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Real analysis - Was Cantor aware of Lebesgue theory of ...

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The following quote is from Joseph Dauben (in his article Georg Cantor: The Personal Matrix of His Mathematics, Isis, Vol. 69, No. 4, Dec., 1978, pp. 534-550). When he suddenly suffered his first breakdown in May 1884, Cantor had just returned from an apparently successful, quite enjoyable trip to Paris.

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Ag.algebraic geometry - When is a pair of space curves ...

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Browse other questions tagged ag.algebraic-geometry algebraic-curves complete-intersection or ask your own question. Featured on Meta Opt-in alpha test for a new Stacks editor

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Big list - Not especially famous, long-open problems which ...

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Question: I'm asking for a big list of not especially famous, long open problems that anyone can understand. Community wiki, so one problem per answer, please. Motivation: I plan to use this list in my teaching, to motivate general education undergraduates, and early year majors, suggesting to them an idea of what research mathematicians do. Meaning of "not too famous" Examples of problems ...

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Convex optimization - Maximization of log-sum-exp function ...

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1 Answer1. This question is answered mostly by simple algebra and calculus, so here is a sketch of how the second expression is derived. Set y 1 = u and y 2 = 1 − u in the conjugate function expression for the log-exp-sum. Simplify what is obtained after using the conjugate function expression to replace the log-exp-sum in the original ...

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Inequalities - Generalisation of the squared sum minus the ...

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This is a generalisation from $\mathbb{R}^n$ to $\mathbb{C}^n$ of the inequality which was proved in Minimising the squared sum minus the sum of squares inequalities oc.optimization-and-control convex-optimization

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Books - Ask for recommendations for textbook on ...

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I studied mathematical logic using a book not written in English. I would now like to study it again using a textbook in English. But I hope I can read a text that is similar to the one I used before, so I ask here for recommendations. Any recommendation will be appreciated. The characters of the mathematical logic book I used before is as follows:

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Matrices - Derivative of matrix logarithm w.r.t. real ...

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A common definition of the logarithm for (finite dimensional) matrices is via the Dunford-Taylor integral: ln. ⁡. ( T) := 1 2 π i ∮ Γ ln. ⁡. ( z) ( z − T) − 1 d z, Where Γ is a simple closed smooth curve that contains all the eigenvalues of T in anticlockwise direction. Note that the above is a seemingly natural generalization of ...

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Linear algebra - Derivative of log determinant - MathOverflow

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Derivative of log determinant [closed] Ask Question Asked 2 months ago. Active 2 months ago. Viewed 158 times -2 $\begingroup$ Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it's on-topic for MathOverflow ...

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Matrices - Derivative of log determinant and inverse ...

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Derivative of log determinant and inverse. Ask Question Asked 8 years, 2 months ago. Active 5 years, 4 months ago. Viewed 15k times 1 1 $\begingroup$ I have a matrix $\Sigma$ with element $(i,j)$ $$\Sigma_{i,j}= \exp(-h_{i,j}\rho).$$ The matrix is positive definite and symmetric (it is a covariance matrix). ...

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$\\log(x)$ or $\\ln(x)$ to denote the natural logarithm in ...

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$\begingroup$ There is an implicit convention to use trigraphs rather than digraphs to denote standard functions ($\exp$, $\cos$, $\tan$, $\log$, $\operatorname{det}$, $\lim$, $\sup$, $\operatorname{adj}$, $\operatorname{vol}$, etc.), except in those rare cases in which there is no obvious pronounceable trigraph available (e.g. $\operatorname{tr}$ for the trace, or $\operatorname{st}$ for the ...

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Notation - What does ! above = mean - MathOverflow

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5 Answers5. In my classes I use it to indicate anxiety. So an equals with ! over it means "we want to show this equality is true". An equals without ! means "I am asserting this is true". I don't know how universal this convention is, though. I do know I'm not the only person to use this convention.

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$\\log(x)$ or $\\ln(x)$ to denote the natural logarithm in ...

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$\begingroup$ There is an implicit convention to use trigraphs rather than digraphs to denote standard functions ($\exp$, $\cos$, $\tan$, $\log$, $\operatorname{det}$, $\lim$, $\sup$, $\operatorname{adj}$, $\operatorname{vol}$, etc.), except in those rare cases in which there is no obvious pronounceable trigraph available (e.g. $\operatorname{tr}$ for the trace, or $\operatorname{st}$ for the ...

