two month time frame or period. Let's customize it up top and then I'm going to increase the size to let's bring it up to like 1414. Okay. Yes. And okay. Let's also open up the balance sheet. The other primary report financial statement report that is reports drop down. We're going to go then to the company financial this time the balance sheet standard. I'm going to customize first and then change the date range going from 010123 to 022823. I'm going to make it from totals to months again so we could see both months and OK. Well not OK yet. Hold on a second. Let's go to the fonts and numbers while we are here changing the font. Let's bring it up to 14 to match what we did on the P and L profit and loss. Now we're going to say OK. There we have it. So next we want to be considering the budgeting process. So first let's just locate where the installation of the budget will be and the reports related to them. And then we'll talk more about when you might create a budget and how the budget kind of fits in with the accounting process and accounting department. So let's go up top and say OK. The budget can be found by going to the company drop down and then you're going to go into planning and budgeting. It's set up a budget from here. If I go into the set up budget gives me basically a little widget to help me set up a budget. Now in here we do have the profit and loss. We've got the balance sheet will actually start up the budget in a future presentation. But for now I just want to show that process and how you would start the budgeting process. And then we're going to have a data input field from that point. Once the budget is in place then you'll have reports which is the other side of things that can be found in the reports drop down and we can go down to the budgets. And we've got the budget reports the budget overview and the budget versus actual those being the primary two reports. So now now that we know kind of where those things are located for the data input and the reports let's consider when the budget would be in place how it fits in with the accounting department. So first thing to note is that budgeting in general is not just something that an accountant would do like automatically or if you're like doing bookkeeping for a customer then you wouldn't assume that you're just going to be doing budgeting automatically because the budgeting process is going to require some input from the management of the company beyond just the financial statement reporting in order to make projections into the future. So that's the first thing to note if you're doing bookkeeping the budgeting would be an added kind of piece that you might take on. But accounting in general is thought of as taking the past data the stuff that has already happened the stuff that we don't have any kind of question about it's not like there's uncertainty about it. And then reporting that in accordance with some rules or regulations in accordance with generally accepted accounting principles accrual principles or tax or cash basis however it is that we're entering that data into the system. And we'll be doing that of course with our forms here on the home page and that will then be used to create the major financial statements balance sheet and income statement as well as the subsidiary type of reports. So the accounting process is there to get those financial statements reports made from past data and to do the day to day routine activities such as collections and whatnot if you're involved in that kind of stuff as the time passes. The budgeting process of course is looking into the future. Now one of the primary tools that you have to look into the future is to take the past data. So clearly the past data is going to be important. Clearly accounting concepts are going to be important because you're going to need the accounting concepts to build the budget because the future budget will look like a budgeted financial statement balance sheet and income statement. So you're going to need that information but you can't do it basically by yourself. So an accountant for example could create a speculative budget on nothing else rather than past performance but that's not really the best budget that you want to be doing. What you want to do is take the past performance use it first as a tool a guideline and then make any changes that you're going to make which means you're going to need management in the business and if you if it's your business then you got to be thinking about what you're going to do in the future. Changes such as are we going to increase advertising? What's the economic environment going to look like? Are we going to decrease advertising? Are we going to add another department? Are we going to remove a department? Are we going to change the prices of stuff and what kind of changes are those things going to have on our projective incomes going forward because the whole point of making those changes is to try to think about what's going to be the result of those changes on future performance. Once we have that information in place then we can put it into QuickBooks. What QuickBooks is good at doing then is taking that information and making reports with it which means we're now can run reports such as budget versus actual as time has passed. So the general process that you might do with a budgeting process is say hey I'm an accountant, I'm on the accounting department, I'm doing the bookkeeping stuff. If I'm working with someone who's in a business or as a bookkeeper for a business I need the person that's making future decisions to help us determine things about the budget. And so then what I can do is take the past performance on the income statement or possibly with a trial balance, export it maybe to Excel, that's what I would do typically, and then make a budget out of past performance and then adjust that budget for any changes that we are thinking are going to happen in the future. The easiest way to kind of think about your baseline budget would be to take last year's income statement stuff typically because the profit and loss report is the performance report. So the first thing we think about with budgeting usually is what's the performance we're going to do in the future. It's kind of like if I was trying to see how far I can drive in a day. That means well I'm going to reset the odometer on day two and see if I can basically get further than I did in day one. That's what the income statement is. It's going to reset. We're going to see how far we can go say in a month or in a year. So we can take last year's performance and I can divide it by 12 on each line item for example and say this is basically my average performance on a monthly basis. That would be like the starting point of a budget and then we can try to get into more detail about what changes are going to happen going forward. And then once you have it mapped out in Excel then I would import it into QuickBooks using your data input and then the budget and planning and the company dropdown here making a budget which is just data inputting it into the system. The reason you want it in QuickBooks and not just in Excel is because QuickBooks can then run these nice reports as time passes the budget reports which are going to be where are the budget reports the budget reports. There they are. And so they have these budget versus actual reports. So as time passes then we can make these comparative reports which QuickBooks does quite well. So also just know you can get way into a lot more detail on the budget because the balance sheet for example shows where we stand at a point in time. So if you look at the balance sheet before the year begins. So if we were looking at the current year of 2023 and I looked at the balance sheet as of the end of last year 1231-22 that's where we currently stand. The income statement in essence is like the performance statement. So that's the one we're thinking how far are we going to go. That's where our focus is on. But then the balance sheet is going to show us where we stand after the performance. So if I'm looking at January 1st 2023 where do we stand after that time frame had passed. The balance sheet is a little bit more difficult to construct. You know to kind of think about how where are you going to end up at the end of the period. There's a lot of different methods that we can get into more detail with budgeting. We get into managerial accounting to talk more about that kind of stuff. If you want to dive into different kinds of budgets in more detail. We also have some issues with the budgets in regards to the profit and loss. For example could be on an accrual basis versus a cash basis. So we could have an accrual based budget and then we might want a cash based budget right. And so you could have differences in that kind of stuff with regards to budgeting so we can drive we could dive way deeper into a rabbit hole on budgeting in general. We won't focus on that mainly here. Our focus mainly here will be what's the role of the accounting department. What's the general process for creating a budget. We'll think about exporting the information so that we can construct the budget like in Excel. And then importing that data back into QuickBooks so that we can use it to generate reports to hopefully improve performance in the future and then continue the process over and over again. So that's what we'll dive into in future presentations.


