Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control

Based on the stability theory of fractional order systems, this paper analyses the synchronization conditions of the fractional order chaotic systems with activation feedback method. And the synchronization of commensurate order hyperchaotic Lorenz system of the base order 0.98 is implemented based on this method. Numerical simulations show the effectiveness of this method in a class of fractional order chaotic systems.     

Mean residual life order of convolutions of heterogeneous exponential random variables

In this paper, we study convolutions of heterogeneous exponential random variables with respect to the mean residual life order. By introducing a new partial order (reciprocal majorization order), we prove that this order between two parameter vectors implies the mean residual life order between convolutions of two heterogeneous exponential samples. For the 2-dimensional case, it is shown that there exists a stronger equivalence. We discuss, in particular, the case when one convolution involves identically distributed variables, and show in this case that the mean residual life order is actually associated with the harmonic mean of parameters. Finally, we derive the “best gamma bounds” for the mean residual life function of any convolution of exponential distributions under this framework.     

Some new results on convolutions of heterogeneous gamma random variables

Convolutions of independent random variables often arise in a natural way in many applied areas. In this paper, we study various stochastic orderings of convolutions of heterogeneous gamma random variables in terms of the majorization order [p-larger order, reciprocal majorization order] of parameter vectors and the likelihood ratio order [dispersive order, hazard rate order, star order, right spread order, mean residual life order] between convolutions of two heterogeneous gamma sets of variables wherein they have both differing scale parameters and differing shape parameters. The results established in this paper strengthen and generalize those known in the literature.     

The Geometry of Systems of Third Order Differential Equations Induced by Second Order Regular Lagrangians

A system of third order differential equations, whose coefficients do not depend explicitly on time, can be viewed as a third order vector field, which is called a semispray, and lives on the second order tangent bundle. We prove that a regular second order Lagrangian induces such a semispray, which is uniquely determined by two associated Poincaré-Cartan one-forms. To study the geometry of this semispray, we construct a horizontal distribution, which is a Lagrangian subbundle for an associated Poincaré-Cartan two-form. Using this semispray and the associated nonlinear connection we define dynamical covariant derivatives of first and second order. With respect to this, the second order dynamical derivative of the Lagrangian metric tensor vanishes.     

一类高阶周期系数线性微分方程解的性质

本文主要研究了一类高阶周期系数线性微分方程解的超级,e-型级,相关性等问题,并得到了e-型级与超级之间的一些关系,以及这两种级与系数的精确关系．本文是首次使用e-型级来估计方程解的增长性,这种估计比级,超级更为精确．     

Projective planes of order 12 do not have a collineation group of order 4

In this paper, we prove that there are no projective planes of order 12 admitting a collineation group of order 4. This yields that the order of any collineation group of a projective plane of order 12 is 1, 2, or 3.     

Steiner triple systems of order 19 and 21 with subsystems of order 7

Steiner triple systems (STSs) with subsystems of order 7 are classified. For order 19, this classification is complete, but for order 21 it is restricted to Wilson-type systems, which contain three subsystems of order 7 on disjoint point sets. The classified STSs of order 21 are tested for resolvability; none of them is doubly resolvable.     

Estimates for The Hyper-Order of Solutions of Certain Linear Differential Equations

In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered.     

On the number of edges of cyclic subgroup graphs of finite groups

Archiv der Mathematik - In this note, we show that among finite nilpotent groups of a given order or finite groups of a given odd order, the cyclic group of that order has the minimum number of...     

Construction of usc Solutions for a Multivalued Iterative Equation of Order n

Without Lipschitz condition, only the second order polynomial-like iterative equation was discussed for monotone usc multivalued solutions under the assumption that the coefficient of the first order iterate is large. In this paper without this assumption we give a general construction of infinitely many increasing usc multivalued solutions for multivalued iterative equation of order n.     