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Lie algebras - Logarithm of a matrix - MathOverflow

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I am looking for a reference to study logarithm of an invertible triangular matrix. What is a good algorithm? Are there any good reference which studies this topic both theoretically and from an algorithm view point? I am also looking for structure of the logarithm of an upper/lower triangular invertible matrix.

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Set of Positive Definite matrices with determinant > 1 ...

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− log det is a smooth convex function on the PSD cone (this is a standard fact, and follows from the Chandler Davis theorem -- see, e.g., my arXiv preprint on "another proof of the Davis theorem", or see Boyd and Vanderberghe's convex optimization for deep significance of this fact in convex programming), so the set log

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Linear algebra - A problem about convex optimization and ...

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Active 4 years, 5 months ago. Viewed 546 times. 2. Please prove or disprove that, for symmetric matrix A = A T, we have. max x ∈ { ± 1 } n x T A x ≥ Tr ( A) linear-algebra convex-optimization. Share. Improve this question. edited Dec 29 '16 at 10:15.

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Linear algebra - Derivative of log determinant - MathOverflow

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Derivative of log determinant [closed] Ask Question Asked 2 months ago. Active 2 months ago. Viewed 158 times -2 $\begingroup$ Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it's on-topic for MathOverflow ...

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Linear algebra - Derivative of a determinant of a matrix ...

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3 Answers3. this identity is known as Jacobi's formula. Another proof, using the characteristic polynomial where is the -th characteristic coefficient. Namely, assume that is invertible. Then Thus Where is the adjugate of which satifies Cramer's rule . Since invertible matrices are dense, the formula follows.

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Matrices - Derivative of matrix logarithm w.r.t. real ...

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A common definition of the logarithm for (finite dimensional) matrices is via the Dunford-Taylor integral: ln. ⁡. ( T) := 1 2 π i ∮ Γ ln. ⁡. ( z) ( z − T) − 1 d z, Where Γ is a simple closed smooth curve that contains all the eigenvalues of T in anticlockwise direction. Note that the above is a seemingly natural generalization of ...

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The "interplay" between additive and multiplicative ...

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The theory of fields is an undecidable theory, and so one cannot give a computable procedure for deciding whether a given statement in the formal language of fields is true or not in all fields.This is a sense in which this theory is not fully understood. Indeed, the situation is that we have proved that we can have no computably complete understanding of the theory of fields.

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At.algebraic topology - Prove that $S^{2n}$ doesn't admit ...

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Stack Exchange network consists of 177 Q&A; communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange

