User soheil malekzadeh - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T20:51:01Z http://mathoverflow.net/feeds/user/3124 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/12827/cone-in-a-metric-space Cone in a metric space Soheil Malekzadeh 2010-01-24T07:19:05Z 2013-03-16T17:59:45Z <p>Hi everybody,</p> <p>We know the definition of a cone in a Real Banach Space. I want to know if there is any definition for a cone in an abstract metric space. Have you ever seen such definition anywhere?</p> <p>Thanks in advance.</p> http://mathoverflow.net/questions/123045/estimating-l1-functions-over-the-ball-with-radius-2r Estimating L1 functions over the ball with radius 2r Soheil Malekzadeh 2013-02-26T23:48:53Z 2013-03-15T20:48:28Z <p>Let $f$ be in $L^1(\Omega)$ where $\Omega$ is an open subset of $\mathbb{R}^n$. Also, assume that $B(x_i,r_i)$ is a collection of disjoint open balls in $\Omega$ such that $B(x_i,2r_i) \subseteq \Omega$. I was wondering if there is a way that we can find a function $g \in L^1(\Omega)$ and possibly a constant $C$ such that</p> <p>$\int_{B(x_i,2r_i)} | f | \le C\int_{B(x_i,r_i)} | g |$, for all $i \in \mathbb{N}$</p> <p>(If $f \in L^p(\Omega)$ with $p > 1$, then I can find such $g$ via the Hardy-Littlewood maximal function.)</p> <p>Thank you so much.</p> http://mathoverflow.net/questions/26950/making-sure-that-you-have-comprehended-a-concept Making sure that you have comprehended a concept Soheil Malekzadeh 2010-06-03T19:16:03Z 2011-09-12T02:28:10Z <p>Hi, <br> I have a question that I've been thinking about for a long time. <br><br> How can you assure yourself that you've fully comprehended a concept or the true meaning of a theorem in mathematics? <br> I mean how can you realize that you totally get the concept and it's time to move on to the next pages of the book you're reading? <br><br> Thanks in advance for your responses.</p> http://mathoverflow.net/questions/13555/a-book-for-problems-in-functional-analysis A book for problems in Functional Analysis Soheil Malekzadeh 2010-01-31T11:28:33Z 2010-06-25T10:32:49Z <p>Hello everybody,</p> <p>I want to know if there's any book that categorizes problems by subjects of Functional Analysis. I'm studying Functional Analysis now a days and I really need to solve some problems in order to assure myself that I've really understood the concepts and definitions. For example: problems related to the Hahn-Banach theorem or Banach Spaces or Hilbert Spaces or ...</p> <p>Thanks in advance.</p> http://mathoverflow.net/questions/27901/does-cauchy-continuity-imply-uniform-continuity-no/27918#27918 Answer by Soheil Malekzadeh for Does Cauchy continuity imply uniform continuity? [No.] Soheil Malekzadeh 2010-06-12T09:23:25Z 2010-06-12T09:23:25Z <p>No it's not true.</p> <p>f(x) = x^2 on whole real line.</p> <p>It maps Cauchy sequences to Cauchy sequences but it's not uniformly continuous on the whole real line.</p> http://mathoverflow.net/questions/20968/rules-for-operator-commutativity/20994#20994 Answer by Soheil Malekzadeh for rules for operator commutativity? Soheil Malekzadeh 2010-04-11T09:39:59Z 2010-04-11T09:39:59Z <p>Hi, I suppose this book will be useful for you:</p> <p>Banach Algebra Techniques in Operator Theory (R. Douglas)</p> http://mathoverflow.net/questions/18794/how-to-start-game-theory How to start Game theory? Soheil Malekzadeh 2010-03-19T20:42:40Z 2010-03-21T03:37:37Z <p>Hi everybody,</p> <p>I recently got interested in Game Theory but I don't know where should I start. Can anyone recommend any references and textbooks? And what are the prerequisites of Game Thoery?</p> <p>Thanks in advance.</p> http://mathoverflow.net/questions/11761/why-sin-and-cos-in-the-fourier-series Why sin and cos in the Fourier Series? Soheil Malekzadeh 2010-01-14T16:01:07Z 2010-03-08T02:42:45Z <p>Is there any special reason that we use the sines and cosines functions in the Fourier Series, while we know that if we chose any maximal orthonormal system in L2, we would get the same result? Is it something historical or what?</p> <p>Thanks in advance.</p> http://mathoverflow.net/questions/7155/famous-mathematical-quotes/11983#11983 Answer by Soheil Malekzadeh for Famous mathematical quotes Soheil Malekzadeh 2010-01-16T13:50:31Z 2010-01-16T13:50:31Z <p>"In mathematics you don't understand things. You just get used to them."