a second wronskian formulation of the boussinesq equation a wronskian formulation leading to rational solutions is presented for the boussinesq equation it involves third order linear partial differential equations whose representative systems are systematically solved the resulting solutions formulas provide a direct but powerful approach for constructing rational solutions positon solutions and complexiton solutions to the boussinesq equation various examples of exact solutions of those three kinds are computed the newly presented wronskian formulation is different from the one previously presented by li et al which does not yield rational solutions

fuzzy linear programming and applications abstract this paper presents a survey on methods for solving fuzzy linear programs first lp models with soft constraints are discussed then lp problems in which coefficients of constraints and or of the objective function may be fuzzy are outlined pivotal questions are the interpretation of the inequality relation in fuzzy constraints and the meaning of fuzzy objectives in addition to the commonly applied extended addition based on the min operator and used for the aggregation of the left hand sides of fuzzy constraints and fuzzy objectives a more flexible procedure based on yager s parametrized t norm t p is presented finally practical applications of fuzzy linear programs are listed

on lie gradings ii abstract to obtain fine gradings of gl n c it is necessary to study maximal abelian subgroups mad subgroups of diagonizable automorphisms in a ut gl n c we described two finite sets h n and k n such that each mad subgroup consisting only from inner automorphisms is conjugated to some element of h n and each mad subgroup containing at least one outer automorphism is conjugated to some element of k n using these results concerning k n we then easily find all mad subgroups in a ut o n c for n 8 and in a ut sp 2n c

random fuzzy dependent chance programming and its hybrid intelligent algorithm abstract a fuzzy random variable is a measurable function from a probability space to a collection of fuzzy sets while a random fuzzy variable is a function from a collection of random variables to 0 1 this paper provides a spectrum of random fuzzy dependent chance programming in which the underlying philosophy is based on selecting the decision with maximal chance to meet the event in order to speed up the solution process we train a neural network to approximate chance functions based on the training data generated by the random fuzzy simulation finally we integrate random fuzzy simulation neural network and genetic algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving random fuzzy dependent chance programming models and illustrate its effectiveness by some numerical examples

deformations and contractions of lie algebras in this contributed presentation we discuss and compare the mutually opposite procedures of deformations and contractions of lie algebras we suggest that with approp riate combinations of both procedures one may construct new lie algebras we first discuss low dimensional lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation the converse is not true in general also we note that some lie algebras belonging to parameterized families are singled out by the irreversibility of defor mations and contractions after reminding that global deformations of the witt virasoro and affine kac moody algebras allow one to retrieve lie algebras of krichever novikov type we contract the latter to find new infinite dimensional lie algebras

a numerical study of the 3 periodic wave solutions to kdv type equations abstract in this paper by using the direct method of calculating periodic wave solutions proposed by akira nakamura we present a numerical process to calculate the 3 periodic wave solutions to several kdv type equations the korteweg de vries equation the sawada koterra equation the boussinesq equation the ito equation the hietarinta equation and the 2 1 dimensional kadomtsev petviashvili equation some detailed numerical examples are given to show the existence of the three periodic wave solutions numerically

universality in fully developed turbulence we extend the numerical simulations of she et al phys rev lett 70 3251 1993 of highly turbulent flow with 15 taylor reynolds numbers re lambda 200 up to re lambda approx equals 45 000 employing a reduced wave vector set method introduced earlier to approximately solve the navier stokes equation first also for these extremely high reynolds numbers re lambda the energy spectra as well as the higher moments when scaled by the spectral intensity at the wave number kp of peak dissipation can be described by one universal function of k kp for all re lambda second the k space inertial subrange scaling exponents zeta m of this universal function are in agreement with the 1941 kolmogorov theory the better the larger re lambda is as is the re lambda dependence of kp only around kp viscous damping leads to a slight energy pileup in the spectra as in the experimental data bottleneck phenomenon

contractions of low dimensional lie algebras theoretical background of continuous contractions of finite dimensional lie algebras is rigorously formulated and developed in particular known necessary criteria of contractions are collected and new criteria are proposed a number of requisite invariant and semi invariant quantities are calculated for wide classes of lie algebras including all low dimensional lie algebras an algorithm that allows one to handle one parametric contractions is presented and applied to low dimensional lie algebras as a result all one parametric continuous contractions for both the complex and real lie algebras of dimensions not greater than 4 are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases levels and colevels of low dimensional lie algebras are discussed in detail properties of multiparametric and repeated contractions are also investigated

