奇素数函数及应用

定义了奇素数函数和简化素数函数,证明了奇素数函数的值域是奇素数全集,简化素数函数的值域是不小于5的素数集合.同时应用这一结果,给出了素数判别函数,分析了孪生素数、梅森素数、费马素数、高斯素数、艾森斯坦素数、等差素数、偶变量素数、奇变量素数等的分布规律.说明了素数除了偶素数2之外,奇素数及其各类素数都有分布规律.

关于Smarandache素数可加补数列

研究著名的Smarandache素数可加补函数SPAC(n)的均值1/n sum from a=1 to n SPAC(a)的敛散性.利用初等及解析方法,给出了均值1/n sum from a=1 to n SPAC(a)一个较强的下界估计.证明均值1/n sum from a=1 to n SPAC(a)是发散的,从而解决了由数论专家Kenichiro Kashihara提出的一个关于函数SPAC(n)的猜想.

一类素数问题等对PA的条件独立性——对一些数论问题的逻辑讨论(Ⅳ)

用模型论方法证明了 2次函数素数值问题及一种 3重完美数问题对于PA的条件独立性 ,以及一些更一般的结论 .

素数

根据对自然数的排列,可得到两个含有素数的数列.从这两个数列中找出内在联系,归纳出两个素数函数.由于某些素数相差2这一性质,可得到孪生素数对函数.运用这些函数可以轻松方便地找到任一素数.

数论中切比雪夫不等式的一点补充

利用Wallis不等式,得到素数计算函数的一个下界估计.

整除在初等数论中的应用

利用格点图内因子的分布规律,推导出素数判断函数,孪生素数判断函数,歌德巴赫素数判断函数;推导出可计算不大于某正整数的素数个数,不大于某正整数的孪生素数个数和大偶数包含的歌德巴赫素数个数精确和近似的计算公式.

Optimal choice of parameters for particle swarm optimization

The constriction factor method (CFM) is a new variation of the basic particle swarm optimization (PSO), which has relatively better convergent nature. The effects of the major parameters on CFM were systematically investigated based on some benchmark functions. The constriction factor, velocity constraint, and population size all have significant impact on the per- formance of CFM for PSO. The constriction factor and velocity constraint have optimal values in practical application, and im- proper choice of these factors will lead to bad results. Increasing population size can improve the solution quality, although the computing time will be longer. The characteristics of CFM parameters are described and guidelines for determining parameter values are given in this paper.

Practical Model of Sea Ice Thickness of Bohai Sea Based on MODIS Data

Sea ice thickness is one of the most important input parameters in the studies on sea ice disaster prevention and mitigation. It is also the most important content in remote sensing monitoring of sea ice. In this study, a practical model of sea ice thickness(PMSIT) was proposed based on the Moderate Resolution Imaging Spectroradiometer(MODIS) data. In the proposed model, the MODIS data of the first band were used to estimate sea ice thickness and the difference between the second-band reflectance and the fifth-band reflectance in the MODIS data was calculated to obtain the difference attenuation index(DAI) of each pixel. The obtained DAI was used to estimate the integrated attenuation coefficient of the first band of the MODIS at the pixel level. Then the model was used to estimate sea ice thickness in the Bohai Sea with the MODIS data and then validated with the actual sea ice survey data. The validation results showed that the proposed model and corresponding parameterization scheme could largely avoid the estimation error of sea ice thickness caused by the spatial and temporal heterogeneity of sea ice extinction and allowed the error of 18.7% compared with the measured sea ice thickness.

On the Pseudo-Primeness of Meromorphic Functions of Infinite Order

In this paper the pseudo -primeness of meromorphic functions of infinite order is dissoussed in detail and quite a few result are obtained, which are improvments of that of Ozawa.

Two-Component Description for Relativistic Fermions

We propose a two-component form to describe massive relativistic fermions in gauge theories. Relations between the Green＇s functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the γ-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion is a scalar function. As examples, we use this form to reproduce the relativistic spectrum of hydrodron atom, the S-matrix of e＋e-→μ＋μ- and QED one-loop vacuum polarization of photon.

Halton-type sequences from global function fields

For any prime power q and any dimension s≥1, a new construction of (t, s)-sequences in base q using global function fields is presented. The construction yields an analog of Halton sequences for global function fields. It is the first general construction of (t, s)-sequences that is not directly based on the digital method. The construction can also be put into the framework of the theory of (u, e, s)-sequences that was recently introduced by Tezuka and leads in this way to better discrepancy bounds for the constructed sequences.

Permutation polynomials with low differential uniformity over finite fields of odd characteristic

In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q≡3(mod 4).

Prime number theorems for Rankin-Selberg L-functions over number fields

In this paper we define a Rankin-Selberg L-function attached to automorphic cuspidal represen-tations of GLm(AE) × GLm (AF ) over cyclic algebraic number fields E and F which are invariant under the Galois action,by exploiting a result proved by Arthur and Clozel,and prove a prime number theorem for this L-function.

The Generalized Prime Number Theorem for Automorphic L-Functions

Let π and π' be automorphic irreducible cuspidal representations of GLm(QA) and GLm'(QA),respectively,and L(s,π×■) be the Rankin-Selberg L-function attached to π and π'.Without assuming the Generalized Ramanujan Conjecture(GRC),the author gives the generalized prime number theorem for L(s,π×■) when π≌π'.The result generalizes the corresponding result of Liu and Ye in 2007.

Dynamics of a Function Related to the Primes

Let n = p1p2 ··· pk, where pi(1 ≤ i ≤ k) are primes in the descending order and are not all equal. Let Ωk(n) = P(p1 + p2)P(p2 + p3) ··· P(pk-1+ pk)P(pk+ p1), where P(n) is the largest prime factor of n. Define w0(n) = n and wi(n) = w(wi-1(n)) for all integers i ≥ 1. The smallest integer s for which there exists a positive integer t such thatΩs k(n) = Ωs+t k(n) is called the index of periodicity of n. The authors investigate the index of periodicity of n.

Density Results in Sobolev Spaces Whose Elements Vanish on a Part of the Boundary

This paper is devoted to the study of the subspace of Wm＇＂ of functions that vanish on a part γ0 of the boundary. The author gives a crucial estimate of the Poincare constant in balls centered on the boundary of γ0. Then, the convolution-translation method, a variant of the standard mollifier technique, can be used to prove the density of smooth functions that vanish in a neighborhood of γ0, in this subspace. The result is first proved for m = 1, then generalized to the case where m 〉 1, in any dimension, in the framework of Lipschitz-continuous domain. However, as may be expected, it is needed to make additional assumptions on the boundary of γ0, namely that it is locally the graph of some Lipschitz-continuous function.

Solvable base change and Rankin-Selberg convolutions

Let π and π′ be unitary automorphic cuspidal representations of GL_n(A_E) and GL_m(A_F), and let E and F be solvable Galois extensions of Q of degrees ? and ?′, respectively. Using the fact that the automorphic induction and base change maps exist for E and F, and assuming an invariance condition under the actions of the Galois groups, we attach to the pair(π, π′) a Rankin-Selberg L-function L(s, π×E,Fπ′) for which we prove a prime number theorem. This gives a method for comparing two representations that could be defined over completely different extensions, and the main results give a measure of how many cuspidal components the two representations π and π′ have in common when automorphically induced down to the rational numbers. The proof uses the structure of the Galois group of the composite extension EF and the character groups attached to the fields via class field theory. The second main theorem also gives an indication of when the base change of π up to the composite extension EF remains cuspidal.