Energies,group-invariant kernels and numerical integration on compact manifolds

The purpose of this paper is to derive quadrature estimates on compact, homogeneous manifolds embedded in Euclidean spaces, via energy functionals associated with a class of group-invariant kernels which are generalizations of zonal kernels on the spheres or radial kernels in euclidean spaces. Our results apply, in particular, to weighted Riesz kernels defined on spheres and certain projective spaces. Our energy functionals describe both uniform and perturbed uniform distribution of quadrature point sets.     

Weights of twisted exponential sums

Let k be a finite field of characteristic p, l a prime number different from p, a nontrivial additive character, and a character on . Then ψ defines an Artin-Schreier sheaf on the affine line , and χ defines a Kummer sheaf on the n-dimensional torus . Let be a Laurent polynomial. It defines a k-morphism . In this paper, we calculate the weights of under some non-degeneracy conditions on f. Our results can be used to estimate sums of the form

Parametric Mulholland-type inequalities

By means of the weight functions and the idea of introducing parameters, a discrete Mulholland-type inequality with the general homogeneous kernel and the equivalent form are given. The equivalent statements of the best possible constant factor related to some parameters, the operator expressions and some particular examples are considered.     

Primitive idempotents of irreducible cyclic codes and self-dual cyclic codes over Galois rings

Let $R$ be the Galois ring $GR(p^k,s)$ of characteristic $p^k$ and cardinality $p^{sk}$. Firstly, we give all primitive idempotent generators of irreducible cyclic codes of length $n$ over $R$, and a $p$-adic integer ring with $gcd(p,n)=1$. Secondly, we obtain all primitive idempotents of all irreducible cyclic codes of length $r{l}^m$ over $R$, where $r,l,$ and $t$ are three primes with $2?l$, $r|(q^t?1)$, $l^v\parallel (q^t?1)$ and $gcd(rl,q(q?1))=1$. Finally, as applications, weight distributions of all irreducible cyclic codes for $t=2$ and generator polynomials of self-dual cyclic codes of length $l^m$ and $r{l}^m$ over $R$ are given.     

A3钢在芽孢杆菌作用下的腐蚀行为

采用表面分析技术、失重法和电化学测试技术研究了A3钢在芽孢杆菌(Bacillus)作用下的腐蚀行为.扫描电子显微镜(SEM)分析结果表明,浸泡7d时,芽孢杆菌会在A3钢表面形成致密的生物膜,有效阻隔了溶液对基体的腐蚀,抑制了腐蚀过程.电化学交流阻抗测试结果显示,含菌体系中的试样表面经历了2个时间常数→3个时间常数→2个时间常数的变化过程.失重法和极化曲线测试结果表明,芽孢杆菌的细菌活性对生物膜的保护作用有着决定性的影响,当微生物活性下降,生物膜的保护能力也会大幅降低.     

Almost subadditive weight functions form Braun-Meise-Taylor theory of ultradistributions

As it is known, Roumieu-Komatsu theory of ultradistributions is strictly larger than Beurling-Björck one and that the latter theory is established by the class of all subadditive weight functions. In its own turn, Roumieu-Komatsu theory is equivalent to Braun-Meise-Taylor one which is given by the class of all weight functions. We prove that the class of all almost subadditive weight functions forms Braun-Meise-Taylor theory of ultradistributions.     

Cantor sets and cyclicity in weighted Dirichlet spaces

We treat the problem of characterizing the cyclic vectors in the weighted Dirichlet spaces, extending some of our earlier results in the classical Dirichlet space. The absence of a Carleson-type formula for weighted Dirichlet integrals necessitates the introduction of new techniques.     

一个零齐次核的Hilbert型积分不等式及其逆

通过引入参数和应用权函数的方法,建立了一个核为零齐次的Hilbert型积分不等式及其等价形式和它们的逆向形式,并证明其常数因子为最佳值.最后,本文给出了一个评注。