energy decay for timoshenko systems of memory type abstract linear systems of timoshenko type equations for beams including a memory term are studied the exponential decay is proved for exponential kernels while polynomial kernels are shown to lead to a polynomial decay the optimality of the results is also investigated

exponential stability of laminated timoshenko beams with boundary internal controls abstract for a laminated timoshenko system with slip along the interface we study existence and boundary interior stabilization of solutions our first main result using resolvent estimates in the frequency domain is to show that interior damping created by the interfacial slip in companion with boundary feedback controls acting on the complementary displacements traverse and rotation angle drives the solution to zero with exponential decay rate we impose neither conditions on the physical parameters of the model nor on the damping coefficients our second main result is to investigate the asymptotic behavior of solutions for partially dissipative problems assuming the condition that the waves travel at the same speed we prove the decay of solutions with exponential rate finally the same condition allows us to show that dissipative effect created by the interfacial slip is strong enough to exponentially stabilizes the solutions to zero

a nonlinear thermoelastic bresse system global existence and exponential stability abstract in this paper we study a dissipative bresse system with nonlinear motion equation where the dissipation is given by thermal effects acting in the shear equation under general hypothesis on the nonlinearities we prove the existence and uniqueness of small global solutions as well as the exponential stability

an approximation scheme for a class of risk averse stochastic equilibrium problems we consider two models for stochastic equilibrium one based on the variational equilibrium of a generalized nash game and the other on the mixed complementarity formulation each agent in the market solves a single stage risk averse optimization problem with both here and now investment variables and production wait and see variables a shared constraint couples almost surely the wait and see decisions of all the agents an important characteristic of our approach is that the agents hedge risk in the objective functions on costs or profits of their optimization problems which has a clear economic interpretation this feature is obviously desirable but in the risk averse case it leads to variational inequalities with set valued operators a class of problems for which no established software is currently available to overcome this difficulty we define a sequence of approximating differentiable variational inequalities based on smoothing the nonsmooth risk measure in the agents problems such as average or conditional value at risk the smoothed variational inequalities can be tackled by the path solver for example the approximation scheme is shown to converge including the case when smoothed problems are solved approximately an interesting by product of our proposal is that the smoothing approach allows us to show existence of an equilibrium for the original problem to assess the proposed technique numerical results are presented the first set of experiments is on randomly generated equilibrium problems for which we compare the proposed methodology with the standard smooth reformulation of average value at risk minimization using additional variables to rewrite the associated max function the second set of experiments deals with a part of the real life european gas network for which dantzig wolfe decomposition can be combined with the smoothing approach

inference of fuzzy relational tableaux from fuzzy exemplifications the paper describes a method for deriving fuzzy relational tableaux from fuzzy exemplifications in particular the work by thole zimmerman and zysno 4 is cited as they derive an operator for and using data derived from human subjects the method results in an operator or operators which is a maximal restriction of the operators implied by the data results showing the process are described and a value of and is derived using data presented in 4

a solution to an open problem on the t product of tl fuzzy subgroups many studies have investigated necessary and sufficient conditions whereby fuzzy subgroups of a cartesian product of groups are a cartesian product of fuzzy subgroups chon fuzzy subgroups as products fuzzy sets and systems 141 2004 505 508 found such conditions under minimum operation he pointed out that the problem of finding necessary and sufficient conditions for t fuzzy subgroups under a t norm operation is still open in this study we solve the problem and identify necessary and sufficient conditions under t norm operation

the stability number of the timoshenko system with second sound abstract in this work we consider the timoshenko beam model with second sound we introduce a new number 0 that characterizes the exponential decay we prove that the corresponding semigroup associated to the system is exponentially stable if and only if 0 0 otherwise there is a lack of exponential stability in this case we prove that the semigroup decays as t 1 2 moreover we show that the rate is optimal

on timoshenko type systems with type iii thermoelasticity asymptotic behavior abstract in this study we consider a thermoelastic beam system where the oscillations are defined by the timoshenko model and heat conduction is given by the green and naghdi theories we provide an explicit characterization of the decay rate which can be exponential or polynomial depending on the relationship between the coefficients of the wave propagation speed

solving monotone stochastic variational inequalities and complementarity problems by progressive hedging the concept of a stochastic variational inequality has recently been articulated in a new way that is able to cover in particular the optimality conditions for a multistage stochastic programming problem one of the long standing methods for solving such an optimization problem under convexity is the progressive hedging algorithm that approach is demonstrated here to be applicable also to solving multistage stochastic variational inequality problems under monotonicity thus increasing the range of applications for progressive hedging stochastic complementarity problems as a special case are explored numerically in a linear two stage formulation

a unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi discretized vibrating damped systems the liapunov method is celebrated for its strength to establish strong decay of solutions of damped equations extensions to infinite dimensional settings have been studied by several authors see e g haraux 1991 11 and komornik and zuazua 1990 17 and references therein results on optimal energy decay rates under general conditions of the feedback is far from being complete the purpose of this paper is to show that general dissipative vibrating systems have structural properties due to dissipation we present a general approach based on convexity arguments to establish sharp optimal or quasi optimal upper energy decay rates for these systems and on comparison principles based on the dissipation property and interpolation inequalities in the infinite dimensional case for lower bounds of the energy we stress the fact that this method works for finite as well as infinite dimensional vibrating systems and as well as for applications to semi discretized nonlinear damped vibrating pde s a part of this approach has been introduced in alabau boussouira 2004 2005 1 2 in the present paper we identify a new simple and explicit criteria to select a class of nonlinear feedbacks for which we prove a simplified explicit energy decay formula comparatively to the more general but also more complex formula we give in alabau boussouira 2004 2005 1 2 moreover we prove optimality of the decay rates for this class in the finite dimensional case this class includes a wide range of feedbacks ranging from very weak nonlinear dissipation exponentially decaying in a neighborhood of zero to polynomial or polynomial logarithmic decaying feedbacks at the origin in the infinite dimensional case we establish a comparison principle on the energy of sufficiently smooth solutions through the dissipation relation this principle relies on suitable interpolation inequalities it allows us to give lower bounds for the energy of smooth initial data for the one dimensional wave equation with a distributed polynomial damping which improves haraux 1995 12 lower estimate of the energy for this case we also establish lower bounds in the multi dimensional case for sufficiently smooth solutions when such solutions exist we further mention applications of these various results to several classes of pde s namely the locally and boundary damped multi dimensional wave equation the locally damped plate equation and the globally damped coupled timoshenko beams system but it applies to several other examples furthermore we show that these optimal energy decay results apply to finite dimensional systems obtained from spatial discretization of infinite dimensional damped systems we illustrate these results on the one dimensional locally damped wave and plate equations discretized by finite differences and give the optimal energy decay rates for these two examples these optimal rates are not uniform with respect to the discretization parameter we also discuss and explain why optimality results have to be stated differently for feedbacks close to linear behavior at the origin

mildly dissipative nonlinear timoshenko systems global existence and exponential stability we consider nonlinear systems of timoshenko type in a one dimensional bounded domain the system has a dissipative mechanism being present only in the equation for the rotation angle it is a damping effect through heat conduction the global existence of small smooth solutions as well as the exponential stability are investigated

boundary stabilization of solutions of a nonlinear system of timoshenko type in this paper we are concerned with a multidimensional timoshenko system subjected to boundary conditions of memory type we establish general rate decay results the usual exponential and polynomial decay rates are only special cases

fuzzy generators and fuzzy direct sums of abelian groups abstract we define the concept of a fuzzy generating set and describe the fuzzy subgroup which it generates we introduce the notion of a minimal fuzzy generating set and we show that any fuzzy subgroup whose support is cyclic has a minimal fuzzy generating set we show by examples that this result breaks down if the support of a is a direct sum of two or more cyclic groups these examples also show that a fuzzy subgroup of a group g need not be a fuzzy direct sum of subgroups whose supports are cyclic even if g is a direct sum of cyclic groups we show that every fuzzy subgroup is a fuzzy direct sum of p primary fuzzy subgroups

on the stability of damped timoshenko systems cattaneo versus fourier law we consider hyperbolic timoshenko type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction while exponential stability under the fourier law of heat conduction holds it turns out that the coupling via the cattaneo law does not yield an exponentially stable system this seems to be the first example that a removal of the paradox of infinite propagation speed inherent in fourier s law by changing to the cattaneo law causes a loss of the exponential stability property actually for systems with history the fourier law keeps the exponential stability known for the pure timoshenko system without heat conduction but introducing the cattaneo coupling even destroys this property

