A model for determining early retirement incentives

The salary savings resulting from the early retirement of an employee and his replacement by a less highly paid employee are analysed. Results are presented for two special cases. Firstly, the case is considered where pre-retirement terminations can be neglected. Secondly, the case is considered where termination rates are so high that the probability of a new entrant reaching retirement is small enough to be neglected. The results should be of assistance in solving actual problems, and a numerical example is given.     

Planning computations in a multiprocessor system with unfixed parameters

The problem of constructing a feasible preemptive multiprocessor schedule is considered for a case where directive intervals are assigned, processors can have arbitrary performance, and the amount of tasks depends linearly on the volume of additional resources allocated for them. In cases where a feasible schedule is not found with an allocated volume of additional resources, the problem of optimally correcting the directive intervals is considered. The solution is based on an analysis of the necessary and sufficient conditions of a feasible schedule’s existence.     

Outliers in Multivariate Regression Models

Likelihood ratio tests for detecting a single outlier in multivariate linear models are considered, where an observation is called an outlier if there has been a shift in the mean. The test statistics are the maximum of n nonindependent statistics, where n is the number of observations. Relevant distributions to use upper and lower Bonferroni's inequalities are given.     

Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance

A problem of decision making under uncertainty in which the choice must be made between two sets of alternatives instead of two single ones is considered. A number of choice rules are proposed and their main properties are investigated, focusing particularly on the generalizations of stochastic dominance and statistical preference. The particular cases where imprecision is present in the utilities or in the beliefs associated to two alternatives are considered.     

Discontinuous periodic behaviour in a looped macroscopic model of traffic dynamics

A whole link model of traffic flow in which the link trip time varies linearly with link volume is investigated in the case where a fraction of the flow exiting the link is ‘re-injected’ as inflow, thus forming the link into a loop. The scenario where the fraction of flow re-injected linearly decreases as the volume of traffic on the link increases is considered. It is found that for certain parameter choices a continuous periodic inflow can lead to sharp post-transient discontinuities in periodic outflow. The conditions under which this type of behaviour can occur are considered.     

On the one-commodity pickup-and-delivery traveling salesman problem with stochastic demands

This paper studies how to set the vehicle capacity for traveling Salesman Problems where some of the customer demands are stochastic. The analyses are done for the one-commodity pickup-and-delivery TSP, as this problem also includes the setting of the initial load. The paper first considers feasibility issues. This includes finding the smallest vehicle capacity and some initial load such that a given tour is feasible for all scenarios. Different variants are considered as a function of the time when information becomes available. The paper then analyzes the case where some penalties are paid for routing a tour unable to handle customer demands. Various types of penalties are considered. The paper studies properties of the minimal expected penalty of a given tour, which are then used to provide approaches to find near-optimal tours. Computational results are presented.     

Trajectory Modeling of Robot Manipulators in the Presence of Obstacles

This paper presents two different strategies for the problem of the optimal trajectory planning of robot manipulators in the presence of fixed obstacles. The first strategy is related to the situation where the trajectory must pass through a given number of points. The second strategy corresponds to the case where only the initial and final points are given. The optimal traveling time and the minimum mechanical energy of the actuators are considered together to build a multiobjective function. The trajectories are defined using spline functions and are obtained through offline computation for online operation. Sequential unconstrained minimization techniques (SUMT) have been used for the optimization. The obstacles are considered as three-dimensional objects sharing the same workspace performed by the robot. The obstacle avoidance is expressed in terms of the distances between potentially colliding parts. Simulation results are presented and show the efficiency of the general methodology used in this paper.     

A stochastic programming model to find optimal sample sizes to estimate unknown parameters in an LP

An LP is considered where the technology coefficients are unknown and random samples are taken to estimate them. A stochastic programming problem is formulated to find the optimal sample sizes where it is required that a confidence interval should cover the unknown deterministic optimum value by a given probability and the cost of sampling be minimum.     

Global solvability and uniform decays of solutions to quaslinear equation with nonlinear boundary dissipation

A n-dimensional quasiliner wave equation with nonlinear boundary dissipation is considered. Global existence, uniqueness and uniform decay rates are established for the model, under the assumption that the H¹(Ω)xL₂(Ω') norms of the initial data are sufficiently small. The result presented in this paper extends/generalizes those obtained those obtained recently in (13), where, by contrast, interior nonlinear damping was considered; and those obtained in (31), where the one-dimensional wave equation with linear boundary damping was treated.     

