A microbial continuous culture system with diffusion and diversified growth

A reaction-diffusion model is presented to describe the microbial continuous culture with diversified growth. The existence of nonnegative solutions and attractors for the system is obtained, the stability of steady states and the steady state bifurcation are studied under three growth conditions. In the case of no growth inhibition or only product inhibition, the system admits one positive constant steady state which is stable; in the case of growth inhibition only by substrate, the system can have two positive constant steady states, explicit conditions of the stability and the steady state bifurcation are also determined. In addition, numerical simulations are given to exhibit the theoretical results.     

A Characterization of π-Complemented Algebras

π-complemented algebras are defined as those algebras (not necessarily associative or unital) such that each annihilator ideal is complemented by other annihilator ideal. Let A be a semiprime algebra. We prove that A is π-complemented if, and only if, every idempotent in the extended centroid of A lies in the centroid of A. We also show the existence of a smallest π-complemented subalgebra of the central closure of A containing A. In the case that A is a C*-algebra, this subalgebra turns out to be a norm dense *-subalgebra of the bounded central closure of A. It follows that a C*-algebra is boundedly centrally closed if, and only if, it is π-complemented.     

Defect indices and definiteness conditions for a class of discrete linear Hamiltonian systems

This paper is concerned with a class of discrete linear Hamiltonian systems in finite or infinite intervals. A definiteness condition and its equivalent statements are discussed and three sufficient conditions for the definiteness condition are given. A precise relationship between the defect index of the minimal subspace generated by the system and the number of linearly independent square summable solutions of the system is established. In particular, they are equal if and only if the definiteness condition is satisfied. Finally, two criteria for the limit point case and one criterion for the limit circle case are obtained.     

Gaussian Trivial Ring Extensions and FQP-rings

Let A be a commutative ring and E a nonzero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either arithmetical or Gaussian. The possibility for R to be Bézout is also studied, but a response is only given in the case where pSpec(A) (a quotient space of Spec(A)) is totally disconnected. Trivial ring extensions which are fqp-rings are characterized only in the local case. To get a general result we intoduce the class of fqf-rings satisfying a weaker property than fqp-ring. Moreover, it is proven that the finitistic weak dimension of a fqf-ring is 0, 1 or 2 and its global weak dimension is 0, 1, or ∞.     

A multivariate nonparametric test of independence

A new nonparametric approach to the problem of testing the joint independence of two or more random vectors in arbitrary dimension is developed based on a measure of association determined by interpoint distances. The population independence coefficient takes values between 0 and 1, and equals zero if and only if the vectors are independent. We show that the corresponding statistic has a finite limit distribution if and only if the two random vectors are independent; thus we have a consistent test for independence. The coefficient is an increasing function of the absolute value of product moment correlation in the bivariate normal case, and coincides with the absolute value of correlation in the Bernoulli case. A simple modification of the statistic is affine invariant. The independence coefficient and the proposed statistic both have a natural extension to testing the independence of several random vectors. Empirical performance of the test is illustrated via a comparative Monte Carlo study.     

Auflösbare Gruppen auf denen nicht auflösbare Gruppen operieren

Let G be a finite solvable group and A a subgroup of Aut G such that ¦G¦ and ¦A¦ are coprime. A conjecture states: The nilpodent length of G is bounded by terms depending only on A and the fixed point group G_A={g∈G¦g^A=g}. For abelian, nilpotent or solvable A various bounds are known. In this paper we study the nonsolvable case and prove the conjecture for wide classes of nonsolvable groups A, especially in the fixed point free case G_A=1.     

On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings

The ring decomposition technique of part I is extended to the case when the factors in the direct product decomposition are no longer fields but arbitrary chain rings. This includes not only the case of quasi-cyclic codes over rings but also the case of quasi-cyclic codes over fields whose co-index is no longer prime to the characteristic of the field. A new quaternary construction of the Leech lattice is derived.     

Convergence in measure of multivariate Pade approximants

Convergence conclusions of Padé approximants in the univariate case can be found in various papers. However, results in the multivariate case are few. A. Cuyt seems to be the only one who discusses convergence for multivariate Pade approximants, she gives in [2] a de Montessus de Bollore type theorem. In this paper, we will discuss the zero set of a real multivariate polynomial, and present a convergence theorem in measure of multivariate Padé approximant. The proof technique used in this paper is quite different from that used in the univariate case. Supported by National Science Foundation of China for Youth     

Representability in mixed integer programmiing,I: Characterization results

We define the concept of a representation of a set of either linear constraints in bounded integers, or convex constraints in bounded integers. A regularity condition plays a crucial role in the convex case. Then we characterize the representable sets (Theorem 2.1) and provide several examples of our representations.A consequence of our characterization is that the only representable sets are those from ‘either/or’ constraints. This latter case can be treated by generalizations of techniques from the disjunctive methods of cutting-plane theory (e.g. [2] and [30]).The representations given here are intended for use as part of the constraints of a larger optimization problem, where they often can serve to tighten the (linear or convex) relaxation.The study of representations was initiated by Meyer and in the linear case we continue the development in [35].     

