# All Questions

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### Identifying modes in circular data

I have some circular data (ie, angles in $[0, 2\pi)$), and I need to analyze it in terms of its modes. I hope this is the right place to ask for help solving this. The main thing I need to be able to ...
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### Chains and cochains: integer versus real coefficients

Let a real, smooth manifold $M$ be given. For each non-negative integer $k$, let a singular $k$-cube on $M$ be a continuous mapping $c:[0,1]\to M$. Let $C_k(M,\mathbb Z)$ denote the set of formal ...
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### Does this quadratic form represent 1?

I am stuck on the following question in Lam's quadratic forms for a few days now. Let $a,b,c$ be three elements of a field $F$ such that $0 \neq a^2+b^2 \neq c^2$. Show that the quadratic form ...
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### Finding an invariant polynomial under a matrix action

I asked this question as a mathematica question: http://mathematica.stackexchange.com/questions/41689/finding-a-certain-invariant-polynomial-using-matrix-coordinates but maybe it will get more ...
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### Vector bundle on a transversal intersection

Consider a curve $X$ (over a field $k$), which is an union of two smooth and connected curves $C$ and $D$ meeting at exactly one point $P \in X$ transversally. Let $E$ be a vector bundle on $X$ such ...
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### How to prove orbit periodicity in some conservative systems?

Good afternoon, I have some trouble proving periodicity with a conservative system. The problems is that I don't know how to make a formal demonstration although I can see it quite true. I have the ...
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### How to solve the following equality

Is it possible to solve the following equation analytically for $\beta$: $$y'(A+\beta B)^{-1}y = \alpha,$$ where $A$ and $B$ are both positive-semidefinite and symmetric matrices (essentially, some ...
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### Question on stochastic process

let $(\Omega, \mathcal{F},\pi)$ be a probability space with $\sigma$-algebra $\mathcal{F}$ and measure $\pi$. Let $$X:[0,+\infty)\times \Omega\rightarrow \mathbb{R}$$ a family of random variables ...
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### Quotient rule for the Jacobian

Is there an analog to the quotient rule that can be applied to the calculation of the Jacobian? Example: Can the jacobian of a quotient of two functions be decomposed into some series of linear ...
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### Estimate distance between approximated posterior and true posterior

I'm working on a paper about using graphical models to do some prediction tasks with known observations. Since the model is complicated, finding the maximum a posteriori on the true posterior ...
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### Equations for Intersection of Plane and circle

I am having a problem in getting the related equations for an intersection between a point on a plane and the edge of a circle in 3D space. Any suggestions? Or also a tangent plane and a point on a ...
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### maximization over a max operator

My question is as follows $$\max_W\max_{D_k}D_kW$$ where D_k = ((x_{i}^{1}-x_{j}^{1})^{2},(x_{i}^{2}-x_{j}^{2})^{2},...(x_{i}^{n}-x_{j}^{n})^{2}) ...
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### Should I find the angle between a normal vector and a line to find the angle between the line and a plane?

I'm asked to find the angle between a line and a plane. I've calculated the normal vector of the plane to be $[7,4,-5]$ and the direction vector of the line to be $[3,-2,4]$. Is it right to find the ...
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### Balls and their cardinality

Let metric space $X$ and fixed point $a\in X$ be given. I search for not restrictive assumption under what all balls in metric space $X$ with center in $a$ have the cardinality equal the carinality ...
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### Eigenvalues of $B$ and $-B$

For a real symmetric matrix $B$, if we assume $QBQ^{T}=-B$ for some orthogonal matrix $Q$, then we know that the eigenvalues of $B$ and $-B$ are the same. My question is whether matrices of this ...
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### Minimum Number of piles

Suppose we have N stones. They have the same size and weight, but they might have different strength.The $i$-th stone can hold at most $x_i$ stones on its top (we'll call xi the strength of the ...
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### Describing a point in im $\Bbb P_A^n/I \rightarrow$ Spec $A$ as those $p$ for which $\emptyset \neq V(I) \subset$ Proj $\kappa(p)[x_0,…,x_n]$

