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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

User Authentication: Understanding The Basics & Top Tips

The most important aspect of website users is the authentication of human to computer interactions. Hence, user authentication is important to understand when someone is creating a website login procedure. Therefore, whether you are looking to be up the internal security or increasing the customer acquisition, or providing a better experience for exploring your site, it is important to know about the authentication process basics. Therefore, we are presenting you with this guide. In this way, you can understand: With the help of better understanding, your organization can understand the better understanding. With the help of a better understanding, your organization can be more effective with the registration and the login processes that can go past the traditional offerings. Moreover, when you go for more different types of authentications, you can get several conventional offerings. Furthermore, when you go for more user authentications, you can get the passwords and more options with fewer alternatives. What can User Authentication Do? The authentication process is the security process that can cover the human to computer interactions that will require the login and can register there. Furthermore, simply the authentications can ask each user about "who are you?" and verifies the response. Moreover, when users can ask for the account, they must create a unique ID and the key that will allow them to access the account later. Mostly the password and username are used as the key and ID. However, the credentials that can include various types of user authentication as well. How Does the User's Authentication Work? The authentications are mostly interchangeable with two separate terms that can work together and create a secure login process. To put the user authentication, you must have three up to the mark tasks: Manage the user connection between the website user and the human user. Verify the identities of the users Decline or approve from the authentication so that the user can identify the user. Importance of User Authentication Understanding the user's authentication is important because it is the key step process that can keep unauthorized users access to every sensitive information. Moreover, they strengthen the authentication process because one user has sensitive information, and another user can only have access to that information if they want. Top User's Authentication Methods Some methods are also called the authentication factor, and for that reason, there are three types. Knowledge Factors: The foremost factor in this regard is the knowledge factor. It can be anything the password, username, and PIN. Furthermore, the challenge with such characteristics is that they can be weak in security because they can be guessed or shared. Possession Factors: Anything that the user must have to log in is the possession factor. Moreover, the one-time password tokens are sometimes the link. Furthermore, there can be physical tokens, ID cards, and possession factors. Inheritance Factors: For a person using the biological characteristics, it is known as the inheritance factor. It can be facial recognition and finger scanning. It can fall into the category. User Authentication with No Password Having the password-less login system is the authentication method that mostly does not require password authentication. Moreover, this sort of authentication has become more famous in the past years, and you are more experienced in the few. Moreover, the most common ways of password-less login in this article are the two most essential cover methods. Biometrics: Fingerprints, facial recognition, iris scanning, and other types of verification through biological characteristics fall under the category of biometrics that can be considered under the inheritance authentication factor. Email Authentication: Email authentication is the most important and password-less user authentication. It mainly because anyone with an email account can use this method. Stronger Password: We encourage you to get the improved security and the stronger vulnerabilities that they used to bring due to the insecure user-generated credentials. It can take to get the password-free online password experience. Implement SSO Authentication: If you do not know about or you can go for the single sign-on, with the authentication, it is a process that can make you logged into the account even when you. Multi-factor Authentication Strategy: Multi-factor authentication is the one that uses the identification with the help of several authentications. For instance, a user can input their password, username, which will then email the link to get the security code. Exploring the Password-less Authentication You can implement a password-less option of login to your website. Moreover, security to the passwords and the security experts can become unreliable and obsolete for user authentication. Furthermore, the password-less logins will not require anything to remember anything. Moreover, the login process is completed with the help of the biological characteristics or through another account. Way to improve user authentication To make your login process more secure, user-friendly, you should know how to create stronger passwords to improve security. As we know, that passwords are not completely safe, they have various vulnerabilities, still, migrating the entire internet to a completely password-free online experience will take your long time. The best way is to create better passwords. Conclusion All in all, this is the best way to authenticate the password to get the optimum security. If you are going to apply the above-discussed user authentications and the given tips you can secure your system.
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Best Ways to Register an English Online Courses