When I used to teach medical students at Tufts, I gave a lecture about this amazing new therapeutic called ilocore B. I talked about all the new signs, all the things they could do, excellent safety profile, and just as they were all scrambling to buy stock in the company and prescribe it to all their patients, I did the big reveal, apologizing for my dyslexia. I had gotten it backwards all this time. I had been talking about broccoli. Sulforaphane is thought to be the active ingredient in broccoli, which may protect our brain, protect our eyesight, protect our free radicals, induce our toxification enzymes, help prevent cancer, as well as help treat it. For example, I've talked about how sulforaphane can target breast cancer stem cells, but then I talked about how the formation of this compound is like a chemical flare reaction requiring the mixing of a precursor compound with an enzyme in broccoli, which is destroyed by cooking. This may explain why we get dramatic suppression of cancer cell growth from raw broccoli, cauliflower, or Brussels sprouts, but hardly anything from boiled microwave or steamed, except for microwave broccoli that actually retains some cancer-fighting abilities. But who unsteat raw Brussels sprouts? I shared a strategy, though, for how to get the benefits of raw in cooked form. In raw broccoli, when the sulforaphane precursor, called glucoraphanin, mixes with the enzyme, called myrosinase, because you chopped or chewed it, given enough time, sitting in your upper stomach, for example, waiting to get digested, sulforaphane is born. Now the precursor is resistant to heat, and so is the final product. But the enzyme is destroyed, and with no enzyme, there is no sulforaphane production. That's why I describe the hack-and-hold technique. If you chop the broccoli, Brussels sprouts, or kale, collards, cauliflower first, and then wait 40 minutes, then you can cook them all you want. The sulforaphane is already made. The enzyme has already done its job, so you don't need it anymore. When most people make broccoli soup, for example, they're doing it wrong. Most people cook the broccoli first, then blend it, but now we know it should be done the exact opposite way. Blend it first, wait, then cook it. What if we're using frozen broccoli, though? Here's the amount of sulforaphane found in someone's body after the broccoli soup made from fresh broccoli. It's their bloodstream within minutes. Here's after frozen. Commercially produced, frozen broccoli lacks the ability to form sulforaphane because vegetables are blanched, flash-cooked, before they're frozen for the very purpose of deactivating enzymes. This prolongs shelf life in the frozen food section, but the enzyme is dead by the time you take it out of your freezer, so it doesn't matter how much you chop it or how long you wait, no sulforaphane has got to be made. This may be why fresh kale suppresses cancer cell growth up to 10 times more than frozen. The frozen is still packed with the precursor. Remember, that's heat-resistant, and they can make lots of sulforaphane out of frozen broccoli by adding some exogenous enzyme, but where are you going to get myrosinase enzyme from? Now, they bought theirs at a chemical company, but we can just walk into any grocery store. This is another cruciferous vegetable, mustard greens. All cruciferous vegetables have this enzyme. Mustard greens grow out of little mustard seeds, which you can buy ground up in the spice aisle as mustard powder. So if you sprinkled some mustard powder on your cooked frozen broccoli, would it start churning out sulforaphane? We didn't know until now. Boiling broccoli prevents the formation of any significant levels of sulforaphane due to the inactivation of the enzyme. However, addition of powdered mustard seeds to the heat-processed broccoli significantly increased the formation of sulforaphane. Here's the amount of sulforaphane in boiled broccoli. This is how much you get if you add a teaspoon of mustard powder. That's a lot, though. How about just a half teaspoon? Worked about just as well, suggesting maybe we could use even less. Domestic cooking leads to enzyme inactivation of myrosinase, and hence stops sulforaphane formation. But addition of powdered mustard seeds to cooked cabbage family vegetables provides a natural source of the enzyme, and then it's like you're practically just eating it raw. So if you forget to chop your greens of the morning for the day, or are using frozen, just sprinkle some mustard powder out on the top at the dinner table and you're all set. Or some daikon radish, or horseradish, or wasabi, all cruciferous vegetables packed with the enzyme. Here they just used like a quarter teaspoon for seven cups of broccoli, so just a tiny pinch can do it. Or you can add a small amount of fresh greens to your cooked greens, right? Because the fresh greens have that enzyme that can go to work on the precursor in the cooked greens. One of the first things I used to do in the morning is chop my greens for the day, and so when lunch and supper rolls around they're good to go, as per the hack and hold strategy. But now with the mustard powder plan, I don't have to pre-chop.