Let $Z$ be a closed subset of $\Bbb P_A^n$ cut out by functions $f_i$. Consider the map $\pi: \Bbb P_A^n \rightarrow \operatorname{Spec} A$. I am trying to see why the points $p\in \pi (Z)$ are ...
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Given that $\Omega$ is bounded and $a_{ij}(u_{k}) \rightarrow a_{ij}(u)$ in $L^{1}(\Omega)$, $a_{i0}(u_{k}) \rightarrow a_{i0}(u)$ in $L^{1}(\Omega)$, $\frac{\partial u_{k}}{\partial x_{j}} ... 0answers 53 views ### Definition of Manifold's Orientation I am reading the book of manifold. And I find there are many definitions about one object, such as orientation, Euler character and degree of map. I am confused with the conception of orientation. ... 0answers 52 views ### A quantity depending on two independent variables must be a constant, why? I'm studying about Fourier analysis and there is one part in my book about partial differential equations I don't understand. It states that a quantity, which depends on two independent variables$x$... 0answers 27 views ### What is the dot product of two randomly generated 0-mean unit-vectors? Given pairs of random 0-mean unit vectors, what kind of distribution is generated by their dot products? Judging from a number of results I've generated myself, the distributions appear to be ... 0answers 30 views ### Obtaining estimates for$|I(f)|$Let$R >0$and$R\neq 1$, set$I(f)=\int_{|z|=R}\frac{Log z}{z^2+1}\,dz.$By obtaining estimates on$|I(f)|$proves$I(f)\to 0$as$R \to 0$and also as$R\to \infty$. Using$z=Re^{i\theta}$... 0answers 125 views ### Is this a correct way to prove what the derivative of a polynomial function is? After trying a polynomial long division problem with a lot of wondering how to go about answering it I proceeded by most likely overcomplicating things but the equation derived seems to work at ... 0answers 21 views ### Linear Gaussian system, covariance of the normalisation constant If we have the following multivariate Gaussian distributions: $$p(x) = N(x|\mu_x,\Sigma_x)$$ $$p(y|x) = N(y|Ax + b, \Sigma_y)$$ Now how can you deduce p(y) ? p(y) is called the normalisation ... 0answers 120 views ### About$f(s)=\sum_{a^2+b^2>0} \frac{(-1)^{a^2+b^2}}{(a^2+b^2)^s}=0$and the Extended Riemann Hypothesis. Let$s$be a complex number with a strictly positive real part ($Re(s)>0$). Let$f(s)=\sum_{a^2+b^2>0} \dfrac{(-1)^{a^2+b^2}}{(a^2+b^2)^s}$where the sum runs over all positive integers$a,b$... 0answers 182 views ### Algebra trick question, multiple choice, choosing one suggests a subgroup of$S_4$has order 6!? - is it a trick question or am I silly First: Let$G=S_4$- the group of all permutations of {1,2,3,4}. I must prove$N=\{1,(1,2)(3,4),(1,3)(2,4),(1,4)(2,3)\}$is a subgroup of$G$- this is easy, each transposition is its own inverse, ... 0answers 64 views ### How does SVD work? Trying to find information, and, no-one seems to know the answers. I have a time-series, represented by$T = [0, 1, 1, 0, \ldots, n]$the time series is then transformed into the Spectral results: ... 0answers 39 views ### Does this Gamma posterior make sense? quick question about the form of a posterior distribution. Suppose that$\theta \sim Gamma(a, b)$and that, given$\theta$,$Y\$ has CDF $$F(Y\mid\theta) = 1 - e^{-\theta(e^y - 1)},\quad ... 0answers 32 views ### Litterature: Convex Geometry using differential forms I've been looking for papers or books that discuss/use differential forms in convex geometry. I have been very unsuccessful in my search and was wondering if anybody here had come across such ... 0answers 132 views ### Rings, annihilators and (maximal) ideals Let R be a unital, associative, non-commutative ring. If P is an ideal of R, what is the annihilator of quotients R/PR and of R/P? Does something change if P is supposed to be a maximal ... 0answers 59 views ### Tanget space to manifold via curves without map I define tangent space T to differentiable manifold, in point p, via equivalence class of curves. The condition for this equivalence is (\varphi\circ\gamma_1)'(0)=(\varphi\circ\gamma_2)'(0) for some ... 0answers 47 views ### Continuity domain for momentum operator The momentum operator in one dimension in quantum mechanics is P=-i\frac{d}{dx} (with \hbar=1). Consider it as an operator on L_2(0,2\pi), the space of square-integrable functions on (0,2\pi). ... 0answers 37 views ### proving that the series  1+2^{s}+3^{s}++  is divergent but borel summable suppose that in the sense of distribution  \int_{0}^{\infty}dxx^{n}T(x,s) =n^{s}  for some distribution  T(x)  i do not know :( so if we apply borel generalized resummation$$ ...

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