Jacobson-Chevalley稠密定理的一个推广

我们在[1]中证明了,一个半环(hemiring)关于它的Jacobson关系根的商同构于完全本原半环的亚直和。这使我们有兴趣对这个特殊的半环类——完全本原半环的结构作进一步的讨论。本文的主要结果是:一个半环是完全本原的当且仅当它是一个半模上的亚稠密自同态半环。这个定理给出了完全本原半环的结构,推广了Jacobson—Chevalley稠密定理。     

几种类型的K~*空间的特征

<正> §1.引言 假设非平坦的 n 维黎曼空间的曲率张量 R_(hijk)在每一点恒满足下列关系(?)其中(?)是某一向量场,同时也满足     

Coorbits of Quantum Homogeneous Spaces

The notion of coorbits for spaces with quantum group actions is introduced. A space with a quantum group action is given by a pair of algebras: an associative algebra which is the analog of a classical topological space, and a Hopf algebra which is the analog of a classical topological group. The Hopf algebra acts on the associative algebra via a comodule structure mapping which is also an algebra homomorphism. For a space with a quantum group action, a coorbit is a pair of spaces given by the image and the kernel of an algebra homomorphism from the associative algebra to the Hopf algebra. The coorbits of several types of quantum homogeneous spaces are discussed. In the case when the associative algebra is the group algebra of a group and the Hopf algebra is a quotient of the group algebra, the connection between the set of coorbits and the character group is established.     

Formulation of the problem of the flutter of a shell of revolution and a shallow shell in a high-velocity supersonic gas flow

Aero-elastic vibration is investigated in the case of a shallow shell of revolution or a cylindrical panel, which respectively occupy a part of a thin cylindrical body or a thin profile, in a high-velocity supersonic gas flow at zero angle of attack. Particular attention is paid to finding the pressure interaction and this problem is solved within the framework of the law of plane sections in boundary-layer theory. An expression is obtained which refines and supplements the well-known formula of “piston” theory. A linearized formulation of the problem of the panel flutter of a shallow shell is presented. Using the example of a plate located on one of the sides of a wedge, it is shown that the formula of “piston” theory is complemented with a term which has the meaning of a compressive force in the plane of the plate. It is shown that, when account is taken of this term, there is a reduction in the critical flow velocity.     

Adaptive Control of a Partially Observed Discrete Time Markov Process

An adaptive control problem of a discrete time Markov process that is completely observed in a fixed recurrent domain and is partially observed elsewhere is formulated and a solution is given by constructing an approximately self-optimal strategy. The state space of the Markov process is either a closed subset of Euclidean space or a countable set. Another adaptive control problem is solved where the process is always only partially observed but there is a family of random times when the process evaluated at these times is a family of independent, identically distributed random variables. Accepted 26 April 1996     

Matrices as sums of squares

How many squares are needed to represent elements in a matrix ring? A matrix over a field of characteristic two is a sum of two squares if and only if its trace is a square, otherwise it is not a sum of squares. Any proper matrix over a field of characteristic not two is always a sum of three squares. If the order of a matrix is even the matrix is a sum of two squares, but an odd order matrix which is q times the identity matrix is a sum of two squares if and only ifq is a sum of two squares in the field. Matrices of order 2,3 and 4 over the integers can always be written as the sum of three squares.     

Optimal detection of a recurring tuple of reference fragments in a quasiperiodic sequence

An a posteriori (off-line) approach to solving the problem of maximum-likelihood detection of a recurring tuple containing reference fragments in a numerical quasiperiodic sequence is studied. The case is analyzed where (1) the total number of fragments in a sequence is unknown; (2) the index of a sequence term corresponding to the beginning of a fragment is a deterministic (not random) value; (3) a sequence distorted by additive uncorrelated Gaussian noise is available for observation. It is shown that the problem under consideration is reduced to testing a set of simple hypotheses about the mean of a random Gaussian vector. The cardinality of this totality grows exponentially as the vector dimension (i.e., the length of the sequence under study) increases. It is established that searching for a maximum-likelihood hypothesis is equivalent to finding arguments that yield a maximum for an auxiliary objective function. It is shown that maximizing the objective function reduces to solving a special optimization problem, which is proved to be solvable in polynomial time. An exact algorithm for solving this problem, which underlies the optimal (maximum-likelihood) detection algorithm for a recurring tuple, is substantiated. The kernel of the exact algorithm is an algorithm for solving a special (basic) optimization problem. Results of numerical simulations are presented.     

