Good B-quasi-Ehresmann semigroups

A semigroup S with a sub-band B is called a good B-quasi-Ehresmann semigroup if it is a Bsemiabundant semigroup satisfying the congruence condition such that B((ab)+)abB((ab)*)aB(a*)B(b+)b for all a,b ∈S.We show that every good B-quasi-Ehresmann semigroup has a global representation and a standard representation.As a special case,the structure of good quasi-adequate semigroups is described.     

Finite p-groups all of whose proper subgroups have small derived subgroups

Let G be a finite p-group.If the order of the derived subgroup of each proper subgroup of G divides pi,G is called a Di-group.In this paper,we give a characterization of all D1-groups.This is an answer to a question introduced by Berkovich.     

AVERAGE ONESIDED WIDTHS OF SOBOLEV AND BESOV CLASSES

The article concerns the average onesided widths of the Sobolev and Besov classes and the classes of functions with bounded moduli of smoothness. The weak asymptotic results are obtained for the corresponding quantities.     

SUBNORMAL SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

In this article, we apply the concept of hyper-order to higher order linear differential equations with periodic coefficients, investigate the existence and the form of its subnormal solution, and estimate the growth of all other solutions, and answer the question raised by Gundersen and Steinbart for more general periodic differential equations.     

ON BLOCK MATRICES ASSOCIATED WITH DISCRETE TRIGONOMETRIC TRANSFORMS AND THEIR USE IN THE THEORY OF WAVE PROPAGATION

Block matrices associated with discrete Trigonometric transforms （DTT＇s） arise in the mathematical modelling of several applications of wave propagation theory including discretizations of scatterers and radiators with the Method of Moments, the Boundary Element Method, and the Method of Auxiliary Sources. The DTT＇s are represented by the Fourier, Hartley, Cosine, and Sine matrices, which are unitary and offer simultaneous diagonalizations of specific matrix algebras. The main tool for the investigation of the aforementioned wave applications is the efficient inversion of such types of block matrices. To this direction, in this paper we develop an efficient algorithm for the inversion of matrices with U-diagonalizable blocks （U a fixed unitary matrix） by utilizing the U- diagonalization of each block and subsequently a similarity transformation procedure. We determine the developed method＇s computational complexity and point out its high efficiency compared to standard inversion techniques. An implementation of the algorithm in Matlab is given. Several numerical results are presented demonstrating the CPU-time efficiency and accuracy for ill-conditioned matrices of the method. The investigated matrices stem from real-world wave propagation applications.     

An analytical and numerical study of peristaltic transport of a Johnson-Segalman fluid in an endoscope

In the present study, we discuss the peristaltic flow of a Johnson-Segalman fluid in an endoscope. Perturbation, homotopy, and numerical solutions are found for the non-linear differential equation. The comparative study is also made to check the validity of the solutions. The expressions for pressure rise frictional forces, pressure gradient, and stream lines are presented to interpret the behavior of various physical quantities of the Johnson-Segalman fluid.     

Shape optimization of the caudal fin of the three-dimensional self-propelled swimming fish

Shape optimization of the caudal fin of the three-dimensional self-propelled swimming fish,to increase the swimming efficiency and the swimming speed and control the motion direction more easily,is investigated by combining optimization algorithms,unsteady computational fluid dynamics and dynamic control in this study.The 3D computational fluid dynamics package contains the immersed boundary method,volume of fluid method,the adaptive multi-grid finite volume method and the control strategy of fish swimming.Through shape optimizations of various swimming speeds,the results show that the optimal caudal fins of different swimming modes are not exactly the same shape.However,the optimal fish of high swimming speed,whose caudal fin shape is similar to the crescent,also have higher efficiency and better maneuverability than the other optimal bionic fish at low and moderate swimming speeds.Finally,the mechanisms of vorticity creation of different optimal bionic fish are studied by using boundary vorticity-flux theory,and three-dimensional wake structures of self-propelled swimming of these fish are comparatively analyzed.The study of vortex dynamics reveals the nature of efficient swimming of the 3D bionic fish with the lunate caudal fin.     

Arbitrary-state solutions of the Dirac equation for a Möbius square potential using the Nikiforov-Uvarov method

We inquire into spin and pseudospin symmetries of the Dirac equation under a Mbius square-type potential using the Nikiforov-Uvarov method to calculate the bound state solutions. We numerically discuss the problem and include various explanatory figures.     

带加法白噪声的随机Boussinesq方程组的解的渐近行为

考虑速度和温度同时在加法白噪声扰动下的随机Boussinesq方程组的解的渐近特征.可以接轨道得到该随机方程组的唯一解,并可以验证该解生成随机动力系统,进而证明了该随机动力系统存在随机吸引子.     

确定环形Markov链的Q-矩阵

给出了Markov链中任一状态集的逗留时间或击中时间的分布(混合指数分布),以及其分布的各阶微分与Q-矩阵之间的约束方程组.利用该约束关系及环形链结构的先验信息,采用Markov链反演方法证明了:对于有限状态环形Markov链,其Q-矩阵能由其中任意两个相邻状态的逗留时间和击中时间分布唯一决定,并给出了相应的算法.