a characterization of fuzzy subgroups abstract an ordinary subgroup of a group g is 1 a subset of g 2 closed under the group operation in a fuzzy subgroup it is precisely these two notions that lose their deterministic character a fuzzy subgroup of a group g associates with each group element a number the larger the number the more certainly that element belongs to the fuzzy subgroup the closure property is captured by the inequality x y t x y in a rosenfeld s original definition t was the function minimum however any t norm t provides a meaningful generalization of the closure property two classes of fuzzy subgroups are investigated the fuzzy subgroups in one class are subgroup generated those in the other are function generated each fuzzy subgroup in these classes satisfies the above inequality with t given by t a b max a b 1 0 while the two classes look different each fuzzy subgroup in either is isomorphic to one in the other it is shown that a fuzzy subgroup satisfies the above inequality with t minimum if and only if it is subgroup generated of a very special type finally these notions are applied to some abstract pattern recognition problems

global existence asymptotic behavior and uniform attractors for a non autonomous timoshenko system of thermoelasticity of type iii with a time varying delay abstract in this paper we first establish the global existence by using the variable norm technique of kato and semigroup method second under suitable assumptions on the data we obtain the asymptotic behavior of the solution last we prove the existence of a uniform attractor by using the method of uniform contractive functions

scenario reduction in stochastic programming given a convex stochastic programming problem with a discrete initial probability distribution the problem of optimal scenario reduction is stated as follows determine a scenario subset of prescribed cardinality and a probability measure based on this set that is the closest to the initial distribution in terms of a natural or canonical probability metric arguments from stability analysis indicate that fortet mourier type probability metrics may serve as such canonical metrics efficient algorithms are developed that determine optimal reduced measures approximately numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty for instance it turns out that after 50 reduction of the scenario tree the optimal reduced tree still has about 90 relative accuracy

a stability result of a timoshenko system with a delay term in the internal feedback abstract in this paper we consider a timoshenko system with a delay term in the feedback and prove a stability result the beam is clamped at the endpoints and has in addition to an internal damping a feedback with a delay under an appropriate assumption on the weights of the two feedbacks we prove the well posedness of the system and establish an exponential decay result for the case of equal speed wave propagation

polynomial stability of the timoshenko system by one boundary damping abstract in this paper we study the indirect boundary stabilization of the timoshenko system with only one dissipation law this system which models the dynamics of a beam is a hyperbolic system with two wave speeds assuming that the wave speeds are equal we prove non uniform stability and an optimal polynomial energy decay rate is obtained otherwise if the ratio of the wave speeds is a rational number we show that the decay rate is of polynomial type

divide to conquer decomposition methods for energy optimization modern electricity systems provide a plethora of challenging issues in optimization the increasing penetration of low carbon renewable sources of energy introduces uncertainty in problems traditionally modeled in a deterministic setting the liberalization of the electricity sector brought the need of designing sound markets ensuring capacity investments while properly reflecting strategic interactions in all these problems hedging risk possibly in a dynamic manner is also a concern the fact of representing uncertainty and or competition of different companies in a multi settlement power market considerably increases the number of variables and constraints for this reason usually a trade off needs to be found between modeling and numerical tractability the more details are brought into the model the harder becomes the optimization problem for structured optimization and generalized equilibrium problems we explore some variants of solution methods based on lagrangian relaxation and on benders decomposition throughout we keep as a leading thread the actual practical value of such techniques in terms of their efficiency to solve energy related problems

expected residual minimization formulation for a class of stochastic linear second order cone complementarity problems abstract this paper considers a class of stochastic linear second order cone complementarity problems slsoccp noticing that the slsoccp does not have a solution suitable to all realizations in general we present a deterministic formulation called the expected residual minimization erm formulation for it the coercive property of the erm problem and the robustness of its solutions are discussed due to the existence of expectation in the erm problem we employ the monte carlo approximation techniques to approximate the erm problem and show that under mild conditions this approximation approach possesses exponential convergence rate then we extend the above results to a general mixed slsoccp furthermore we apply the theoretical results to a stochastic optimal power flow model in radial network and report some numerical dispatching experiments for real world southern california edison 47 bus network

decay rate estimates for the quasi linear timoshenko system with nonlinear control and damping terms in this work we consider a class of quasi linear timoshenko systems with nonlinear control and damping terms we investigate the stabilization of weak solutions to the initial boundary value problem and obtain explicit decay rate estimation depending on control and damping terms

general energy decay in a timoshenko type system of thermoelasticity of type iii with a viscoelastic damping in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove a general decay result from which the exponential and polynomial decays are only special cases

fuzzy subgroups as products we find necessary and sufficient conditions for a fuzzy subgroup of a cartesian product of groups to be a cartesian product of fuzzy subgroups

