Estimating a survival function with incomplete cause-of-death data

We propose a random censorship model which permits uncertainty in the cause of death assessments for a subset of the subjects in a survival experiment. A nonparametric maximum likelihood approach and a “self-consistency” approach are considered. The solution sets corresponding to both approaches are found. They are infinite and identical. Only some of the solutions are consistent; i.e., the MLEs and self-consistent estimators are not consistent in general. Two estimates are thus proposed and their asymptotic properties are studied. It is shown that both estimates are strongly consistent and converge to Gaussian processes. The covariance structures of these Gaussian processes are derived.     

A network flow-based method to solve performance cost and makespan open-shop scheduling problems with time-windows

This paper deals with several bicriteria open-shop scheduling problems where jobs are pre-emptable and their corresponding time-windows must be strictly respected. The criteria are a performance cost and the makespan. Network flow approaches are used in a lexmin procedure with a bounded makespan and the considered bicriteria problems are solved. Finally, the computational complexity of the algorithm and a numerical example are reported.     

Optimal strategies for a class of adaptive search processes

Optimal strategies are investigated for a class of one-dimensional search processes in which the objective is to find a point which is near, but not beyond, a boundary of uncertain location. Problems of this type are encountered in the analysis of mining operations. Upper and lower bounds for the optimal expected payoff are derived, and the optimal search strategies are described explicitly for a large subclass of these processes. Results are obtained by formulating the search as a multistage decision process and using a dynamic programming approach.     

Duality and Lipschitzian selections in best approximation from nonconvex cones

Duality relationships in finding a best approximation from a nonconvex cone in a normed linear space in general and in the space of bounded functions in particular, are investigated. The cone and the dual problems are defined in terms of positively homogeneous super-additive functional on the space. Conditions are developed on the cone so that the duality gap between a pair of primal and dual problems does not exist. In addition, Lipschitz continuous selections of the metric projection are identified. The results are specialized to a convex cone. Applications are indicated to approximation problems.     

Exact and asymptotic solutions of the equation of internal gravity waves in a wedge-shaped region

The field of internal gravity waves in a wedge-shaped region of a stratified medium is considered. Using a Kantorovich–Lebedev transformation, exact solutions are obtained which describe an individual mode and the complete wave field. The asymptotics of an individual wave mode are constructed by the WKB method, and are expressed in terms of a hypergeometric function, as well as the asymptotics of the complete wave field, which are expressed in terms of a semilogarithmic function. The results of numerical calculations of the wave field using the exact and asymptotic formulae are presented for the parameters of a stratified medium, characteristic for the dynamics of the ocean. The limits of their applicability are estimated.     

On degenerate elliptic equations of high order and pseudodifferential operators with degeneration

Problems for high-order degenerate elliptic equations in a half-space are studied. Coercive a priori estimates and existence theorems for solutions of such problems in special weighted Sobolev-type spaces are obtained. The norms in these spaces are defined with the help of a special integral transform. Pseudodifferential operators with degeneration constructed using a special integral transform are studied. Pseudodifferential operators with degeneration are used to factorize the symbol of a high-order degenerate elliptic operator and to construct a separating operator of the Leray–Sakamoto type.     

Allocation rules for hypergraph communication situations

This paper considers hypergraph communication situations, where for a group of agents the economic possibilities are described by a coalitional game and the communication possibilities are described by a hypergraph in which the nodes are the agents and the edges are the subgroups of agents who can effect communication. Axiomatic characterizations are provided for two allocation rules, the Myerson value and the position value.     

Greedy algorithm and symmetric matroids

Symmetric matroids are set systems which are obtained, in some sense, by a weakening of the structure of a matroid. These set systems are characterized by a greedy algorithm and they are suitable for dealing with autodual properties of matroids. Applications are given to the eulerian tours of 4-regular graphs and the theory ofg-matroids.     

