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    Stable Scheme

    The scheme of the form $$\alpha v_{m+1}^{n+1}+\beta v_{m-1}^{n+1}=v_m^n$$ are they stable if $||\alpha|-|\beta||\ge 1$? Thank you.
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    A PDE solution: We define ϕ(x,r)=1nα(n)∫∂B(0,1)f(x+rz)dS(z)

    let f\in C^2(\mathbb{R}^n). We define \phi(x,r)=\frac{1}{n\alpha(n)}\int_{\partial B(0,1)}f(x+rz)dS(z) where \alpha(n) is the volume of B(0,1). I calculated \partial_r\phi=\frac{r}{n\alpha(n)}\int_{ B(0,1)}\Delta_xf(x+rz)dS(z) Please help me to show that...
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    Simple module: Let R be a ring with 1 and F a family of simple left R modules.

    Please help me to prove the following result: Let R be a ring with 1 and \mathcal{F} a family of simple left R modules. Let M=\oplus_{S\in \mathcal{F}} S and suppose that T is a simple submodule of M. Show that T\cong S for some S\in \mathcal{F}. Thanks
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    Taylor's series: A(t) = [1-cos(t*sqrt{4v-1})]/[4v-1] - (cosh(t)-1), g(t) = ...

    Let \nu\ge 1 be a parameter. For all t>0, we consider . . . . .\begin{align} A(t) & =\frac{1-\cos(t\sqrt{4\nu-1})}{4\nu-1}-(\cosh(t)-1) \\[10pt] g(t) & =\frac{\frac{\sin(t\sqrt{4\nu-1})}{\sqrt{4\nu-1}}+\sinh(t)}{A(t)} \end{align} By using Taylor's series, I want to prove that there exists...
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    number of orbits of a group: is map well-defined and surjective?

    For that i defined the map $\mathcal{O}_{X\times X}\to \mathcal{O}_X\times \mathcal{O}_X$, $[(x,y)] \mapsto ([x],[y])$ where $O_Z$ denotes the set of orbits of $Z$ and $[z]$ denotes the orbit $\{g\cdot z : g\in G\}$ I want to check that this map is well-defined and surjective. Please hepl me
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    number of orbits of a group: is map well-defined and surjective?

    Let $G$ be a finite group acting on a finite set $X$. Let $m$ be a number of orbits of $G$ on $X$ and $M$ be the number of orbits of $G$ on $X\times X$. Show that $m^2\le M$ with equality if and only if G acts trivialy on $X$. I need your help to solve this problem. Thanks.
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    frobenius group

    Let p be a prime number. We define the frobenius group by F_{p(p-1}=\left\{\begin{pmatrix}a&b\\0&1\end{pmatrix}, a\in \mathbb{F}_p^{\times}, b\in \mathbb{F}_p\right\} I want to identify the center Z(F_{p(p-1)}) and F'_{p(p-1)}=[F_{p(p-1)}:F_{p(p-1)}] with I will be gratefull if you could...
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    solution du prolème de Dirichlet

    This is what i wrote; The solution $u$ of the Dirichlet problem in $G$ with the boundary values $f$ is given by: $u:\bar{G}\to \mathbb{R}$ with $ u(z) = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{1-|z|^2}{|1 - e^{-it}z|^2} f ( e^{it}) \, dt, \qquad z \in {\mathbb{G}}. \tag{1}$ Then for all $z...
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    solution du prolème de Dirichlet

    solution du prolème de Dirichlet I want to unswer the following problem please help me: Let $G:=\left\{z\in \mathbb{C},\;-a<Re\;z<a,\;-b<Im\;z<b\right\}$, where $a,b>0$. Suppose that $f:\partial G\to\mathbb{R}$ is a continuous function satisfifying $f(\bar z)=-f(z)$,$\;z\in\partial G$...
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    V∈ E_r={P∈R[X_1,X_2,..,X_d]∣degP≤r} If exp^{−V(x)} ∈ L^2(R^d) then V admits local min

    Hi Ishuda, this is what i wrote but i don't know if that will help: if we prove the following implication does it help to answer the initial question?: If exp−V(x)∈L2(Rd) then the limit of V(x) as |x|goes to $+\infty$ is $+\infty$+∞ is+∞
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    V∈ E_r={P∈R[X_1,X_2,..,X_d]∣degP≤r} If exp^{−V(x)} ∈ L^2(R^d) then V admits local min

    V∈ E_r={P∈R[X_1,X_2,..,X_d]∣degP≤r} If exp^{−V(x)} ∈ L^2(R^d) then V admits local min Can someone please help me to answer this question: we consider V∈ E_r={P∈R[X_1,X_2,..,X_d]∣degP≤r} If exp^{−V(x)} ∈ L^2(R^d) then V admits a local minimum. Thanks in advance
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    spectral theory: prove equivalence of "A is essentially maximally accretive" and...

    Hi I mean : The equivalence of the next statements can easily be checked : 1. A is essentially maximally accretive. 2. A is maximally accretive. 3. There exists λ0 > 0 such that A∗ + λ0I is injective. 4. There exists λ1 > 0 such that the range of A + λ1I is dense in H. If you can help me ,thanks...
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    spectral theory: prove equivalence of "A is essentially maximally accretive" and...

    spectral theory: prove equivalence of "A is essentially maximally accretive" and... hi i want to prove the proposition in page 9 here :http://cermics.enpc.fr/~stoltz/MATHERIALS/nier1.pdf this is what i tried to do for 2)imply 3) we proceede by contraposition. let us suppose that for any a>0 we...
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    heat equation

    I want to know if the solution of heat equation verifies the estimate 0<u(t,x)<||u0||∞,(where u0 is the initil data u(0,x)) then this estimate is sufficient to prove that the maximum time of existance of u is infinity.Can someone help?
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    heat equation on a torus

    Can someone please help me to solve the following problem about the existance of a unique solution of the heat equation:
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    linear elliptic equation

    Hi can someone please help me show that if A c Rn a domain C2 smooth and f an application is in L2 (A) and u is a weak solution of the linear elliptic equation. if f is in Cb (A) with b in (0,1), then u is a classical solution of the linear elliptic equation. thank you in advance.
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    field: Suppose k has characteristic p>0 and is algebraic over Fp

    Suppose k has characteristic p>0 and is algebraic over Fp,prove that Every nonzero element of k is a root of unity this is what i wrote: let α ∈ k\{0}. Since k is algebraic, there exists a polynomial f ∈ Fp[x] such that f(α) = 0 moreover k has characteristic p>0 implis that p.1=0 but i couldn't...
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    density of S(R)

    we consider the operator A=1/√2(∂x+x) with domain D(A)={ u ∈ L2(R) such that Au ∈L2(R)} I am trying to solve the following question but i didn't manage to do that: Using the basic functions of Hermit and the harmonic oscillator ?(-Δ+/x/2 -1)/2 = = A*A, remember why S (R) (Schwartz functions) is...
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    height of prime ideal

    can someone please help me to show this result: Let A be a factoriel ring,and P included in A be a prime ideal show this equivalence: a)p is a principal ideal b) ht(p) ≤1 thanks in advance
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    localisation of ring

    Hi. Can someone please help me to prove this equivalence? Let A be a commutative ring and "a" is in A. We note Aa the localisation of A by S = {an, n dans N}. Knowing that A[x]/(ax-1) is isomorphic to Aa, show that Aa #0 if and only if a is not nilpotent Thanks in advance.
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