Hello everybody, Andrea Mayesca here with Dental L Mobile Hygiene. So why would somebody get their teeth cleaned by a mobile dental hygienist? Meaning, why not just go to a dental office and get your teeth cleaned? So that is a question that I do get asked often. Even when I first opened up the business, a lot of people said, a mobile what? A mobile hygienist? What is that exactly? So I thought, well, you know, it may be obvious to me, but it's not obvious, obviously, to everybody else. So basically, since 2007, dental hygienists have been allowed to open up their own practice. So we can work on our own. We don't have to work under, I guess, the order of a dental, or sorry, of a dentist. But you do have to be of a certain type of dental hygienist to be able to do that. So it is called a self-initiating dental hygienist. And to become self-initiated, you have to be practicing for a number of years. Plus, you need to take a course to say that you are capable to work on your own. Because we have to know certain things about the medical history. We have to know medical emergencies. We have to basically know and be prepared for anything to happen. Any type of medical emergency, not going wood, any special needs patient. We have to know the pharmacology. We have to know medications. We have to basically just know everything. You know, I mean, not everything, obviously, but we do have to know a lot. But also to own your own practice, you have to go through extensive courses for infection control, instruments, sterilizing, again, pharmacology or pathology. We have to apply for a business license, so all kinds of things. So not just any dental hygienist can do it, you have to be motivated. You have to go through a lot, but it is completely worth it. But why would you see me, let's say, opposed to just going to your dentist and seeing them? Well, the nice thing what I like to provide is that I come to you. So I am a mobile dental hygienist, meaning I bring all of my stuff and I set up my stuff in your home, office, just pretty much wherever you are. So I basically have a chair for you, I have a stool for myself, I have my instruments, my cassettes, my dental supplies, my compressor unit, which is about 30 pounds. It's tiny though, which is nice, it's just heavy. My compressor unit with the air, the water, all of that. So I come to you like a little mini dental office. And the nice thing is you guys is that you are in the comfort of your own home. So you don't have to smell those dental office smells, hear the dental office noises. You do not have to be sitting there in a waiting room super nervous, waiting to come in and the dental office is half an hour behind, you know, I come to you, so there's no waiting because I'm always on time because I don't book patients back to back either. So even if I'm over there and I have a patient, let's just say till about 10 o'clock, I don't book another patient till about 12.30 so that I have plenty of time to take my time and then go to the next area. So I don't book patients back to back because I do have to account for my travel time. So you also save time and money because you don't have to travel to a dental office. You don't have to worry about being bad, whether if your office is out of town, you don't have to worry about having to take the highway, you don't have to worry about taking time off of work either because I will come to you when it suits you. I do a morning appointments, evening, afternoon, everything.  Plus I have about 14 years experience now, so there's no question that you can ask me that I won't know. And if for some reason I don't, I will find the answer for you. Plus I've been a tutor for dental hygiene students and dental assisting students since about 2005. So I'm constantly being kept on my toes because I need to know the latest of what's happening because I tutor students almost every single day. So I do do a lot also and it's just, it's just nicer. Plus it's a little bit less expensive too because being a dental hygienist who owns her own clinic, we have a certain fee guide that we follow and our costs are a little bit less than if you were to go to a dentist's office because we don't hire staff. We don't have a dentist on staff either where we have to pay them for their time. It's just me. It's just me. So I do follow the fee guide, but my costs are a lot less than if you were to go to a dentist's office. So if you're in my area, just as an example, a cleaning depending on how long it's been since you've had your teeth cleaned is about $120 for children. It's about $65 to $100. If you're 15, it will probably be closer to $100 for teeth whitening. I do have a promo on this month, which is $90. Even then the regular price is about $200. That's it. If you were to go to a dentist's office, a cleaning is at least $165. Like that's the minimum, where my minimum is $120, so that's a lot less. So I think whitening in a dental office is anywhere from $300 to $500, depending on the type of system that they use. My system's excellent. It works. It's amazing. I do have a lot of before and after pictures on my Facebook page, so have a look. They're amazing. I charge $200 regular price for the whitening, whereas a dental office charges $300 to $500, depending on the system that they use. For a dentist's exam, for them to just kind of come in to have a look is about $28, which isn't bad, but you don't always need a dentist's exam. I suggest, I mean, everybody's different, but I suggest having one at least once a year, but there are so many people out there that just simply won't go to the dentist because they're nervous. Well, I can help you because you don't have to go to a dentist because I'm not a dentist, right? I can come to you, clean your teeth, make sure that everything looks nice, nice and healthy. If I see a cavity in there or something that I don't like, I will let you know and tell you you should see a dentist, but I also might say, you know what, things look pretty good. You don't have to see a dentist right away because you are doing a good job. Things look good. Now, I'm not perfect. I can't diagnose. I was trying to think of the word.  You should really get that looked at versus, oh, you're having pain. Well, let me have a look at that. Oh, the pain is to chewing only. Well, it could be this. It could be this. I suggest having that looked at. So that's a big difference than having to go to the dentist knowing you will be charged to have a look at it, whereas at least I can kind of help you that way too. But again, it's still important to go to the dentist if you have pain. So let me just say that, okay? And even if you don't have pain, something might still be happening. So go see a dentist for a checkup at least once a year. That's what I do suggest to everybody. But again, there's so many people out there that just won't go to the dentist. So at least they can feel better. I'm looking at them, letting them know kind of how things look. What else did I want to talk about with you guys? Plus, I do fully accept insurance, which is amazing. A lot of insurance companies say, well, yeah, she's a dental hygienist. She cleans teeth. Yes, it is covered by insurance. So what I do is covered by insurance, which is fantastic. So you're paying less. And if you do have insurance, it is covered. If you don't have insurance, that's okay, because I do charge less than a dental office. Dental L mobile hygiene is perfect for students, you know, seniors, adults, children, teen. It doesn't matter because I come to you. When I was a student, it would have been so nice to have a dental hygienist come to me to clean my teeth. I was a student in many different cities away from home. I didn't necessarily want to go to another dentist because when I came home, well, I did have one there. But if I could have had a dental hygienist come to me just to tell me that things looked okay, have my teeth cleaned, whitened, that would have been amazing. So I am so happy to be offering this to everybody. So come see me. I'm so happy to help because I come to you in the comfort of your own home. It costs less. You don't have to hear the dental sounds, the dental smells, any of that.  If you have any questions, please let me know. Feel free to check out my website. I will leave the link for you on the bottom. And I do also have a page as well at www.facebook.com slash dental L mobile hygiene. Thank you guys so much for watching and if you have any questions, let me know.