graded contractions of the affine lie algebra a1 1 its representations and tensor products and an application to the branching rule a1 1 contains implies a1 1 we describe all contractions of the affine kac moody algebra a1 1 which preserve various gradings by the cyclic groups z2 and z3 as well as a grading by z2 z3 together with the contractions of simultaneously graded representations of a1 1 and their tensor products an application is given to the branching rules for a1 1 contains implies a1 1 for a number of distinct embeddings each associated with a particular grading

a systematic approach to the soliton equations of a discrete eigenvalue problem the ablowitz ladik al problem is a linear vector difference equation whose isospectral flow equations include several important soliton equations e g the discrete nonlinear schrodinger equation iqn qn 1 2qn qn 1 qn 2 qn 1 qn 1 there is an established procedure for describing the soliton hierarchy of the more familiar akns ablowitz kaup newell and segur problem it is based on the notion of a generator for the hierarchy in this paper the soliton equations of the al hierarchy are described and characterized by a generator pair a new continuous spectral problem is introduced and the akns hierarchy is embedded in its hierarchy as a specialization

an extension to possibilistic linear programming abstract this paper proposes an extension to the solution of possibilistic linear programming problems with fuzzy number parameters introduced by buckley fuzzy sets and systems31 1989 329 341 the method relies on cuts of the fuzzy number parameters to generate a succession of pairs of classical linear programs the solutions of these linear programs produce a convex possibility distribution of the optimal objective values with the corresponding levels of the decision variables the approach is illustrated with an imprecise water quality management problem

graded contractions of the gell mann graded sl 3 c the gell mann grading one of the four gradings of sl 3 c that cannot be further refined is considered as the initial grading for the graded contraction procedure using the symmetries of the gell mann grading the system of contraction equations is reduced and solved each non trivial solution of this system determines a lie algebra which is not isomorphic to the original algebra sl 3 c the resulting 53 contracted algebras are divided into two classes the first is represented by the algebras which are also continuous inonu wigner contractions the second is formed by the discrete graded contractions

contractions from grading we note that large classes of contractions of algebras that arise in physics can be understood purely algebraically via identifying appropriate zm gradings and their generalizations on the parent algebra this includes various types of flat space carroll limits of finite and infinite dimensional a ds algebras as well as galilean and galilean conformal algebras our observations can be regarded as providing a natural context for the grassmann approach of krishnan et al j high energy phys 2014 3 36 we also introduce a related notion which we call partial grading that arises naturally in this context

interactive decision making in fuzzy linear optimization problems abstract this paper presents an interactive method for solving a multi criteria linear program where coefficients of the objective functions and or of the constraints are known exactly but imprecisely assuming fuzzy aspiration levels for each of the goals and basing on a comparison of flat fuzzy numbers the original fuzzy problem is transformed into a crisp satisfactory model to determine a suitable compromise solution we will maximize the minimum of the surpluses over the aspiration levels this induces a problem with a nonlinear objective function which is equivalent to a linear program

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

fuzzy stochastic linear programming survey and future research directions in many real life problems one has to base decision on information which is both fuzzily imprecise and probabilistically uncertain although consistency indexes providing a union nexus between possibilistic and probabilistic representation of uncertainty exist there are no reliable transformations between them this calls for new paradigms for incorporating the two kinds of uncertainty into mathematical models fuzzy stochastic linear programming is an attempt to fulfill this need it deals with modelling and problem solving issues related to situations where randomness and fuzziness co occur in a linear programming framework in this paper we provide a survey of the essential elements methods and algorithms for this class of linear programming problems along with promising research directions being a survey the paper includes many references to both give due credit to results in the field and to help readers obtain more detailed information on issues of interest

soliton and antisoliton interactions in the good boussinesq equation the solitary wave interaction mechanism for the good boussinesq equation is investigated and found to be far more complicated than was previously thought three salient features are that solitary waves only exist for a finite range of velocities that large solitons can turn into so called antisolitons and that it is possible for solitons to merge and split small solitons however appear to be stable the existence of a potential well is linked to the different behaviors observed between small and large initial conditions

on the problem of possibilistic optimization abstract this paper is a continuation on the author s investigation on possibilistic optimization problems which are considered from general methodological positions of possibility theory and managing uncertainty as well to tackle optimization tasks under uncertainty a calculus for possibilities is developed leading to classic and interval valued optimization