Choosing an English online course can be a daunting task. It would be best if you considered several things, for example, audio, videos, and in any of the other cases that are a better fit for you. What will work perfectly for you? It would be best to consider some points, like knowing the language, knowing how to read and work with your schedule and from the country do you belong. The answer will determine what course you want. When to take the short course? If you wish to know how to survive your short vacation, a video or audio might be sufficient for you. Furthermore, it will allow you to understand everything with the flexibility to study whatever you want to master your test. Therefore, you must own whenever you want to master the language to get to the point where you must be comfortable in the situation whenever the situation you wish to have. Similarly, these sort of watch videos and then the online courses you wish to have in every answer and question that must-watch videos. These sorts of English typically utilize chatrooms, and the conference calls you must have. English online videos The online videos are ideal for whatever English-speaking course you know with the flexibility, but you need to sure about the master English language. Here your answer and the question sessions are not that flexible, but the opportunity you might have can make you on the right track. It is the option when you are on the video calls like Skype and other instructors to check the pronunciation. If you are working with Skype's help, there must be certain information you must have to pronounce the things more clearly for the tongue and formation placements. Things you must find while opting for the English The English course needs to be fully mastered, and for this reason, one must master the session completely. Moreover, with the help of lost in scheduling live in the course, they can be lost time, and there might be such advantages. Moreover, the largest advantages of instructions, feedback, questions, and instruction can easily happen in one session. Such a session will allow you to deal with questions and the issues that need to be done after watching the videos to learn about the mastery exam to tell you about the success of the issues.  Online English learning trend Several students are learning English now online. Moreover, some platforms and schools can connect students from all over the well-refined online English tutors. If you plan to follow the trend, you need to follow if you got the time to do so.  Study anywhere, any time Learning English online must give you freedom in terms of location and time. Furthermore, you can learn English class on the school's busy day or sign up for the weekend lessons. Moreover, time is flexible so you always up to this. Moreover, there are several things you can sign up for in the evening class, and there are several tutors during the day to help. Online platform The best thing is that you can get it with the help of your phone. Many lessons are doing with the help of Skype, WeChat, Zoom, and others. However, in such a case having an excellent connection to the internet is important. Also, several students may ask you to come online, and only after some minutes, you will see if your internet connection is working or not. Moreover, if you are serious about learning English online, you must have an external microphone and headset. Place It might be possible that you can take online lectures anytime and anywhere, but you must ensure to have a quiet place during the lessons. If you want to know what the online tutors are saying to you but might be distracted by the working of the internet, it might be possible. Furthermore, you can learn to have your concentration online.  Learning with experts No one can make you learn English online; therefore, you must go for the platform to only serve experts that can make you learn English online. It includes experts like teachers that can make you learn English online with the real knowledge and skills as the expertise of only to learn English online with the help of technology. Most importantly, teachers are the only professional who will be guiding you to take every step wisely. Affordable one to one lesson Online lessons in English are super affordable. Moreover, students have the option to enroll in every lesson they can. Several students can help you learn lessons hourly and per week as the way you want. Furthermore, this beat will help you learn language schools whenever you must sit or on the other students. Moreover, you can get to know about one-to-one lessons. Furthermore, you can get the tutor's attention, which is undivided too. Conclusion All in all, learning online English is important if it is not your native language. Learning English can be the easiest way if you are opting for online option.
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Tips to Fix Login Activity on Instagram

Instagram is famous among real users and among hackers and spammers trying to access random accounts. In these situations, the app alerts you of a suspicious login attempt, which is very serious and safer for you. Read more news and guidelines on Instagram on the separate section of our website. Certainly, you can also find some helpful tutorials on anything you need to know to fix Instagram Login Errors. PC Repair Tool This program can correct common computer errors, defend against the loss of file, malware, hardware failure, and improve your PC's performance. Delete viruses and repair PC problems in 3 simple steps now. Download the Proprietary Technologies Restore PC Repair Kit. To identify Windows problems that can cause PC problems, press Start Search. Click Repair Everything to correct problems that affect the protection and efficiency of your machine. This month, 550,106 readers downloaded Restoro. For general security purposes, Instagram alerts users of any suspicious behavior or stops spammers from deleting fake accounts and preventing hackers. Every once in a while, many Instagram users get an alert that an odd login attempt has been identified. The app also includes such choices: helping you log in, getting a security code via an SMS, or confirming your account. This alert typically happens when you attempt to register from another computer. When Instagram detects an IP address different from the normal one, changes the usual location (often driving, moving to another country), or someone is attempting to access your account for various reasons. Accept security tests That is, check whether or not it was you. Maybe from another IP address or unrecognized device or machine, you or anyone else tried to access your account. If you were, you would be permitted to use your account; press the option. Don't worry if it isn't you, as your attempt probably failed. Click this, not me.  Click this. You can then change your password using the app. Now you should try replacing your password with a better password and a password you have never used before. We encourage you to use a password manager to help preserve complex passwords for both applications and computers. You tap the Submit option and should be good to go after changing your password and checked twice. Insert protection code Instagram will need a security code to login if you have enabled the 2-factor authentication process. The code is sent to your Instagram account's email address. You need to use the code, and you will have access to your account. This phase is only necessary occasionally and only if the additional security layer is enabled. Again, particularly if you frequently have a suspicious login attempt, you should allow this choice.  Tap your profile, select Settings in your account, and then click on the Authentication two-factor option. Allow the Security Code Require choice. The app will give you a code via text message any time you log in to your Instagram account. In reality, at first, it might be a bit irritating, but better safe than sorry. Any comments or suggestions in the dedicated area below are welcome. Instagram showing the wrong log in location An incorrect registration location is something you can try to grasp and see if your account will not be used unauthorized. It may be because Instagram uses your IP position rather than the location of your screen. Your telephone network may be situated near the heart of the city rather than your city. You can even have a VPN on your network, and you do not know. I have also found that in Europe and in various Asian countries in which the whole network in the neighboring country would be on a VPN. If you suspect that a possible security risk might be a problem where someone is logging in from far away, you can make sure you are in a safe network and help contacts and improve the account to secure your account. UNUSUAL LOGIN ATTEMPT WARNING Instagram does have some pretty slick security tests that allow you to cause this "unusual log-in attempt" or the "suspect log-in attempt" when you see your log-in from a remote location or try to log in to your account. In both cases, Instagram sees something atypical and needs to make sure everything is alright. You should appreciate Instagram's efforts to help you ensure that your account doesn't lose access to a catastrophic hacker, possibly far away across the globe. I know this feeling of panic doesn't ease. Let's take the easy steps of handling the odd login and tighten up the security of your Instagram account once we've finished. I know I haven't visited Moscow over the past couple of weeks or ever, so that's sure a Russo hacker is trying to break into my account. Or, more likely, some program that simultaneously attempts to divide thousands of stores. Anyway, certainly not a good thing. I'm going to tap the Blue, "This Wasn't Me," because I haven't been trying to reach my Moscow account. It means my account is safe against Russian login attempts by Instagram. If not, you will succumb to the popular strategy of using the same password on many or even hundreds of websites. I highly advise you to use your password manager or track your passwords in a protected file or folder elsewhere. If any of them are infected, all your accounts are hackable.
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How to fix Server Login Issues?

