fuzzy inventory model with two warehouses under possibility constraints a multi item inventory model with two storage facilities is developed with advertisement price and displayed inventory level dependent demand in a fuzzy environment purchase cost investment amount and storehouse capacity are imprecise the model is formulated as a single multi objective programming problem under fuzzy constraint constraints are satisfied with some pre defined necessity and the problem is solved via the goal programming method gpm when crisp equivalents of the constraints are available and by a fuzzy simulation based single multi objective genetic algorithm fsga fsmoga otherwise the model is illustrated with some numerical examples and results from different methods are compared in some particular cases

fuzzy portfolio optimization under downside risk measures this paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return we assume that the rates of returns on securities are approximated as lr fuzzy numbers of the same shape and that the expected return and risk are evaluated by interval valued means we establish the relationship between those mean interval definitions for a given fuzzy portfolio by using suitable ordering relations finally we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form

calculus for interval valued functions using generalized hukuhara derivative and applications this paper is devoted to studying differential calculus for interval valued functions by using the generalized hukuhara differentiability which is the most general concept of differentiability for interval valued functions conditions examples and counterexamples for limit continuity integrability and differentiability are given special emphasis is set to the class f t c g t where c is an interval and g is a real function of a real variable here the emphasis is placed on the fact that f and g do not necessarily share their properties underlying the extra care that must be taken into account when dealing with interval valued functions two applications of the obtained results are presented the first one determines a delta method for interval valued random elements in the second application a new procedure to obtain solutions to an interval differential equation is introduced our results are relevant to fuzzy set theory because the usual fuzzy arithmetic extension functions and mathematical analysis are done on a cuts which are intervals

numerical solution method for general interval quadratic programming abstract recently liu and wang described an interesting numerical method to a special class of interval quadratic programming where the linear term in objective function and constraints involved interval coefficients s t liu r t wang a numerical solution method to interval quadratic programming applied mathematics and computation 189 2007 1274 1281 in this paper we generalize liu and wang s method to general interval quadratic programming where all coefficients in the objective function and constraints are interval numbers although the interval quadratic programming model considered in this paper is more general the proposed method requires less computing compared with liu and wang s method numerical examples are presented to illustrate the whole idea

satisficing solutions and duality in interval and fuzzy linear programming in this paper we introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions the necessary tools for dealing with such problems in this way we show that the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems we define the concept of duality and prove the weak and strong duality theorems further we define a class of interval linear programming problems as a special subclass of flp problems and apply the previous results to this special case

generalized calabi yau manifolds and the chiral de rham complex abstract we show that the chiral de rham complex of a generalized calabi yau manifold carries n 2 supersymmetry we discuss the corresponding topological twist for this n 2 algebra we interpret this as an algebroid version of the super sugawara or kac todorov construction

strong optimal solutions of interval linear programming abstract this paper considers optimal solutions of general interval linear programming problems the new concepts of optimal solutions are introduced in a unified framework some existed optimal solution concepts of interval linear program such as weak and strong optimal solutions are special cases in this framework necessary and sufficient conditions for checking optimality are developed also the features of the proposed methods are illustrated by some examples

model evaluation for robust tracking under unknown upper bounds on perturbations and measurement noise this technical note addresses a problem of model evaluation in the framework of robust steady state tracking in the l1 setup the upper bounds on measurement noise exogenous disturbance and coprime factor perturbations in a discrete time linear time invariant siso system are assumed to be unknown for a given nominal model and a given tracking controller three different model validation tests are considered and the complexity of computing upper bounds on the worst case steady state tracking error consistent with these tests is analysed

multiobjective programming in optimization of the interval objective function abstract in this paper the mathematical programming problem whose objective function has interval coefficients is investigated to maximize the interval objective function the order relations which represent the decision maker s preference between interval profits are defined by the right limit the left limit the center and the width of an interval the maximization problem with the interval objective function is converted into a multiobjective problem using the order relations the minimization problem is also converted into a multiobjective problem using the order relations which represent the decision maker s preference between interval costs

on the elliptic genus of generalised kummer varieties borisov and libgober 2 recently proved a conjecture of dijkgraaf moore verlinde and verlinde see 6 on the elliptic genus of a hilbert scheme of points on a surface we show how their result can be used together with our work on complex genera of generalised kummer varieties 17 to deduce the following formula conjectured by kawai and yoshioka 15 on the elliptic genus of a generalised kummer variety a n of dimension 2 n 1 here is the weak jacobi form of weight 1 and index and v n is the hecke operator sending jacobi forms of index r to jacobi forms of index nr see 7

applications of homological mirror symmetry to hypergeometric systems duality conjectures abstract homological mirror symmetry for crepant resolutions of gorenstein toric singularities leads to a pair of conjectures on certain hypergeometric systems of pdes we explain these conjectures and verify them in some cases

checking strong optimality of interval linear programming with inequality constraints and nonnegative constraints this paper considers optimal solutions of interval linear programming problems in a unified framework necessary and sufficient conditions for checking a b strong optimality and a b c strong optimality of interval linear programming with inequality constraints are developed the features of the proposed methods are illustrated by some examples