fuzzy and stochastic programming abstract fuzzy mathematical programming is considered on the basis of the concept of fuzzy variable 5 that is one of the most complete patterns of fuziness statements of problems under consideration are analogous to those in stochastic programming equivalent precise analogues are derived for these problems the relationship between fuzzy programming and stochastic programming is determined

measuring efficiency by a fuzzy statistical approach methods of measuring economic efficiency of input output systems by employing a fuzzy statistical approach are explored here in the context of the recent technique of data envelopment analysis which utilizes a nonparametric approach to measure efficiency three applied fuzzy measures are illustrated here e g fuzzy linear programs fuzzy linear regressions and finally the fuzzy entropy measures in the context of a two person game theory model

a fuzzy systems approach in data envelopment analysis abstract the use of fuzzy set theoretic measures is explored here in the context of data envelopment analysis which utilizes a nonparametric approach to measure efficiency three types of fuzzy statics are employed here e g fuzzy mathematical programme fuzzy regression and fuzzy entropy to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is inexact and imprecise

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

water quality management with imprecise information abstract the application of fuzzy set and possibility theories for the representation of imprecise information in water quality management problems is investigated imprecision is associated with fuzziness which is non statistical in nature and refers to the absence of sharp boundaries in the information imprecise parameters in water quality decision making can be represented by possibility distributions defining maximum achievable probabilities the corresponding possibilistic programming problem is viewed as an alternative to the stochastic one where the parameters are modeled as fuzzy variables instead of random variables the possibilistic problem can be solved through a succession of classical linear programs the resulting possibility distributions of the objective value provide a possibilistic assessment of the risk based on possibility levels

a class of fuzzy random optimization expected value models fuzzy random variable is a measurable mapping from a probability space to a collection of fuzzy variables this concept may be regard as an extension of both random variable and fuzzy variable in this paper the linearity of a scalar value expected value operator of fuzzy random variable is discussed and a fuzzy random simulation approach is suggested to evaluate the expected value of a fuzzy random variable in addition three types of fuzzy random expected value models are presented to model fuzzy random decision systems moreover a hybrid intelligent algorithm which incorporates simulation neural network and genetic algorithm is designed in order to solve general fuzzy random expected value models at the end of this paper the effectiveness of this algorithm is showed via three numerical examples

fuzzy random chance constrained programming by fuzzy random programming we mean the optimization theory dealing with fuzzy random decision problems this paper presents a new concept of chance of fuzzy random events and constructs a general framework of fuzzy random chance constrained programming we also design a spectrum of fuzzy random simulations for computing uncertain functions arising in the area of fuzzy random programming to speed up the process of handling uncertain functions we train a neural network to approximate uncertain functions based on the training data generated by fuzzy random simulation finally we integrate the fuzzy random simulation neural network and genetic algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving fuzzy random programming models and illustrate its effectiveness by some numerical examples

a general concept for solving linear multicriteria programming problems with crisp fuzzy or stochastic values for modelling imprecise data the literature offers two different methods either the use of probability distributions or the use of fuzzy sets in our opinion these two concepts should be used in parallel or in combination dependent on the real situation moreover in many economic problems the well known probabilistic or fuzzy solution procedures are not suitable because the stochastic variables do not have a simple classical distribution and the fuzzy values are not fuzzy intervals for example in case of investment problems the coefficients may often be described by means of more complex distributions or more general fuzzy sets in this case we propose to distinguish several scenarios and to describe the parameters of the different scenarios by fuzzy intervals for solving such stochastic linear programs with fuzzy parameters we propose a new method which retains the original objective functions dependent on the different states of nature it is based on the integrated chance constrained program introduced by klein haneveld on integrated chance constraints in gargnano ed stochastic programming springer berlin 1986 pp 194 209 and the interactive solution process fulpal see rommelfanger fuzzy decision support systeme entscheiden bei unscharfe second ed springer berlin heidelberg 1994 fulpal an interactive method for solving multiobjective fuzzy linear programming problems in r slowinski j teghem eds stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty reidel publishing company dordrecht 1990 pp 279 299 fulpal 2 0 an interactive algorithm for solving multicriteria fuzzy linear programs controlled by aspiration levels in d scheigert ed methods of multicriteria decision theory pfalzakademie lamprecht 1995 pp 21 34 the advantages of fuzzy optimization models in practical use fuzzy optim decision making 3 2004 295 310 and rommelfanger and slowinski fuzzy linear programming with single or multiple objective functions in r slowinski ed fuzzy sets in decision analysis operations research and statistics kluwer academic publishers norwell ma 1998 pp 179 213 an extensive numerical example illustrates the efficiency and the generality of the proposed new method