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Saving Tips

Common Twitter Login Issues

Here we are talking about the common Twitter login issues. Twitter is a social networking site launched in 2006, and it is one of the most popular social media platforms which is available today with 100 million daily active users and 500 million tweets sent daily. Nowadays, people are using Twitter to receive news, follow high profile celebrity, or stay in touch with an old friend by using Twitter. Why Use Twitter? Nowadays, millions of peoples are using Twitter for real-time communication. Twitter allows you to stay interconnected by posting the updates which are known as a tweet. Tweet consists of 140 characters or fewer and contains ideas and other various information, such as photos, videos, and links to the articles. Most people use Twitter to discover information and stay connected with others. This social network is the gateway to share ideas, exciting content and currently updated in real-time. Twitter the information gathering tool Some people think that Twitter is only a social platform, but Twitter is also an information-gathering tool and broadcasting resource that help a person stay relevant. A user can easily receive any breaking news updates, track trends and discover hot topics by following tweets from anyone or anything, such as political figures, the media, or local businesses. A person can start a conversation with a friend or the organization over personal thoughts or a particular topic by tweeting or retweeting. The issue that you have to face during logging into Twitter Like other platforms, many users have to face up with the common login issue on Instagram, Facebook,... Twitter is the same. There are some problems that you have to face during logging into Twitter. The issues are created due to some point. The questions are given below with their relative solutions. These issues will make that mistake you are driving while logging into Twitter and also tell you the resolution of these issues.      Common Username Issue Everyone uses their account email address and password to log into Twitter. In case you forget the password or your password is not working then the simple solution to this problem is to request a new password by entering your email in our reset form. If our system does not find the email address, then you may be entering the wrong one. Is your Browser up to Date Many issues can be resolved by ensuring that you are using the recent of your browser. If you are not sure that the browsers you are using are up to date, then download the latest version to solve this issue. You can download the newest version of your selected browser. If a browser upgrade does not solve your problem, then you can also try downloading an alternate browser. Problem Create due to Cache and Cookies The most problem that occurs on Twitter is due to cache and cookies. For solving this problem, you have to clear cache and cookies when you feel that they are creating a problem with your Twitter. You can quickly clear cache and cookies from the settings menu for your mobile browser and solve your problem. Incorrect Username If you are not still log in, then make sure that you have used the correct login username and password. For checking the password is correct or incorrect, try logging in from a computer. In case you can’t log in to the computer it is mean that the password or user name you are using is not correct. In case you logged in on your Pc then turn off your mobile for 5 seconds to reset the connection. How to Reset your Twitter or any other Password?  From your logged in account, click on the More icon in the navigation bar and select setting and privacy.  Then from the account tab, click on password.  Enter your current password.  Then finally choose your new password.  Then at last save your changes by clicking save. Note if you can log in but can’t remember your password, then you can send yourself a password reset email from the password setting page. Furthermore, you are also able to log out of all your active Twitter session from the one that you choose to change your password. Twitter Most Common Problem Depending on the different devices that you are using, you may have to face other problems while accessing Twitter. To solve this problem, the solution will be helpful to you.  In case you are may facing a problem due to using a VPN and proxy and by disabling it, your issue may be solved. The problem also occurs due to incorrect internet sources. So for solving the problem, make sure that the internet source is working correctly.  If you still fail to solve the problem, then go ahead and report to Twitter.  Most of the problems can be avoided by using a strong password and restrict access to the third-party app by allowing only trusted third-party programs and applications to be associated with your Twitter account.  
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How to Fix "Face ID not working" Problems on iPhone?

iPhone is one of the most famous phone brands, recently the iPhone launched a great feature of facial ID, replace fingerprint. In case any issue raises in this feature, you should know How to Fix "Face ID not working" Problems on iPhone. However, you can instantly sign into apps or authenticate your buying details. It is undoubtedly a fantastic technology, but it will fair enough frustrate you in the case of malfunctioning in your iPhone. Therefore, in the first hand, you should check that your iPhone model supports face ID or not. There are a lot of causes that "Face ID is not working", firstly you need to check your iPhone thoroughly. Which iPhone Models Support Face ID?   Facial ID technology is the latest feature for the iPhone. That's why only some models on the market feature it relatively. Only iPhone XS Max, iPhone XR, iPhone XS, or iPhone X allows this feature, so you can set up as well as using facial ID on your phone if you have one of those models. However, the previous models do not have this feature. Check for the Latest Updates Once you have analyzed that your iPhone is one of the models supporting facial ID, you should check for any updates to iOS. Therefore, make sure to back up your iPhone by using iTunes or iCloud before any updates to be done if you do not want to lose your data. Plug your device into an outlet. Connect to the internet that has high-speed Wi-Fi. Tap to Settings options. Click on "General". If it appears that there is a software update, immediately hit on Install button.  A message will appear which asks you to temporarily remove apps because iOS required additional space for an update.  You are allowed to tap on "Continue" to respond that you want to reinstall the apps later. Check to determine if the facial ID is fixed after you have installed the update. If it has not done its task, then switch to the next option. Check Your Face ID Settings Properly If you check the face ID settings on your iPhone regularly, it will help you evaluate whether the phone is configured, which enables you to use this feature. The setting can be changed by keeping in mind the steps given as under: Go to Settings Go ahead for Face ID and Passcode. Check it out if Face ID is set up in the correct format. Therefore, you should check to determine if the features you are trying to use Face ID, such as iPhone unlock or Apple Pay, are turned off. Solution if Face ID is not Set-Up If you have not set up your Face ID still, you are required to do that before you enable to use any of the features with which it is associated. Follow these steps to set up your Face ID: Go to Settings. Go ahead for Face ID and Passcode. You will have to enter your passcode there when prompted to do so. Tap the message prompted to Set Up Face ID. Ensure that your holding position of iPhone is in portrait orientation position. Head your face in front of the iPhone, then press "Get Started". Head your face in a way that it is entirely inside the frame. Slowly move your head to complete the circle. On the other hand, if you cannot transfer your head as directed, then instantly tap Accessibility Options. Tap Continue after accomplishing the Face ID scan. Slowly move your head around to complete the second circle. If you have not still set a passcode, then a message will be prompted to do so at the moment; Tap "Done". It is a substitutive way to verify your identity if the Face ID features malfunction ever. Check to determine if the True Depth Camera is Covered Have you reached this point and have tried the options we have discussed above? Still, the facial ID is not working? Now you should check if the True Depth camera is not covered in any way. It is what the iPhone uses for this feature. The True Depth camera is located near the top of the front of your iPhone. If your phone has a screen protector that is blocking the camera, you will have to remove the protector for this feature to work correctly. Furthermore, check for any dirt, grime, or other buildup.  You should check to see if the camera is in landscape mode as well. If it happens, ensure that your palm or finger is not blocking it while trying to use it. If this situation raises continuously, you should look for the alert at the top of the screen, which prompted that "Camera Covered," with the arrow pointing in the True Depth camera direction. Ensure Your Face is Uncovered You should further check to ensure that you face open and not covered at any mean that is keeping the True Depth camera from recognizing you. Therefore, your eyes, nose, and mouth area must be evident to the camera.
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What To Do If You Forget Face Book Login Details?