interval quadratic programming for day ahead dispatch of uncertain predicted demand in this paper we propose an interval quadratic programming method for the day ahead scheduling of power generation and battery charge cycles where the prediction uncertainty of power consumption and photovoltaic power generation is described as a parameter vector lying in an interval box the interval quadratic programming is formulated as the problem of finding the tightest box i e interval hull that encloses the image of a function of the minimizer in parametric quadratic programming to solve this problem in a computationally efficient manner we take a novel approach based on a monotonicity analysis of the minimizer in the parametric quadratic programming in particular giving a tractable parameterization of the minimizer on the basis of the karush kuhn tucker condition we show that the monotonicity analysis with respect to the parameter vector can be relaxed to the sign pattern analysis of an oblique projection matrix the monotonicity of the minimizer is found to be essential in the day ahead dispatch problem where uncertain predicted demand described by a parameter vector is dispatched to power generation and battery charge cycles while the economic cost is minimized finally we verify the efficiency of the proposed method numerically using experimental and predicted data for power consumption and photovoltaic power generation

on the rigidity theorems of witten in this paper we prove the rigidity theorems predicted by witten in 1986 about the index of certain elliptic operators on manifolds with an s1 action w witten s insight was the culmination of an interesting interchange of ideas between him and hopkins landweber ochanine and stong for the detailed history we refer the reader to la the present account is essentially a reinterpretation of the second author s taubes t original proof of the theorem the senior author s contribution was solely to notice that the rather densely written arguments of the original manuscript could be formulated in terms of the well known fixed point formulae of equivariant index theory and equivariant cohomology in this context the final proof then appears in direct lineage of the atiyah hirzebruch theorem concerning the vanishing of the a genus of spin manifolds admitting a circle action a h and of the even older idea of lusztig concerning circle actions in the complex case there remains however the beautiful physics inspired novelty of connecting these techniques with elliptic function theory

projective elliptic genera and elliptic pseudodifferential genera abstract in this paper we construct for the first time the projective elliptic genera for a compact oriented manifold equipped with a projective complex vector bundle such projective elliptic genera are rational q series that have topological definition and also have analytic interpretation via the fractional index theorem in 25 without requiring spin condition we prove the modularity properties of these projective elliptic genera as an application we construct elliptic pseudodifferential genera for any elliptic pseudodifferential operator this suggests the existence of putative s 1 equivariant elliptic pseudodifferential operators on loop space whose equivariant indices are elliptic pseudodifferential genera

superconformal structures on generalized calabi yau metric manifolds we construct an embedding of two commuting copies of the n 2 superconformal vertex algebra in the space of global sections of the twisted chiral anti chiral de rham complex of a generalized calabi yau metric manifold including the case when there is a non trivial h flux and non vanishing dilaton the 4 corresponding brst charges are well defined on any generalized kahler manifold this allows one to consider the half twisted model defining thus the chiral de rham complex of a generalized kahler manifold the classical limit of this result allows one to recover the celebrated generalized kahler identities as the degree zero part of an infinite dimensional lie superalgebra attached to any generalized kahler manifold as a byproduct of our study we investigate the properties of generalized calabi yau metric manifolds in the lie algebroid setting

robust performance unknown disturbances and known fixed inputs this paper addresses the robust performance problem when the system under consideration is subjected to norm bounded time varying uncertainty different performance objectives are considered and computable bounds are obtained for the worst case performance in various norms in some important cases it is shown that these bounds are tight giving simple exact formulas for computing robust performance measures one of the important features of these formulas is that they enable the direct and exact calculation of a number of worst cast performance measures while avoiding entirely the iterations needed for computing these measures by existing methods that rely on repeated scalings and spectral radius bound evaluations

elliptic genera of singular varieties the notions of orbifold elliptic genus and elliptic genus of singular varieties are introduced and the relation between them is studied the elliptic genus of singular varieties is given in terms of a resolution of singularities and extends the elliptic genus of calabi yau hypersurfaces in fano gorenstein toric varieties introduced earlier the orbifold elliptic genus is given in terms of the fixed point sets of the action we show that the generating function for the orbifold elliptic genus ellorb x 6n p for symmetric groups 6n acting on n fold products coincides with the one proposed by r dijkgraaf g moore e verlinde and h verlinde the two notions of elliptic genera are conjectured to coincide