modified variational iteration method for boussinesq equation this paper applies the modified variational iteration method to solve a class of nonlinear partial differential equations boussinesq equation is used as a case study to illustrate the simplicity and effectiveness of the method comparison between variational iteration method and adomian decomposition method is made

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

the kp equation with quasiperiodic initial data abstract the kadomtsev petviashvili kp equation is known to admit exact quasiperiodic solutions that can be written in terms of riemann theta functions with a finite number of phases in each solution in this paper we propose a method to solve the initial value problem for the kp equation for initial data taken from this class of quasiperiodic functions

graded contractions of affine lie algebras the method of graded contractions based on the preservation of automorphisms of finite order is applied to the affine lie algebras and their representations to yield a new class of infinite dimensional lie algebras and representations after the introduction of the horizontal and vertical gradings and the algorithm to find the horizontal toroidal gradings some general properties of the graded contractions are discussed and compared with the inonu wigner contractions the example of is discussed in detail

fuzziness and randomness in an optimization framework abstract a semi infinite approach for linear programming in the presence of fuzzy random variable coefficients is described as a byproduct a way for dealing with optimization problems including both fuzzy and random data is obtained numerical examples are provided for the sake of illustration

periodic solutions of the kdv equation in this paper we construct a large family of special solutions of the kdv equation which are periodic in x and almost periodic in t these solutions lie on n dimensional tori very likely they are dense among all solutions the special solutions are characterized variationally they minimize fn u subject to the constraints fj u aj j 1 n 1 here fj denote the remarkable sequence of conserved functionals discovered by kruskal and zabusky the above minimum problem was originally suggested by them in exploring the manifold of solutions of this minimum problem we make essential use of gardner s discovery that these functionals are in involution with respect to a suitable poisson bracket gardner greene kruskal and miura have shown that the eigenvalues of the schrodinger operator are conserved functionals if the potential is a function of t and satisfies the kdv equation in section 6 a new set of conserved quantities is constructed which serve as a link between the eigenvalues of the schrodinger operator and the fj another result in section 6 is a slight sharpening of an earlier result of the author and j moser for the special solutions constructed above all but 2n 1 eigenvalues of the schrodinger operator are double the simplest class of special solutions n 1 are cnoidal waves in an appendix m hyman describes the results of computing numerically the next simplest case n 2 these calculations show that the shape of these solutions recurs exactly after a finite time in a shifted position the theory verifies this fact

optimisation under hybrid uncertainty abstract fuzzy stochastic optimisation is emerging as a subfield of mathematical programming the disciplinary matrix of which consists of analysis of mathematical programs under fuzziness and randomness along with methods for solving them the primum movens of this paper is to describe a unifying methodological approach that is suitable for finding a satisfying solution of a mathematical program in the presence of fuzzy data and random variables properties of fuzzy random variables frvs serve as the backdrop to this approach which also lends itself better to handling mathematical programs with fuzzy random coefficients for the paper to be somewhat self contained the notion of frv is briefly discussed and a synopsis of fuzzy stochastic optimisation provided a systematically solved example aimed at illustrating the proposed approach is also included

graded contractions of bilinear invariant forms of lie algebra we introduce a new construction for bilinear invariant forms on lie algebras based on the method of graded contractions the general method is described and the z2 z3 and z2 x z2 contractions are found the results can be applied to all lie algebras and superalgebras finite or infinite dimensional which admit the chosen gradings we consider some examples contractions of the killing form toroidal contractions of sl 3 c and we briefly discuss the limit to new wess zumino witten actions

linear programming under randomness and fuzziness this paper is concerned with the use of fuzzy sets theory well suited for nuanced human behavior to extend the applicability of linear programming in a way to let both randomness and fuzziness uncertainties be taken into account a fuzzy stochastic linear programming problem is considered and ways to handle it suggested the basic idea behind our approaches is to translate the original problem in deterministic terms via tools provided by fuzzy sets theory to get a classical one some conditions for the resulting problems to be solved without extra computational effort are stressed and illustrative examples given

