fractional laplacian phase transitions and boundary reactions a geometric inequality and a symmetry result we deal with symmetry properties for solutions of nonlocal equations of the type sv f v in rn where s 0 1 and the operator s is the so called fractional laplacian the study of this nonlocal equation is made via a careful analysis of the following degenerate elliptic equation div x u 0on rn 0 x ux f u on rn 0 where 1 1 y rn x 0 and u u y x this equation is related to the fractional laplacian since the dirichlet to neumann operator u r n 1 x ux r n 1 is 1 2 more generally we study the so called boundary reaction equations given by div x u g x u 0on rn 0 x ux f u on rn 0 under some natural assumptions on the diffusion coefficient and on the nonlinearities f and g we prove a geometric formula of poincare type for stable solutions from which we derive a symmetry result in the spirit of a conjecture of de giorgi

on the possibilistic mean value and variance of multiplication of fuzzy numbers in this paper we introduce the definitions of the possibilistic mean variance and covariance of multiplication of fuzzy numbers and show some properties of these definitions then we apply these definitions to build the possibilistic models of portfolio selection under the situations involving uncertainty over the time horizon by considering the portfolio selection problem from the point of view of possibilistic analysis moreover numerical experiments with real market data indicate that our approach results in better portfolio performance

the hardy inequality and the asymptotic behaviour of the heat equation with an inverse square potential we study the well posedness and describe the asymptotic behavior of solutions of the heat equation with inverse square potentials for the cauchy dirichlet problem in a bounded domain and also for the cauchy problem in rn in the case of the bounded domain we use an improved form of the so called hardy poincare inequality and prove the exponential stabilization towards a solution in separated variables in rn we first establish a new weighted version of the hardy poincare inequality and then show the stabilization towards a radially symmetric solution in self similar variables with a polynomial decay rate this work complements and explains well known work by baras and goldstein on the existence of global solutions and blow up for these equations in the present article the sign restriction on the data and solutions is removed the functional framework for well posedness is described and the asymptotic rates calculated examples of non uniqueness are also given

high order essentially nonsocillatory schemes for hamilton jacobi equations hamilton jacobi h j equations are frequently encountered in applications e g in control theory and differential games h j equations are closely related to hyperbolic conservation laws in one space dimension the former is simply the integrated version of the latter similarity also exists for the multidimensional case and this is helpful in the design of difference approximations in this paper high order essentially nonoscillatory eno schemes for h j equations are investigated which yield uniform high order accuracy in smooth regions and sharply resolve discontinuities in the derivatives the eno scheme construction procedure is adapted from that for hyperbolic conservation laws the schemes are numerically tested on a variety of one dimensional and two dimensional problems including a problem related to control optimization and high order accuracy in smooth regions good resolution of discontinuities in the derivatives and convergence to viscosity solutions are observed

a simple proof of hardy lieb thirring inequalities we give a short and unified proof of hardy lieb thirring inequalities for moments of eigenvalues of fractional schrodinger operators the proof covers the optimal parameter range it is based on a recent inequality by solovej sorensen and spitzer moreover we prove that any non magnetic lieb thirring inequality implies a magnetic lieb thirring inequality with possibly a larger constant

sharp constants in the hardy rellich inequalities optimal constants are found in hardy rellich inequalities containing derivatives of arbitrary not necessarily integer order l some new inequalities of this type are also obtained

optimal multiple objective resource allocation using hybrid particle swarm optimization and adaptive resource bounds technique the multiple objective resource allocation problem morap seeks for an allocation of resource to a number of activities such that a set of objectives are optimized simultaneously and the resource constraints are satisfied morap has many applications such as resource distribution project budgeting software testing health care resource allocation etc this paper addresses the nonlinear morap with integer decision variable constraint to guarantee that all the resource constraints are satisfied we devise an adaptive resource bound technique to construct feasible solutions the proposed method employs the particle swarm optimization pso paradigm and presents a hybrid execution plan which embeds a hill climbing heuristic into the pso for expediting the convergence to cope with the optimization problem with multiple objectives we evaluate the candidate solutions based on dominance relationship and a score function experimental results manifest that the hybrid pso derives solution sets which are very close to the exact pareto sets the proposed method also outperforms several representatives of the state of the art algorithms on a simulation data set of the morap

