企业人力资本所有者与所有权安排的博弈分析

我们利用博弈论的基本思想和基本方法，从人力资本所有与非人力资本所有以及人力资本所有之间博弈关系的角度，构建企业人力资本所有与所有权安排的博弈模型，从博弈的视角对企业人力资本所有与所有权安排进行分析，探究企业人力资本所有与所有权安排中参与人之间的合约关系，给出一个关于企业人力资本所有分享所有权的一般性解释。     

模糊子坡代数、模糊等价关系及模糊同余关系的序方面

证明了坡代数(X,+,*)上所有模糊子坡代数构成的集合(SI[0.1](X,+,*),≤),所有模糊理想构成的集合(Id[0.1](X,+,*),≤),所有模糊滤子构成的集合(Fil[0.1](X,+,*),≤)都是([0,1]x,≤)的子完备格,所有模糊等价关系构成的集合(Equ[0.1](X,+,*),≤),所有模...     

利用格蕴涵代数找出所有LI-理想的方法

利用格蕴涵代数中理想的定义未找出所有的理想需要花费大量的时间.给出了利用格蕴涵代数的蕴涵运算表找出格蕴涵代数所有理想的方法;再利用析取运算表找出格蕴涵代数中所有sl_理想的方法;最后,利用蕴涵否运算表找出格蕴涵代数中所有LI-理想的方法.     

二阶非齐次线性微分方程解的平方可积性与有界性

本文借助于辅助函数，得到了二阶非齐次线性微分方程所有解均平方可积及所有解都有界的判定准则．     

广义映射Schr?dinger-Virasoro代数的二上同调群

该文给出了广义映射Schr?dinger-Virasoro代数的所有二上同调群,并且给出了这类李代数的所有泛中心扩张.     

常微分方程的通解

给出常微分方程通解的定义,研究常微分方程的通解和所有解之间的关系,给出通解包含所有解的若干充分性条件.     

理想簇和根理想

关于环的理想的根有两种定义,一种是所有包含I的极大理想的交,另一种是所有包含I的素理想交,本文主要研究后者定义的一些性质,以及和理想簇V(I)(所有包含I的素理想的集合)的关系.     

新题征展(79)

A题组新编1.已知函数y=f(x)存在反函数y=f-1(x).(1)若方程f(x)-m 1 x=0的所有实根和方程f-1(x-1)-m x=0的所有实根的集合为k元集合A,则集合A中所有元素的和为.(2)若方程f(x)-mx 1=0(m>0)的所有正根与f-1(x-1)-mx=0(m>0)的所有正根组成一个k元集合A,则集合A中所有元素的积为.(3)     

几类常见图形的对称变换

一个图形的对称性通常是用对称变换来描述,因此,要弄清图形的对称性,就需要找出它的所有对称变换.人教A版教材的诸多例题与习题中要求找出几类常见图形的所有对称变换,但却没有给出找所有对称变换的方法,本文说明找几类常见图形的     

D_l和E_6型Weyl群的扭子群的扩群

本文决定了 Dl 和 E6 型 Weyl群扭子群的所有扩群 ,这为确定相应 Chevalley群扭子群的所有扩群奠定了基础 .     

On a mapping of a projective space into a sphere

We obtain an exact estimate for the minimum multiplicity of a continuous finite-to-one mapping of a projective space into a sphere for all dimensions. For finite-to-one mappings of a projective space into a Euclidean space, we obtain an exact estimate for this multiplicity for n = 2, 3. For n ≥ 4, we prove that this estimate does not exceed 4. Several open questions are formulated.     

Evolution to a steady state for a rarefied gas flowing from a tank into a vacuum through a plane channel

A kinetic equation (S-model) is used to solve the nonstationary problem of a monatomic rarefied gas flowing from a tank of infinite capacity into a vacuum through a long plane channel. Initially, the gas is at rest and is separated from the vacuum by a barrier. The temperature of the channel walls is kept constant. The flow is found to evolve to a steady state. The time required for reaching a steady state is examined depending on the channel length and the degree of gas rarefaction. The kinetic equation is solved numerically by applying a conservative explicit finite-difference scheme that is firstorder accurate in time and second-order accurate in space. An approximate law is proposed for the asymptotic behavior of the solution at long times when the evolution to a steady state becomes a diffusion process.     

Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance

We study the asymptotic behavior at large time of a solution to a system of nonlinear integro-differential equations which arises in mathematical modeling of diffusion of a magnetic field into a substance. We establish the corresponding stabilization rate.     

Motion of a container as a nonholonomous system in a curved section of a horizontal pipeline

The problem of the motion of a container in a curved section of a horizontal pipeline is solved using second-order Lagrange equations in the presence of nonholonous couplings. The special case of the motion of a container in a circular curve is examined.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 90–95, 1987.     

Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait

We consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypic trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative, we investigate the existence of travelling wave solutions. We identify a minimal speed c* > 0, and prove the existence of waves when c ≥ c* and the nonexistence when 0 ≤ c < c*.     

Symmetry-based solution of a model for a combination of a risky investment and a riskless investment

Benth and Karlsen [F.E. Benth, K.H. Karlsen, A note on Merton's portfolio selection problem for the Schwartz mean-reversion model, Stoch. Anal. Appl. 23 (2005) 687-704] treated a problem of the optimisation of the selection of a portfolio based upon the Schwartz mean-reversion model. The resulting Hamilton-Jacobi-Bellman equation in 1+2 dimensions is quite nonlinear. The solution obtained by Benth and Karlsen was very ingenious. We provide a solution of the problem based on the application of the Lie theory of continuous groups to the partial differential equation and its associated boundary and terminal conditions.     

Choosing a leader on a complex network

In many real life applications a group of people interact through a communication network, mathematically modelled as a connected graph linking each element of the group. These participants may have diverse objectives and play very different roles depending on their knowledge and privileges. We focus on a particular scenario, in which a certain node is absolutely essential for completing the intended task. Moreover, if a technical failure results in disconnection of a participant to this leader node, this participant can no longer take part in the group's performance.     

Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution

We investigate the behavior of a diserete dynamical system in a neighborhood of a quasiperiodic trajeetory for the case of an infinite-dimensional Banach space We find conditions sufficient for the system considered to reduce, in such a neighborhood, to a system with quasiperiodic coefficients. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1661–1676, December, 1997.     

Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

Locating a robber on a graph

Consider the following game of a cop locating a robber on a connected graph. At each turn, the cop chooses a vertex of the graph to probe and receives the distance from the probe to the robber. If she can uniquely locate the robber after this probe, then she wins. Otherwise the robber may either stay put or move to any vertex adjacent to his location other than the probe vertex. The cop’s goal is to minimize the number of probes required to locate the robber, while the robber’s goal is to avoid being located. This is a synthesis of the cop and robber game with the metric dimension problem. We analyse this game for several classes of graphs, including cycles and trees.