Polynomial Optimization of Stochastic Feedback Control for Stable Plants

A rigorous derivation is given of the polynomial method foroptimizing the stationary stochastic feedback control of linearmultivariable plants. The same approach is used for both discrete-timeand continuous-time control. In each case, the method involvestwo spectral factorizations and, by considering only stableplants, the solution of one diophantine equation.     

Nekhoroshev estimates for finitely differentiable quasi-convex Hamiltonians

A major result about perturbations of integrable Hamiltonian systems is the Nekhoroshev theorem, which gives exponential stability for all solutions provided the system is analytic and the integrable Hamiltonian is generic. In the particular but important case where the latter is quasi-convex, these exponential estimates have been generalized by Marco and Sauzin if the Hamiltonian is Gevrey regular, using a method introduced by Lochak in the analytic case. In this paper, using the same approach, we investigate the situation where the Hamiltonian is assumed to be only finitely differentiable, for which it is known that exponential stability does not hold but nevertheless we prove estimates of polynomial stability.     

Methods for solving unstable equilibrium programming problems with coupled variables

Regularization (stabilization, residual and quasisolution) methods for solving an unstable equilibrium programming problem are proposed for the case when not only the objective function but also the set determined by coupled inequality constraints are given inexactly. The convergence of these methods is studied. A regularizing operator is constructed.     

Average optimality in a Poissonian bandit with switching arms

A symmetric Poissonian two-armed bandit becomes, in terms of a posteriori probabilities, a piecewise deterministic Markov decision process. For the case of the switching arms, only of one which creates rewards, we solve explicitly the average optimality equation and prove that a myopic policy is average optimal.Supported by NSF grant DMS-9404177     

A parallel algorithm to solve the stable marriage problem

In this paper a parallel algorithm to solve the stable marriage problem is given. The worst case performance of this algorithm is stated. A theoretical analysis shows that the probability of the occurrence of this worst case is extremely small. For instance, if there are sixteen men and sixteen women involved, then the probability that the worst case occurs is only 10^–45. Possible future research is also discussed in this paper.     

The string merging problem

The string merging problem is to determine a merged string from a given set of strings. The distinguishing property of a solution is that the total cost of editing all of the given strings into this solution is minimal. Necessary and sufficient conditions are presented for the case where this solution matches the solution to the string-to-string correction problem. A special case where deletion is the only allowed edition operation is shown to have the longest common subsequence of the strings as its solution.This research was supported by the U.S. Army Research Office.     

Single machine scheduling subject to precedence delays

A single-machine scheduling problem with precedence delays is analyzed. A set of n tasks is to be scheduled on the machine in such a way that the makespan is minimized. The executions of the tasks are constrained by precedence delays, i.e., a task can start its execution only after any of its predecessors has completed and the delay between the two tasks has elapsed. In the case of unit execution times and integer lengths of delays, the problem is shown to be NP-hard in the strong sense. In the case of integer execution times and unit length of delays, the problem is polynomial, and an O(n²) optimal algorithm is provided. Both preemptive and non-preemptive cases are considered.     

Tracking nonperiodic trajectories with the overtaking criterion

A tracking problem on an infinite time interval is studied, where the plant is linear with quadratic cost, and the tracked trajectory is not necessarily period. Optimal solutions with respect to the overtaking criterion are studied. Existence and uniqueness of such optimal solutions are proved and they are shown to be given by a linear feedback law which is the same as in the periodic case. A close relation between the solutions of tracking problems where the tracked trajectories are different only for very large times is established.     

A replacement model for an additive damage model with restoration

A system existing in a random environment receives shocks at random points of time. Each shock causes a random amount of damage which accumulates over time. A breakdown can occur only upon the occurrence of a shock according to a known failure probability function. Upon failure the system is replaced by a new identical one with a given cost. When the system is replaced before failure, a smaller cost is incurred. Thus, there is an incentive to attempt to replace the system before failure. The damage process is controlled by means of a maintenance policy which causes the accumulated damage to decrease at a known restoration rate. We introduce sufficient conditions under which an optimal replacement policy which minimizes the total expected discounted cost is a control limit policy. The relationship between the undiscounted case and the discounted case is examined. Finally, an example is given illustrating computational procedures.     

Needle Variations and Almost Lower Semicontinuous Differential Inclusions

It is shown that the construction of needle variations can be carried out for almost lower semicontinuous differential inclusions rather than for the case of ordinary single-valued continuously differentiable vector fields usually considered in the literature. The construction leads to needle variations whose flows are in general set-valued but still have good differentiability properties. The variations are constructed by using single-valued selections that are not necessarily continuous with respect to the state variable, but have instead a much weaker 'integral continuity' property, somewhat more general that the 'directional continuity' considered in previous work by A. Cambini and S. Querci, A. Pucci, and A. Bressan. The existence of many such selections is proved by slightly adapting an argument due to Bressan, extending it from the lower semicontinuous to the almost lower semicontinuous case, and strengthening it to yield not only directional continuity at all points but also full continuity at a specified point.     

S-半正规性在有限群中可传递的判别

一个有限群G被称为ST-群,如果对于它的子群 H、K和L有H在K中S-半正规,K在L中S-半正规,则H总在L中S-半正规,本文证明:有限群G是一个可解ST-群的充要条件是G的任一 Sylow子群的每个子群皆在 G中 S-半正规或 Abnormal。