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

elliptic genera of symmetric products and second quantized strings in this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the n fold symmetric product m n sn of a manifold m to the partition function of a second quantized string theory on the space m s 1 the generating function of these elliptic genera is shown to be almost an automorphic form for o 3 2 z in the context of d brane dynamics this result gives a precise computation of the free energy of a gas of d strings inside a higher dimensional brane

lagrangian approach to sheaves of vertex algebras we explain how sheaves of vertex algebras are related to mathematical structures encoded by a class of lagrangians the exposition is focused on two examples the wzw model and the 1 1 supersymmetric model we conclude by showing how to construct a family of vertex algebras with base the barannikov kontsevich moduli space thus furnishing the b model moduli for witten s half twisted model

a nonlinear interval number programming method for uncertain optimization problems in this paper a method is suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints based on an order relation of interval number the uncertain objective function is transformed into two deterministic objective functions in which the robustness of design is considered through a modified possibility degree the uncertain inequality and equality constraints are changed to deterministic inequality constraints the two objective functions are converted into a single objective problem through the linear combination method and the deterministic inequality constraints are treated with the penalty function method the intergeneration projection genetic algorithm is employed to solve the finally obtained deterministic and non constraint optimization problem two numerical examples are investigated to demonstrate the effectiveness of the present method

robust steady state tracking this paper addresses the robust performance problem when the performance measure is the steady state value of an error signal necessary and sufficient conditions are derived for robust steady state tracking of fixed inputs in the presence of structured time varying uncertainty are derived these conditions are easily computable and fit well with existing conditions on stability robustness and performance robustness when the performance measure is the level of disturbance rejection using these conditions it is shown that time varying perturbations of a nominal linear time invariant plant can result in large steady state tracking errors to fixed inputs even if the nominal plant and controller give zero steady state tracking errors the derived expressions for the worst case steady state tracking error give insight into how the time variation in the plant affects tracking errors and suggest that certain transfer function norms should be minimized to reduce the effect of these perturbations on the steady state value of error signals

some results on the upper bound of optimal values in interval convex quadratic programming one of the fundamental problems in interval quadratic programming is to compute the range of optimal values for minimized problem with equality constraint computing the upper bound of the optimal values is known to be np hard one kind of the effective methods for computing the upper bound of interval quadratic programming is so called dual method based on the dual property of the problem to obtain the exact upper bound the dual methods require that the duality gap is zero however it is not an easy task to check whether this condition is true when the data may vary inside intervals in this paper we first present an easy and efficient method for checking the zero duality gap then some relations between the exact upper bound and the optimal value of the dual model considered in dual methods are discussed in detail we also report some numerical results and remarks to give an insight into the dual method s behavior

elliptic genus of phases of n 2 theories we discuss an algebro geometric description of witten s phases of n 2 theories and propose a definition of their elliptic genus provided some conditions on singularities of the phases are met for landau ginzburg phase one recovers elliptic genus of lg models proposed in physics literature in early 1990s for certain transitions between phases we derive invariance of elliptic genus from an equivariant form of mckay correspondence for elliptic genus as special cases one obtains landau giznburg calabi yau correspondence for elliptic genus of weighted homogeneous potentials as well as certain hybrid cy correspondences

necessary and sufficient conditions of some strong optimal solutions to the interval linear programming abstract this paper considers optimal solutions of general interval linear programming problems necessary and sufficient conditions of a b strong and a b c strong optimal solutions to the interval linear programming with inequality constraints are proposed the features of the proposed methods are illustrated by some examples

an eigenvector method for generating normalized interval and fuzzy weights crisp comparison matrices produce crisp weight estimates it is logical for an interval or fuzzy comparison matrix to give an interval or fuzzy weight estimate in this paper an eigenvector method em is proposed to generate interval or fuzzy weight estimate from an interval or fuzzy comparison matrix which differs from csutora and buckley s lambda max method in several aspects first the proposed em produces a normalized interval or fuzzy eigenvector weight estimate through the solution of a linear programming model while the lambda max method gives a series of nonnormalized interval eigenvector weight estimate through an iterative solution process next the em directly solves the principal right eigenvector of an interval or fuzzy comparison matrix while the lambda max method needs transforming a fuzzy comparison matrix into a series of interval comparison matrices using a level sets and the extension principle and therefore needs the solution of a series of eigenvalue problems finally the lambda max method needs the help of the principal right eigenvector of a crisp comparison matrix to determine the final interval weights while the em has no such requirement it is also found that not all interval or fuzzy comparison matrices can generate normalized interval or fuzzy eigenvector weights situations where the em is inapplicable are analyzed and the aggregation of local interval or fuzzy weights into global interval or fuzzy weights is also discussed three numerical examples including a hierarchical structure decision making problem are examined using the em to demonstrate its applications

a goal programming method for obtaining interval weights from an interval comparison matrix crisp comparison matrices lead to crisp weight vectors being generated accordingly an interval comparison matrix should give an interval weight estimate in this paper a goal programming gp method is proposed to obtain interval weights from an interval comparison matrix which can be either consistent or inconsistent the interval weights are assumed to be normalized and can be derived from a gp model at a time the proposed gp method is also applicable to crisp comparison matrices comparisons with an interval regression analysis method are also made three numerical examples including a multiple criteria decision making mcdm problem with a hierarchical structure are examined to show the potential applications of the proposed gp method

