calculating some inverse linear programming problems in this paper we consider some inverse lp problems in which we need to adjust the cost coefficients of a given lp problem as less as possible so that a known feasible solution becomes the optimal one a method for solving general inverse lp problem including upper and lower bound constraints is suggested which is based on the optimality conditions for lp problems it is found that when the method is applied to inverse minimum cost flow problem or inverse assignment problem we are able to obtain strongly polynomial algorithms

a note on the null condition for quadratic nonlinear klein gordon systems in two space dimensions we consider the cauchy problem for quadratic nonlinear klein gordon systems in two space dimensions with masses satisfying the resonance relation under the null condition in the sense of j m delort d fang and r xue j funct anal 211 2004 no 2 288 323 we show the global existence of asymptotically free solutions if the initial data are sufficiently small in some weighted sobolev space our proof is based on an algebraic characterization of nonlinearities satisfying the null condition 2012 wiley periodicals inc

multiparametric linear programming support set and optimal partition invariancy traditional sensitivity and parametric analysis in linear optimization was based on preserving optimal basis interior point methods however do not converge to a basic solution vertex in general recently there appeared new techniques in sensitivity analysis which consist in preserving so called support set invariancy and optimal partition invariancy this paper reflects the renascence of sensitivity and parametric analysis and extends single parametric results to the case when there are multiple parameters in the objective function and in the right hand side of equations multiparametric approach enables us to study more complex perturbation occurring in linear programs than the simpler sensitivity analysis does we present a description of the set of admissible parameters under the mentioned invariances and compare them with the classical optimal basis concept

calculation of exact bounds for the solution set of linear interval systems abstract this paper presents some topological and graph theoretical properties of the solution set of linear algebraic systems with interval coefficients based on these properties we describe a method which in a finite number of steps either calculates exact bounds for each component of the solution set or finds a singular matrix within the interval coefficients the calculation of exact bounds of the solution set is known to be np hard our method needs p calls of a polynomial time algorithm where p is the number of nonempty intersections of the solution set with the orthants frequently due to physical or economical requirements many variables do not change the sign in those cases p is small and our method works efficiently

a numerical model for the raman amplification for laser plasma interaction in this paper we continue the study of the raman amplification initiated in m colin t colin on a quasi linear zakharov system describing laser plasma interactions differential integral equations 17 3 4 2004 297 330 we use a dispersive quasi linear system the quasi linear part is not hyperbolic and this difficulty is overcome using the dispersion we give an asymptotic result on a reduced system we then introduce a simple robust and efficient numerical scheme on the whole system that takes into account the non hyperbolicity of the quasi linear part as well as the nonlinear saturation of the raman growth the scheme is validated thanks to the asymptotic result finally we present 1 d and 2 d simulations

properties of rule interestingness measures and alternative approaches to normalization of measures we are considering properties of interestingness measures of rules induced from data these are bayesian confirmation property two properties related to the case of entailment or refutation called ex 1 and logicality l and a group of symmetry properties we propose a modification of properties ex 1 and l called weak ex 1 and weak l that deploy the concept of confirmation in its larger sense we demonstrate that properties ex 1 and l do not fully reflect such understanding of the confirmation concept and thus we propose to substitute ex 1 by weak ex 1 and l by weak l moreover we introduce four new approaches to normalization of confirmation measures in order to transform measures so that they would obtain desired properties the analysis of the results of the normalizations of the confirmation measures takes into account all considered properties we advocate for two normalized confirmation measures measure z considered in the literature and newly proposed measure a finally we provide some ideas for combining them in a single measure keeping all desirable properties

theoretical aspects of fuzzy set qualitative comparative analysis fsqca fuzzy set qualitative comparative analysis fsqca is a methodology for obtaining linguistic summarizations from data that are associated with cases it has recently been described as a collection of 13 steps 7 in this paper we focus on how to greatly speed up some of the computationally intensive steps of fsqca and show how to use the speed up equations to obtain some interesting and important properties of fsqca these properties not only provide additional understanding about fsqca but also lead to different ways to implement fsqca one of the properties is so important section 8 that unless its results are adopted when a variable is described by more than one term e g low and high fsqca will provide incorrect results

quadratic nonlinear derivative schrodinger equations part 2 in this paper we consider the local well posedness theory for the quadratic nonlinear schrodinger equation with low regularity initial data in the case when the nonlinearity contains derivatives we work in 2 1 dimensions and prove a local well posedness result for small initial data with low regularity