Flows op a reacting mixture in laval nozzles under conditions op a quasi-frozen process : PMM vol. 39, n 6, 1975, pp. 1068–1072

Flows of a chemically active gas mixture are considered in a small region of a La val nozzle, where their mode changes from subsonic to supersonic (the frozen speed of sound is considered) are analyzed. Continuous solutions and solutions with shock waves are derived. Conditions of shock-free flows are obtained.     

How to Speed up Optimization Algorithm in Topology Optimization of Continuum Structure

The problem of obtaining the optimal topology within very small step number during the optimization process is considered. The optimization procedure cuts the density in these design points where the energy decreases and adds the mass to these design points where the energy increases. To improve and speed up the process of moving mass the border functions are introduced.     

Stability of Epidemic Models with Evolution

Epidemic models are considered where the diffusion of individuals is influenced by intraspecific competition pressures and are weakly affected by different classes. The nonlinear stability of some of the models is proved by introducing new Liapunov functions.     

Asymptotics of Eigenvalues of Differential Operator With Alternating Weight Function

We study a differential operator of the sixth order with an alternating weight function. The potential of the operator has a first-order discontinuity at some point of the segment, where the operator is being considered. The boundary conditions are separated. We study the asymptotics of solutions to the corresponding differential equations and the asymptotics of eigenvalues of the considered differential operator.     

Large Eddy Simulation of a flow through circular tube bundle

The Large Eddy Simulation approach is used to perform a numerical simulation of a flow around a circular tube bundle. The model uses the immersed boundaries technique to represent tube geometry in the Cartesian grid. Simulation is conducted in an area away from the boundaries, where the flow is considered homogenous and, thus, the three Cartesian directions are considered periodic. The results are compared with experimental data in terms of mean velocity and turbulence quantities, showing good agreement in general.     

Symmetry group classification of three-dimensional Hamiltonian systems

We present some results on the symmetry group classification for an autonomous Hamiltonian system with three degrees of freedom. The potentials considered are natural, i.e., depend on the position variables only and the symmetries considered are Lie point symmetries. With the exception of the harmonic oscillator or a free particle where the dimension is 24, we obtain all dimensions between 1 and 12, except 8.     

Production,remanufacturing and waste disposal models for the cases of pure and partial backordering

Production, remanufacture and waste disposal models in the literature assume that produced and recovered (repaired or remanufactured) items are of the same quality. However, a recent study considered a more realistic situation where produced and remanufactured items are incompatible. That is, they are not perceived by customers to have the same quality characteristics. This results in a lost sales situation for produced (remanufactured) items when they are requested by customers during the remanufacturing (production) period. In today’s competitive market, where firms thrive to sustain or increase the market share for their products, a stock-out situation where demand is completely lost seems to go contrary to the objectives of these firms. In reality, a firm may choose to either backorder fully or partially their unsatisfied demand. This paper extends along this line of research by modelling these stock-out situations. Several stock-out cases are considered for which mathematical models are developed and numerical examples are provided with their results discussed.     

Block and asynchronous two-stage methods for mildly nonlinear systems

Block parallel iterative methods for the solution of mildly nonlinear systems of equations of the form are studied. Two-stage methods, where the solution of each block is approximated by an inner iteration, are treated. Both synchronous and asynchronous versions are analyzed, and both pointwise and blockwise convergence theorems provided. The case where there are overlapping blocks is also considered. The analysis of the asynchronous method when applied to linear systems includes cases not treated before in the literature. Received June 5, 1997 / Revised version received December 29, 1997     

Propagation of Seismic Waves in Block Elastic-Fluid Media. II

A two-dimensional medium consisting of alternating elastic and fluid blocks along the x and z axes is considered. For this block medium, an effective model described by a system of equations is constructed by the method of matrix averaging. An investigation of the equations of this model enables one to separate two body waves from the wave field, to construct their fronts, and to obtain expressions for their velocities along the axes. The effective model is considered in the cases where the block medium is converted to a layered elastic-fluid medium, where all the blocks are of the same size, and where an elastic or a fluid medium occupies the entire volume. Bibliography: 7 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 254–271.     

Light rays having extreme points with the same spatial coordinates

In this paper we deal with lightlike geodesics in Lorentzian manifolds which are closed with respect to the spatial coordinates. We consider the case where the initial point is fixed or moves on a level of a given time function. The case where the initial point is free is also considered, under a periodicity condition on the metric.