When beginning IBM SPSS Statistics on a macOS-based host machine, appears 'Domain Login' and 'Local Computer.' Or in the lower-left corner of the product launching, a Red x on Local Server is given. Not get the window "What would you like to do" but get an error finally. Symptoms When IBM SPSS stats or modeler is started on a Mac computer, a window will be displayed on the 'Computer Local Server Login' screen. 'OK and 'Cancel' are the only response choices. No shift is made by clicking the 'OK' button. The window closing results in 'Cancel,' but the IBM SPSS Statistics product's installation doesn't work. Or when starting the product at the local stage, at the bottom left corner of the server, the red x is on Server Local Server; do not get the window. The problem of diagnosing For this action, there are many reasons. The following are the most common causes of conduct and treatments for behavior—operating systems for Apple Macintosh (Mac). See Technote 1992861 for your Statistics version 23. The following method applies to all other versions (or when Statistics 23 problem has not been solved by Technote 1992861). Open statistics. Open statistics. The window will show 'Domain Login.' Choose the menu entry 'Utility.' Launch 'Control of Operation' Choose 'Pace' (at the top of the window). Check that the following entries are present. If you're not on the list of an active program in 'SPSS statistics' AND ' spssengine,' go to the 'Resolution of a problem' but close the data and go to. Issue Resolution Test compatibility with your operating system by product compatibility report. For instructions, see the following document: Technote 1986726. The probable cause of the 'Server Login: Local Machine' message if the host operating system NOT lists compatible operating systems this is likely. When the host machine's operating system is specified in the operating systems compatible, go to. Open 'Track Activity' From the list of available choices, pick the 'Memory' option. The 'Domain Login' is likely to trigger IF 'free' RAM to equal, or to be less than, 1GB of RAM, insufficient RAM. To solve either add physical RAM to the host or to recognize and end redundant context program to release adequate RAM. If 'free' RAM reaches 1GB of RAM, then go to it. Carry out the Technote 1993131 operation. If 'Domain Login' does NOT exist, the issue is solved THEN. If 'login server' DOES is open, then go to. The platform has a strong history The problems can be triggered by cookies and temporary data already saved on your computer. Then test them for your problem, delete them. On your toolbar, click on the 57-icon library icon. Tap History, then click on the All-History Bar at the bottom to open the library window. (If you don't see it, click an fx57 menu button, then click library.) Type the website's name in the search history area in the top-right corner and press the Enter button. From the list, you want to forget, right-click, and pick Forget about this place. Clear all cache cookies If the issue is not resolved to delete cookies for the domain, uninstall and clear the Firefox cache from any cookies you have saved into your device. On your toolbar, click on the 57-icon library icon. Tap on History and pick Recent History. (If you don't see it, click the fx47 menu button, then click the library.) Pick Everything in the Time range to clear: drop-down. Pick all Cookies and Cache under the drop-down menu. Make sure you don't pick other things you want to hold. Application protection blocks cookies Some Internet protection and privacy apps have cookie-blocking functionality. Check your software manual or access the software provider's support site to see if your program contains a cookie check function and how these settings can be modified. Delete Fixed File Cookies You could have a compromised cookie file in your Firefox profile folder if you are unable to log into websites after deleted the related cookies, removed your Firefox Cache, and reviewed your Firefox extensions plugins, and have verified the safety program. The issue with the server An error on the web site you are attempting to reach is an internal server error. This server is in some way misconfigured to prevent it from correctly reacting to what you are asking for. View it as a blue screen version of the Internet. There was something on the server so wrong it couldn't tell you what the problem was. Besides the site owners' warning (which may be included in the error message on the Webmaster's email address), there is probably no solution to that problem. It must be fixed by the person responsible for the website. The fault of the server Although it is the server's fault if anything is not done correctly, it can be triggered by scenarios. For instance, it can be caused by URL errors. One example is that you see a link in an email or website, and you copied and pasted it in a web browser instead of clicking it. You will see this message if you did not mistakenly pick the full link and left out a number of important characters. You may also see this message if you type and do not type it precisely in a URL from a book or other source.
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