Forget FaceBook Login Details is one of the most frequent error users often meet when logging in, in case you have forgotten your Facebook account logging details, It would be frustrating for you. In this article, I would like to help you as possible. If you have forge logging information of your Facebook account, you can recover it with the help of Facebook security features. When you are doing recover or change a forgotten password, it can be solved within some minutes. Recovering a forgotten username, that can take up to 24 hours to retrieve if you have not used the Facebook account for a long time. Suppose you have not used email, which signed up with Facebook using an Alienator, Maildrop, Guerrilla Mail, 10 minutes mail, and other email addresses. It may be difficult to retrieve, but nothing impossible, for this condition you have to add your friends to be trusted contact. You can get help from the Facebook help page.  You can get help from the Facebook help page, by searching for How can I recover my Facebook login details. Follows the instruction given by Facebook to use your trusted contact to re-back into your account. You will receive the page of instructions that contains a URL. This URL includes a specific safety code that can be approached by your trusted friend contact and provide them with this URL. You will open this URL link and send you the provided security code. Use the security code from your friend's device to recover your account. If you not settled, your friend trusted contacts, keep set up immediately.   Recover Facebook Password Facebook will never provide you with your password because it is your privacy and the reason for captivating analytical wizardry. If they allow for then, it will be a wrong security way. There are two accesses to try: one is the official way, and the other is no official way. Either you have not used a non-official method, but you know about it because it shows the other power security threat. The traditional method to recover your Facebook login is Facebook's own account it recovers automatically. It uses such information that you had provided before to confirm you are eligible. If you don't offer current information, you can't access to recover your account. If you organized your password in your browser to remember, then you can view what it's saved. Password Reset Facebook Login Note the steps that alternate suddenly, Facebook-based personal change along with the appropriate of your condition. You can follow the steps which are provided to you on Facebook, however, it may be a little bit different than what I had discussed here.  If you forgot your password, you require retrieving your account.  Just log in your password in the boxes of the entry field of the Facebook login page. Select forget account, and you get a page where you insert the email address or mobile number with the version. Then Facebook page presents you with a list of account recovery options related to your account. You have to select one that you want to use and click on the continue box.  Set a New Password Suppose you do have the reach to the option of the account recovery or way you have chosen, Facebook will provide you with a code. You have to enter that code as per request and click on the continue option. This way proves that you are the right Facebook account holder. The Facebook page may ask you to choose a new password. It is the official and appropriate method to recover access to your Facebook login. With the response to the password recovery option, you makeup initially and then set a unique password. Password Recovery If you are looking to recover your current password, I want to clear you that are cannot or be able to. If you set your browser to remember the password for you, then it is so risky and straightforward also. You will have to use Firefox, but most of the browser has similar functionality. You have to click on the hamburger menu at the right corner end of the Firefox toolbar, and then select the preferences option, according to your version.  You can use the search box on the resulting page to find out the password and when it displays, click on Login saved. After a little more obsession: The dialogue box of saved password updates with more columns that show the actual password for all to see. Security Issue If your browser displays your password:   Go forward and feel comfortable if you can recover your Facebook in this method. You have to be very, very anxious. If you set your browser to save the password, then someone with utilization to your device he can do what we just discussed.  Use this procedure to recover all your saved passwords. It is the only reason; I am recommending you to keep your password in your browser. If you want to do, make sure that your device will always be secure.
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How to Fix Account Login Issue in PUBG Mobile?

