共查询到20条相似文献,搜索用时 0 毫秒
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We establish the limit system for the Gross–Pitaevskii equations when the segregation phenomenon appears, and shows this limit is the one arising from the competing systems in population dynamics. This covers and verifies a conjecture of S. Terracini et al., both in the parabolic case and the elliptic case. 相似文献
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In this paper, we consider the Fischer–Marsden conjecture within the frame-work of K-contact manifolds and \((\kappa ,\mu )\)-contact manifolds. First, we prove that a complete K-contact metric satisfying \(\mathcal {L}^{*}_g(\lambda )=0\) is Einstein and is isometric to a unit sphere \(S^{2n+1}\). Next, we prove that if a non-Sasakian \((\kappa ,\mu )\)-contact metric satisfies \(\mathcal {L}^{*}_g(\lambda )=0\), then \( M^{3} \) is flat, and for \(n > 1\), \(M^{2n+1}\) is locally isometric to the product of a Euclidean space \(E^{n+1}\) and a sphere \(S^n(4)\) of constant curvature \(+\,4\). 相似文献
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In this paper, we would like to formulate a conjecture on a relation between a certain period of automorphic forms on special orthogonal groups and some L-value. Our conjecture can be considered as a refinement of the global Gross–Prasad conjecture. 相似文献
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The Gross conjecture over ? was first claimed by Aoki in 1991. However, the original proof contains too many mistakes and false claims to be considered as a serious proof. This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki. We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of ?. 相似文献
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《Expositiones Mathematicae》2020,38(4):430-479
The Bateman–Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green–Tao theorem, along with many famous conjectures, such the twin prime conjecture and Landau’s conjecture. We discuss the Bateman–Horn conjecture, its applications, and its origins. 相似文献
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Bäcklund transformations are applied to study the Gross–Pitaevskii equation. Supported by previous results, a class of Bäcklund transformations admitted by this equation are constructed. Schwarzian derivative as well as its invariance properties turn out to represent a key tool in the present investigation. Examples and explicit solutions of the Gross–Pitaevskii equation are obtained.
相似文献12.
Jiaqun Wei 《Mathematische Zeitschrift》2012,272(1-2):431-441
We studied the properties of tilting complexes and proved that derived equivalences preserve the validity of the Auslander–Reiten conjecture. 相似文献
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Jesse Thorner 《Archiv der Mathematik》2014,103(2):147-156
Let \({f(z) = \sum_{n=1}^\infty a(n)e^{2\pi i nz} \in S_k^{\mathrm{new}}(\Gamma_0(N))}\) be a newform of even weight \({k \geq 2}\) that does not have complex multiplication. Then \({a(n) \in \mathbb{R}}\) for all n; so for any prime p, there exists \({\theta_p \in [0, \pi]}\) such that \({a(p) = 2p^{(k-1)/2} {\rm cos} (\theta_p)}\) . Let \({\pi(x) = \#\{p \leq x\}}\) . For a given subinterval \({[\alpha, \beta]\subset[0, \pi]}\) , the now-proven Sato–Tate conjecture tells us that as \({x \to \infty}\) , $$ \#\{p \leq x: \theta_p \in I\} \sim \mu_{ST} ([\alpha, \beta])\pi(x),\quad \mu_{ST} ([\alpha, \beta]) = \int\limits_{\alpha}^\beta \frac{2}{\pi}{\rm sin}^2(\theta) d\theta. $$ Let \({\epsilon > 0}\) . Assuming that the symmetric power L-functions of f are automorphic, we prove that as \({x \to \infty}\) , $$ \#\{p \leq x: \theta_p \in I\} = \mu_{ST} ([\alpha, \beta])\pi(x) + O\left(\frac{x}{(\log x)^{9/8-\epsilon}} \right), $$ where the implied constant is effectively computable and depends only on k,N, and \({\epsilon}\) . 相似文献
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Rishi Nath 《Journal of Algebra》2009,321(6):1632-1642
A recent refinement of the McKay conjecture is verified for the case of the alternating groups. The argument builds upon the verification of the conjecture for the symmetric groups [P. Fong, The Isaacs–Navarro conjecture for symmetric groups, J. Algebra 250 (1) (2003) 154–161]. 相似文献
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An \(n\) -poised set in two dimensions is a set of nodes admitting unique bivariate interpolation with polynomials of total degree at most \(n\) . We are interested in poised sets with the property that all fundamental polynomials are products of linear factors. Gasca and Maeztu (Numer Math 39:1–14, 1982) conjectured that every such set necessarily contains \(n+1\) collinear nodes. Up to now, this had been confirmed only for \(n\le 4\) , the case \(n=4\) having been proved for the first time by Busch (Rev Un Mat Argent 36:33–38, 1990). In the present paper, we prove the case \(n=5\) with new methods that might also be useful in deciding the still open cases for \(n\ge 6\) . 相似文献
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Victor Beresnevich Glyn Harman Alan Haynes Sanju Velani 《Mathematische Zeitschrift》2013,275(1-2):127-133
In 2012 the authors set out a programme to prove the Duffin–Schaeffer conjecture for measures arbitrarily close to Lebesgue measure. In this paper we take a new step in this direction. Given a non-negative function $\psi : \mathbb N \rightarrow \mathbb R $ , let $W(\psi )$ denote the set of real numbers $x$ such that $|nx -a| < \psi (n) $ for infinitely many reduced rationals $a/n \ (n>0) $ . Our main result is that $W(\psi )$ is of full Lebesgue measure if there exists a $c > 0 $ such that $$\begin{aligned} \sum _{n\ge 16} \, \frac{\varphi (n) \psi (n)}{n \exp (c(\log \log n)(\log \log \log n))} \, = \, \infty \, . \end{aligned}$$ 相似文献
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Mathematical Notes - The author attempts to change and supplement the standard scheme of partitions of integers in number theory to make it completely concur with the Bohr–Kalckar... 相似文献
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Given , the Fox–Kleitman conjecture from 2006 states that there exists a nonzero integer such that the -variable linear Diophantine equation is -regular. This is best possible, since Fox and Kleitman showed that for all , this equation is not -regular. While the conjecture has recently been settled for all , here we focus on the case and determine the degree of regularity of the corresponding equation for all . In particular, this independently confirms the conjecture for . We also briefly discuss the case . 相似文献