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

two approximations of solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games the associated initial value problems almost never have global time classical solutions and one must deal with suitable generalized solutions the correct class of generalized solutions has only recently been established by the authors this article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates analogous results are proved by similar means for the method of vanishing viscosity author

nonexistence of distributional supersolutions of a semilinear elliptic equation with hardy potential abstract in this paper we study nonexistence of non negative distributional supersolutions for a class of semilinear elliptic equations involving inverse square potentials

integral representation of solutions using green function for fractional hardy equations abstract our main aim is to study green function for the fractional hardy operator p s x 2 s in r n where 0 n s and n s is the best constant in the fractional hardy inequality using green function we also show that the integral representation of the weak solution holds

nonexistence results for a class of fractional elliptic boundary value problems abstract in this paper we study a class of fractional elliptic problems of the form s u f x u in u 0 in r n where s 0 1 we prove nonexistence of positive solutions when is star shaped and f is supercritical we also derive a nonexistence result for subcritical f in some unbounded domains the argument relies on the method of moving spheres applied to a reformulated problem using the caffarelli silvestre extension caffarelli and silvestre 2007 11 of a solution of the above problem

a geometrical optics based numerical method for high frequency electromagnetic fields computations near fold caustics part i this paper presents an eulerian numerical method for the computation of a bi valued solution of hamilton jacobi type equation in a particular geometric setting more precisely we consider high frequency electromagnetic fields in the vicinity of fold caustics

order allocation and procurement transport planning in apparel supply chain a utility based possibilistic flexible programming approach abstract the purpose of this paper is to study the integrated decisions of the physical supply channel on the global scale including the supplier selection order allocation and transportation planning under uncertainty in detail this study addresses the supply decision making problem in a multi source multi product and multi mode transportation in accordance with the price discounts to this end a multi objective mixed integer linear programming model is developed to jointly determine the best suppliers and purchasing quantities along with the number and type of transportation modes three important objective functions i e total logistics costs total late deliveries and total value of purchasing are optimized in our proposed mathematical model then a fuzzy multi choice goal programming model with the utility function is presented to solve the multi objective formulation a novel flexible possibilistic programming approach is proposed to cope with the epistemic uncertainty and the flexibility of constraints based on the expected value and chance constraint programming concept finally a numerical study in the apparel supply chain is carried out to show the model usefulness and the solution algorithm effectiveness

a reformulation of the conservative level set reinitialization equation for accurate and robust simulation of complex multiphase flows abstract this paper presents an accurate and robust reinitialization equation for the conservative level set that does not significantly deform stationary surfaces the compression and diffusion term of the reinitialization equation are reformulated to use a distance level set directly mapped from the conservative level set the normals are calculated using a distance level set reconstructed from the interface using a fast marching method increasing robustness and allowing the use of high order non tvd transport schemes using this new reinitialization equation we present results for canonical test cases such as zalesak s disk and spurious currents which show significant improvement a simulation of a liquid gas jet with r e 5000 is also presented to demonstrate the volume conservation properties of the method in more complex flows

the algorithmic analysis of hybrid systems we present a general framework for the formal specification and algorithmic analysis of hybrid systems a hybrid system consists of a discrete program with an analog environment we model hybrid systems as finite automata equipped with variables that evolve continuously with time according to dynamical laws for verification purposes we restrict ourselves to linear hybrid systems where all variables follow piecewise linear trajectories we provide decidability and undecidability results for classes of linear hybrid systems and we show that standard program analysis techniques can be adapted to linear hybrid systems in particular we consider symbolic model checking and minimization procedures that are based on the reachability analysis of an infinite state space the procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space we also present approximation techniques for dealing with systems for which the iterative procedures do not converge

semilinear dirichlet problem for the fractional laplacian abstract we give a general framework and results on existence representation and uniqueness of solutions to the semilinear problem for the fractional laplacian with dirichlet conditions on the complement and at the boundary of general open sets