Logical regularities in pattern recognition (Parametric Approach)

The search for logical regularities of classes in the recognition by precedents problems and the use of logical regularities for solving recognition and prediction problems are considered. Logical regularities of classes are defined as conjunctions of one-place predicates that determine the membership of a value of a feature in a certain interval of the real axis. The conjunctions are true on the subsets of reference objects of a certain class and are optimal. Various optimality criteria are considered and the problem of finding logical regularities is formulated as an integer programming problem. A qualitative analysis of these problems is performed. Models for evaluating estimates on the basis of systems of logical regularities are considered. Modifications of linear decision rules for finding estimates of how close the reference objects are to classes are proposed that are based on the search for the maximum gap. Approximations of logical regularities of classes by smooth functions is proposed. The concept of the dynamic logical regularity of classes is introduced, an algorithm for finding dynamic logical regularities is proposed, and a prediction method is developed.     

Equilibrium solutions for multiobjective bimatrix games incorporating fuzzy goals

Equilibrium solutions in terms of the degree of attainment of a fuzzy goal for games in fuzzy and multiobjective environments are examined. We introduce a fuzzy goal for a payoff in order to incorporate ambiguity of human judgments and assume that a player tries to maximize his degree of attainment of the fuzzy goal. A fuzzy goal for a payoff and the equilibrium solution with respect to the degree of attainment of a fuzzy goal are defined. Two basic methods, one by weighting coefficients and the other by a minimum component, are employed to aggregate multiple fuzzy goals. When the membership functions are linear, computational methods for the equilibrium solutions are developed. It is shown that the equilibrium solutions are equal to the optimal solutions of mathematical programming problems in both cases. The relations between the equilibrium solutions for multiobjective bimatrix games incorporating fuzzy goals and the Pareto-optimal equilibrium solutions are considered.     

Mixed convection boundary layer flow over a permeable vertical surface with prescribed wall heat flux

The effects of suction/injection on the laminar mixed convection boundary-layer flow on a vertical wall with a prescribed heat flux are considered. The conditions which allow the equations to be reduced to similarity form are derived and numerical solutions of the resulting equations are obtained for a range of values of the suction/injection and buoyancy parameters. Two specific cases, corresponding to a stagnation point flow and uniform wall heat flux, are treated in detail. Results are presented in terms of the skin friction and wall temperature with a selection of velocity and temperature profiles also being given. Dual solutions are found to exist for assisting flow, these are an addition to what has been reported previously for opposing flows. Solutions for some limiting values of the parameters are also derived.     

Distribution planning in a turbulent environment

This paper looks at planning within the present distribution environment, paying particular attention to recent trends and developments. The idea of a depot as the traditional building block of a distribution network is questioned and the various functions of a regional depot are explored.The concept of a transit point as a simple alternative to a depot is developed and examples are given of its use in practice. Several refinements are available, particularly in the area of trailer technology, and these are discussed. The necessary support system for transit point operation is identified and finally the implications for distribution planning are considered.     

Capacitated location allocation problem with stochastic location and fuzzy demand: A hybrid algorithm

In this article, a capacitated location allocation problem is considered in which the demands and the locations of the customers are uncertain. The demands are assumed fuzzy, the locations follow a normal probability distribution, and the distances between the locations and the customers are taken Euclidean and squared Euclidean. The fuzzy expected cost programming, the fuzzy β-cost minimization model, and the credibility maximization model are three types of fuzzy programming that are developed to model the problem. Moreover, two closed-form Euclidean and squared Euclidean expressions are used to evaluate the expected distance between customers and facilities. In order to solve the problem at hand, a hybrid intelligent algorithm is applied in which the simplex algorithm, fuzzy simulation, and a modified genetic algorithm are integrated. Finally, in order to illustrate the efficiency of the proposed hybrid algorithm, some numerical examples are presented.     

Workstage repair policies for sequential manufacturing systems

Dynamic stage repair policies where the stage repair probabilities are determined by the number of items in the buffer are examined through a model of a manufacturing system with two unreliable workstages connected by a minimal intermediate storage buffer. Definitions for workstage availability and line balance are extended for sequential manufacturing systems with dynamic repair policies. A measure for stage repair inputs and a general form of dynamic stage repair policies are presented. The steady-state probabilities of the resultant state-inhomogeneous Markov chain are computed by an efficient solution procedure. Insights obtained from extensive numerical studies are illustrated and discussed.     

