Customer selection problem with profit from a sideline

This paper deals with the problem of selecting profitable orders to accept out of customers sequentially arriving at companies operating in service industries which provide specialized services designed to meet the various needs of their customers. When all the orders accepted up to a point of time are completed and delivered, the companies provide subsidiary services as a sideline in order to prevent their system from being idle, and to yield extra income, referred to as the profit from a sideline. Further, a cost is paid to search for customers, called the search cost. We discuss the admission control problem and pricing control problem in an identical framework. Properties of the optimal decision rule maximizing the total expected present discounted net profit gained over an infinite planning horizon are examined and clarified. It is shown that when the profit from the sideline is large, the optimal policies may not be monotone in the number of orders in the system.     

A note on a diffusive predator-prey model and its steady-state system

In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.     

The coupled problem of a solid oscillating in a viscous fluid under the action of an elastic force

The torsional oscillations are studied of a solid of revolution under the action of elastic torque inside a container with a viscous incompressible fluid. We prove the asymptotic stability of the static equilibrium. We use the two approaches: the direct Lyapunov and linearization methods. The global asymptotic stability is established using a one-parameter family of Lyapunov functionals. Then small oscillations are studied of the fluid-solid system. The linearized operator of the problem of a solid oscillating in a fluid can be realized as an operator matrix obtained by appending two scalar rows and two columns to the Stokes operator. This operator is therefore a two-dimensional bordering of the Stokes operator and inherits many properties of the latter; in particular, the spectrum is discrete. The eigenvalue problem for the linearized operator is reduced to solving a dispersion equation. Inspection of the equation shows that all eigenvalues lie inside the right (stable) half-plane. Basing on this, we justify the linearization. Using an abstract theorem of Yudovich, we prove the asymptotic stability in a scale of function spaces, the infinite differentiability of solutions, and the decay of all their derivatives in time.     

A finite differences method for a two-dimensional nonlinear hyperbolic equation in a class of discontinuous functions

A numerical scheme is proposed for a scalar two-dimensional nonlinear first-order wave equation with both continuous and piecewise continuous initial conditions. It is typical of such problems to assume formal solutions with discontinuities at unknown locations, which justifies the search for a scheme that does not rely on the regularity of the solution. To this end, an auxiliary problem which is equivalent to, but has more advantages then, the original system is formulated and shown that regularity of the solution of the auxiliary problem is higher than that of the original system. An efficient numerical algorithm based on the auxiliary problem is derived. Furthermore, some results of numerical experiments of physical interest are presented.     

Controlled multistage selection procedures for comparison with a standard

Comparison with a standard is a general multiple comparison problem, where each system is required to be compared to a single system, referred to as a “standard”, as well as to other alternative systems. The goal is to determine the best system among a number of systems that are better than the standard, or to select the standard when it is equal to or better than the other alternatives. Kim (2005) proposed an efficient fully sequential procedure for comparison with a standard, that obtains a single observation at each stage from the surviving systems, and is one of the most efficient existing procedures. We develop two provably valid multistage selection procedures that take a number of observations from each system and update the variance estimators at each stage. We also employ appropriate control variate technique for each procedure to further improve the efficiency. Empirical results are provided to demonstrate that the proposed procedures are statistically and computationally more efficient than existing fully sequential procedures.     

Numerical resolution of an exact heat conduction model with a delay term

In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.     

Asymptotic Behavior for Global Smooth Solution to a One-dimensional Nonlinear Thermoviscoelastic System

This paper is concerned with asymptotic behavior, as time tends to infinity, of globally defined smooth (large) solutions to the system in one-dimensional nonlinear thermoviscoelasticity. Our results show that the global smooth solution approaches to the solution in the H¹ norm to the corresponding stationary problem, as time tends to infinity.     

矩阵的初等标准形与线性方程组

指出矩阵的初等标准形理论是线性方程组问题的理论基础     

On the existence of an element with given deviations from an expanding system of subspaces

The problem as to whether a Banach space contains an element with given deviations from an expanding system of strictly nested subspaces (which are not necessarily finite-dimensional) is solved under additional restrictions on the deviations or subspaces.     

Asymptotic Normality of Cross-correlogram Estimates of the Response Function

The problem of estimation of an unknown response function of a time-invariant continuous linear system is considered. Discrete-time sample input–output cross-correlograms are taken as estimates of the response function. The inputs are supposed to be zero-mean stationary Gaussian processes close, in some sense, to a white noise. Both asymptotic normality of finite-dimensional distributions of the estimates and their asymptotic normality in spaces of continuous functions are studied. Our basic tool is a new integral representation for cumulants of the estimate as a finite sum of integrals involving cyclic products of kernels. Some inequalities for these integrals are obtained and their asymptotic behaviour is studied.     

Numerical solution to systems of delay integrodifferential algebraic equations

The numerical solution of the initial value problem for a system of delay integrodifferential algebraic equations is examined in the framework of the parametric continuation method. Necessary and sufficient conditions are obtained for transforming this problem to the best argument, which is the arc length along the integral curve of the problem. The efficiency of the transformation is demonstrated using test examples.     

Global Smooth Solutions and the Asymptotic Behavior of the Motion of a Viscous,Heat-conductive,One-dimensional Real Gas

The system of balance laws of mass, momentum and energy for a viscous, heal-conductive, one-dimensional real gas is considered. The existence of globally defined smooth solution to an initial boundary value problem is established. Because of the boundary conditions' effect, vacuum will be developped as time tends to infinity.     

