All Questions

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How to express a Poisson regression equation as a quasi-Poisson

I was reading this paper: http://www.researchgate.net/publication/13878515_A_simple_non-linear_model_in_incidence_prediction and was wondering whether the equations 1 and 3 presented in the paper to ...
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What is the value of $x$ such that $\frac{\text{d}^2y}{\text{d}x^2}=0$ where $\frac{\text{d}y}{\text{d}x}=-ae^{-bx}y-cy+d$?

How can you find the values of $x$ such that $$\frac{\text{d}^2y(x)}{\text{d}x^2}=0$$ where $$\frac{\text{d}y}{\text{d}x}=-ae^{-bx}y-cy+d$$ with $$y(0)=y_0$$ and $$a,b,c,d>0$$ If it helps I can ...
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Is the inverse of a bijective connectedness preserving map , on a complete real inner product space , also connectedness preserving?

Let $X$ be a complete real inner-product space and $f:X \to X$ be a bijection which maps connected sets to connected sets ; then is it necessarily true that $f^{-1}$ also maps connected sets to ...
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Mathematical structures textbook recommendation

I am busy doing an undergraduate course called "Fundamentals of Mathematics". It is not well-defined as there is no syllabus nor recommended textbook (there are lectures and notes), but the course ...
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Hessian Matrix of an Angle in Terms of the Vertices

I am attempting to derive the analytical formula for the Hessian matrix of a the second derivatives of the value of an angle in terms of the (9) coordinates of the 3 3D points that define it. While I ...
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Configurations of eleven (or more) points in the Euclidean plane, such that out of any four there is a pair at unit distance.

Inspired by this question, I was wondering the following: What is the maximal size of a subset $C$ of the Euclidean plane such that out of any four points in $C$ there are two at unit distance ...
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Integers $n$ for which the digit sum of $n$ exceeds the digit sum of $n^5$

This question is strongly inspired by The smallest integer whose digit sum is larger than that of its cube? by Bernardo Recamán Santos. The number $n=124499$ has digit sum $1+2+4+4+9+9=29$ while its ...
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For all $n$ there exists $x$ such that $\varphi(x)<\varphi(x+1)<\ldots<\varphi(x+n)$

Let $\varphi$ be the Euler's function, i.e. $\varphi(n)$ stands for the number of integers $m \in \{1,\ldots,n\}$ such that $\text{gcd}(m,n)=1$. Let $n\ge 2$ be a positive integer. Show that there ...
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How can I indicate that n and k are natural numbers in ∀n[(∀k < n P(k)) → P(n)].

$∀\, x \, \{x\in\mathbb N\rightarrow P(x)\}$ can be abbreviated to $∀ \hspace{.1cm} x∈ℕ[P(x)].$ But, I am not sure how I can indicate "concisely" that n and k are natural numbers in ∀n[(∀k < n ...
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Bounding 2nd-smallest eigenvalue of the Laplacian of the binary tree

I am reading on my own the notes of this lecture series from 2012: http://www.cs.yale.edu/homes/spielman/561/2012/lect04-12.pdf. In section 4.7.2 (page 8) it's mentioned that we can prove a lower ...
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Invariant points and lines under homography

Given a matrix representation of an homography in a real projective space $P(\mathbb{R^3})$, what is the general procedure to calcule the invariant subspaces? A brief description would be enough.
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Injury-free proof of Cof being $\Sigma^0_3$-complete

How can I prove, without using priority argument, that Cof, the set of indices of cofinite c.e. sets, is $\Sigma^0_3$-complete? I know an injury-free proof of Rec being $\Sigma^0_3$-complete, where ...
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How can I solve this stochastic system of equation?

$(B_1(t),B_2(t))$ is a 2-dimensional standard Brownian motion. $\alpha , \beta$ are constant. The system of equations is: $$dX_1(t)=X_2(t)dt+\alpha dB_1(t)\\dX_2(t)=-X_1(t)dt+\alpha dB_2(t)$$ I tried ...
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Research in algebra.

First of all, I don't know if this is the right place to ask about this. If not, please direct me somewhere I can get more help. I like algebra a lot as a mathematics undergraduate student on his 3rd ...
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Weierstrass's M-test example for uniform convergence and switching Sum and Integral.

How would I go about finding $M_n$ in $$\sum_{n=1}^{\infty} \int_{0}^\infty x^{\frac{s}{2}-1}e^{-\pi n^{2}x}dx$$ to show that it is uniformly convergent? UPDATE: Just ...
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Element of Grothendieck group is eigenvector of operator

Let $K_\mathbb{C}(G)$ be the Grothendieck group (over $\mathbb{C}$) of finite dimensional representations of a finite group $G$. Associated with any such representation $V$, there is a linear ...
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Product of 2 dirac delta functions

Find the functional form of the Green function G(x,t) for a parabolic differential equation (i.e. heat diffusion etc):  ...
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construct a triangle with a compass and a ruler, given $a, B, t_a$

$a,b,c$ the sides of the triangles; $A,B,C$ the angles of the triangles; $t_a, t_b, t_c$ the internal bisectors of the angles $A,B,C$. How to construct a triangle with a compass and a ruler(a ...
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Proving the Ideal Generated by the Coefficients of $f(X)\cdot g(X)\in R[X]$ is $R$.

Let $R$ be a commutative ring with unity, and let $f(X),g(X)\in R[X]$. Assume the ideals generated by the coefficients of $f(X),g(X)$ are both $R$. Prove that the ideal generated by the ...
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Correlation between an event and a time series

I have a time series, e.g. the daily number of visitors on my blog. I have a set of events of some class, like the days when I made a new posting. I want to measure the effect of a new posting on the ...
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3D projection coordinates onto 2D plane to determine transformation matrix?

I'm not sure if there is an actual solution to this problem or not, but thought I would give it a shot here to see if anyone has any ideas. So here goes: I basically have three vertices of a rigid ...
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Kernel, Green function and the functional derivative.

I am pretty new to the subject of differential equations and am reading about Green functions and Kernels for the first time. I am more familiar with functional differentiation and am comfortable with ...
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Prove Euler characteristic is a homotopy invariant without using homology theory

I was flipping through May's Concise Course in Algebraic Topology and found the following question on page 82. Think about proving from what we have done so far that $\chi(X)$ depends only on ...
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Cauchy induction: are there examples of cases where choosing an integer other than $2$ is a better strategy?

Cauchy induction, sometimes called backwards induction, works as follows: show that $p(1)$ is true show that $p(n)$ implies $p(2n)$ (which inductively implies $p(2^n)$ is true) show that $p(n)$ ...
I recently was passing some time on Project Euler, when I came across this question. It deals with finding Pentagonal Numbers $P_j$ and $P_k$ such that $P_j+P_k$ and $P_j-P_k$ are also pentagonal ...