the expected value of a function of a fuzzy variable with a continuous membership function in this paper a formula for the expected value of a function of a fuzzy variable is presented with which the exact expected value of the function of the fuzzy variable can be obtained directly the proposed formula holds provided that the function is monotonic on the assumption that the fuzzy variable has a continuous membership function furthermore some examples showing how to apply the formula are given

a fast marching like algorithm for geometrical shock dynamics we develop a new algorithm for the computation of the geometrical shock dynamics gsd model the method relies on the fast marching paradigm and enables the discrete evaluation of the first arrival time of a shock wave and its local velocity on a cartesian grid the proposed algorithm is based on a first order upwind finite difference scheme and reduces to a local nonlinear system of two equations solved by an iterative procedure reference solutions are built for a smooth radial configuration and for the 2d riemann problem the link between the gsd model and p systems is given numerical experiments demonstrate the efficiency of the scheme and its ability to handle singularities

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

three objective fuzzy chance constrained programming model for multiproject and multi item investment combination this paper presents a new fuzzy chance constrained programming model to find the solution for multiproject and multi item investment combination in investment combination problems the proposed 0 1 integer programming model has three objectives with fuzzy constraints and nsga ii is applied to solve the optimization model with a small modification of the constraint handling rule a simulation experiment illustrating the application of the proposed model is presented and pareto optimal solutions are obtained through a modified nsga ii algorithm a comparison among nsga ii pso and de shows that modified nsga ii has some advantages over pso and de

hybrid control synthesis for eventuality specifications using level set methods this paper is concerned with the extraction of controllers for hybrid systems with respect to eventuality specifications given a hybrid system modelled by a hybrid automaton and a target set of states the objective is to compute the maximal set of initial states together with the hybrid control policy such that all the trajectories of the controlled system reach the target in finite time due to the existence of set valued disturbance inputs the problem is studied in a game theoretic framework having shown that a least restrictive solution does not exist we propose a dynamic programming algorithm that computes the maximal initial set and a controller with the desired property to implement the algorithm reachable sets of pursuit evasion differential games need to be computed for that reason level set methods are employed where the boundary of the reachable set is characterized as the zero level set of a hamilton jacobi equation the procedure for the numerical extraction of the controller is presented in detail and examples illustrate the methodology finally to demonstrate the practical character of our results a control design problem in the benchmark system of the batch evaporator is considered as an eventuality synthesis problem and solved using the proposed methodology

minimax chance constrained programming models for fuzzy decision systems abstract the existing chance constrained programming for fuzzy decision systems is essentially a kind of maximax models optimistic models which maximize the maximum possible return this paper presents a spectrum of minimax models as opposed to maximax models based on chance constrained programming as well as chance constrained multi objective programming and chance constrained goal programming in which the minimax models will select the alternative that provides the best of the worst possible return finally a fuzzy simulation based genetic algorithm will be designed for solving minimax models and illustrated by some numerical examples

regularity estimates for the solution and the free boundary of the obstacle problem for the fractional laplacian we use a characterization of the fractional laplacian as a dirichlet to neumann operator for an appropriate differential equation to study its obstacle problem we write an equivalent characterization as a thin obstacle problem in this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary

time optimal control systhesis for discrete time hybrid automata in this paper the problem of time optimal control for hybrid systems with discrete time dynamics is considered the hybrid controller steers all trajectories starting from a maximal set to a given target set in minimum time we derive an algorithm that computes this maximal winning set also algorithms for the computation of level sets associated with the value function rather than the value function itself are presented we show that by solving the reachability problem for the discrete time hybrid automata we obtain the time optimal solution as well the control synthesis is subject to hard constraints on both control inputs and states for linear discrete time dynamics linear programming and quantifier elimination techniques are employed for the backward reachability analysis emphasis is given on the computation of operators for non convex sets using an extended convex hull approach a two tank example is considered in order to demonstrate the techniques of the paper

discrete time high order schemes for viscosity solutions of hamilton jacobi bellman equations a general method for constructing high order approximation schemes for hamilton jacobi bellman equations is given the method is based on a discrete version of the dynamic programming principle we prove a general convergence result for this class of approximation schemes also obtaining under more restrictive assumptions an estimate in l infty of the order of convergence and of the local truncation error the schemes can be applied in particular to the stationary linear first order equation in bbb r n we present several examples of schemes belonging to this class and with fast convergence to the solution