In this video I'm going to teach you how to become a better defender by understanding your positioning, defending your man out of the game knowing when to press, when to cover, and what to do when your team is in possession of the ball.  You can learn from analyzing and understanding other positions.  So you need to know what to do when you're in those situations. Today's tutorial, we're focusing on defending. So I've put a back four and two defensive midfielders and just a few red attackers to demonstrate some situations. So this first tip, it's not actually a tactic. This is a mentality, but it's very important to understand and play with this mentality every time you step on the field. I always say good defending usually comes down to two things. Number one, positioning and number two, passion. Be passionate about your defending. Don't let your man score or don't even let your man create a chance. Even more so if you can, don't let your teammates man score or create a chance. Take pride in your defending. Be passionate about stopping attackers. Don't let someone jog past you.  Don't let someone dribble past you.  When you're in a one-on-one situation, have the mentality that there is no way that this guy is getting past me. If the ball comes into the striker's feet and he's trying to turn, there is no way that he's going to get a shot off on my net. You need to take pride in your defending and that happens all over the field. You're going to learn and develop the defensive skills necessary to be a good defender. You're going to understand when to press and when to tackle and when not to. But it all starts with this mentality. You need to be passionate about your defending. No one gets past you. No one puts a cross into your box. No one beats you in a one-on-one situation. No one scores a goal on your net. This is your field. This is your ball. This is your game. So if he's going to try to score against you, he's really going to have a difficult time today. Most players get caught out of position because they are ball-watching. They're only watching the ball. They're not aware of where their teammates are. They're not aware of where the man they're marking is. And they're only focusing on the ball. They're not aware of what's going on around them. And that's a recipe for defensive disaster. Whenever your team is defending, you should always be focusing on your positioning, asking yourself, where should I be, and adjusting as the play moves. Now there's three things you need to think about. Number one is the ball. Where is the ball? Number two, where are your teammates? And number three, where is the man that I am responsible for? When defending, you want to get behind the ball as quickly as possible. So if we lost the ball, how do we need to get behind the ball as quickly as possible? You want to get close to your teammates. You don't want to have big gaps like this. You want to get close to your teammates, and you want to get in your defensive shape. So however your team was set up on the team sheet, that's the shape that you want to look like when you're defending on the field. You also want to be aware of where the man that you're marking is. So when that ball comes to him, you can get to him closely. So get ball side, get into good team shape, nice and close together, and get goal side inside of your man. So if this is my man, I want to be goal side of him, closer to my goal. If he's here and I'm here, he's goal side on me. I need to be goal side of him. I want to be inside of him. If this is my man, now I'm goal side inside of him. This is my goal, I'm closer, I'm inside on the goal. If he's here and I'm there, he's inside of me. So I want to be somewhere like this. So ball side, goal side inside in your team defensive shape, nice and tight moving together. Now as the ball moves, we are going to move as a unit. So the ball gets shifted out here. If it goes to the right, we're all going to move as a unit to the right. If the ball gets shifted and it comes to the left, we're quickly going to move as a unit to the left. Everyone moves together, keeping good defensive shape. If the ball goes up the field, we have to get up and we have to keep in a line. You don't want to be staying back and then suddenly you're keeping everyone offside and they just play a little ball over the top. So you need to get up, move as a unit. You should be keeping your shape as you move around the field. If the ball gets shifted down, everyone needs to get back behind the ball in good defensive shape. So we're always moving left, right, up and down together. When you do this, you're protecting yourself.  You're protecting a ball over the top because we're in good shape and we're keeping a good line. We can defend that. We can get there quicker than the attacker.  So because we're close together, if he gets beaten, we're here to protect each other. If there's big gaps, we can't protect each other if he gets beat. And you're protecting yourself in one-on-one situations because you know where your man is and you can get there quickly if the ball gets to him. It requires everyone to focus on their positioning for the entire game but it makes it extremely difficult for the opposition to get through this well-structured defense. When there are large gaps in the team and players lose their concentration, especially when you start to get tired, you get out of position and then suddenly our shape doesn't look so good. We have big gaps like this. Now it's easy to play through and the other team is going to create lots of goal-scoring chances. So always focus on your positioning in relation to where the ball is, to where your teammates are, and to where the man that you're marking is. Ballside, goal-side, inside. Always focus moving together as the ball moves around the field. The further the ball is away from the man that you're marking, the more space you can afford him. So if I'm supposed to be marking this man, I'm responsible for him, and the ball is on this side of the field, I can give him more space. As that ball comes, then I'll adjust and I'll get there quickly because it will take time to get there in the air or take time to get shifted around the back. But I need to anticipate and as I realize that the ball is getting potentially closer to the man that I'm marking, I am giving him less and less space because as he receives that ball, I want to be very close to him and also everyone else has to be anticipating where the ball is going. So we're all close in a nice tight unit. Anticipate rather than react. You're already getting good at reading the play because you're watching the ball, you know where your teammates are, and you know where the man that you're responsible for is. Now you want to get in the habit of reading the player on the ball. Look at his eyes, look at his body shape. Most of the time you can tell where he's going to play the pass before he even does. You want to anticipate when this pass is being played to the man that you're marking or when it might be played into the space that you're responsible for. When you can do this, you can either read the pass and intercept it before your opponent gets to it or worst case, you can arrive as the man that you're marking receives the ball and force him to go backwards. When you give your opponents lots of time and space, that's when they can hurt you. If you don't give them this luxury, you become in control of the situation.  As the ball is coming to your man, anticipate that and get there right as he receives it. Force him to panic, force him to have a bad touch and then our midfielder can win it and we'll gain possession of the ball. Worst case, he does have a good touch and our midfielder can come and double up and hopefully will win the ball and keep possession. Or he's forced to go backwards and that's fine as well because we're still doing a good job of defending our net, defending our defensive zone. If you can get good at this and you can anticipate that the ball is coming and you catch him waiting for the ball, you can even jump in and win possession of that ball. However, you need to be cautious and really pick your spots. Only do that if you know that you're going to win the ball.  