PUBG mobile game is notoriously famous for all its glitches and bugs that you can see throughout the game. Mostly PUBG mobile game users are fed up with the issues they use to face while logging with the Facebook ID's help.  Likewise, there are several errors that you can see through this game. In this article, you will know how to fix all those errors and how you can resolve them.  The Problem for Logging in with the Help of Facebook ID Mostly, people who have signed in with the help of their linked Facebook account cannot sign in the back due to the login problem they face. Moreover, whenever a player encounters a problem, the notification appears on the screen of "Authentication failed." However, such a message will continue to pop up on the screen. Moreover, the error message will continue to pop up on the screen with the social media platform's help.  Solution: Such an issue was persistent during the last update, but the issue was then solved from the mobile. Moreover, the players do not need to change their account without changing their password.  Problem Persists If the problem is there and you want to improve then the PUBG mobile game, you can log in with Google ID help. It can be a problem due to the authentication error due to Facebook, and the G-play account might still be there, but you can be good to go there. Moreover, those who have linked their account to Facebook until they want PUBG to solve the issue. The PUBG mobile game problem can be solved in a few hours. Moreover, the PUBG mobile game has rolled out the next update on the 7th of May.  Solution with Update: PUBG mobile game update brings exciting content for all their users. However, the recent content can serve with the bugs that are already known to the users. The recent update also has a problem related to the login, so you can easily solve it in some hours.  Log in with the Help of Google Play Whenever you are playing PUBG with the help of google play games or the Facebook account. In this way, you can also back up the progress on your cloud. However, the recent update can solve the issue by signing into the accounts. Whenever they are trying to log in, the dialogue box will appear there, and the account will be rechecked. Sometimes you can no longer sign in to the new account with the new version of the game. But if the issue is persisting, then you need to update the account.  Check the Game Mailbox Sometimes the game guidelines can appear in the game mailbox. Moreover, it will ask the players to log out of their accounts. Sometimes it isn't easy to log back in. For all those who are having this issue, they can load the query from the loading screen. Also, you go into the settings from there, and you can get the customer service from there. Once you have got there, you can use the contact us key word for the account lost. With the help of the issue, you can also help to follow steps. Moreover, PUBG mobile is also not stable. Therefore, it is better to unlink accounts. If you have the same problems, then following the steps mentioned earlier. With the help of these tips, you can know about the features that are available to the registered users: Features of PUBG Solution Dashboard From the player dashboard, get the entire information of your past 20 to 50 matches Recent statistics of matches: averages, get totals, and other match statistics for the last 10 to 30 matches.  Current statistics for weapons: Information of weapons and the statistics for the last 30 matches.  Scoreboards: live competitions comparison for the competition of up to 4 to 10 matches.  Tournaments BETA: these matches can be easily manageable for the tournaments with the custom, team statistics, and public leaderboards.  Follow other players: moreover, you can also follow another player with the squamates or the favorite streamer for quick access to the match reports and the stats.  Save matches reports: It can help the later matches; furthermore, you can also save all your matches reports that are not on their standard matches.  How to Solve the PUBG Problem more Effectively?  For this purpose, you can also use the services. The email address that you can share with anyone for any reason You cannot ask for an email from PUBG unless you look for one.  The only ask information about this is the one when you use for your login account Moreover, it is free Conclusion All in all, if you are a wonder to know about the PUBG login problem, then you can easily cope up with it in no time. You can easily solve the problem of PUBG. Therefore, in this way, you can easily pursue playing the PUBG game in the ideal scenario.
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