genetic algorithm for asymmetric traveling salesman problem with imprecise travel times this paper presents a variant of the asymmetric traveling salesman problem atsp in which the traveling time between each pair of cities is represented by an interval of values wherein the actual travel time is expected to lie instead of a fixed deterministic value as in the classical atsp here the atsp with interval objective is formulated using the usual interval arithmetic to solve the interval atsp i atsp a genetic algorithm with interval valued fitness function is proposed for this purpose the existing revised definition of order relations between interval numbers for the case of pessimistic decision making is used the proposed algorithm is based on a previously published work and includes some new features of the basic genetic operators to analyze the performance and effectiveness of the proposed algorithm and different genetic operators computational studies of the proposed algorithm on some randomly generated test problems are reported

interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming abstract the modern trend in operations research methodology deserves modelling of all relevant vague or uncertain information involved in a real decision problem generally vagueness is modelled by a fuzzy approach and uncertainty by a stochastic approach in some cases a decision maker may prefer using interval numbers as coefficients of an inexact relationship as a coefficient an interval assumes an extent of tolerance or a region that the parameter can possibly take however its use in the optimization problems is not much attended as it merits this paper defines an interval linear programming problem as an extension of the classical linear programming problem to an inexact environment on the basis of a comparative study on ordering interval numbers inequality constraints involving interval coefficients are reduced in their satisfactory crisp equivalent forms and a satisfactory solution of the problem is defined a numerical example is also given

chiral de rham complex we define natural sheaves of vertex algebras over smooth manifolds which may be regarded as semi infinite de rham complexes of certain d modules over the loop spaces for calabi yau manifolds they admit n 2 supersymmetry connection with wakimoto modules is discussed

l1 robust performance of discrete time systems with structured uncertainty abstract this paper addresses the robust performance problem when a linear time invariant system is subjected to both norm bounded time varying uncertainty and worst case external bounded input the tightest upper bounds for steady state robust performance measures over classes of finite memory and fading memory perturbations are computed in the regulation and tracking problems since the classes of finite memory and fading memory perturbations are inappropriate to the purposes of model validation and adaptive control approximating subclasses of bounded memory perturbations and perturbations with exponentially decreasing impulse responses are considered it is shown that the robust performance bounds obtained are nonconservative in the case of bounded memory perturbations the worst case steady state robust performance measures for siso system under coprime factor perturbations are computed for illustration

a new multi section based technique for constrained optimization problems with interval valued objective function in this paper an efficient optimization technique is proposed for constrained optimization problems with interval valued objective function at first the significance of interval valued objective function and the meaning of the interval valued solution of the proposed problem have been explained with graphical interpretation generally this type of problems has infinitely many compromise solutions the aim of this approach is to obtain one of such solutions with higher accuracy and lower computational cost the proposed technique is mainly based on the splitting criterion of the accepted prescribed search region calculation of the interval inclusion functions and the selection of subregion depending on the modified interval order relations in the context of the decision makers point of view novel interval oriented constraint satisfaction rules are used for non interval equality and inequality constraints clearly the proposed technique is nothing but an imitation of well known interval analysis based branch and bound b b optimization approach the modified multi section division criterion with some new interval oriented constraint satisfaction rules for non interval valued equality and inequality constraints and some novel interval order relations in the context of the decision makers point of view have been applied to increase the efficiency of the proposed algorithm finally the technique is applied for solving some test problems and the results are compared with the same obtained from the existing methods

a sequential nonlinear interval number programming method for uncertain structures a sequential nonlinear interval number programming sninp method is suggested to deal with the uncertain optimization problems a general uncertain optimization model is investigated in which the objective function and constraints are both nonlinear and uncertain a nonlinear interval number programming ninp method is employed to transform the uncertain optimization problem into a deterministic two objective optimization problem then using the linear combination method and the constraint penalty function method a deterministic single objective and non constraint optimization problem is formulated in terms of a penalty function combining this ninp method with a modified approximation management framework amf an efficient sninp method is then constructed at each iterative step an approximation optimization problem is created based on the latin hypercube design lhd and the quadratic polynomial response surface approximation rsa and it can then be solved by the ninp method efficiently the trust region method is used to manage the sequence of the approximation optimization problems based on a reliability index an efficient method is suggested to calculate the actual penalty function and whereby the reliability index and based on it the current design space can be updated two numerical examples are presented to demonstrate the effectiveness of the present method

numerical methods for interval and fuzzy number comparison based on the probabilistic approach and dempster shafer theory there are many different methods for interval and fuzzy number comparison proposed in the literature which provide the results of comparison in the form of a real or boolean value in this paper we use the dempster shafer theory of evidence with its probabilistic interpretation to justify and construct the method which provides the result of comparison in the form of an interval or fuzzy number the complete and consistent set of expressions for inequality and equality relations between intervals and fuzzy numbers has been obtained in the framework of the probabilistic approach these relations make it possible to compare intervals and fuzzy numbers with real values and may be considered as an asymptotic limit of the results we obtain using the dempster shafer theory a natural fuzzy extension of the proposed approach is considered and discussed using some illustrative examples