You are the player closest to the ball. You want to press. If you're worried about getting beat, you just want to slow this player down and force him to go sideways or backwards. If you are not the player pressing the ball closest to the ball, you want to cover the space in behind because if we get multiple players going to the same ball, we create space for other attackers to get into. We leave gaps and we compromise our team's defensive shape. As the player closest to the ball goes to press, you want to keep your shape and you want to protect the space in behind him because if he does get beat, for example, let's say he gets beat and this player is in this space, you'll be there to cover his position.  Don't waste a second complaining. Quickly turn and get back into your team shape. Now, what you may have to do is cover the position of the player who went to cover you. One more important example I want to illustrate is what happens if you press your opponent when he's on the ball and he plays a pass and then makes a forward run. In this situation, what happens is most players go to press the ball and as this ball is passed, they make the mistake of watching the ball and they move towards the ball rather than worrying about their man who is making the dangerous run. What I want you to do in this situation instead is, yes, close the man who's on the ball, go to press him, but as that ball is being passed into here, you need to track the run of the man that you are marking. Let this player worry about him. Unless you know you can win this pass because he made a bad pass or this player had a really heavy touch, so say that ball is played into here and he plays it into there. If you know you can win it, then yes, go for it. But if he quickly plays that pass and then he's making a forward run, drop off immediately and try to stay goal-side inside of this player. Let this defender handle this, let the mid-feelers come to double up. You need to mark the dangerous run that this player can make because if he plays that pass and gets in behind, so he gets the ball here, you go to press, you close, he plays that pass, you go here, he comes in behind, now he's in a very dangerous position all by himself. I've made an individual defending technique video that I want to share with you and I'll post that link in the description of this video. But I just want to give you a few ideas about individual defending and some tips that will help you be more successful. Number one, don't give up your goal-side position because you're trying to win the ball. So let's say you're defending this player. What you don't want to do is try to win the ball on this side of him, being overambitious and lunging in on this side of the player. Worst case, you force him to go backwards, but you don't want to give up your goal-side position because if he turns you, then he's in behind and there's no one there to protect the space. So keep your goal-side position when you're defending. Don't dive in or approach the attacker with too much speed because all it takes is a little touch and he's going to get past you. Yes, you do want to jockey to a certain degree. You need to realize that there's a big difference between jockeying, staying with your man and giving him too much space so he can put a cross into the box or make a dangerous forward pass. So I want you to close down quickly. Yes, be cautious and don't dive in, but close down that space. Be confident in your ability to defend and your ability to move laterally quickly. Stay light on your toes and if he does try to take you on, be ready to move with him. So close down that space, don't dive in, but if this player has a heavy touch, he shows too much of the ball to you, don't feel like you always have to jockey. Sometimes the best move is just to stick a hard tackle and win possession for your team. When you're on the ball, keep things simple, but don't be afraid to join in the attack and start attacks from the back. First of all, get your width. Yes, when we are defending, we want to be nice and compact. We don't want to give them space to play through us, but when we're attacking, we want to do the opposite. We want to get really wide to force the opposition to chase the ball. So the full backs are going to get nice and wide. Center backs are going to spread. Then we're just going to move the ball around the back, mostly to touch, moving the ball quickly, forcing the opposition to chase, keeping that ball and using a lot of pace on your passes to ensure that that ball moves quickly. Now, as a defender, you need to know your role.  You'll get your chances to attack and you'll get your chances to score, but you need to know your role and you need to play the ball to the attackers and let the attackers attack. However, that doesn't mean you can't support the attack, especially as a full back. You need to be getting forward all of the time. Play the ball into your attackers, let them do the attacking, but give them supporting options.  Specifically as a center back, always think about creating angles of support. So as any player on the field, whenever my teammate has the ball, I should always be thinking about creating passing angles, places where he can get me the ball rather than hiding behind defenders. But especially as a center back, you always want to think about giving good supportive angles. So if the ball goes into my full back and he gets closed down, this is not a good supporting angle. I want to be somewhere like here. If the ball goes into my central midfielder and he's getting closed down, or even if he's not getting closed down, I still want to give good supporting angles from both center backs. You want to give options. If the ball goes into my goalkeeper, I want to give those options right away and give opportunities for people to give us passes. If your team is on the ball and our center backs aren't giving supportive angles for a pass, we're forced to play the ball forward either by dribbling when we shouldn't be dribbling or just clipping the ball over the top. So when your team has the ball, always think about where should I be to support this play. And as this other center back, you can already anticipate that that ball is going to come to him and then it's going to come to me and then I'm already in a position. I'm already in a supportive angle and I can switch the play and start the attack. As a full back, you also want to be creating angles for your teammates to pass you the ball and help them get out of trouble. If the ball goes into defensive midfielder, again, you want to support and give an angle so he can get out of trouble. You do, however, have more license to get forward. So let's say that ball went into my winger. If he's going inside, I'm going to take that as an invitation to overlap and get on the outside. And when you do get into these good attacking areas, make sure you take a deep breath and you focus on your quality, whether that's whipping a good ball into the back post for someone to attack or just putting a ball across the face of goal inviting someone to come and score. If my winger does get on the ball and he's attacking and he gets closed down, again, I want to be a supporting the attack, creating an angle for pass to get the ball so we can quickly switch it or I can even dribble into this space and start attacking. You can also dribble out from the back if there's no options. However, you need to be very cautious when you're doing this because losing the ball in this situation can be extremely dangerous. So dribble into this space. If that's your option, be confident, dribble into this space, then release a pass and again, focus on creating those supporting angles. Everyone gets up the field. You can also play more forward passes, whether you're playing center back or full back.  