# Tagged Questions

Mathematical analysis. Consider a more specific tag instead: (real-analysis), (complex-analysis), (functional-analysis), (fourier-analysis), (measure-theory), (calculus-of-variations), etc. For data analysis, use (data-analysis).

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### integrate over a contour

Please help me with this: Find the value of $\displaystyle\int_{\gamma}\frac{e^z}{z-Logz}dz$, $\gamma$ is the positively oriented contour consisting of four vertices at $2, 4, 4+3i, 2+3i$
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### Uniqueness of Fourier Coefficients

I'm reading through Stein & Shakarchi's book on Fourier Analysis on my own, and have a question about the proof of the following theorem: Suppose that $f$ is an integrable function on the circle ...
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### Logistic regression eye treacting data (need model)

I have two sets of time course data, they are for an eye-tracking study. The data is 20 100ms chunks, one category being percent fixations for canonical sentences, and the other being percent looks ...
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I find it difficult to remember the different forms of summation by parts: where the indices begin, end, whether to take forward/backward differences, etc. For example, Wikipedia has one form $$\sum_{... 1answer 52 views ### Is norm of a differentiable function continuous? The following argument is from my class notes. "Suppose \gamma(s): I\rightarrow \mathbb R^3 is a regular curve. Fix t_0 and define s(t) = \int_{t_0}^t \|\gamma'(t)\|dt. That is, s(t) is the ... 1answer 59 views ### Convex continuous functions [duplicate] $$w \left (\dfrac{x+y}{2} \right ) \le \dfrac{1}{2}(w(x) +w(y)) \quad \mbox{for all} \quad x,y \in \Omega,$$ is a sufficient condition to a continuous function w \in C^0(... 1answer 365 views ### Alternatives to Rudin I'm taking an advanced calculus class this semester and we've been using Rudin's Principles of Mathematical Analysis. I was wondering if anyone could suggest some good analysis textbooks aimed toward ... 1answer 52 views ### Interesting question about functions I saw the following question and I would like to share. I don't know the answer. Suppose that the function f:\Bbb{N}\to\Bbb{N} has the property f(f(n))<f(n+1) for any n\in\Bbb{N}. Prove that ... 1answer 84 views ### Polygons circumscribed to a circle with the smallest circumference Let n \geq 3. Prove that among all n-polygons circumscribed to a (particular) circle, the regular n-polygon has the smallest circumference. It shouldn't be difficult, but I don't even know how ... 2answers 260 views ### Strange Property of Ultrametric Spaces and Metric Completion The following property of ultrametric spaces seems quite strange: (No new values of the metric after completion) Let x_1, x_2, \ldots be a sequence in X converging to x \in X. Suppose a \in ... 0answers 88 views ### Integration by parts on a sum of a product of partial derivatives Let \Omega be a region \subset \subset \mathbb{R}^{n}, and suppose that both u_{\infty} and \varphi \in C_{0}^{\infty}(\Omega). Then, I want to perform integration by parts on the following:... 1answer 64 views ### Is every separately continuous function on R^2 continuous? My friend asked me this question a few days ago. I felt it's not right but couldn't find a single counterexample. Any comment is appreciated. 1answer 40 views ### Count PI with analytical methods Is there a differential equation which can be used to count the value of pi? I was able to describe pi only with sequences based on polygons with infinite corners. I think I'll need a continuous ... 2answers 61 views ### Can an integral be proved to have a finite value if an upper bound of the integrand has a finite value for improper integrals? Can we say  \int_{0}^{\infty} f(x) \text{dx} < \infty if \exists \quad g(x) : \quad g(x)\geq f(x)\; \forall x \in \mathbb{R} and  \int_{0}^{\infty} g(x) \text{dx} is finite. If yes, ... 0answers 24 views ### Verifying an algebra Consider the metric space of bounded, continuous functions from [0,1] to \mathbb{R}, and a subset E: E=\left\{\sum_{i=0}^N a_ie^{b_ix}\mid a_i,b_i\in\mathbb{R}\right\} \end{... 0answers 42 views ### (g,f)_{L^2} \le C||g||_{H^{-s}}||f||_{H^s} right or wrong? I am proving something, and I may need the following inequality:$$ (g,f)_{L^2} \le C||g||_{H^{-s}}||f||_{H^s}  where $(g,f)_{L^2}$ is inner product and $f$ and $g$ have higher enough regularity ...
Let $\mu , \nu$ be two probability measures on $(\Omega , \mathcal{F}).$ Suppose we have a probability measure $\lambda$ such that both $\mu , \nu$ are absolutely continuous with respect to $\lambda$....
Let $\mu , \nu$ be two probability measures on $(\Omega , \mathcal{F}).$ Suppose we have a probability measure $\lambda$ such that both $\mu , \nu$ are absolutely continuous with respect to $\lambda$....