elliptic genera of toric varieties and applications to mirror symmetry the paper contains a proof that elliptic genus of a calabi yau manifold is a jacobi form finds in which dimensions the elliptic genus is determined by the hodge numbers and shows that elliptic genera of a calabi yau hypersurface in a toric variety and its mirror coincide up to sign the proof of the mirror property is based on the extension of elliptic genus to calabi yau hypersurfaces in toric varieties with gorenstein singularities

characters of topological n 2 vertex algebras are jacobi forms on the moduli space of elliptic supercurves abstract we show that trace functions on modules of topological n 2 super vertex algebras give rise to conformal blocks on elliptic supercurves we show that they satisfy a system of linear partial differential equations with respect to the modular parameters of the supercurves under some finiteness condition on the vertex algebra these differential equations can be interpreted as a connection on the vector bundle of conformal blocks we show that this connection is equivariant with respect to a natural action of the jacobi modular group on the modular parameters and the trace functions in the appendix we prove the convergence of the trace functions

a general model for fuzzy linear programming abstract in the current literature there are several models of fuzzy linear programming problems the aim of this paper is first to describe the more important problems in fuzzy linear programming and second to give a general model of fuzzy linear programming problems involving all of the above ones finally a resolution method for that general model is proposed

a chiral borel weil bott theorem abstract we compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold this is applied to 1 finding the character of g integrable irreducible highest weight modules over the affine lie algebra at the critical level and 2 computing a certain elliptic genus of the flag manifold the main tool is a result that interprets the drinfeld sokolov reduction as a derived functor

a necessary and sufficient condition for the stability of interval matrices consider the linear dynamical system described by the equation xdot t ax t where a is a constant real matrix with dimensions n n and the elements of matrix a are not known precisely we know only the upper and lower bounds of the intervals in which the elements of matrix a are confined in this paper there is proved a necessary and sufficient condition for the stability of solutions of eqn 1 with incomplete information about the elements of matrix a

performance robustness of discrete time systems with structured uncertainty given an interconnection of a nominal discrete time plant and a stabilizing controller together with structured norm bounded nonlinear time varying perturbations necessary and sufficient conditions for robust stability and performance of the system are provided it is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem the resulting stability robustness problem is shown to be equivalent to a simple algebraic one the solution of which provides the desired necessary and sufficient conditions for performance stability robustness these conditions provide an effective tool for robustness analysis and can be applied to a large class of problems in particular it is shown that some known results can be obtained immediately as special cases of these conditions

hodge elliptic genera and how they govern k3 theories the complex hodge elliptic genus and its conformal field theoretic counterpart were recently introduced by kachru and tripathy refining the traditional complex elliptic genus we construct a different so called chiral hodge elliptic genus which is expected to agree with the generic conformal field theoretic hodge elliptic genus in contrast to the complex hodge elliptic genus as originally defined for k3 surfaces x the chiral hodge elliptic genus is shown to be independent of all moduli moreover employing kapustin s results on infinite volume limits it is shown that it agrees with the generic conformal field theoretic hodge elliptic genus of k3 theories while the complex hodge elliptic genus does not this new invariant governs part of the field content of k3 theories supporting the idea that all their spaces of states have a common subspace which underlies the generic conformal field theoretic hodge elliptic genus and thereby the complex elliptic genus mathematically this space is modelled by the sheaf cohomology of the chiral de rham complex of x it decomposes into irreducible representations of the n 4 superconformal algebra such that the multiplicity spaces of all massive representations have precisely the dimensions required in order to furnish the representation of the mathieu group m 24 that is predicted by mathieu moonshine this is interpreted as evidence in favour of the ideas of symmetry surfing which have been proposed by taormina and the author along with the claim that the sheaf cohomology of the chiral de rham complex is a natural home for mathieu moonshine these investigations also imply that the generic chiral algebra of k3 theories is precisely the n 4 superconformal algebra at central charge c 6 if the usual predictions on infinite volume limits from string theory hold true

necessary and sufficient conditions for unified optimality of interval linear program in the general form abstract this paper considers optimal solutions of general interval linear programming problems the most general concepts of optimal solutions are introduced in a unified framework the existing optimal solution concepts of interval linear program such as weak and strong optimal solutions are all the special cases in this framework necessary and sufficient conditions for checking a class of optimality are developed according to the kkt conditions also the comparison among several conclusions using kkt conditions and tangent core technique in various forms of interval linear programming is proposed

adaptive robust control for siso systems abstract this paper addresses the problem of nonconservative adaptive robust regulating a siso system allowing for model perturbations in the coprime factor representation of the system as well as external additive bounded disturbance signals the perturbations and disturbances are assumed to belong to a particular parameterized class and are norm bounded the norm bounds are not available for control design but the class knowledge is available the performance measure is the worst possible steady state absolute value of the controlled output over the class of allowable disturbances and model perturbations an identification based adaptive control method is proposed where the identification criterion coincides with the control objective the proposed adaptive scheme achieves near optimal performance simulations comparing the new scheme with an adaptive controller based on classical recursive least squares identification are presented

