Human memory as ap-adic dynamic system

We propose a mathematical model of the human memory-retrieval process based on dynamic systems over a metric space ofp-adic numbers. The elements of this space represent ideas. We assume that two ideas are close if they have a sufficiently long initial segment in common. We also assume that this dynamic system is located in the subconscious and is controlled by the conscious, which specifies the system parameters and provides the ideas that initiate the iteration of the dynamic system. We show that even simplep-adic dynamic systems describe essential features of the human memory-retrieval process. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 3, pp. 385–396, December, 1998     

Tree decompositions of graphs: Saving memory in dynamic programming

We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique” is based on a tree-like set covering problem. We substantiate our findings by experimental results. Our strategy has negligible computational overhead concerning running time but achieves memory savings for nice tree decompositions and path decompositions between 60% and 98%.     

Iterative approaches for a dynamic memory allocation problem in embedded systems

Memory allocation has a significant impact on energy consumption in embedded systems. In this paper, we are interested in dynamic memory allocation for embedded systems with a special emphasis on time performance. We propose two mid-term iterative approaches which are compared with existing long-term and short-term approaches, and with an ILP formulation as well. These approaches rely on solving a static version of the allocation problem and they take advantage of previous works for addressing the static problem. A statistic analysis is carried out for showing that the mid-term approach is the best one in terms of solution quality.     

The dynamic discrepancy method for a differential equation with memory

We study the problem of recovering a control for a system of parabolic type with memory. We exhibit a finite-step algorithm for solving the problem, based on the discrepancy method. The algorithm is resistant to informational noise and computational errors. Bibliography: 22 titles. Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 68–74.     

Control problems for weakly coupled systems with memory

We investigate control problems for wave–Petrovsky coupled systems in the presence of memory terms. By writing the solutions as Fourier series, we are able to prove Ingham type estimates, and hence reachability results. Our findings have applications in viscoelasticity theory and linear acoustic theory.     

Control design in problems with an unknown level of dynamic disturbance

Linear differential games for two players with a fixed termination time are considered. The objective of player 1 is to bring the motion of the system into an assigned terminal set or fairly close to it at the termination time. Player 2 (the disturbance) opposes this. The control of player 1 is scalar and its absolute value is subject to a constraint. One special feature of the formulation is that no constraint on the control of player 2 is specified a priori. A method of designing the feedback control of player 1 that works satisfactorily over a broad range of disturbance levels and corresponds to a small magnitude of the control input at a low level of disturbance is proposed and verified. A numerical program is written for the case of small dimensionality of the phase variable. The results of the simulation of a system that describes a conflict-controlled pendulum are presented.     

Control problems with state constraints for shape memory alloys

In this paper, two different control problems with state constraints for shape memory alloys are considered: in the non-isothermal case, we study boundary control problems, and in the isothermal situation, a dynamical shape optimization problem is considered. In both cases, the transverse displacement is the constrained state variable. The first-order conditions of optimality are derived.     

Control of the thermoelastic model of a plate activated by shape memory alloy reinforcements

In the paper we study the problem of control by means of a heat source g for a thermoelastic system of equations u_tt − ρ∇· p (θ, ∇u) − νΔu_t + DΔ² u = f, c_v(θ, ∇u)θ_t − κΔθ − ρθ[ p _θ (θ, ∇u)·∇u_t] − ν∣∇u_t∣² = g, in a two-dimensional domain, where both viscosity ν and rigidity D are positive. Such a system has been considered in our former papers, and existence of solutions as well as uniqueness have been obtained. Here we prove the continuity and differentiability of solutions under somewhat stronger assumptions. An example of a control problem and necessary optimality conditions are presented. The system has an interpretation as a plate reinforced with shape memory alloy (SMA) wire mesh. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Unilateral dynamic contact of von Kármán plates with singular memory

The solvability of the contact problem is proved provided the plate is simply supported. The singular memory material is assumed. This makes it possible to get a priori estimates important for the strong convergence of gradients of velocities of solutions to the penalized problem. Dedicated to Jiří V. Outrata on the occasion of his 60th birthday. The work presented here was partially supported by the Czech Academy of Sciences under grant IAA1075402 and under the Institutional research plan AVOZ 10190503, and by the grant 1/4214/07 of the Grant Agency of the Slovak Republic.     

Lipschitz continuity and duality for dynamic oligopolistic market equilibrium problem with memory term

We are concerned with an infinite dimensional variational inequality which is connected with the dynamic oligopolistic market equilibrium problem. We will provide existence theorems and show, under minimal assumptions on the data, the Lipschitz continuity of the solution. Moreover a general duality theory is provided overcoming the difficulty of the voidness of the interior of the ordering cone which defines the cone constraints.     