some comments on fuzzy variables abstract nahmias introduced the concept of a fuzzy variable as a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed in this paper we attempt to shed more light on fuzzy variables in analogy with random variables in particular we study the problem if x1 x2 xn are mutually unrelated fuzzy variables with common membership function and 1 2 n are real numbers satisfying i o for every i and i 1n i 1 when does does z i 1n ixi have the same membership function

inonu wigner contraction of kac moody algebras inonu wigner contractions of affine kac moody algebras are discussed here the sugawara construction for the contracted affine algebra exists only for a fixed value of the level k which is determined in terms of the dimension of the uncontracted part of the starting lie algebra and the quadratic casimir in the adjoint representation further contractions of the g h coset spaces are discussed and an affine translation algebra is obtained which yields a virasoro algebra via a goddard kent olive gko construction with a central charge given by dim g h

application of fuzzy sets to aggregate production planning with multiproducts and multitime periods the objective of this study is to develop a fuzzy mathematical programming method to solve aggregate production planning app decision problems that involve multiproducts and multitime periods in a fuzzy environment the fuzzy app model that is developed here attempts to minimize total cost with respect to inventory carrying levels available labor levels machine capacity and warehouse space and the constraint of available budget the proposed app method evaluates monetary interest of related operating cost categories and provides greater computational efficiency and flexibility by adopting triangular fuzzy numbers and piecewise linear membership functions to represent both imprecise data and fuzzy goals the actual performance of an industrial company was used to demonstrate the feasibility of applying the proposed method to real world app decisions the proposed method yields an efficient solution and presents overall decision maker satisfaction with the given goal values this paper also presents several significant management implications that are related to the practical application of the proposed method

on fuzzy stochastic optimization abstract this paper extends the applicability of optimization models to situations where both fuzzy and random data are in the state of affairs the major mathematical tool used to this end is the concept of fuzzy random variables which provides a synergistic way for dealing with the two kinds of imprecision the extension principle is canonically extended to fuzzy random variables and exploited to derive a way for handling robust fuzzy stochastic mathematical programming problems finally we provide some possible avenues for further fruitful developments in this field

discrete and continuous graded contractions of representations of lie algebras simultaneous grading of lie algebras and their representation spaces is used to develop a new theory of grading preserving contractions of representations of all lie algebras admitting the chosen grading the theory is completely different from the traditional ways of contracting representations the graded contractions fall naturally into two classes discrete and continuous ones related respectively to 2 cocycles and coboundaries of the grading group

principal agent problem in a fuzzy environment this paper studies implementation of a classical principal agent problem in which the agents characteristics are supposed to be unknown to the principal it is reasonable for us to employ fuzzy variables to denote these hidden characteristics since generally they are fuzzy by nature a fuzzy expected value model which aims to maximize the utility function of the principal under the incentive constraints is developed from the principal s point of view pontryagin maximum principle is adopted in this paper to find the optimal solutions to the fuzzy expected value model

portfolio selection problems with random fuzzy variable returns this paper considers several portfolio selection problems including probabilistic future returns with ambiguous expected returns assumed as random fuzzy variables random fuzzy portfolio selection problems are formulated as nonlinear programming problems based on both stochastic and fuzzy programming approaches since there is no efficient solution method to solve these problems directly main problems are transformed into equivalent deterministic quadratic programming problems using probabilistic chance constraints possibility measure and fuzzy goals and their efficient solution methods to find a global optimal solution of each problem is constructed furthermore numerical examples of portfolio selection problems are provided to illustrate our proposed models and solution methods compared with several previous basic models and to show that our proposed model is a versatile model to be applicable to various unexpected conditions

a new technique of using homotopy analysis method for second order nonlinear differential equations abstract in this paper a new technique of homotopy analysis method nham is proposed for solving second order nonlinear differential equations this method improves the convergence of the series solution eliminates the unneeded terms and reduces time consuming in the standard homotopy analysis method ham the proposed provides an approximate solution by rewriting the second order nonlinear differential equation in the form of two first order differential equations the solution of these two differential equations is obtained as a power series solution this scheme is tested on four non linear exactly solvable differential equations three of the examples are initial value problems and the fourth is boundary value problem the results demonstrate reliability and efficiency of the algorithm developed