set theoretic methodology using fuzzy sets in rule extraction and validation consistency and coverage revisited abstract the use of set theoretic concepts of consistency and coverage and their fuzzified versions needs to be accompanied with an extension of the general non fuzzy methodology in the fuzzy context the same piece of data can provide partial evidence in favour of the existence of a given relationship and at the same time contribute to its disproof which constitutes a significant interpretation and methodological issue we point out the possible problems of the use of these measures fuzzified in direct analogy to their non fuzzy counterparts in the investigation of relationships and causality we propose two alternative fuzzifications of these measures to be used in the set theoretic framework and fuzzy set qualitative comparative analysis fsqca we also introduce novel degree of support and degree of disproof measures to handle simultaneous subset relations in this way simultaneous partial support for and disproof of a given rule by the given set of data can be analyzed in detail the suggested measures can enhance the insights needed in theory building and be widely used in research using fuzzified set theoretic methods for the assessment of the plausibility of the rules we compare the newly suggested consistency and coverage measures with standard ones and discuss their properties in practical examples

a hormander type multiplier theorem for multilinear operators abstract in this paper we prove a hormander type multiplier theorem for multilinear operators as a corollary we can weaken the regularity assumption for multilinear fourier multipliers to assure the boundedness

null structure and almost optimal local well posedness of the maxwell dirac system we uncover the full null structure of the maxwell dirac system in lorenz gauge this structure which cannot be seen in the individual compo nent equations but only when considering the system as a whole is expressed in terms of tri and quadrilinear integral forms with cancellations measured by the angles between spatial frequencies in the 3d case we prove frequency localized l 2 space time estimates for these integral forms at the scale invariant regularity up to a logarithmic loss hence we obtain almost optimal local well posedness of the system by iteration

algorithms for linear programming problems with interval objective function coefficients this paper presents three algorithms for solving linear programming problems in which some or all of the objective function coefficients are specified in terms of intervals which algorithm is applicable depends upon a the number of interval objective function coefficients b the number of nonzero objective function coefficients and c whether or not the feasible region is bounded the algorithms output all extreme points and unbounded edge directions that are multiparametrically optimal with respect to the ranges placed on the objective function coefficients the algorithms are most suitable to linear programs in which the objective function coefficients are deterministic but are likely to vary from time period to time period as for example in blending problems

sensitivity analysis in linear optimization invariant support set intervals abstract sensitivity analysis is one of the most interesting and preoccupying areas in optimization many attempts are made to investigate the problem s behavior when the input data changes usually variation occurs in the right hand side of the constraints and or the objective function coefficients degeneracy of optimal solutions causes considerable difficulties in sensitivity analysis in this paper we briefly review three types of sensitivity analysis and consider the question what is the range of the parameter where for each parameter value an optimal solution exists with exactly the same set of positive variables that the current optimal solution has this problem is coming from managerial requirements managers want to know in what range of variation of sources or prices in the market can they keep the installed production lines active and only production s levels would change

well posedness for a quadratic derivative nonlinear schrodinger system at the critical regularity abstract we consider the cauchy problem for a quadratic derivative nonlinear schrodinger system in sobolev space h s in this paper under the null condition and the mass resonance relation we prove large data local well posedness if the space dimension d 3 and s s c d 2 and s s c or d 1 and s 0 where s c is the scaling critical regularity moreover under the same assumptions we also prove small data global well posedness and scattering in h s if d 3 and s s c our proof is based on a contraction argument using the u p and v p type function spaces

inverse linear programming with interval coefficients the paper deals with the inverse linear programming problem over intervals more precisely given interval domains for the objective function coefficients and constraint coefficients of a linear program we ask for which scenario a prescribed optimal value is attained using continuity of the optimal value function under some assumptions we propose a method based on parametric linear programming techniques we study special cases when the interval coefficients are situated in the objective function and or on the right hand sides of the constraints as well as the generic case when possibly all coefficients are intervals we also compare our method with the straightforward binary search technique finally we illustrate the theory by an accompanying numerical study called matrix casino showing some approaches to designing a matrix game with a prescribed game value

sharp well posedness and ill posedness results for a quadratic non linear schrodinger equation abstract we establish that the quadratic non linear schrodinger equation iu t u xx u 2 where u r r c is locally well posed in h s r when s 1 and ill posed when s 1 previous work in c kenig g ponce l vega quadratic forms for the 1 d semilinear schrodinger equation trans amer math soc 346 1996 3323 3353 had established local well posedness for s 3 4 the local well posedness is achieved by an iteration using a modification of the standard x s b spaces the ill posedness uses an abstract and general argument relying on the high to low frequency cascade present in the non linearity and a computation of the first non linear iterate

