Central limit behavior in the Kuramoto model at the “edge of chaos”

We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the “edge of chaos” (i.e. in a regime with vanishing Lyapunov exponents), robust q-Gaussian-like limit distributions naturally emerge, consistently with recently proved generalizations of the CLT.     

What is a Quotient Map with Respect to a Closure Operator?

It is shown that there is no good answer to the question of the title, even if we restrict our attention to S et-based topological categories. Although very closely related, neither the natural notion of c-finality (designed in total analogy to c-initiality) nor the notion of c-quotient (modelled after the behaviour of topological quotient maps) provide universally satisfactory concepts. More dramatically, in the category T op with its natural Kuratowski closure operator k, the class of k-final maps cannot be described as the class of c-quotient maps for any closure operator c, and the class of k-quotients cannot be described as the class of c-final maps for any c. We also discuss the behaviour of c-final maps under crossing with an identity map, as in Whitehead's Theorem. In T op, this gives a new stability theorem for hereditary quotient maps.     

O—连通性的樊畿定理

借助分子的领域给出O－连通性的樊畿定理型刻画。     

Karlin定理的推广和应用

Ｋａｒｌｉｎ定理是研究估计量的容许性的有效工具,但是这个定理是建立在单参数指数族分布下的,本文在多参数指数族分布下给出了Ｋａｒｌｉｎ定理的一个推广,并将它应用到正态分布,Ｐｏｉｓｓｏｎ分布,二项分布,指数分布,逆二项分布和Ｗｉｓｈａｒｔ分布,得到了一些有意义的结果。     

关于"圆盘定理的改进与弱连对角占优矩阵"一文的注记

本文指出《应用数学学报》中一文的错误,分析了产生错误的原因,同时给出修正的矩阵谱包含域及特征值定理,推广与改进了佟文廷（１９７７）以及叶伯英（１９８５）的相应结果。     

Quasilinear elliptic problems with multivalued terms

We study the quasilinear elliptic problem with multivalued terms.We consider the Dirichlet problem with a multivalued term appearing in the equation and a problem of Neumann type with a multivalued term appearing in the boundary condition. Our approach is based on Szulkin's critical point theory for lower semicontinuous energy functionals.     

THE CAUCHY-KOVALEVSKAYA THEOREM-OLD AND NEW

The paper surveys interactions between complex and functional-analytic methods in the Cauchy-Kovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions of the Cauchy-Kovalevskaya Theorem. Recent trends in the Cauchy-Kovalevskaya theory are based on the concept of associated differential operators. Since an evolution operator may posses several associated operators, initial data may be decomposed into components belonging to different associated spaces. This technique makes it also possible to solve ill-posed initial value problems.     

Classical Fourier Analysis over Homogeneous Spaces of Compact Groups

This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G andμ be the normalized G-invariant measure on G/ H associated to the Weil's formula.Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L~2(G/H,μ).     

On the strong maximum principle

This paper presents a necessary and sufficient condition on the convex function in order that continuous solutions to

satisfy a Strong Maximum Principle on any open connected .

     

A one-parameter quadratic-base version of the Baillie-PSW probable prime test

The well-known Baillie-PSW probable prime test is a combination of a Rabin-Miller test and a ``true' (i.e., with The well-known Baillie-PSW probable prime test is a combination of a Rabin-Miller test and a ``true' (i.e., with ) Lucas test. Arnault mentioned in a recent paper that no precise result is known about its probability of error. Grantham recently provided a probable prime test (RQFT) with probability of error less than 1/7710, and pointed out that the lack of counter-examples to the Baillie-PSW test indicates that the true probability of error may be much lower.

In this paper we first define pseudoprimes and strong pseudoprimes to quadratic bases with one parameter: , and define the base-counting functions:

and

Then we give explicit formulas to compute B and SB, and prove that, for odd composites ,

and point out that these are best possible. Finally, based on one-parameter quadratic-base pseudoprimes, we provide a probable prime test, called the One-Parameter Quadratic-Base Test (OPQBT), which passed by all primes and passed by an odd composite odd primes) with probability of error . We give explicit formulas to compute , and prove that

The running time of the OPQBT is asymptotically 4 times that of a Rabin-Miller test for worst cases, but twice that of a Rabin-Miller test for most composites. We point out that the OPQBT has clear finite group (field) structure and nice symmetry, and is indeed a more general and strict version of the Baillie-PSW test. Comparisons with Gantham's RQFT are given.