A Free Boundary Problem Arising in Smoulder Combustion

The smouldering combustion is modeled as a free boundary problem here. By using the Duvaut's transform, the problem is reduced to a variational inequality. Existence and uniqueness are established. Tbe properties of the free boundary are studied in various cases. The asymptotic behavior of the free boundary with respect to the parameter is rigorously proved, which confirms the result of a previous work by J. Adler and D. M. Herbert, obtained by using asymptotic expansion. Furthermore, we show that the time dependent problem will actually converge to a travelling wave solution if the boundary data converge to the corresponding travelling wave solution.     

L2,μ(Q)-estimates for Parabolic Equations and Applications

In this paper we derive a priori estimates in the Campanato space L^{2,\mu}(Q_T) for solutions of tbe following parabolic equation u_t - \frac{∂}{∂x_i}(a_{ij}(x,t)u_x_j+a_iu) + b_iu_x_i + cu = \frac{∂}{∂_x_i}f_i + f_0 where {a_{ij}(x, t)} are assumed to be measurable and satisfy the ellipticity condition. The proof is based on accurate DeGiorgi-Nash-Moser's estimate and a modified Poincare's inequality. These estimates are very useful in the study of the regularity of solutions for some nonlinear problems. As a concrete example, we obtain the classical solvability for a strongly coupled parabolic system arising from the thermistor problem.     

An a priori error analysis of a type III thermoelastic problem with two porosities

In this work, we study, from the numerical point of view, a type III thermoelastic model with double porosity. The thermomechanical problem is written as a linear system composed of hyperbolic partial differential equations for the displacements and the two porosities, and a parabolic partial differential equation for the thermal displacement. An existence and uniqueness result is recalled. Then, we perform its a priori error numerical analysis approximating the resulting variational problem by using the finite element method and the implicit Euler scheme. The linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are shown to demonstrate the accuracy of the approximations and the dependence of the solution on a coupling coefficient.     

Chaos in a restricted problem of rotation of a rigid body with a fixed point

In this paper, we consider the transition to chaos in the phase portrait of a restricted problem of rotation of a rigid body with a fixed point. Two interrelated mechanisms responsible for chaotization are indicated: (1) the growth of the homoclinic structure and (2) the development of cascades of period doubling bifurcations. On the zero level of the area integral, an adiabatic behavior of the system (as the energy tends to zero) is noted. Meander tori induced by the break of the torsion property of the mapping are found.      

Decentralized optimal control of a group of dynamical objects

The problem of optimal control of a group of coupled dynamical objects is considered. The cases are examined in which the centralized control of a group of objects is impossible. Fast real-time optimal control algorithms of each of the dynamical systems are described that use information exchanged between group members in the course of control. The proposed methods supplement the earlier developed real-time optimal control methods for an individual dynamical system. The results are illustrated using optimal control of two coupled mathematical pendulums as an example.     

Computing Voronoi skeletons of a 3-D polyhedron by space subdivision

We tackle the problem of computing the Voronoi diagram of a 3-D polyhedron whose faces are planar. The main difficulty with the computation is that the diagram's edges and vertices are of relatively high algebraic degrees. As a result, previous approaches to the problem have been non-robust, difficult to implement, or not provenly correct.

We introduce three new proximity skeletons related to the Voronoi diagram: (1) the Voronoi graph (VG), which contains the complete symbolic information of the Voronoi diagram without containing any geometry; (2) the approximate Voronoi graph (AVG), which deals with degenerate diagrams by collapsing sub-graphs of the VG into single nodes; and (3) the proximity structure diagram (PSD), which enhances the VG with a geometric approximation of Voronoi elements to any desired accuracy. The new skeletons are important for both theoretical and practical reasons. Many applications that extract the proximity information of the object from its Voronoi diagram can use the Voronoi graphs or the proximity structure diagram instead. In addition, the skeletons can be used as initial structures for a robust and efficient global or local computation of the Voronoi diagram.

We present a space subdivision algorithm to construct the new skeletons, having three main advantages. First, it solves at most uni-variate quartic polynomials. This stands in sharp contrast to previous approaches, which require the solution of a non-linear tri-variate system of equations. Second, the algorithm enables purely local computation of the skeletons in any limited region of interest. Third, the algorithm is simple to implement.     

Preemptive Scheduling with Two Minimax Criteria

Two preemptive single-machine bicriteria scheduling problems with release dates and deadlines are considered in this paper. Each criterion is formulated as a maximum cost. In the first problem the cost of both criteria depends on the completion time of the tasks. This problem can be solved by enumerating all the Pareto optimal points with an approach proposed by Hoogeveen (1996) for the nonpreemptive problem without release dates. In the second problem, the costs of one criterion are dependent on the completion times of the tasks and the costs of the other criterion are dependent on the start times. This problem is more difficult but an efficient algorithm is proposed for a sub-problem with heads, tails, release dates and deadlines that appears in the job-shop scheduling problem.     

Effect of vertical vibrations on a two-layer system with a deformable interface

The effect of single- and two-frequency vibrations on the behavior of a system consisting of two homogeneous viscous fluids bounded by rigid walls is analyzed. It is assumed that the system as a whole is under vertical vibrations obeying a certain law. An eigenvalue problem is obtained in order to analyze the stability of the relative equilibrium. The case of finite frequencies and arbitrary modulation amplitudes is treated along with the case of high frequencies and small modulation amplitudes. In the former case, the parametric resonance domains are examined depending on the parameters of the system. In the latter case, the high-frequency vibration is shown to create effective surface tension, thus flattening the interface, and can suppress instability when the heavy fluid is over the light one.