bibo stability robustness in the presence of coprime factor perturbations a necessary and sufficient condition for robustly stabilizing a family of plants described by perturbations of fixed coprime factors of a plant is given the computation of the largest stability margin is discussed via solving a nonsquare l sup 1 optimal control problem an algorithm for obtaining lower approximations of the minimum value of the optimization problem mu sub 0 is proposed this together with the standard algorithm which provides upper approximations allows mu sub 0 to be computed within any degree of accuracy

control oriented model validation and errors quantification in the spl lscr sub 1 setup a priori information required for robust synthesis includes a nominal model and a model of uncertainty the latter is typically in the form of additive exogenous disturbance and plant perturbations with assumed bounds if these bounds are unknown or too conservative they have to be estimated from measurement data in this paper the problem of errors quantification is considered in the framework of the spl lscr sub 1 optimal robust control theory associated with the spl lscr sub spl infin signal space the optimal errors quantification is to find errors bounds that are not falsified by measurement data and provide the minimum value of a given control criterion for model with unstructured uncertainty entering the system in a linear fractional manner the optimal errors quantification is reduced to quadratic fractional programming for system under coprime factor perturbations the optimal errors quantification is reduced to linear fractional programming

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

toric varieties and modular forms let n r be a lattice and let deg n be a piecewise linear function that is linear on the cones of a complete rational polyhedral fan under certain conditions on deg the data n deg determines a function f that is a holomorphic modular form of weight r for the congruence subgroup 1 l moreover by considering all possible pairs n deg we obtain a natural subring l of modular forms with respect to 1 l we construct an explicit set of generators for l and show that l is stable under the action of the hecke operators finally we relate l to the hirzebruch elliptic genera that are modular with respect to 1 l

generalized hukuhara gâteaux and frechet derivatives of interval valued functions and their application in optimization with interval valued functions abstract in this article the notions of gh directional derivative gh g teaux derivative and gh frechet derivative for interval valued functions are proposed the existence of gh frechet derivative is shown to imply the existence of gh g teaux derivative and the existence of gh g teaux derivative is observed to indicate the presence of gh directional derivative for an interval valued gh lipschitz function it is proved that the existence of gh g teaux derivative implies the existence of gh frechet derivative it is observed that for an interval valued convex function on a linear space the gh directional derivative exists at any point for every direction concepts of linear and monotonic interval valued functions are studied in the sequel further it is shown that the proposed derivatives are useful to check the convexity of an interval valued function and to characterize efficient points of an optimization problem with interval valued objective function it is observed that at an efficient point of an interval valued function none of its gh directional derivatives dominates zero and the gh g teaux derivative must contain zero the entire study is supported by suitable illustrative examples

berglund hubsch mirror symmetry via vertex algebras we give a vertex algebra proof of the berglund hubsch duality of nondegenerate invertible potentials we suggest a way to unify it with the batyrev borisov duality of reflexive gorenstein cones

necessary and sufficient conditions for stability of symmetric interval matrices it is shown that a family of symmetric interval matrices is schur if and only if the vertex matrices are schur this result is also applicable to hurwitz stability and aperiodic properties of linear systems

localized solutions to interval linear equations in this paper we propose a new type of solutions localized solutions to interval linear equations ax b the new solutions are based on l localized solutions and r localized solutions the concepts of the three solutions are given and the characteristics of the new solutions to the interval linear equations are described by means of nonlinear inequality as is similar to the well known oettli prager inequality which is related to the mid point and interval radius some necessary conditions of the three types of solutions to the equations are given

on globally stable adaptive control providing l 1 tracking performance for linear discrete time systems abstractexisting adaptive control algorithms at best guarantee that the tracking error is a l2 sequence this paper presents globally stable adaptive control algorithms for linear discrete time systems providing l1 tracking performance two algorithms with different degree of complexity are proposed one for the case of known control directions and a separate algorithm for the case of unknown control directions it is demonstrated that in both cases the tracking error is l1 sequence while the input and output signals are uniformly bounded

a two stage logarithmic goal programming method for generating weights from interval comparison matrices a two stage logarithmic goal programming tlgp method is proposed to generate weights from interval comparison matrices which can be either consistent or inconsistent the first stage is devised to minimize the inconsistency of interval comparison matrices and the second stage is developed to generate priorities under the condition of minimal inconsistency the weights are assumed to be multiplicative rather than additive in the case of hierarchical structures a nonlinear programming method is used to aggregate local interval weights into global interval weights a simple yet practical preference ranking method is investigated to compare the interval weights of criteria or rank alternatives in a multiplicative aggregation process the proposed tlgp is also applicable to fuzzy comparison matrices when they are transformed into interval comparison matrices using a level sets and the extension principle six numerical examples including a group decision analysis problem with a group of comparison matrices a hierarchical decision problem and a fuzzy decision problem using fuzzy comparison matrix are examined to show the applications of the proposed methods comparisons with other existing procedures are made whenever possible

a ga based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components in this paper we have considered the problem of constrained redundancy allocation of series system with interval valued reliability of components for maximizing the overall system reliability under limited resource constraints the problem is formulated as an unconstrained integer programming problem with interval coefficients by penalty function technique and solved by an advanced ga for integer variables with interval fitness function tournament selection uniform crossover uniform mutation and elitism as a special case considering the lower and upper bounds of the interval valued reliabilities of the components to be the same the corresponding problem has been solved the model has been illustrated with some numerical examples and the results of the series redundancy allocation problem with fixed value of reliability of the components have been compared with the existing results available in the literature finally sensitivity analyses have been shown graphically to study the stability of our developed ga with respect to the different ga parameters

a multicriteria fuzzy linear programming method for water supply system development planning abstract a method is presented for solving a multicriteria linear program where the coefficients of the objective functions and the constraints are fuzzy numbers of the l r type assuming the aspiration levels for particular criteria to be fuzzy and basing on comparison of fuzzy numbers the original problem is transformed into a multicriteria linear fractional program the latter is solved using an interactive technique involving a linear programming procedure in the calculation phase this method has been elaborated with a view to the application to the development of a water supply system

new method for computing the upper bound of optimal value in interval quadratic program we consider the interval quadratic programming problems the aim of this paper is to present a new method to compute the upper bound of the optimal values under weaker conditions moreover we discuss the relations between the new method and previous results the features of the proposed methods are illustrated by some examples

characteristic classes of singular toric varieties in this paper we compute the motivic chern classes and homology hirzebruch characteristic classes of possibly singular toric varieties which in the context of complete toric varieties fit nicely with a generalized hirzebruch riemann roch theorem as important special cases we obtain new or recover well known formulae for the baum fulton macpherson todd or macpherson s chern classes of toric varieties as well as for the thom milnor l classes of simplicial projective toric varieties we present two different perspectives for the computation of these characteristic classes of toric varieties first we take advantage of the torus orbit decomposition and the motivic properties of the motivic chern and respectively homology hirzebruch classes to express the latter in terms of dualizing sheaves and respectively the dual todd classes of closures of orbits this method even applies to torus invariant subspaces of a given toric variety the obtained formula is then applied to weighted lattice point counting in lattice polytopes and their subcomplexes yielding generalized pick type formulae second in the case of simplicial toric varieties we compute our characteristic classes by using the lefschetz riemann roch theorem of edidin graham in the context of the geometric quotient description of such varieties in this setting we define mock hirzebruch classes of simplicial toric varieties which specialize to the mock chern mock todd and mock l classes of such varieties and investigate the difference between the actual homology hirzebruch class and the mock hirzebruch class we show that this difference is localized on the singular locus and we obtain a formula for it in which the contribution of each singular cone is identified explicitly finally the two methods of computing characteristic classes are combined for proving several characteristic class formulae originally obtained by cappell and shaneson in the early 1990s 2015 wiley periodicals inc

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

analysis and design for robust performance with structured uncertainty abstract necessary and sufficient conditions for stability and performance robustness of discrete time systems are provided in terms of the spectral radius of a certain nonnegative matrix the conditions are easily computable and provide a simple and efficient method for computation of the robustness conditions for siso as well mimo perturbations the problem of robust controller synthesis is explored and an iteration scheme for controller synthesis is introduced

vertex algebras and mirror symmetry mirror symmetry for calabi yau hypersurfaces in toric varieties is by now well established however previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror we are able to calculate explicitly vertex algebras that correspond to holomorphic parts of a and b models of calabi yau hypersurfaces and complete intersections in toric varieties we establish the relation between these vertex algebras for mirror calabi yau manifolds this should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra as well as some basic results of the theory of vertex algebras ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties

chiral rings of vertex algebras of mirror symmetry we calculate chiral rings of the n 2 vertex algebras constructed from the combinatorial data of toric mirror symmetry and show that they coincide with the description of stringy cohomology conjectured previously in a joint work with a mavlyutov this constitutes an important reality check of the vertex algebra approach to mirror symmetry

chiral differential operators on supermanifolds the first part of this paper provides a new description of chiral differential operators cdos in terms of global geometric quantities the main result is a recipe to define all sheaves of cdos on a smooth cs manifold its ingredients consist of an affine connection and an even 3 form that trivializes p1 with fixed two suitable 3 forms define isomorphic sheaves of cdos if and only if their difference is exact moreover conformal structures are in one to one correspondence with even 1 forms that trivialize c1 applying our work in the first part we then construct what may be called chiral dolbeault complexes of a complex manifold m and analyze conditions under which these differential vertex superalgebras admit compatible conformal structures or extra gradings by fermion numbers when m is compact their cohomology computes in various cases the witten genus the two variable elliptic genus and a spinc version of the witten genus this part contains some new results as well as provides a geometric formulation of certain known facts from the study of holomorphic cdos and models