Control methods for dynamic time-based manufacturing under customized product lead times

For manufacturers, the integration of high performance manufacturing with customer-oriented practices plays an important role in improving the performance of their business system. The benefits from such integration can only be maximized when the two parts are designed to work cooperatively. Though previous research has contributed much to manufacturing control algorithms and customer service practices, there has been little consideration of the two parts as a whole; consequently, the methods proposed may not be well supported by the other practices adopted in the system. This study develops production control methods that support a customer-oriented lead time policy, and aims to increase the performance of both manufacturing and customer service. The control methods are proposed for hybrid flow shops handling orders arriving dynamically. Computer simulations are conducted on a large number of problem instances, and the results show that the designed distributed feedback and decision-making functions enable the proposed methods to significantly outperform existing methods in achieving just-in-time (JIT) job completion under customized product lead times. Even taking into account the possible tradeoff between JIT job completion and flow time length, the proposed methods still deliver competitive performance.     

Control of a family of nonlinear dynamic systems under measurements with bounded disturbances

We consider a control synthesis problem for nonlinear dynamic systems under parametric uncertainty and bounded measurement noises. Because of bounded disturbances in measurements of the state vector and the nonlinearity in the control object, the initially formulated control synthesis problem for a family of nonlinear systems as a generalized Zubov problem is transformed into a symbiosis of generalized Zubov–Bulgakov problems. The main result of the paper is the analytic solution of a minimax synthesis problem, which yields a constructive method for finding an invariant set.     

Control of linear processes with distributed lags using dynamic programming from first principles

A simple dynamic programming argument is presented for the quadratic-cost controller synthesis problem for discrete-time linear processes with delay. Distributed delays are allowed in both state and control. The solution obtained has a discrete-time Riccati difference structure closely analogous to the Riccati differential structure associated with delay problems in continuous time. Extensions are provided for the cases of varying lag-limits, performance criterion dependent on past variables, and the time-invariant regulator problem. A feedback solution is also obtained for a continuous-time problem with distributed delays in the control, by passage to limit from the discrete results.This work was supported by the Operations Research Center, University of California, Berkeley, California, under NSF Grant No. GP-30961X2. The author would like to thank Professor S. E. Dreyfus for guidance and helpful suggestions.     

A dynamic visualization system for multiprocessor computers with common memory and its application for numerical modeling of the turbulent flows of viscous fluids

Basic design principles of the architecture of a dynamic visualization system for multiprocessor computers with common memory are described. Analysis of the results of calculation of 3D nonstationary multivortical turbulent flows of viscous fluids and gases is performed for the systems whose behavior can be analyzed using the Navier-Stokes and difference methods involving grids with several millions of nodes. Such a large number of nodes results from a great complexity of the vortical structures arising and changing in the process of calculation. The software tools necessary for the analysis of the results are considered and a technique of interaction between a supercomputer and the workstation used for visualization is proposed. As an example, a procedure for processing of the calculation results obtained from the numerical investigation of 3D nonstationary flows of a viscous incompressible fluid in a channel with a square cross section is presented.     

Representation theorems in the mechanics of materials with memory

Zusammenfassung Es wird gezeigt, wie das Stone-Weierstrass'sche Theorem zur Aufstellung von Stoffgleichungen von Materialien mit Gedächtnis benützt werden kann, wenn diese im Bezugszustand gewisse Symmetrien aufweisen.     

On the rate of decay in interacting continua with memory

This paper is concerning the linear theory of isothermal interacting continua with memory. We consider anti-plane shear deformations in a mixture of two elastic solids where the dissipation mechanisms can be the viscosity in one of the components and the viscosity with respect to the relative displacement. We have seen that when the only dissipation mechanism applies on the relative displacement we cannot expect the exponential decay for the solutions. We have also analyzed the case when the viscosity mechanism applies on a constituent. We have seen that generically the decay is of exponential type. However if the coupling constitutive parameter vanishes the decay is slow.     

Dedicated to the memory of Stefan Bergman

Solutions in H¹ _loc of Dirichlet's problem for a linear second-order elliptic equation are considered. The nature of singularities which higher derivatives of such solutions may have near the boundary is investigated     

Solvability of the electromagneticelasticity problem with memory

Questions are studied of the solvability of boundary value problems of electromagneticelasticity for media with memory. Theorems are proved on the existence and uniqueness of the solution of the indicated problems in the spaces C(0, T; W₂ ¹()) and C(0, T; {329-01}). In proving the existence theorem, we use the property of connected fields, the compactness method, monotonicity and generalized Gronwall-Bellman inequalities.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 365–374, March, 1991.