investment models based on clustered scenario trees abstract stochastic programming is widely applied in financial decision problems in particular when we need to carry out the actual calculations for portfolio selection problems we have to assign a value for each expected return and the associated conditional probability in advance these estimated random parameters often rely on a scenario tree representing the distribution of the underlying asset returns one of the drawbacks is that the estimated parameters may be deviated from the actual ones therefore robustness is considered so as to cope with the issue of parameter inaccuracy in view of this we propose a clustered scenario tree approach which accommodates the parameter inaccuracy problem in the context of a scenario tree

benders decomposition for multi stage stochastic mixed complementarity problems applied to a global natural gas market model abstract this paper presents and implements a benders decomposition type of algorithm for large scale stochastic multi period mixed complementarity problems the algorithm is applied to various multi stage natural gas market models accounting for market power exertion by traders due to the non optimization nature of the natural gas market problem a straightforward implementation of the traditional benders decomposition is not possible the master and subproblems can be derived from the underlying optimization problems and transformed into complementarity problems however to complete the master problems optimality cuts are added using the variational inequality based method developed in gabriel and fuller 2010 in this manner an alternative derivation of benders decomposition for stochastic mcp is presented thereby making this approach more applicable to a broader audience the algorithm can successfully solve problems with up to 256 scenarios and more than 600 thousand variables and problems with over 117 thousand variables with more than two thousand first stage capacity expansion variables the algorithm is efficient for solving two stage problems the computational time reduction for other stochastic problems is considerable and would be even larger if a parallel implementation of the algorithm were used the paper concludes with a discussion of infrastructure expansion results illustrating the impact of hedging on investment timing and optimal capacity sizes

solving stochastic complementarity problems in energy market modeling using scenario reduction in this paper we analyze market equilibrium models with random aspects that lead to stochastic complementarity problems while the models presented depict energy markets the results are believed to be applicable to more general stochastic complementarity problems the contribution is the development of new heuristic scenario reduction approaches that iteratively work towards solving the full extensive form stochastic market model the methods are tested on three representative models and supporting numerical results are provided as well as derived mathematical bounds

spectrum and stability for elastic systems with global or local kelvin voigt damping in this paper we study the mathematical properties of a variational second order evolution equation which includes the equations modelling vibrations of the euler bernoulli and rayleigh beams with the global or local kelvin voigt k v damping in particular our results describe the semigroup setting the strong asymptotic stability and exponential stability of the semigroup the analyticity of the semigroup as well as characteristics of the spectrum of the semigroup generator under various conditions on the damping we also give an example to show that the energy of a vibrating string does not decay exponentially when the k v damping is distributed only on a subinterval which has one end coincident with one end of the string

on the stabilization of timoshenko systems with memory and different speeds of wave propagation in this work we consider a one dimensional timoshenko system with different speeds of wave propagation and with only one control given by a viscoelastic term on the angular rotation equation for a wide class of relaxation functions and for sufficiently regular initial data we establish a general decay result for the energy of solution unlike the past history and internal feedback cases the second energy is not necessarily decreasing to overcome this difficulty a precise estimate of the second energy in terms of the initial data and the relaxation function is proved

products of fuzzy subgroups fuzzy subgroups are different from ordinary subgroups in that one cannot tell with certainty which group elements belong and which do not of course this requires an appropriate modification of the closure property which takes the form of an inequality in this paper a study of products of fuzzy subgroups is begun some results are expected the product of fuzzy subgroups is a fuzzy subgroup products with the same but permuted factors are isomorphic and there is a natural isomorphism from any factor into the product functions called t norms are used to construct products of fuzzy subgroups different t norms yielding different products since a fuzzy subgroup must satisfy an inequality generalizing closure and the strength of that inequality is important some results relate the t norm used in forming the product to the strength of the ensuing inequality when can complicated fuzzy subgroups be expressed as products of simple ones this question is addressed for fuzzy subgroups of finite abelian groups

stability of timoshenko systems with past history we consider vibrating systems of timoshenko type with past history acting only in one equation we show that the dissipation given by the history term is strong enough to produce exponential stability if and only if the equations have the same wave speeds otherwise the corresponding system does not decay exponentially as time goes to infinity in the case that the wave speeds of the equations are different which is more realistic from the physical point of view we show that the solution decays polynomially to zero with rates that can be improved depending on the regularity of the initial data

on the spectrum of evolution operators generated by hyperbolic systems abstract we prove that the asymptotic behavior of semigroups generated by mixed initial value problems for hyperbolic systems in one space variable is determined by the zeroes of the characteristic equation the proof is based on the following reduction principle we construct a reduced system which is much simpler than the given one such that the difference of the semigroups is a compact operator the construction of the reduced system is presented in the non autonomous case because it has implifications in the study of systems which are time periodic