共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove that for each prime p, positive integer \(\alpha \), and non-negative integers \(\beta \) and \(\gamma \), the Diophantine equation \(X^{2N} + 2^{2\alpha }5^{2\beta }{p}^{2\gamma } = Z^5\) has no solution with N, X, \(Z\in \mathbb {Z}^+\), \(N > 1\), and \(\gcd (X,Z) = 1\). 相似文献
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Neena Gupta 《Inventiones Mathematicae》2014,195(1):279-288
We show that the Cancellation Conjecture does not hold for the affine space $\mathbb{A}^{3}_{k}$ over any field k of positive characteristic. We prove that an example of T. Asanuma provides a three-dimensional k-algebra A for which A is not isomorphic to k[X 1,X 2,X 3] although A[T] is isomorphic to k[X 1,X 2,X 3,X 4]. 相似文献
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R. Cavazzoni 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(2):193-204
In this paper we present a parabolic approach to studying the diffusive long time behaviour of solutions to the Cauchy problem:
where u0 and u1 satisfy suitable assumptions.
After an appropriate scaling we obtain the convergence to a stationary solutio n in Lq norm (1 ≤ q < ∞). 相似文献
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Given a Lie group G with a bi-invariant metric and a compact Lie subgroup K, Bittencourt and Ripoll used the homogeneous structure of quotient spaces to define a Gauss map ${\mathcal{N}:M^{n}\rightarrow{\mathbb{S}}}$ on any hypersupersurface ${M^{n}\looparrowright G/K}$ , where ${{\mathbb{S}}}$ is the unit sphere of the Lie algebra of G. It is proved in Bittencourt and Ripoll (Pacific J Math 224:45–64, 2006) that M n having constant mean curvature (CMC) is equivalent to ${\mathcal{N}}$ being harmonic, a generalization of a Ruh–Vilms theorem for submanifolds in the Euclidean space. In particular, when n = 2, the induced quadratic differential ${\mathcal{Q}_{\mathcal{N}}:=(\mathcal{N}^{\ast}g)^{2,0}}$ is holomorphic on CMC surfaces of G/K. In this paper, we take ${G/K={\mathbb{S}}^{2}\times{\mathbb{R}}}$ and compare ${\mathcal{Q}_{\mathcal{N}}}$ with the Abresch–Rosenberg differential ${\mathcal{Q}}$ , also holomorphic for CMC surfaces. It is proved that ${\mathcal{Q}=\mathcal{Q}_{\mathcal{N}}}$ , after showing that ${\mathcal{N}}$ is the twisted normal given by (1.5) herein. Then we define the twisted normal for surfaces in ${{\mathbb{H}}^{2}\times{\mathbb{R}}}$ and prove that ${\mathcal{Q}=\mathcal{Q}_{\mathcal{N}}}$ as well. Within the unified model for the two product spaces, we compute the tension field of ${\mathcal{N}}$ and extend to surfaces in ${{\mathbb{H}}^{2}\times{\mathbb{R}}}$ the equivalence between the CMC property and the harmonicity of ${\mathcal{N}.}$ 相似文献
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Nicolae Popescu Marian Vâjâitu Alexandru Zaharescu 《Algebras and Representation Theory》2006,9(1):47-66
Let T be a transcendental element of
and
the orbit of T. On
we have a Haar measure
. The goal of this paper is to characterize all the elements of
for which the integral
, called the trace of T, is well defined.Presented by A. Verschoren 相似文献
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We consider the following Liouville equation in
For each fixed and a
j
> 0 for 1 ≤ j ≤ k, we construct a solution to the above equation with the following asymptotic behavior:
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We consider the (pure) braid groups $B_{n}(M)$ and $P_{n}(M)$ , where $M$ is the $2$ -sphere $\mathbb S ^{2}$ or the real projective plane $\mathbb R P^2$ . We determine the minimal cardinality of (normal) generating sets $X$ of these groups, first when there is no restriction on $X$ , and secondly when $X$ consists of elements of finite order. This improves on results of Berrick and Matthey in the case of $\mathbb S ^{2}$ , and extends them in the case of $\mathbb R P^2$ . We begin by recalling the situation for the Artin braid groups ( $M=\mathbb{D }^{2}$ ). As applications of our results, we answer the corresponding questions for the associated mapping class groups, and we show that for $M=\mathbb S ^{2}$ or $\mathbb R P^2$ , the induced action of $B_n(M)$ on $H_3(\widetilde{F_n(M)};\mathbb{Z })$ is trivial, $F_{n}(M)$ being the $n^\mathrm{th}$ configuration space of $M$ . 相似文献
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N. M. Ivochkina 《Journal of Mathematical Sciences》1983,21(5):689-697
One gives an a priori estimate of \(\parallel u\parallel _{c^2 (\overline \Omega )}\) for the convex solutions of the Dirichlet problem for the Monge-Ampère equation (Uij=f(x,u,ux)in a strictly convex bounded domain det,ΩcRn 相似文献
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Consider the perturbation analysis for positive definite solution of the nonlinear matrix equation $X-\sum_{i=1}^{m}A_{i}^{*}X^{-1}A_{i}=Q$ which arises in an optimal interpolation problem. Two perturbation bounds for the unique positive definite solution are obtained, and an explicit expression of the condition number for the unique positive definite solution is derived. The theoretical results are illustrated by several numerical examples. 相似文献
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Mohamed A. Ramadan Mokhtar A. Abdel Naby Ahmed M. E. Bayoumi 《Journal of Applied Mathematics and Computing》2014,44(1-2):99-118
This paper is concerned with iterative solution to general Sylvester-conjugate matrix equation of the form $\sum_{i = 1}^{s} A_{i}V + \sum_{j = 1}^{t} B_{j}W = \sum_{l = 1}^{m} E_{l}\overline{V}F_{l} + C$ . An iterative algorithm is established to solve this matrix equation. When this matrix equation is consistent, for any initial matrices, the solutions can be obtained within finite iterative steps in the absence of round off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm. 相似文献
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S. V. Fomin 《Journal of Mathematical Sciences》1984,27(5):3152-3160
Sufficient conditions for convergence in the central limit theorem (for identically distributed random variables) with respect to the topology specified in the title are given. These conditions hold for the uniform distribution although there exist distributions with smooth densities concentrated on a bounded interval for which the convergence result does not hold. 相似文献