</p> <p>John von Neumann</p> http://mathoverflow.net/questions/2340/what-is-the-first-interesting-theorem-in-insert-subject-here/11762#11762 Answer by Soheil Malekzadeh for What is the first interesting theorem in (insert subject here)? Soheil Malekzadeh 2010-01-14T16:10:03Z 2010-01-14T16:10:03Z <p>In real analysis, I would say The intermediate value theorem.</p> http://mathoverflow.net/questions/4994/fundamental-examples/11365#11365 Answer by Soheil Malekzadeh for Fundamental Examples Soheil Malekzadeh 2010-01-10T20:46:57Z 2010-01-10T20:46:57Z <p>I suppose the <strong>discrete metric space</strong> is a crucial example in the metric spaces theory and in the introductory mathematical analysis. It shows many aspects and pathological behavior of metric spaces in general.</p> http://mathoverflow.net/questions/4023/text-for-an-introductory-real-analysis-course/11352#11352 Answer by Soheil Malekzadeh for Text for an introductory Real Analysis course. Soheil Malekzadeh 2010-01-10T17:21:52Z 2010-01-10T20:20:43Z <p>I recommend this book: Principles of Mathematical Analysis (by W.Rudin)</p> <p>By studying this book, you're gonna be able to achieve an accurate, as well as, an abstract view of concepts like continuity or Riemann-Stieltjes Integral ...</p> <p>By the way, Mathematical Analysis (by Tom M.Apostol) is a FANTASTIC book for one who wants to start the course. I personally taught this book once and the result was great.</p> http://mathoverflow.net/questions/13555/a-book-for-problems-in-functional-analysis Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-06-27T06:39:03Z 2010-06-27T06:39:03Z Thanks Paul. I have this book and I have to say that it's a fantastic one. http://mathoverflow.net/questions/18794/how-to-start-game-theory/18810#18810 Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-03-22T20:03:24Z 2010-03-22T20:03:24Z Thank you, your answer was very helpful. Upvoated. http://mathoverflow.net/questions/18794/how-to-start-game-theory Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-03-19T21:58:39Z 2010-03-19T21:58:39Z What's wrong with the game theory Georges? http://mathoverflow.net/questions/18794/how-to-start-game-theory Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-03-19T20:54:23Z 2010-03-19T20:54:23Z Actually I already did what you said but there were a lot of references and I didn't know which one I should choose. That's why I came here and asked this question. http://mathoverflow.net/questions/13555/a-book-for-problems-in-functional-analysis/13563#13563 Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-02-11T19:20:13Z 2010-02-11T19:20:13Z This is exactly what I was searching for. Thanks. http://mathoverflow.net/questions/12827/cone-in-a-metric-space Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-01-24T20:20:27Z 2010-01-24T20:20:27Z I need to define a partial order relation in a metric space via a cone like the real Banach space's case: If P is a cone in a real Banach space, then we have: x &lt;= y iff x-y belongs to P I'm so sorry if my question was not clear. http://mathoverflow.net/questions/12827/cone-in-a-metric-space/12834#12834 Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-01-24T20:18:53Z 2010-01-24T20:18:53Z I need to define a partial order relation in a metric space via a cone like the real Banach space's case: If P is a cone in a real Banach space, then we have: x &lt;=y iff x-y belongs to P I'm so sorry if my question was not clear. http://mathoverflow.net/questions/12827/cone-in-a-metric-space Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-01-24T07:48:56Z 2010-01-24T07:48:56Z Actually the feature of a cone that I want to use is that a cone induces a partial ordering relation. http://mathoverflow.net/questions/7155/famous-mathematical-quotes/11983#11983 Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-01-16T14:39:49Z 2010-01-16T14:39:49Z Oh, I'm so sorry ... I didn't acknowledge ... http://mathoverflow.net/questions/11761/why-sin-and-cos-in-the-fourier-series Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-01-14T16:17:46Z 2010-01-14T16:17:46Z Got it ... So you're saying that there are reasons beyond the historical ones that make the basis of complex exponentials the preferable one. Thanks a lot my friend. http://mathoverflow.net/questions/11761/why-sin-and-cos-in-the-fourier-series Comment by Soheil Malekzadeh Soheil Malekzadeh 2010-01-14T16:06:09Z 2010-01-14T16:06:09Z Actually by sines and cosines, I had the basis of complex exponentials in my mind. Thank you.