charles ragin s fuzzy set qualitative comparative analysis fsqca used for linguistic summarizations fuzzy set qualitative comparative analysis fsqca is a methodology for obtaining linguistic summarizations from data that are associated with cases it was developed by the eminent social scientist prof charles c ragin but has as of this date not been applied by engineers or computer scientists unlike more quantitative methods that are based on correlation fsqca seeks to establish logical connections between combinations of causal conditions and an outcome the result being rules that summarize the sufficiency between subsets of all of the possible combinations of the causal conditions or their complements and the outcome the rules are connected by the word or to the output each rule is a possible path from the causal conditions to the outcome this paper for the first time explains fsqca in a very quantitative way something that is needed if engineers and computer scientists are to use fsqca

improving the modified interval linear programming method by new techniques we improve milp method proposed by zhou et al in 2009 solution region resulted from milp method is feasible and no completely optimal we propose two improved milp methods namely iilp and imilp solution region obtained through iilp and imilp methods is feasible and optimal in this study we consider interval linear programming ilp problems which are used to deal with uncertainties resulting from the range of admissible values in problem coefficients in most existing methods for solving ilp problems a part of the solution region is not feasible the solution set obtained through the modified ilp milp method is completely feasible i e it does not violate any constraints but is not completely optimal i e some points of the region are not optimal in this paper two new ilp methods and their sub models are presented these techniques improve the milp method giving a solution region that is not only completely feasible but also completely optimal

measures of rule interestingness in various perspectives of confirmation confirmation is a useful concept for assessing the impact of the premise on the conclusion of a rule induced from data interpretation of probabilistic relationships between premise and conclusion of a rule led to four mathematical formulations of confirmation called perspectives the logical equivalence of these perspectives and the resulting general definition of confirmation underline the known qualitative aspect of the concept of confirmation the quantitative aspect of confirmation is handled by definitions of particular confirmation measures in this paper we relate the qualitative and quantitative aspects by introducing a property of monotonicity of measures with respect to left and right hand side probabilities defining the perspectives this new property permits consideration of confirmation measures in association with particular perspectives we also identify several other properties that valuable confirmation measures should possess particular care is devoted to discussion of behavior of confirmation measures monotonic in different perspectives with respect to symmetry properties taking also into account two new perspectives of bayesian confirmation we also prove that confirmation measures monotonic in the six perspectives are exhaustive in the sense that their set is closed under transformations related to symmetry properties finally we verify which confirmation measures enjoy these properties

weak and strong solvability of interval linear systems of equations and inequalities abstract we consider weak and strong solvability of general interval linear systems consisting of mixed equations and inequalities with mixed free and sign restricted variables we generalize the well known weak solvability characterizations by oettli prager for equations and gerlach for inequalities to a unified framework in the same manner we extend strong solvability theorems to general interval linear systems next we propose a sufficient condition for checking strong solvability we give an application in linear programming with interval data by means of weak and strong solvability we determine limits of the optimal values for any form of the problem setting

the inverse optimal value problem this paper considers the following inverse optimization problem given a linear program a desired optimal objective value and a set of feasible cost vectors determine a cost vector such that the corresponding optimal objective value of the linear program is closest to the desired value the above problem referred here as the inverse optimal value problem is significantly different from standard inverse optimization problems that involve determining a cost vector for a linear program such that a pre specified solution vector is optimal in this paper we show that the inverse optimal value problem is np hard in general we identify conditions under which the problem reduces to a concave maximization or a concave minimization problem we provide sufficient conditions under which the associated concave minimization problem and correspondingly the inverse optimal value problem is polynomially solvable for the case when the set of feasible cost vectors is polyhedral we describe an algorithm for the inverse optimal value problem based on solving linear and bilinear programming problems some preliminary computational experience is reported

what are fuzzy rules and how to use them abstract fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in fuzzy logic however there does not exist a unique kind of fuzzy rules nor is there only one type of fuzzy logic this diversity has caused many a misunderstanding in the literature of fuzzy control the paper is a survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory it is pointed out that the interpretation of fuzzy rules dictates the way the fuzzy rules should be combined the various kinds of fuzzy rules considered in the paper gradual rules certainty rules possibility rules and others have different inference behaviors and correspond to various intended uses and applications the representation of fuzzy unless rules is briefly investigated on the basis of their intended meaning the problem of defining and checking the coherence of a block of parallel fuzzy rules is also briefly addressed this issue has been neglected in the fuzzy control literature although it looks important for validation purposes