log barrier method for two stage quadratic stochastic programming in this paper we present a log barrier method for solving two stage quadratic stochastic programs the mathematical model considered here can be used to present several real world applications including financial and production planning problems we discuss fundamental properties associated with the proposed algorithm and analyze the convergence and complexity of the algorithm

adaptive suboptimal control of a linear system with bounded disturbance abstract an adaptive suboptimal control of a linear discrete system with unknown parameters is proposed an additive disturbance v t acting on the system is supposed to be uniformly bounded the criterion is sup v t i y 1 u 1 where y t is the output u t is the control the adaptive control law gives almost the same guaranteed value of the criterion as the optimal linear feedback does for a system with known parameters

a general evidential reasoning algorithm for multi attribute decision analysis under interval uncertainty abstract evidential reasoning er is one of the important approaches used to solve multi attribute decision analysis mada problems under uncertainty involving both quantitative and qualitative attributes the er approach provides a distributed modeling framework fusing several types of uncertain and incomplete information including ignorance and vagueness to work out the optimum alternative rationally in this paper we review the original er algorithm and recursive interval evidential reasoning ier algorithm and derive a general analytical algorithm for ier thus enabling an aggregation of attributes assessments in an explicit manner then a more complicated uncertain occasion is investigated where it is possible to conduct evaluation assessments including quantitative data belief degrees grades and weights in the form of an interval a pair of nonlinear optimization models based on the new algorithm is established to solve this problem under interval uncertainty and the maximum and minimum expected utilities of each alternative are calculated and ranked accordingly additionally we prove that the original er and recursive ier algorithms are special cases of the new algorithm finally a numerical example is used to demonstrate the steps involved in the proposed approach

a numerical solution method to interval quadratic programming quadratic programming has been widely applied to solving real world problems the conventional quadratic programming model requires the parameters to be known constants in the real world however the parameters are seldom known exactly and have to be estimated this paper discusses the interval quadratic programming problems where the cost coefficients constraint coefficients and right hand sides are represented by interval data since the parameters are interval valued the objective value is interval valued as well a pair of two level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the interval quadratic program based on the duality theorem and by applying the variable transformation technique the pair of two level mathematical programs is transformed into conventional one level quadratic program solving the pair of quadratic programs produces the interval of the objective values of the problem an example illustrates the whole idea and sheds some light on interval quadratic programming

on the geometry of a siegel modular threefold introduction 317 1 compactifications 318 2 humbert surfaces 324 3 the chern numbers of s n 331 4 symmetric quartic threefolds 334 5 the modular threefold of level 2 335 6 kummer surfaces 338 7 prym surfaces 340 8 humbert surfaces again 345

mckay correspondence for elliptic genera we establish a correspondence between orbifold and singular elliptic genera of a global quotient while the former is defined in terms of the fixed point set of the action the latter is defined in terms of the resolution of singularities as a byproduct the second quantization formula of dijkgraaf moore verlinde and verlinde is extended to arbitrary kawamata log terminal pairs

adaptive suboptimal tracking for the first order plant with lipschitz uncertainty a tracking problem for the first order discrete time plant with time invariant uncertainty of the lipschitz type and bounded exogenous disturbance is considered in the adaptive setting and two different adaptive laws are proposed the first law is based on a natural estimation of the unknown linear part of the plant and introduces some conservatism in stability margin and tracking performance the second adaptive law is suboptimal and includes additionally the estimation of the unknown lipshitz constant and the unknown norm of exogenous disturbance the suboptimality is achieved by exploiting a cone estimation algorithm and the linearity of the control criterion with respect to unknown parameters both adaptive laws utilize the nonlinear feedback by xie and guo based on nonparametric estimation of the uncertainty

l sub 1 optimal robust controller for siso plant under coprime factor perturbations the problem of synthesis of l sub 1 optimal robust controller for siso plant under coprime factor perturbations and bounded external disturbance is considered a geometric interpretation of l sub 1 optimal robust controller standard l sub 1 optimal controller and two other optimal robust controllers is presented the existence of l sub 1 optimal robust linear controller is proved and an algorithm for approximate solution of the problem is proposed the algorithm is reduced to approximate solution of finite family of standard l sub 1 optimization problems

elliptic classes of schubert varieties we introduce new notions in elliptic schubert calculus the twisted borisov libgober classes of schubert varieties in general homogeneous spaces g p while these classes do not depend on any choice they depend on a set of new variables for the definition of our classes we calculate multiplicities of some divisors in schubert varieties which were only known for full flag varieties before our approach leads to a simple recursions for the elliptic classes comparing this recursion with r matrix recursions of the so called elliptic weight functions of rimanyi tarasov varchenko we prove that weight functions represent elliptic classes of schubert varieties

an algorithm for checking stability of symmetric interval matrices a branch and bound algorithm for checking hurwitz and schur stability of symmetric interval matrices is proposed the algorithm in a finite number of steps either verifies stability or finds a symmetric matrix which is not stable it can also be used for checking positive definiteness of asymmetric interval matrices