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

approximation based fuzzy multi objective models with expected objectives and chance constraints application to earth rock work allocation in this paper we introduce a measure me which is more suitable for real life decision making problems under fuzzy environments then we establish a general fuzzy multi objective model with expected objectives and chance constraints ecm based on the me to handle the model and obtain solutions we propose two approximation models by dividing the fuzzy feasible region using rough set theory in particular we focus on a linear ecm and several properties and two equivalent models are presented finally as an illustration we apply the proposed models and approaches to an earth rock work allocation problem at the longfeng hydropower construction project

the heat equation with a singular potential of concern is the singular problem du dt au c x 2 iz x tz x 0 u0 x and its generalizations here c 0 x g rn t 0 and and t 0 are nonnegative and not both identically zero there is a dimension dependent constant c n such that the problem has no solution for c ct n for c s ct a necessary and sufficient conditions are found for and u0 so that a nonnegative solution exists

minimax resource allocation problems optimization and parametric analysis abstract we consider a linear minimax resource allocation problem with single variable terms in the objective function and multiple knapsack type resource constraints all variables are continuous and nonnegative efficient algorithms for such large scale problems have been developed by luss and smith and by tang this paper describes an enhanced algorithm that provides a more efficient search for the optimal solution further we develop post optimization schemes and parametric analysis that are employed once an optimal solution for the original minimax problem is obtained post optimization provides a perturbed optimal solution under a specified change in the data whereas parametric analysis provides a continuum of optimal solutions when some data elements are changed over a given interval

ellipsoidal techniques for reachability analysis internal approximation for the reach tube of a linear time varying system with ellipsoidal bounds on the control variable consider the following approximation problem find a tight ellipsoid valued tube inside the reach tube that touches it along any prespecified smooth curve on the boundary we construct this ellipsoidal tube and show that if the given curve is itself a system trajectory the tube can be calculated recursively with minimum computational burden

a novel multi stage possibilistic stochastic programming approach with an application in relief distribution planning proposing a novel multi stage possibilistic stochastic programming approach considering fuzzy probabilities in the scenario tree s arcs accounting for deep uncertainty of sdps at the early stages of the scenario tree through random fuzzy variables providing a real post disaster relief distribution planning case study in this paper a novel multi stage possibilistic stochastic programming mspsp approach is developed at the early stages there is little information on how to pursue mspsp the optimal decision while in the course of time new series of information become unfolded which further necessitate the model to be updated compared to other competent uncertainty programming approaches i e the classical two stage stochastic programming tssp and multi stage stochastic programming mssp and enhanced versions of tssp and mssp approaches the proposed mspsp method relaxes the subjectively setting the deterministic occurrence probabilities and allows possible perturbation in their values as fuzzy probabilities it further enables these values to be updated so that the updated values do not conflict with each other and their summation does not exceed one also given the existence of several sources of uncertainty and the deep level of uncertainty in the early stages the scenario dependent variables at such stages are treated as random fuzzy variables finally it takes into account the effect of unfolded information in an on going fashion in the course of time applicability of the proposed approach is tested on a real case study for the post disaster relief distribution planning in tehran finally useful managerial insights are provided through conducting several sensitivity analyses

an eulerian approach for computing the finite time lyapunov exponent we propose efficient eulerian methods for approximating the finite time lyapunov exponent ftle the idea is to compute the related flow map using the level set method and the liouville equation there are several advantages of the proposed approach unlike the usual lagrangian type computations the resulting method requires the velocity field defined only at discrete locations no interpolation of the velocity field is needed also the method automatically stops a particle trajectory in the case when the ray hits the boundary of the computational domain the computational complexity of the algorithm is o dx d 1 with d the dimension of the physical space since there are the same number of mesh points in the x t space the computational complexity of the proposed eulerian approach is optimal in the sense that each grid point is visited for only o 1 time we also extend the algorithm to compute the ftle on a co dimension one manifold the resulting algorithm does not require computation on any local coordinate system and is simple to implement even for an evolving manifold