a further study on inverse linear programming problems abstract in this paper we continue our previous study zhang and liu j comput appl math 72 1996 261 273 on inverse linear programming problems which requires us to adjust the cost coefficients of a given lp problem as less as possible so that a known feasible solution becomes the optimal one in particular we consider the cases in which the given feasible solution and one optimal solution of the lp problem are 0 1 vectors which often occur in network programming and combinatorial optimization and give very simple methods for solving this type of inverse lp problems besides instead of the commonly used l1 measure we also consider the inverse lp problems under l measure and propose solution methods

extracting easily interpreted diagnostic rules abstract diagnosis support systems are often disregarded because of their high costs complicated inference and inability to modify the knowledge base the aim of this work is to propose a method that helps to resolve these problems by extracting diagnostic rules that can be easily interpreted and verified by experts the rules can be obtained from data even if the latter are imperfect which is usual in medical databases next intuitively clear reasoning is suggested to elaborate on the diagnosis rules are focal elements in the framework of the dempster shafer theory they include fuzzy sets in their premises thus a measure of imprecision as a fuzzy membership function and a measure of uncertainty as the basic probability value are used moreover a rule selection algorithm and a rule evaluation method that prevent some of the imperfections of the existing methods are proposed particular attention is paid to the evaluation of the extracted rule set according to its reliability and clarity for a human user experimental results obtained for popular medical data sets demonstrate the advantages of the proposed approach for each data set simple and readable rule sets are determined they provide comparable or better results than the approaches published so far

multipulses of nonlinearly coupled schrodinger equations abstract the capacity of coupled nonlinear schrodinger nls equations to support multipulse solutions multibump solitary waves is investigated a detailed analysis is undertaken for a system of quadratically coupled equations that describe the phenomena of second harmonic generation and parametric wave interaction in non centrosymmetric optical materials utilising the framework of homoclinic bifurcation theory and employing a lyapunov schmidt reduction method developed by hale lin and sandstede a novel mechanism for the generation of multipulses is identified which arises from a resonant semi simple eigenvalue configuration of the linearised steady state equations conditions for the existence of multipulses as well as a description of their geometry are derived from the analysis

low level interpretability and high level interpretability a unified view of data driven interpretable fuzzy system modelling this paper aims at providing an in depth overview of designing interpretable fuzzy inference models from data within a unified framework the objective of complex system modelling is to develop reliable and understandable models for human being to get insights into complex real world systems whose first principle models are unknown because system behaviour can be described naturally as a series of linguistic rules data driven fuzzy modelling becomes an attractive and widely used paradigm for this purpose however fuzzy models constructed from data by adaptive learning algorithms usually suffer from the loss of model interpretability model accuracy and interpretability are two conflicting objectives so interpretation preservation during adaptation in data driven fuzzy system modelling is a challenging task which has received much attention in fuzzy system modelling community in order to clearly discriminate the different roles of fuzzy sets input variables and other components in achieving an interpretable fuzzy model a taxonomy of fuzzy model interpretability is first proposed in terms of low level interpretability and high level interpretability in this paper the low level interpretability of fuzzy models refers to fuzzy model interpretability achieved by optimizing the membership functions in terms of semantic criteria on fuzzy set level while the high level interpretability refers to fuzzy model interpretability obtained by dealing with the coverage completeness and consistency of the rules in terms of the criteria on fuzzy rule level some criteria for low level interpretability and high level interpretability are identified respectively different data driven fuzzy modelling techniques in the literature focusing on the interpretability issues are reviewed and discussed from the perspective of low level interpretability and high level interpretability furthermore some open problems about interpretable fuzzy models are identified and some potential new research directions on fuzzy model interpretability are also suggested

gain of regularity for semilinear schrodinger equations we discuss local existence and gain of regularity for semilinear schrodinger equations which generally cause loss of derivatives we prove our results by advanced energy estimates more precisely block diagonalization and doi s transformation together with symbol smoothing for pseudodifferential operators with nonsmooth coefficients apply to systems of schrodinger type equations in particular the sharp garding inequality for pseudodifferential operators whose coefficients are twice continuously differentiable plays a crucial role in our proof

global solutions of nonlinear hyperbolic equations for small initial data on considere des systemes quasilineaires d equations hyperboliques d ordre 2 qui sont des deformations non lineaires de l equation d onde on etudie l existence globale et le comportement asymptotique des solutions du probleme de cauchy quand la donnee initiale est suffisamment petite

quadratic forms for the 1 d semilinear schrodinger equation this paper is concerned with 1 d quadratic semilinear schr6dinger equations we study local well posedness in classical sobolev space hs of the associated initial value problem and periodic boundary value problem our main interest is to obtain the lowest value of s which guarantees the desired local well posedness result we prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered