Fixed Point Theorems in Relational Metric Spaces with an Application to Boundary Value Problems

In this paper, we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of ω-distance in relational metric spaces. Thus we generalize the recent results of Senapati and Dey [J. Fixed Point Theory Appl. 19, 2945-2961 (2017)] and many other important results relevant to this literature. In order to revel the usefulness of such investigations, an application to first order periodic boundary value problem are given. Moreover, we furnish a non-trivial example to demonstrate the validity of our generalization over previous existing results.     

离散数学教材中传递闭包的两个问题

设R和F是有限集合X上的两个关系.借助关系图的概念,本文确定了分别满足t(R∪F)=t(R)∪t(F),t(s(R))=s(t(R))的R和F的充分必要条件,解决了耿素云、曲婉玲和王捍贫2002年编著的《离散数学教程》第40页和44页中的两个遗留问题.     

企业管理系统基本结构的数学定义

基于一般系统结构理论,描述了系统要素之间的关联关系,在此基础上,将企业管理系统的基本结构分为串联型、并联型、反馈型、扩缩型和蕴含型五种类型,并给出了相应的数学定义和图形描述,这将有助于研究由若干基本结构组合而成的复杂管理系统.     

直觉模糊变换半群

首先定义了直觉模糊变换半群的概念,给出了一种特殊的直觉模糊变换半群.其次,引入了直觉模糊变换半群上的直觉容许关系,讨论了两个直觉模糊变换半群间的关系,为直觉模糊有限自动机进一步的理论研究提供了代数方法.     

高阶常系数线性微分方程的一种积分形式特解

利用微分算子及n阶常系数非齐次线性微分方程的特征方程根与系数的关系给出其特解的逐次积分形式,并由此给出自由项f(x)=Pm(x)eλx(其中Pm(x)为m次多项式)时特解的简单递推公式.     

多重Hurwitz-zeta值的恒等式

当k=2,3,4或5且n〉k-1时,利用调和乘积公式我们证明了和∑a1＋a2＋…ak=na1,a2,…ak≥1ζ（2a1,2a2,…,2ak;-2-1,-2-1,…-2-1）与a1,a2,…,……有关的恒等式,这里……是多重Hurwitz—zeta函数,……     

Dispersion characteristics of transverse surface waves in piezoelectric coupled solid media with hard metal interlayer

The propagation of transverse surface waves in a piezoelectric layer/metal substrate system with one or multiple hard metal interlayer(s) is investigated analytically. The general dispersion equations for the existence of the waves are obtained in a simple mathematic form for class 6 mm piezoelectric materials. The presence of a hard metal interlayer can not only get rid of the undesired mode appearing in the case without an interlayer but shorten the existence range of the phase velocity within which a nonleaky but dispersive mode exists. The effects of the hard interlayer on the phase velocity can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.     

Numerical simulation of nonlinear magnetic-mechanical-electric coupling effect in laminated magnetoelectric composites

Considering the significant nonlinear magnetoelectric (ME) characteristics in laminated ME composites, we build a numerical model of magnetic-mechanical-electric coupling effect based on the nonlinear magnetostrictive constitutive relation. The change of the ME field coefficients with bias magnetic field predicted by this model shows good agreement with the experimental result, both qualitatively and quantitatively. Furthermore, this paper considers and predicts the magnetoelectric conversion charateristics of laminated ME composites, calculates and analyzes the influence of the thickness ratio of magnetostrictive layer, the geometrical size of laminated composites, the saturation magnetization, and the types of piezoelectric materials on the ME conversion coefficient of ME laminated composites. We believe that this research provides a theoretical basis for the production of magnetoelectric devices with good magnetoelectric conversion characteristics.     

F-theory grand unification at the colliders

We predict the exact gaugino mass relation near the electroweak scale at one loop for gravity mediated supersymmetry breaking in F-theory SU(5) and SO(10) models with UY(1) and U(1)_B−L fluxes, respectively. The gaugino mass relation introduced here differs from the typical gaugino mass relations studied thus far, and in general, should be preserved quite well at low energy. Therefore, these F-theory models can be tested at the Large Hadron Collider and future International Linear Collider. We present two typical scenarios that satisfy all the latest experimental constraints and are consistent with the CDMS II experiment. In particular, the gaugino mass relation is indeed satisfied at two-loop level with only a very small deviation around the electroweak scale.