Existence and Limiting Behavior of Trajectories Associated with P0-equations

Given a continuous P₀-function F : Rⁿ Rⁿ, we describe a method of constructing trajectories associated with the P₀-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P₀-function lead to P₀-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P₀-equations when the underlying function is P₀. To generate the trajectories, we perturb the given P₀-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem.     

On a Primal-Dual Analytic Center Cutting Plane Method for Variational Inequalities

We present an algorithm for variational inequalities VI( , Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one or sometimes two. Linear equalities that may be included in the definition of the set Y are taken explicitly into account.We report numerical experiments on several well—known variational inequality problems as well as on one where the functional results from the solution of large subproblems. The method is robust and competitive with algorithms which use the same information as this one.     

A combinatorial interior point method for network flow problems

For solving minimum cost flow problems, we develop a combinatorial interior point method based on a variant of the algorithm of Karmarkar, described in Gonzaga [3, 4]. Gonzaga proposes search directions generated by projecting certain directions onto the nullspace ofA. By the special combinatorial structure of networks any projection onto the nullspace ofA can be interpreted as a flow in the incremental graph ofG. In particular, to evaluate the new search direction, it is sufficient to choose a negative circuit subject to costs on the arcs depending on the current solution. That approach results in an O(mn ² L) algorithm wherem denotes the number of vertices,n denotes the number of arcs, andL denotes the total length of the input data.     

The Bell inequalities and the joint measurement of incompatible observables

A quantum-mechanical theory of joint nonideal measurement of incompatible polarization observables is applied to an EPR-like experiment. It is demonstrated that this experiment yields both information satisfying and information violating the Bell inequalities. The measurement is also discussed in the context of a local hidden-variables theory. It is argued that the violation of an additional assumption of reproducibility of the hidden variable rather than violation of locality may be responsible for the violation of the Bell inequalities.     

A relaxed primal-dual path-following algorithm for linear programming

In this paper, we provide an easily satisfied relaxation condition for the primaldual interior path-following algorithm to solve linear programming problems. It is shown that the relaxed algorithm preserves the property of polynomial-time convergence. The computational results obtained by implementing two versions of the relaxed algorithm with slight modifications clearly demonstrate the potential in reducing computational efforts.Partially supported by the North Carolina Supercomputing Center, the 1993 Cray Research Award, and a National Science Council Research Grant of the Republic of China.     

A passive solar heater-refrigerator

Summary In this paper we study the nonequilibrium thermodynamic steady-state behaviour of a model system representing a core surrounded by an envelope in which the envelope interacts with the solar radiation and with an external bath having a given temperature profile. The heat flow between core and envelope can be controlled by varying the thermal conductivity of their interface. We show that this system acts as a passive heat pump raising the core average temperature with respect to the average equilibrium value corresponding to a fixed value of the interface conductivity, at the same time flattening its oscillation in time. By changing the time dependence of the conductivity the systemvice versa acts as a refrigerator. We show how the limits of this performance depend on the passive parameters such as surfaces, conductivities, heat capacities. The periodicity considered in this study is the daily cycle.

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Riassunto In questo lavoro si studia lo stato stazionario di non equilibrio termodinamico per un sistema che rappresenta modellisticamente un corpo circondato da un involucro; questo interagisce con la radiazione solare e con un bagno termico esterno caratterizzato da una temperatura che dipende dal tempo in modo prefissato. Il flusso di calore fra l'interno e l'involucro è controllato variando la conducibilità termica dell'interfaccia. Noi mostriamo che questo sistema funziona come una pompa di calore passiva, cioè innalza la temperatura media dell'interno rispetto a quella che si avrebbe nel caso di conducibilità fissa e, allo stesso tempo, riduce le oscillazioni di codesta temperatura. Semplicemente cambiando la dipendenza oraria del controllo, il sistema funziona come un frigorifero. Si mostra in che modo tale effetto dipenda dai parametri passivi che sono le superfici, i calori specifici, la conducibilità. Consideriamo in questo studio il ciclo giornaliero.

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Резюме В этой работе мы исследуем неравновесное термодинамическое стационарное поведение модельной системы, представляющей ядро, окруженное оболочкой, которая взаимодействует с солнечным излучением и с внешним термостатом, имейщим заданный профиль температур. Поток тепла между ядром и оболочкой можно контролировать посредством изменения теплопровдности их границы раздела. Мы покзываем, что эта система действует, как пассивный тепловой насос, поднимающий среднюю температуру ядра относительно средней равновесной величины, соответствующей фиксировчнной величине теплопроводности границе раздела, и в то же время сглаживающий осцилляции температуры во времени. Изменяя временную зависимость теплопроводности, описанная система может действовать как холодильник. Мы показываем, как указанный эффект зависит от таких пассивных параметров, как поверхности, проводимости, теплоемкости. Периодичность рассмотренной системы представляет суточный цикл.

     

A superdense star model as charged analogue of Schwarzschild’s interior solution

A charged analogue of Schwarzschilds interior solution has been derived by considering the non-gravitational energy density to be constant along with a special choice of electric intensity. The charged fluid sphere so obtained is seen to be more general than that of P.S. Florides and joins smoothly with the Reissner-Nordström metric at the pressure-free interface. Also the new charged fluid sphere is capable of representing a superdense star with surface density of 2×10¹⁴ g cm^–3 which can occupy maximum mass 1.502408 times the solar mass. In the process of deriving the solution, the authors have also come across A. L. Mehras gaseous charged fluid model which is found to be unphysical as it has negative pressure at least at the center of the model.This revised version was published online in April 2005. The publishing date was inserted.     

Enhanced Optical Image Verification Based on Joint Transform Correlator Adopting Fourier Hologram

In this paper two new architectures for optical image verification are proposed. Both architectures are based on conventional joint transform correlators (JTCs) adopting a Fourier hologram and can significantly improve the recovered image quality. First, an input phase-only function is Fourier transformed and then interferes with a reference wave that is diffracted from a plane wave incident on another random phase mask. Second, two phase-only functions are placed at the two input sides of a beamsplitter such that the interference pattern of their Fourier transforms can be detected. To obtain a predefined target image in the output plane, one of the input phase functions is iteratively retrieved by the use of the projection onto constraint sets algorithm. Simulation results show that the less mean squared error and better image quality are obtained for both the binary and grayscale images.