You can play a nice diagonal ball to get the ball to the feet of your winger and start an attack or you can notice the run of a striker whether that's coming to the ball and then spinning, trying to clip a ball in behind or just anticipating his run in behind the last defender. So don't be afraid to play these passes. You don't always have to play nice little passes on the ground out of the back. In fact, it's good to vary your play because it keeps the opposition honest. Most importantly, take care of the ball. I encourage you to play out of the back, move the ball around the back quickly and keep possession of the ball as a defender. Be confident with the ball at your feet but realize that losing the ball as a defender is extremely dangerous. So be cautious when it comes to losing possession.  As long as when you do, you're quickly giving those supporting options and allowing the keeper a way to play out from the back. I just want to give you one little bonus tip that will be helpful whenever you're defending whether you're playing center back or full back or even as a midfielder. When you're going to attack a goal kick or a long ball, you're trying to win a header, just one helpful tip that will help you win way more headers. Instead of this ball being played and we're both jumping from a standstill what you want to do is take a few steps back even one or two steps back and then attack the ball. So instead of jumping flat footed trying to get as high as you can what you want to do is take a few steps back and then as that ball is coming you're moving towards the ball and this forward momentum will allow you to jump higher and attack the ball better than your opponent who's jumping from a standstill or trying to make a shuffle step backwards and then jump. So take that little tip and apply it whenever you're defending goal kicks or long balls take two steps back two steps forward use that forward momentum to come and win the header. Thanks for watching this video please like this video with a thumbs up before you leave if you have any questions on this topic or any topic comment below share this video with your friends and teammates and come back tomorrow because we're going to keep improving and keep moving towards your goals I'll talk to you guys real soon


Hey folks, we're answering frequently asked questions from the Octa customer identity cloud community and today We're troubleshooting a missing user ID when SAML mapping This area is something that can occur with SAML Enterprise Connections And it will occur when the SAML connection on the Auth0 side is configured to generate a user ID based on an attribute that did not appear in the SAML response sent from the identity provider You can configure which attribute you would like to have included in the user ID either with the mappings tab here or on the main settings tab with the user ID attribute To troubleshoot this a good first step is to check the decoded SAML response to make sure all of the expected attributes are coming through To find this you will need to enable debug mode for the connection You can then go back to the log Scroll down to find the SAML response You can copy this value and paste it at SAMLTool.io If you then scroll down you can see the attributes that are coming from the identity provider In this case we have name identifier and email address If there's a value that you're expecting to come that you don't see here You'll need to check with your identity provider for a misconfiguration In this example the identity provider is sending a name identifier with a unique identifier and an email address When we go back to the mapping tab for our connection We see that name identifier is being used for the user ID value So we would expect this to work. However back on the main settings tab Email address is configured as well. If this value is set it takes precedence over the field mapping done on the mappings tab Email underscore address was not the name of any attribute coming from the identity provider Which is why we saw the error message that no user ID was found To resolve this we can go back to the SAML response Copy and paste the name of the value that we would like to use We want the email address so we will copy this We can go back to the settings page here and Paste this value in hit save. We'll now see that a successful login will occur Go to an example log here and the user ID is now set to use the strategy The name of the connection and then the email address for the user So today we went over troubleshooting a missing used ID when SAML mapping If you found this helpful, please like and subscribe to us on YouTube and join us for more content on community.auth0.com Thank you


All right, everyone, welcome back. I hope you had a chance to take a break, refill your coffee, have a glass of water, hug someone you love. We're back for our deep dive session. Well, we will be able to hear from our chapter authors with some more detail, the nitty gritty and the details most of you have probably been waiting to hear more about. And so we'll begin with Professor Richard Laird, who will be taking us through chapter eight, again, on living long and living well, the well be approach. OK. Well, thank you so much. This is a chapter written jointly with Kaccha Arparina. And when we were writing it, I began to think why wasn't this chapter in the first issue of the World Happiness Report? Because surely this is a basic issue for you looking at the amount of happiness, which is being delivered by different nations. It should surely include not only the average well-being at a point in time, but how long each individual manages to experience their well-being. And that really matters not only for policy, but also for the performance of nations and how we evaluate that. So I think it's obvious how we would move to include that. And I'm going to have to test my skill to the limit here. Right. So for each person, we would be concerned about their total experience of well-being, which is the sum of their well-being over all their years of life. We're calling the well-being experience in one year a well be, so for each individual, we are wanting to see the maximum sum of well-bears over their lifetime, which, as I said in the previous session, could be thought of as the average well-being each year times the number of years. And that's a good way of thinking about the performance of different countries. So here is the top of the slide, the basic equation. We think of social welfare as the objective that we value as being equal to the average well-being of the population of the country times the average years of life of each person born there. So we can now apply that equation to thinking about human experience since the Gallup World poll began in 2006, because we are interested in looking at what happened to average well-being, what happened to life expectancy, and then what happened to the product of the two, which is the well-bears per person. So you can see that the average well-being up to 2019, when I did these sums, because we've got the figures exactly, had gone down a bit. But life expectancy had gone up by 3.7 years. And as I mentioned, that's happened in particular in areas which started with low life expectancy and well below average well-being. So it's a hugely equalizing development. If you then ask what happened between 2019 and 2020, John's been explaining average well-being roughly constant up in some countries down in others. But life expectancy, we are estimating, was down about 0.3 years. That's got by an estimation for the US that life expectancy went down by one year. And we know the number of deaths per million. And if we assume the same relation between life expectancy and death per million in all other countries, we find that world life expectancy will have gone down by 0.3 years, which doesn't, in any way, fully offset the gain of 3.7 years. So in that sense, we've seen some progress. So that's the sort of accounting for human experience. And I wonder if we shouldn't be incorporating this kind of analysis in future reports. Now let's go on to policy. Then, of course, we're looking forward. We're wanting to maximize the future well-being per person born with a bit of discounting, but not too much because we want to give proper weight to future generations. So that's the thing which we're wanting to maximize. If the total expenditure