Transformation of high order linear differential-algebraic systems to first order

We study general nonsquare linear systems of differential-algebraic systems of arbitrary order. We analyze the classical procedure of turning the system into a first order system and demonstrate that this approach may lead to different solvability results and smoothness requirements. We present several examples that demonstrate this phenomenon and then derive existence and uniqueness results for differential-algebraic systems of arbitrary order and index. We use these results to identify exactly those variables for which the order reduction to first order does not lead to extra smoothness requirements and demonstrate the effects of this new formulation with a numerical example.Dedicated to Richard S. Varga on the occasion of his 77th birthday.     

Characterization of Approximate Solutions of Vector Optimization Problems with a Variable Order Structure

In this paper, we deal with approximate solutions in vector-optimization problems with respect to a variable order structure. In the case of exact solutions of a vector optimization problem, especially in the variable order case, authors use a cone or a pointed convex cone-valued map in order to describe the solution concepts but in this paper, we use a set-valued map and this map is not a (pointed convex) cone-valued map necessarily. We characterize these solution concepts by a general scalarization method by means of nonlinear functionals. In the last section, an extension of Ekeland’s variational principle for a vector optimization problem with a variable order structure is given.     

On chaos control and synchronization of the commensurate fractional order Liu system

In this work, we study chaos control and synchronization of the commensurate fractional order Liu system. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate fractional order systems are discussed. The existence and uniqueness of solutions for a class of commensurate fractional order Liu systems are investigated. We also obtain the necessary condition for the existence of chaotic attractors in the commensurate fractional order Liu system. The effect of fractional order on chaos control of this system is revealed by showing that the commensurate fractional order Liu system is controllable just in the fractional order case when using a specific choice of controllers. Moreover, we achieve chaos synchronization between the commensurate fractional order Liu system and its integer order counterpart via function projective synchronization. Numerical simulations are used to verify the analytical results.     

Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data

In this paper, we establish some results for the increasing convex comparisons of generalized order statistics. First, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then the remaining generalized order statistics are also ordered in the increasing convex order. This result is extended to the increasing directionally convex comparisons of random vectors of generalized order statistics. For establishing this general result, we first prove a new result in that two random vectors with a common conditionally increasing copula are ordered in the increasing directionally convex order if the marginals are ordered in the increasing convex order. This latter result is, of course, of interest in its own right.     

一种4N阶幻方构造方法的论证

一种 4 N阶幻方构造方法被发现 .本文阐明了 4 N阶幻方构造方法 ,介绍了 12阶幻方构造过程 .     

关于有限Abel p-群的自同构群

从有限Abel p-群P的型不变量出发,给出了其自同构群AutP的阶的计算公式,并利用|AutP|的计算公式得到了下面3个结果:1.由有限Abel p-群的型不变量的两种变换得到了其自同构群的阶的变化规律;2.用群的阶、秩、幂指数三个量界定了有限Abel p-群的自同构的阶;3.对部分Frattini子群为p阶群的有限p-群,确定了其自同构群的阶何时达到最小值和最大值.     

Row-complete latin squares of every composite order exist

A construction for a row-complete latin square of order n, where n is any odd composite number other than 9, is given in this article. Since row-complete latin squares of order 9 and of even order have previously been constructed, this proves that row-complete latin squares of every composite order exist. © 1998 John Wiley & Sons, Inc. J Combin Designs 6:63–77, 1998     

分数阶积分微分方程的近似解

本文给出了分数阶积分微分方程的一种新的解法.利用未知函数的泰功多项式展开将分数阶积分微分方程近拟转化为一个涉及未知函数及其n阶导数的线性方程组.数值例子表明该方法的有效性.     

Laplace-Stieltjes变换所确定的整函数的对数级

研究了全平面上收敛的零级Laplce-Stieltjes变换的增长性问题,通过定义对数级和对数下级,得到了零级Laplace-Stieltjes变换具有对数级和对数下级的特征性质,推广了Dirichlet级数相关结果.     

BOUNDARY LAYER ESTIMATION OF A SINGULAR PROBLEM WITH LIMIT EQUATION OF ORDER 2

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