A Chart for Evaluating Product Research and Development Projects

A method of evaluating research and development projects is described. The method is based on the use of an evaluation chart. The main purpose of the chart is to calculate a project score which is a measure of a selected evaluation criterion. A method of constructing a chart is illustrated using a project index as the evaluation criterion. The chart contains a list of twelve questions, the answers to which are assumed to be the main determinants of the variables in the formula of the index. Each question is followed by a set of answers from which a choice is to be made, and underneath each answer is a numerical score. The numerical scores are logarithmic functions of the answers to which they relate, and when added together give a project score which is a logarithmic function of the index. Various methods of using the chart, and a suggested evaluation procedure, are also described.     

关于凸子集和（绝对）收缩核

讨论了线性度量空间中凸子集在什么情况下为该空间的收缩核，以及在什么情况下为绝对收缩核。     

Mini-Maximizers for Reaction-Diffusion Systems with Skew-Gradient Structure

A reaction-diffusion system with skew-gradient structure is a sort of activator-inhibitor system that consists of two gradient systems coupled in a skew-symmetric way. Any steady state of such a system corresponds to a critical point of some functional. The aim of this paper is to study the relation between a stability property as a steady state of the reaction-diffusion system and a mini-maximizing property as a critical point of the functional. It is shown that a steady state of the skew-gradient system is stable regardless of time constants if and only if it is a mini-maximizer of the functional. It is also shown that the mini-maximizing property is closely related with the diffusion-induced instability. Moreover, by using the property that any mini-maximizer on a convex domain is spatially homogeneous, quite a general instability criterion is obtained for some activator-inhibitor systems. These results are applied to the diffusive FitzHugh-Nagumo system and the Gierer-Meinhardt system.     

Optimal pricing and quantity of products with two offerings

This paper analyzes the decision of a firm offering two versions of a product, a deluxe and a regular. While both products satisfy the same market, the deluxe version is sold at a high price relative to its cost and is aimed at the high end of the demand curve. The regular version is sold at a low price relative to its cost and is targeted to customers at the low end of the demand curve. This two-offering strategy is especially popular with book publishers where a paperback book is introduced some time after the hardbound version is introduced. The time between the introduction of the two versions of the product is accompanied by a downward shift in the demand curve due to customers losing interest in the product or satisfying their demand from a secondary used market. We solve a profit maximization model for a firm using a two-offering strategy. The model is solved for linear and exponential deterioration in demand, which is assumed to be deterministic. Also, a model with linear deterioration in demand, which is assumed to be stochastic, is solved. The results indicate that substantial improvements in profit can be obtained by using the two-offering strategy. Numerical sensitivity analysis and examples are used to illustrate the results.     

Remarks on pseudo-valuation rings

A prime ideal P of a ring A is said to be a strongly prime ideal if aP and bA are comparable for all a,b ε A. We shall say that a ring A is a pseudo-valuation ring (PVR) if each prime ideal of A is a strongly prime ideal. We show that if A is a PVR with maximal ideal M, then every overring of A is a PVR if and only if M is a maximal ideal of every overring of M that does not contain the reciprocal’of any element of M.We show that if R is an atomic domain and a PVD, then dim(R) ≤ 1. We show that if R is a PVD and a prime ideal of R is finitely generated, then every overring of R is a PVD. We give a characterization of an atomic PVD in terms of the concept of half-factorial domain.     

On Two-Phase Flow in a Rotating Boundary Layer

The two-phase flow induced by a rotating disk in a stationary unbounded mixture is considered. The generalized similarity assumption of von Karman reduces the averaged equations of motion with a linear drag between the phases to a system of ordinary differential equations. These are investigated by asymptotic and numerical techniques. The equations display a nontrivial behavior in a sublayer near the boundary, whose thickness is of the order of the particle size. The volume fraction of the dispersed phase is singular unless a small suction is applied on the disk or a small diffusion term is added to the continuity equations. Outside this sublayer, the velocity field is quite similar to a rescaled classical von Karman flow. Good agreement between asymptotic and numerical solution is obtained, although there is considerable stiffness in the equations. The motion of a solid particle in a von Karman flow is also discussed, but the present investigation is restricted to small radii because the shear-lift force is neglected.     