is fixed, policy should be improved if the gain in terms of that expression higher up on the page relative to the net cost is above some cut off value, which exhausts all the available funds. So this is really the approach that we have been pushing in discussions with officials in all kinds of organizations, including EUE, OECD, and, of course, Britain. And of course, you've got to persuade people not only this is philosophically the right way to think, but it's feasible in terms of do we have the numbers to put into these calculations. So going back about five years in our group at LSE, we decided to try and put a lot of numbers together in one place that were internally consistent in the sense that they used the same outcome measure, which was life satisfaction. And they used consistent set of equations on seven or eight different survey bodies of data. And we put that in origins of happiness. So I think we've got quite a good naturalistic understanding of what is generating a person's well-being at a point in time. But that's, of course, not the same as knowing what a policy change would do. And I think where the happiness research literature is weakest is the quite small numbers of experiments where outcomes have been measured in units of happiness or well-being. And I think one of our main objectives is first to get everybody, whether they're part of our world or some other world, to include well-being questions as outcomes in every experimental evaluation. And then, of course, to give that outcome priority at a place when you are evaluating the success or otherwise of the experiment. Now, I just want to end more or less on a thorny issue, which is that, of course, if you're evaluating policies that affect both a person's income or income of the community and length of life against a single criterion, you must be implicitly implying some relative value between money and a life year. Some implicit measure of the monetary value of a life year. You can't avoid that. And here is what the way we are doing these things implies in terms of that implicit value. So if a life year is lost, we simply saying, well, that person didn't live that year, and they would have had, on average, a citizen for a rich country, 7.5 well-biz. So that's the value of a year of life lost. We also know from these equations that if a pound of household consumption is lost, 1 over 100,000 well-biz are lost. So that implies that a year of life is of equal value to $750,000, assuming they're spread widely over people at their existing margin utility of income. That is a very big number. It's much bigger than the numbers which are currently used in both Britain and America. For example, in America, the typical valuation is near, let's say, $250,000. In the UK, the official valuation is $60,000, which is close to coming up to $100,000. These are got by very shaky methods. So the people who use these methods are, of course, shocked when they see what our method is producing. The US one is based on wage differences between jobs with different fatality rates, which, of course, assume perfect information. It's also thinking that you should value things in this ex-ante way rather than what actually happens when somebody dies and what is lost ex-post. The UK method is based on hypothetical questions like willingness to pay for a reduced probability of death. But that's an incredibly different question for anybody to answer. And typically, for example, in one survey, it was found that people gave the same amount of money they were willing to pay for reduced probability of death of four in $100,000 and $12,000 in $100,000. It's so difficult to answer that question. So I think we're entering here a pretty open territory where we can push our own method. And one thing which one can certainly say, and many people have said it, if you use the existing values that the US and Britain use, you would never have any lockdowns. You only get a lockdown to be justified if you're using a method which implies this sort of really high valuation of life. Let me just end with some facts. Using this method, it's interesting to see what has been the impact on social welfare of a few things which we can identify. And it is quite interesting that actually the loss of GDP has caused as much loss of social welfare as the loss of life. But of course, as I think John probably is about to point out, what is interesting is that the GDP has been lost in those countries where life has also been lost because of failures of policy. And the correlation between loss of GDP and the loss of life is positive, quite a large correlation. So I'm with John and Jeff and others who have been speaking that certainly the only correct policy was to try and absolutely stamp out the virus. But for most policies, and Jeff kind of referred to that earlier on, for most policies, there are trade-offs and the well-being approach should be used. Thanks. Thank you very much, Richard. There are a few questions that have come in from the Q&A box, and so I'll pose them here for you because I don't think listeners are unable to unmute themselves. So the first question that's come in is how are well-beings different from qualities? Well, a quality is the so-called one, it's a so-called health-related quality of life. So it's not really how you're feeling. It's based on the EQ5D and some rather weird weights which are applied to the items in the EQ5D, whereas ours is just life satisfaction. That's first the measure. But then there's a question, obviously, of who's affected? The quality doesn't usually take into account even the family members. So we're obviously interested in taking out everybody who's affected. And of course, we're interested in applying this to every kind of policy, not just the health intervention. Thank you. The next question that has come in is how can the well-be approach account for fluctuations of well-being in a country over time? Well, it will measure them. I mean, it can identify them. That's what we want it to do. And I think it ought to become a standard reporting measure. We haven't tried this on our own Office of National Statistics yet, but it occurs to me that's the next thing for us to be doing. Thank you. I see another question here. I believe this one has come in from YouTube. This person writes, I also believe in the use of well-being as finality. In my study, I pointed out the use of well-being for sustainability. Do you believe in the connection between sustainability and well-being? Very good question. Extraordinary important question. I mean, this relates, of course, to the question of the discount rate. And I think that one of the problems which arose in the early stages of the climate change debate was that if you use a sort of typical discount rate that are being used by economists that say four or 5% real, really what happens toward the end of this century is of hardly any importance. And that led to the downplaying of the seriousness of the climate change threat. I think the well-being approach starts from the basic proposition that every human being is equally important, wherever they live, whoever they are, and whenever they live. So a life lived in the future is as important as one lived at the moment. And when it comes actually doing policies, because hopefully human race will go on more or less infinitely, you get into an absurd position if you don't apply some sort of discounting to the future for uncertainty and the general impossibility about looking too far ahead. So a small, mild discounting, I think, pure time preference rate of 1 and 1% is a perfectly reasonable number to use. The result of this, though, is this very interesting thing, that there is a natural partnership between people who are concerned about well-being and people who are concerned about the planet. And I think I see it from our side as arising from the fact that we think all people matter whenever they live. But the fact is that it's very often the same people who care about both these things. Wonderful. Thank you so much, Professor Laird. I think that is the end of our questions, and we'll move on to the next speaker. Thank you.