an a posteriori kam theorem for whiskered tori in hamiltonian partial differential equations with applications to some ill posed equations the goal of this paper is to develop a kam theory for tori with hyperbolic directions which applies to hamiltonian partial differential equations even to some ill posed ones the main result has an a posteriori format that is we show that if there is an approximate solution of an invariance equation which also satisfies some non degeneracy conditions then there is a true solution nearby this allows besides dealing with the quasi integrable case for the validation of numerical computations or formal perturbative expansions as well as for obtaining quasi periodic solutions in degenerate situations the a posteriori format also has other automatic consequences smooth dependence on parameters bootstrap of regularity etc we emphasize that the non degeneracy conditions required are just quantities evaluated on the approximate solution no global assumptions on the system such as twist hence they are readily verifiable in perturbation expansions we will pay attention to the quantitative relations between the sizes of the approximation and the non degeneracy conditions this will allow us to prove what experts call small twist theorems the non degeneracy conditions vanishes as the perturbation goes to zero but much slower than the error of the approximation the method of proof is based on an iterative method for solving a functional equation for the parameterization of the torus expressing that the range of the parameterization admits an evolution and is invariant we also solve functional equations for bundles which imply that are invariant under the linearization the iterative method does not use transformation theory nor action angle variables the main result does not assume that the system is close to integrable more surprisingly we do not need that the equations we study define an evolution for all initial conditions and are well posed even if the systems we study do not admit solutions for all initial conditions we show that there is a systematic way to choose initial conditions on which one can define an evolution which is quasi periodic we first develop an abstract theorem then we show how this abstract result applies to some concrete examples the examples considered in this paper are the scalar boussinesq equation and the boussinesq system both are pde models that aim to describe water waves in the long wave limit for these equations we construct small amplitude time quasi periodic solutions which are even in the spatial variable the strategy for the abstract theorem is inspired by that in fontich et al electron res announc math sci 16 9 22 2009 j differ equ 246 8 3136 3213 2009 the main part of the paper is to study infinite dimensional analogues of dichotomies which applies even to ill posed equations and which is stable under addition of unbounded perturbations this requires that we assume smoothing properties we also present very detailed bounds on the change of the splittings under perturbations

singularities of the complex korteweg de vries flows on etudie le probleme isospectral de l equation de hill complexe etant donne 2g 1 valeurs propres simples dans le plan complexe trouver la classe spectrale correspondante q on considere la caracterisation de la classe isospectrale et ses sections singulieres on construit q a l aide des flots non lineaires de korteweg de vries dans c 1 les fonctions regulieres de periode 1

a possibilistic linear program is equivalent to a stochastic linear program in a special case abstract in this paper we discuss an equivalent condition between a possibilistic linear programming problem with a quadratic membership function and a stochastic linear programming problem with a multivariate normal distribution first the possibilistic linear programming problem is formulated as a usual mathematical programming problem based on maximizing the necessity measure next the stochastic linear programming problem is formulated as a usual mathematical programming problem by introducing the flexible programming approach since these two formulated programming problems are similar in their forms an equivalent condition between these problems is given lastly the equivalence is examined from a geometric viewpoint

discrete and continuous graded contractions of lie algebras and superalgebras grading preserving contractions of lie algebras and superalgebras of any type over the complex number field are defined and studied such contractions fall naturally into two classes the wigner inonu like continuous contractions and new discrete contractions a general method is described for any abelian grading semigroup and any lie algebra or superalgebra admitting such a grading all contractions preserving z2 z3 and z2 z2 gradings are found examples of these gradings and contractions for the simple lie algebra a2 affine kac moody algebra a 1 and the simple superalgebra osp 2 1 are shown

global existence of smooth solutions and stability of solitary waves for a generalized boussinesq equation certain generalizations of one of the classical boussinesq type equations u tt u xx u 2 u xx xx are considered it is shown that the initial value problem for this type of equation is always locally well posed it is also determined that the special solitary wave solutions of these equations are nonlinearly stable for a range of their phase speeds these two facts lead to the conclusion that initial data lying relatively close to a stable solitary wave evolves into a global solution of these equations this contrasts with the results of blow up obtained recently by kalantarov and ladyzhenskaya for the same type of equation and casts additional light upon the results for the original version of this class of equations obtained via inverse scattering theory by deift tomei and trubowitz