Algorithms for Calculating the Inverse of a Given R-Automorphism of R[x]

Associated to a toric variety X of dimension r over a field k is a fan Δ on R¹. The fan Δ is a finite set of cones which are in one-to-one correspondence with the orbits of the torus action on X. The fan Δ inherits the Zariski topology from X. In this article some cohomological invariants of X are studied in terms of whether or not they depend only on Δ and not k. Secondly some numerical invariants of X are studied in terms of whether or not they are topological invariants of the fan Δ. That is, whether or not they depend only on the finite topological space defined on Δ. The invariants with which we are mostly concerned are the class group of Weil divisors, the Picard group, the Brauer group and the dimensions of the torsion free part of the etale cohomology groups with coefficients in the sheaf of units. The notion of an open neighborhood of a fan is introduced and examples are given for which the above invariants are sufficiently fine to give nontrivial stratifications of an open neighborhood of a fan all of whose maximal cones are nonsimplicia.     

School redistricting: embedding GIS tools with integer programming

The paper deals with a school redistricting problem in which blocks of a city must be assigned to schools according to diverse criteria. Previous approaches are reviewed and some desired properties of a good school districting plan are established. An optimization model together with a geographic information system environment are then proposed for finding a solution that satisfies these properties. A prototype of the system is described, some implementation issues are discussed, and two real-life examples from the city of Philadelphia are studied, one corresponding to a relatively easy to solve problem, and the other to a much harder one. The trade-offs in the solutions are analysed and feasibility questions are discussed. The results of the study strongly suggest that ill-defined spatial problems, such as school redistricting, can be addressed effectively by an interaction between objective analysis and subjective judgement.     

Statistical inferences based on INID progressively type II censored order statistics

Suppose that the failure times of the units placed on a life-testing experiment are independent but nonidentically distributed random variables. Under progressively type II censoring scheme, distributional properties of the proposed random variables are presented and some inferences are made. Assuming that the random variables come from a proportional hazard rate model, the formulas are simplified and also the amount of Fisher information about the common parameters of this family is calculated. The results are also extended to a fixed covariates model. The performance of the proposed procedure is investigated via a real data set. Some numerical computations are also presented to study the effect of the proportionality rates in view of the Fisher information criterion. Finally, some concluding remarks are stated.     

基于二重网格的定常Navier-Stokes方程的局部和并行有限元算法

对二维定常的不可压缩的Navier-Stokes方程的局部和并行算法进行了研究．给出的算法是多重网格和区域分解相结合的算法,它是基于两个有限元空间:粗网格上的函数空间和子区域的细网格上的函数空间．局部算法是在粗网格上求一个非线性问题,然后在细网格上求一个线性问题,并舍掉内部边界附近的误差相对较大的解．最后,基于局部算法,通过有重叠的区域分解而构造了并行算法,并且做了算法的误差分析,得到了比标准有限元方法更好的误差估计,也对算法做了数值试验,数值结果通过比较验证了本算法的高效性和合理性．     

非自治动力系统的原像熵

本文对紧致度量空间上的连续自映射序列应用生成集和分离集引入了点原像熵、原像分枝熵以及原像关系熵等几类原像熵的定义并进行了研究.主要结果是:(1) 证明了这些熵都是等度拓扑共轭不变量.(2)讨论了这些原像熵之间及它们与拓扑熵之间的关系,得到了联系这些熵的不等式.(3)证明了对正向可扩的连续自映射序列而言, 两类点原像熵相等,原像分枝熵与原像关系熵也相等.(4)证明了对(a).由闭Riemann 流形上的一个扩张映射经充分小的C1-扰动生成的自映射序列,以及(b).有限图上等度连续的自映射序列,有零原像分枝熵.     

Controllability and stabilization of the programmed motions of a transport robot

A non-linear mathematical model for the motion of a transport robot (TR) with a caterpillar chassis and with drives based on DC motors, which is a non-holonomic electromechanical system, is considered. Non-linear canonical transformations of the coordinates of the state and control space are constructed, which reduce the initial equations of motion of the TR to a simpler canonical form, which is convenient for analysing and synthesizing control systems for the TR. The conditions for the TR to be controllable as a controlled object are found. Algorithms are given for constructing programmed motions (PMs) of the TR. Stabilizing control laws are synthesized under which the PMs of the TR are asymptotically stable and transients of a specified nature are ensured.