Electrodynamics of Magnetoelectric Media and Magnetoelectric Fields

The relationship between magnetoelectricity and electromagnetism is a subject of a strong interest and numerous discussions in microwave and optical wave physics and material sciences. The definition of the energy and momentum of the electromagnetic (EM) field in a magnetoelectric (ME) medium is not a trivial problem. The question of whether electromagnetism and magnetoelectricity can coexist without an extension of Maxwell's theory arises when the effects of EM energy propagation are studied and the group velocity of the waves in an ME medium is considered. The energy balance equation reveals unusual topological structure of fields in ME materials. Together with certain constraints on the constitutive parameters of a medium, definite constraints on the local field structure should be imposed. Analyzing the EM phenomena inside an ME material, the question “what kind of the near fields arising from a sample of such a material can be measured?” should be answered. The visualization of the ME states requires an experimental technique that is based on an effective coupling to the violation of spatial as well as temporal inversion symmetry. To observe the ME energy in a subwavelength region, it is necessary to assume the existence of first-principle near fields—the ME fields. These are non-Maxwellian near fields with specific properties of violation of spatial and temporal inversion symmetry. A particular interest to the ME fields arises in studies of metamaterials with “artificial-atoms” ME elements.     

考虑塑性变形发展程度系数的RC梁开裂弯矩改进计算公式

针对RC梁开裂荷载计算方法尚未统一的现状，首先，结合18根RC梁试验数据对比了已有的6种RC梁开裂弯矩计算公式，发现开裂弯矩理论计算值与试验值的偏差大小和混凝土强度有关；然后，通过提出塑性变形发展程度系数k，推导新的RC梁开裂弯矩计算公式，并进一步基于k值和塑性影响系数计算值γ_k进行改进；最后，选取12根RC试验梁验证改进公式的准确性，证明改进公式的计算值与试验值吻合更好且偏于安全。     

Birnbaum‐Saunders distribution: A review of models,analysis, and applications

Birnbaum and Saunders introduced a two‐parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix‐variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

Central Sets Theorem along filters and some combinatorial consequences

The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions and extensions of this theorem. All of these theorems deal with central sets, and its origin from the algebra of Stone–?ech compactification of arbitrary semigroup, say $\beta S$. It can be proved that every closed subsemigroup of $\beta S$ is generated by a filter. We will show that, under some restrictions, one can derive the Central Sets Theorem for any closed subsemigroup of $\beta S$. We will derive this theorem using the corresponding filter and its algebra. Later we will also deal with how the notions of largeness along filters are preserved under some well behaved homomorphisms and give some consequences.