supervisory control of hybrid systems based on model abstraction and guided search abstract this paper addresses the task of computing supervisory controllers by which hybrid systems with nonlinear continuous dynamics are driven into goal sets while safety specifications are met for this class of systems the conservatively approximative determination of reachable states is an important but also a computationally expensive step of the controller synthesis this contribution proposes a technique aiming at reducing the reach set computation by using abstract models and guided search for a discrete abstraction of the hybrid model candidate paths are determined as possible controlled evolutions which fulfill the given specifications a validation scheme comprising three different techniques is applied to determine whether the candidate path represents a feasible control strategy for the hybrid system if the specification is violated the abstract model is refined according to the validation result the iterative application of the determination of candidate paths the path validation and the model refinement steers the search for a control strategy such that often only a relatively small part of the reachable state space has to be explored the synthesis procedure is illustrated for two examples

on fractional multi singular schrodinger operators positivity and localization of binding abstract in this work we investigate positivity properties of nonlocal schrodinger type operators driven by the fractional laplacian with multipolar critical and locally homogeneous potentials on one hand we develop a criterion that links the positivity of the spectrum of such operators with the existence of certain positive supersolutions while on the other hand we study the localization of binding for this kind of potentials combining these two tools and performing an inductive procedure on the number of poles we establish necessary and sufficient conditions for the existence of a configuration of poles that ensures the positivity of the corresponding schrodinger operator

reachability and optimal control for linear hybrid automata a quantifier elimination approach this paper considers an optimal control problem for linear hybrid automata lha first we present a controller synthesis algorithm based on reachability analysis the algorithm computes the maximal initial set from which the controller drives the system to a given target set it is shown that using quantifier elimination qe an under approximation of the maximal reachable set can be derived next a weighted time optimal control problem is solved by transforming it into a constrained optimization problem whose constraints are a set of inequalities with quantifiers quantifier elimination qe techniques are employed in order to derive the quantifier free inequalities that are shown to be linear thus the optimal cost is obtained using linear programming for any state belonging to the maximal initial set the optimal switching times and the optimal continuous control inputs are computed these are used in order to derive a hybrid controller which is optimal with respect to the cost function our results are applied to an air traffic management example which is of practical interest

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

a unified approach to improved l p hardy inequalities with best constants we present a unified approach to improved l p hardy inequalities in r n we consider hardy potentials that involve either the distance from a point or the distance from the boundary or even the intermediate case where the distance is taken from a surface of codimension 1 k n in our main result we add to the right hand side of the classical hardy inequality a weighted l p norm with optimal weight and best constant we also prove nonhomogeneous improved hardy inequalities where the right hand side involves weighted l q norms q p

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

positive solutions of nonlinear problems involving the square root of the laplacian abstract we consider nonlinear elliptic problems involving a nonlocal operator the square root of the laplacian in a bounded domain with zero dirichlet boundary conditions for positive solutions to problems with power nonlinearities we establish existence and regularity results as well as a priori estimates of gidas spruck type in addition among other results we prove a symmetry theorem of gidas ni nirenberg type

regularity of the obstacle problem for a fractional power of the laplace operator given a function and s 0 1 we will study the solutions of the following obstacle problem u in r n s u 0i nr n s u x 0 for those x such that u x x lim x u x 0 we show that when is c 1 s or smoother the solution u is in the space c 1 for every s in the case where the contact set u is convex we prove the optimal regularity result u c 1 s when is only c 1 for a s we prove that our solution u is c 1 for every c 2006 wiley periodicals inc

mean variance skewness model for portfolio selection with fuzzy returns numerous empirical studies show that portfolio returns are generally asymmetric and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same in order to measure the asymmetry of fuzzy portfolio return a concept of skewness is defined as the third central moment in this paper and its mathematical properties are studied as an extension of the fuzzy mean variance model a mean variance skewness model is presented and the corresponding variations are also considered in order to solve the proposed models a genetic algorithm integrating fuzzy simulation is designed finally several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm

semilinear elliptic equations for the fractional laplacian with hardy potential abstract in this paper we study existence and nonexistence of nonnegative distributional solutions for a class of semilinear fractional elliptic equations involving the hardy potential