Hello friends, so we have taken another question to solve here and we are again solving a quadratic equation by Sridhra Charya's method which is also called quadratic formula method. So we have to solve this given equation where abx square plus b square minus ac times x minus bc equals to 0. So if you notice here there are no numerals in the equation all are in terms of constants represented by ab and c and the variable is x correct. So how do we solve this equation? So before that let's revise what is Sridhra Charya's rule. So there we understood that the solution to a given quadratic equation will be of the form of minus b plus under root d upon 2a and x is equal to minus b minus under root d upon 2a. Now here don't get confused with the a and b which is given in the equation here and the a and b we are writing here. So in the formula a is coefficient of coefficient of x square and b is coefficient of coefficient of x and c is coefficient of or it's a constant term correct so don't get confused. So a b and c here are in the formula this formula when we are talking about this formula then we are talking about abc which are coefficient of x square of bx and constant term respectively okay. But in the given question ab in this equation ab these are different from what we are talking about here okay so hence let us now try to solve it. So first of all d what is d? d is nothing but b square minus 4ac correct. So just to avoid confusion we can write small a as a so hence you can say in this case let us say this is capital A this is equal to capital B and this is equal to capital C where the equation is ax square plus bx plus c equals to 0. So hence what is a? a is given as in this question a is nothing but if you see a is ab what's b? b is b square minus ac and what's c? capital C is minus bc right these are the few things a is ab b is b square minus ac and c is minus bc okay. So let's first find it out find the discriminant discriminant is b square minus 4ac okay so what is b square in this case let me just write I should not write the small letters anymore why because we are using capital letter for the equation right. So hence d is capital B square minus 4 capital ac okay in this case just to avoid confusion and for no other reason we are now treating it as capital A b and c okay because there are small a b and c in the given equation okay. So it is capital B square b square will be nothing but small b square minus ac whole square and whole square minus 4 times a a is ab and c is minus bc okay.  So if you notice this is again giving us a feel of you know square of a binomial so hence this is nothing but if you see this is b square plus ac whole square so d is this much this was our d now what is the solution then x is equal to minus b plus root of d upon 2 a and x is equal to minus b minus root of d upon 2 a both would be the solution again so instead of a b and c I should be writing a sorry for this confusion so I will be writing plus b minus b plus root d upon 2 a and similarly here it will be minus b and here it will be 2 capital a right 2 capital a okay now what let's you know deploy the values and get the solution so x is minus b minus b is my friends minus b what is b here so minus capital b will be simply minus of b square minus ac so hence it is minus b square minus ac plus root of d d is b square plus ac whole squared upon twice of a and a was my dear friends what was a let's see what was a a was a b so a b yep if you see a is a b yep so now next solve this and similarly here x will be equal to nothing but minus b square minus ac then minus root of d so b square plus 4 sorry not 4 ac whole squared under root divided by divided by 2 a b fair enough now what is it this will be nothing but minus b square minus ac and this will be simply there is a square and there's a square root this square will be cancelled by the square root right so hence it is b square plus ac divided by 2 a b and similarly here just the same change of sign nothing else it is minus sorry this will be in the brackets yep minus b square minus ac minus b square plus ac upon 2 a b right so I'm finding both the solutions simultaneously so now open the brackets you'll get minus b square plus ac plus b square plus ac upon 2 a b first solution is this so this is x equals to x equals to and here x equals to minus b square plus ac minus b square minus ac upon 2 a b isn't it so hence what will you get you will get here minus b square plus b square goes so 2 ac sorry this is b here so 2 ac twice ac ac plus ac 2 ac divided by 2 a b and this is one x equals to this much and the other solution is x is equal to this ac and this ac will go so minus 2 b square y 2 a b we can simplify further we get x is equal to this 2 this 2 will go if a is not equal to 0 then this a will also go so hence x is equal to c by b and here x is equal to this 2 and this 2 will go if b is not equal to 0 then this this b and this b will go so minus b upon a okay so these are the two solutions so x is equal to c and c by b and x is equal to mine x equals to minus b by a is the solution so x equals to c by b and x equals to minus b by a is the solution