We consider the problem of frictional contact between an piezoelectric body and aconductive foundation. The electro-elastic constitutive law is assumed to be nonlinear andthe contact is modelled with the Signorini condition, nonlocal Coulomb friction law and aregularized electrical conductivity condition. The existence of a unique weak solution ofthe model is established. The finite elements approximation for the problem is presented,and error estimates on the solutions are derived

We present a user-friendly version of a double operator integration theory which stillretains a capacity for many useful applications. Using recent results from the lattertheory applied in noncommutative geometry, we derive applications to analogues of theclassical Heinz inequality, a simplified proof of a famous inequality ofBirman-Koplienko-Solomyak and also to the Connes-Moscovici inequality. Our methods aresufficiently strong to treat these inequalities in the setting of symmetric operator normsin general semifinite von Neumann algebras.

We present a new method for generating a d-dimensional simplicial meshthat minimizes the L p -norm,p > 0, of the interpolation error or its gradient. The methoduses edge-based error estimates to build a tensor metric. We describe and analyze thebasic steps of our method

A general theorem on the GBDT version of the Bäcklund-Darboux transformation for systemsdepending rationally on the spectral parameter is treated and its applications tononlinear equations are given. Explicit solutions of direct and inverse problems forDirac-type systems, including systems with singularities, and for the system auxiliary tothe N-wave equation are reviewed. New results on explicit construction ofthe wave functions for radial Dirac equation are obtained.

In L 2(ℝd ;ℂn ), we consider a wide class of matrix elliptic secondorder differential operators $\mathcal{A}$ εwith rapidly oscillating coefficients (depending on x/ε).For a fixed τ > 0 and small ε > 0, we findapproximation of the operator exponential exp(− $\mathcal{A}$ ε τ) in the(L 2(ℝd ;ℂn ) →H 1(ℝd ;ℂn ))-operator norm with an error term of orderε. In this approximation, the corrector is taken into account. Theresults are applied to homogenization of a periodic parabolic Cauchy problem.

In this paper, a new hybrid simulated annealing algorithm for constrained globaloptimization is proposed. We have developed a stochastic algorithm called ASAPSPSA thatuses Adaptive Simulated Annealing algorithm (ASA). ASA is a series of modifications to thebasic simulated annealing algorithm (SA) that gives the region containing the globalsolution of an objective function. In addition, Simultaneous Perturbation StochasticApproximation (SPSA) method, for solving unconstrained optimization problems, is used torefine the solution. We also propose Penalty SPSA (PSPSA) for solving constrainedoptimization problems. The constraints are handled using exterior point penalty functions.The combination of both techniques ASA and PSPSA provides a powerful hybrid optimizationmethod. The proposed method has a good balance between exploration and exploitation withvery fast computation speed, its performance as a viable large scale optimization methodis demonstrated by testing it on a number of benchmark functions with 2 - 500 dimensions.In addition, applicability of the algorithm on structural design was tested and successfulresults were obtained

In this paper we present a new hybrid method, called SASP method. We propose thehybridization of two methods, the simulated annealing (SA), which belong to the class ofglobal optimization based on the principles of thermodynamics, and the descent method werewe estimate the gradient using the simultaneous perturbation. This hybrid method givesbetter results. We use the Normal Boundary Intersection approach (NBI) based on the SASPmethod to solve a portfolio optimization problem. Such problem is a multi-objectiveoptimization problem, in order to solve this problem we use three statistical quantities:the expected value, the variance and the Conditional Value-at-Risk (CVaR). The purpose ofthis work is to find the efficient boundary of the considered multi-objective problemusing the NBI method based on the SASP method

We prove the instability of threshold resonances and eigenvalues of the linearized NLSoperator. We compute the asymptotic approximations of the eigenvalues appearing from theendpoint singularities in terms of the perturbations applied to the original NLS equation.Our method involves such techniques as the Birman-Schwinger principle and the Feshbachmap.

The goal of this paper is to apply the Continuous Hopfield Networks (CHN) to thePlacement of Electronic Circuit Problem (PECP). This assignment problem has been expressedas Quadratic Knapsack Problem (QKP). To solve the PECP via the CHN, we choose an energyfunction which ensures an appropriate balance between minimization of the cost functionand simultaneous satisfaction of the PECP constraints. In addition, the parameters of thisfunction must avoid some bad local minima. Finally, some computational experiments solvingthe PECP are included

The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which thefeasible set is determined by the set of optimal solutions of parametric Knapsack Problem.In this paper, we propose two stages exact method for solving the BKP. In the first stage,a dynamic programming algorithm is used to compute the set of reactions of the follower.The second stage consists in solving an integer program reformulation of BKP. We show thatthe integer program reformulation is equivalent to the BKP. Numerical results show theefficiency of our method compared with those obtained by the algorithm of Moore andBard

In the present paper, a general multiobjective optimization problem is stated as a Nashgame. In the nonrestrictive case of two objectives, we address the problem of thesplitting of the design variable between the two players. The so-called territorysplitting problem is solved by means of an allocative approach. We propose two algorithmsin order to find fair allocation tables

In topology optimization problems, we are often forced to deal with large-scale numericalproblems, so that the domain decomposition method occurs naturally. Consider a typicaltopology optimization problem, the minimum compliance problem of a linear isotropicelastic continuum structure, in which the constraints are the partial differentialequations of linear elasticity. We subdivide the partial differential equations into twosubproblems posed on non-overlapping sub-domains. In this paper, we consider the resultingproblem as multilevel one and show that it can be written as one level problem

In this paper, an artificial neural network (ANN) based on hybrid algorithm combiningparticle swarm optimization (PSO) with back-propagation (BP) is proposed to forecast thedaily streamflows in a catchment located in a semi-arid region in Morocco. The PSOalgorithm has a rapid convergence during the initial stages of a global search, while theBP algorithm can achieve faster convergent speed around the global optimum. By combiningthe PSO with the BP, the hybrid algorithm referred to as BP-PSO algorithm is presented inthis paper. To evaluate the performance of the hybrid algorithm, BP neural network is alsoinvolved for a comparison purposes. The results show that the neural network model evolvedby PSO-BP algorithm has a good predictions and better convergence performances

This work concerns an enlarged analysis of the problem of asymptotic compensation for aclass of discrete linear distributed systems. We study the possibility of asymptoticcompensation of a disturbance by bringing asymptotically the observation in a giventolerance zone 𝒞. Under convenient hypothesis, we show the existence and theunicity of the optimal control ensuring this compensation and we give itscharacterization

In this work, we present some concepts recently introduced in the analysis and control ofdistributed parameter systems: Spreadability,vulnerability and protector control. These conceptspermit to describe many biogeographical phenomena, as those of pollution, desertificationor epidemics, which are characterized by a spatio-temporal evolution

In this work we study the optimal control problem for a class of nonlinear time-delaysystems via paratingent equation with delayed argument. We use an equivalence theorembetween solutions of differential inclusions with time-delay and solutions of paratingentequations with delayed argument. We study the problem of optimal control which minimizes acertain cost function. To show the existence of optimal control, we use the maintopological properties of the set solutions of paratingent equation with delayedargument