impulse differential inclusions a viability approach to hybrid systems impulse differential inclusions are introduced as a framework for modeling hybrid phenomena connections to standard problems in the area of hybrid systems are discussed conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion for sets that violate these conditions methods are developed for approximating their viability and invariance kernels that is the largest subset that is viable or invariant under the action of the impulse differential inclusion the results are demonstrated on examples

unconditionally stable methods for hamilton jacobi equations we present new numerical methods for constructing approximate solutions to the cauchy problem for hamilton jacobi equations of the form ut h dxu 0 the methods are based on dimensional splitting and front tracking for solving the associated non strictly hyperbolic system of conservation laws pt dx h p 0 where p dx u in particular our methods depend heavily on a front tracking method for one dimensional scalar conservation laws with discontinuous coefficients the proposed methods are unconditionally stable in the sense that the time step is not limited by the space discretization and they can be viewed as large time step godunov type or front tracking methods we present several numerical examples illustrating the main features of the proposed methods we also compare our methods with several methods from the literature

portfolio selection under different attitudes in fuzzy environment abstract this paper studies stock portfolio selection problem based on varying conservative neutral aggressive attitudes the return rates of stocks are characterized by fuzzy variables the pareto optimal solutions are obtained by maximizing the return and minimizing the risk subject to constraints of transaction cost and value at risk since investors with different attitudes may have different understanding of the likelihoods of occurrence measure me with the ability of reflecting varying conservative neutral aggressive attitudes is adopted based on me the expected value of fuzzy return and the lower absolute deviation are used to quantify the return and risk levels of a portfolio respectively then the constraint method is employed to obtain the efficient frontier finally an empirical study is carried out using the data of 10 stocks in chinese stock market sensitivity comparisons are conducted to demonstrate the effectiveness of the proposed model the results show that different frontiers can be obtained under different attitudes confidence levels and values at risk

a uniformly second order fast sweeping method for eikonal equations a uniformly second order method with a local solver based on the piecewise linear discontinuous galerkin formulation is introduced to solve the eikonal equation with dirichlet boundary conditions the method utilizes an interesting phenomenon referred as the superconvergence phenomenon that the numerical solution of monotone upwind schemes for the eikonal equation is first order accurate on both its value and gradient when the solution is smooth this phenomenon greatly simplifies the local solver based on the discontinuous galerkin formulation by reducing its local degrees of freedom from two 1 d or three 2 d or four 3 d to one with the information of the gradient frozen when considering the eikonal equation with point source conditions we further utilize a factorization approach to resolve the source singularities of the eikonal by decomposing it into two parts either multiplicatively or additively one part is known and captures the source singularities the other part serves as a correction term that is differentiable at the sources and satisfies the factored eikonal equations we extend the second order method to solve the factored eikonal equations to compute the correction term with second order accuracy then recover the eikonal with second order accuracy numerical examples are presented to demonstrate the performance of the method

computation of nonclassical solutions to hamilton jacobi problems this paper is devoted to the construction of numerical methods for the approximation of nonclassical solutions to multidimensional hamilton jacobi equations for both scalar and vectorial problems recent theoretical results have yielded existence of solutions in many cases for which the usual viscosity approach was ill suited or not applicable the selection criterion used here is based on a viscoelasticity capillarity approach common in solid mechanics numerical methods adapted to this framework are built consistency of the model equation with the given selection criterion is essential it is achieved here through the use of high order finite difference schemes by considering applications to potential well problems the convergence of the methods are investigated

fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production optimizing the charge in secondary steel production is challenging because the chemical composition of the scrap is highly uncertain the uncertainty can cause a considerable risk of the scrap mix failing to satisfy the composition requirements for the final product in this paper we represent the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure consequently the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem since the constraints of the model mainly address the specification of the product the crisp equivalent of the fuzzy constraints should be less relaxed than that purely based on the concept of soft constraints based on the application context we adopt a strengthened version of soft constraints to interpret fuzzy constraints and form a crisp model with consistent and compact constraints for solution simulation results based on realistic data show that the failure risk can be managed by proper combination of aspiration levels and confidence factors for defining fuzzy numbers there is a tradeoff between failure risk and material cost the presented approach applies also for other scrap based production processes