Subspaces and quotients of Banach spaces with shrinking unconditional bases

The main result is that a separable Banach space with the weak* unconditional tree property is isomorphic to a subspace as well as a quotient of a Banach space with a shrinking unconditional basis. A consequence of this is that a Banach space is isomorphic to a subspace of a space with a shrinking unconditional basis if and only if it is isomorphic to a quotient of a space with a shrinking unconditional basis, which solves a problem dating to the 1970s. The proof of the main result also yields that a uniformly convex space with the unconditional tree property is isomorphic to a subspace as well as a quotient of a uniformly convex space with an unconditional finite dimensional decomposition.     

Power-series approximations for the optimal feedback control of noisy nonlinear systems

Power-series methods are developed for designing approximately optimal state regulators for a nonlinear system subject to white Gaussian random disturbances. The performance index of the control is an ensemble average of a quadratic form. A perfect observation of the system state is assumed. When the system nonlinearity is small and it is characterized by a polynomial function of the state, a definite method is presented to construct a suboptimal feedback control of a power-series form in a small nonlinearity parameter. If the variance of noise is small, an alternative method is also applicable which yields a suboptimal control in a power series with respect to a variance parameter. A simple one-dimensional problem is examined to make comparison between controls of the two different forms.     

Does contraction preserve triangular meshes?

A triangular graph is a planar graph in which each face is a 3-cycle, except possibly for the exterior face, and without articulation nodes. The embedding of a triangular graph in the plane is called a triangular mesh. More generally, a triangular graph with multiple contours is a planar graph without articulation nodes in which each face is a 3-cycle, except possibly for a fixed number of them. A contraction along an edge in a graph is the result of identifying the two endpoints of the edge. In this paper a necessary and sufficient condition is shown for which triangularity (possibly with multiple contours) is preserved after contraction. Moreover, when a licit contraction is performed, the question to answer is whether or not it is possible to derive the embedding of the contracted triangular graph from the original triangular mesh by redrawing only around the contraction zone.Part of this work was done when the author was in his sabbatical year at the University of California at Los Angeles.     

最小填充问题的可分解性

起源于稀疏矩阵计算和其它应用领域的图G的最小填充问题是在图G中寻求一个内含边数最小的边集F使得G F是弦图.这里最小值|F|称为图G的填充数,表示为f(G).作为NP-困难问题,该问题的降维性质已被研究,其中包括它的可分解性.基本的可分解定理是:如果图G的一个点割集S是一个团,则G经由S是可分解的.作为推广,如果S是一个"近似"团(即只有极少数边丢失的团),则G经由S是可分解的.本文首先给出基本分解定理的另外一个推广:如果S是G的一个极小点割集且G-S含有至少|S|个分支,则G经由S是可分解的;其次,给出了这个新推广定理的一些应用.     

The Toroidal Embedding Arising From an Irrational Fan

A toroidal embedding is defined which does not assume the fan consists of rational cones. For a rational fan, the toroidal embedding is the usual toric variety. If the fan is not rational, the toroidal embedding is in general a quasi-compact noetherian locally ringed space which is not a scheme. A divisor theory exists and a class group is defined. A second construction is also carried out which mimics the gluing construction of the usual toric variety, but which makes no reference to a lattice. The resulting scheme is separated but infinite dimensional. The Picard group is described in terms of the group of real valued locally linear support functions on the fan and the Brauer group is shown to be trivial. Many examples are given throughout the paper; in particular, it is shown that there is associated to a real hyperplane arrangement of full rank a toroidal embedding.     

The stress state of an elastic composite cone with centre of rotation at the apex

The torsion of a composite cone that has a centre of rotation at its apex is investigated in a spherical system of coordinates. A composite cone is a cone with one shear modulus, inserted into a conical funnel having another shear modulus and with ideal mechanical contact between its surface and the inner surface of the conical funnel. The auxiliary problem of a composite cone with its apex truncated by a spherical surface is considered first. The outer surface of such a conical body is not loaded, but a load that reduces to a torque is applied to its spherical surface. The auxiliary problem is reduced to a one-dimensional discontinuous boundary-value problem using a specially constructed integral transformation. The exact solution of this boundary-value problem is constructed. The limit is then taken in the solution obtained as the radius of the spherical surface tends to zero for the purpose of obtaining an exact solution of the problem of the torsion of a composite cone that has a centre of rotation at the apex.     

U-标算子的结构分析

类似与标型谱算子,U-标算子是否拟仿射相似于自伴算子是一“公开问题”．尽管对具纯离散谱的U-标算子答案是肯定的,但一般情况下并不成立．本文继续探讨这一问题,证明了U-标算子在一强范数拓扑意义下是Hermite算子,或者说U-标算子拟仿射相似于Hermite算子,并给出U-标算子是标型谱算子的充要条件．