response surface approximation of pareto optimal front in multi objective optimization a systematic approach is presented to approximate the pareto optimal front pof by a response surface approximation the data for the pof is obtained by multi objective evolutionary algorithm improvements to address drift in the pof are also presented the approximated pof can help visualize and quantify trade offs among objectives to select compromise designs the bounds of this approximate pof are obtained using multiple convex hulls the proposed approach is applied to study trade offs among objectives of a rocket injector design problem where performance and life objectives compete the pof is approximated using a quintic polynomial the compromise region quantifies trade offs among objectives 2006 elsevier b v all rights reserved

multifactorial functions in fuzzy sets theory abstract the multifactorial function is a very important new concept which can be used to many aspects in fuzzy sets theory it appeared firstly in 5 where it was used to define fuzzy perturbation function and where the stability for the solutions of fuzzy relation equations by using fuzzy perturbation was studied in 6 by means of multifactorial functions multifactorial fuzzy sets and the multifactorial degree of nearness which are two new concepts too were given and they were used to multifactorial pattern recognition and clustering analysis with fuzzy characteristics in fact generally speaking most of the mathematical models dependent on several factors should use multifactorial functions especially fuzzy decision making fuzzy games fuzzy programming and fuzzy linear programming with several objective functions should here we study properties of multifactorial functions how to generate a new multifactorial function and we introduce in detail its applications in fuzzy pattern recognition fuzzy decision making fuzzy clustering fuzzy games and fuzzy programming etc

jet schemes of locally complete intersection canonical singularities let x be a variety defined over an algebraically closed field k of characteristic zero the mth jet scheme xm of x is a scheme whose closed points over x x are morphisms ox x k t tm 1 when x is a smooth variety this is an affine bundle over x of dimension m 1 dim x the space of arcs x of x is the projective limit x proj limm xm our main result is a proof of the following theorem which was conjectured by eisenbud and frenkel

the chen ruan cohomology of moduli of curves of genus 2 with marked points in this work we describe the chen ruan cohomology of the moduli stack of smooth and stable genus 2 curves with marked points in the first half of the paper we compute the additive structure of the

the orbifold chow ring of toric deligne mumford stacks the orbifold chow ring of a deligne mumford stack defined by abramovich graber and vistoli 2 is the algebraic version of the orbifold cohomology ring in troduced by w chen and ruan 7 8 by design this ring incorporates numerical invariants such as the orbifold euler characteristic and the orbifold hodge num bers of the underlying variety the product structure is induced by the degree zero part of the quantum product in particular it involves gromov witten invariants inspired by string theory and results in batyrev 3 and yasuda 28 one expects that in nice situations the orbifold chow ring coincides with the chow ring of a resolution of singularities fantechi and g ttsche 14 and uribe 25 verify this conjecture when the orbifold is symn 5 where 5 is a smooth projective surface with ks 0 and the resolution is hilbn the initial motivation for this project was to compare the orbifold chow ring of a simplicial toric variety with the chow ring of a cr pant resolution to achieve this goal we first develop the theory of toric deligne mumford stacks modeled on simplicial toric varieties a toric deligne mumford stack corresponds to a combinatorial object called a stacky fan as a first approximation this object is a simplicial fan with a distinguished lattice point on each ray in the fan more precisely a stacky fan s is a triple consisting of a finitely generated abelian group n a simplicial fan e in q z n with n rays and a map zn n where the image of the standard basis in zn generates the rays in e a rational simplicial fan e produces a canonical stacky fan s n e where n is the distinguished lattice and is the map defined by the minimal lattice points on the rays hence there is a natural toric deligne mumford stack associated to every simplicial toric variety a stacky fan encodes a group action on a quasi affine variety and the toric deligne mumford stack is the quotient if e corresponds to a smooth toric variety x e and s is the canonical stacky fan associated to e then we simply have x z we show that many of the basic concepts such as open and closed toric substacks line bundles and maps between toric deligne mumford stacks correspond to combinatorial notions we expect that many more results about toric varieties lift to the realm of stacks and hope that toric deligne mumford stacks will serve as a useful testing ground for general theories

the algebra of discrete torsion abstract we analyze the algebraic structures of g frobenius algebras which are the algebras associated to global group quotient objects a k a global orbifolds here g is any finite group first we show that these algebras are modules over the drinfel d double of the group ring k g and are moreover k g module algebras and k g comodule algebras we furthermore consider g frobenius algebras up to projective equivalence and define universal shifts of the multiplication and the g action preserving the projective equivalence class we show that these shifts are parameterized by z 2 g k and by h 2 g k when considering of g frobenius algebras up to isomorphism we go on to show that these shifts can be realized by the forming of tensor products with twisted group rings thus providing a group action of z 2 g k on g frobenius algebras acting transitively on the classes g frobenius related by universal shifts the multiplication is changed according to the cocycle while the g action transforms with a different cocycle derived from the cocycle defining the multiplication the values of this second cocycle also appear as a factor in front of the trace which is considered in the trace axiom of g frobenius algebras this allows us to identify the effect of our action by z 2 g k as so called discrete torsion effectively unifying all known approaches to discrete torsion for global orbifolds in one algebraic theory the new group action of discrete torsion is essentially derived from the multiplicative structure of g frobenius algebras this yields an algebraic realization of discrete torsion defined via the perturbation of the multiplication resulting from a tensor product with a twisted group ring additionally we show that this algebraic formulation of discrete torsion allows for a treatment of g frobenius algebras analogous to the theory of projective representations of groups group extensions and twisted group ring modules lastly we identify another set of discrete universal transformations among g frobenius algebras pertaining to their super structure and classified by hom g z 2 z which are essential for the application to mirror symmetry for singularities with symmetries

nonabelian localization in equivariant k theory and riemann roch for quotients abstract we prove a localization formula in equivariant algebraic k theory for an arbitrary complex algebraic group acting with finite stabilizer on a smooth algebraic space this extends to nondiagonalizable groups the localization formulas of nielsen diagonalizably linearized coherent sheaves bull soc math france 102 1974 85 97 and thomason une formule de lefschetz en k theorie equivariante algebrique duke math j 68 3 1992 447 462 as an application we give a riemann roch formula for quotients of smooth algebraic spaces by proper group actions this formula extends previous work of toen theoremes de riemann roch pour les champs de deligne mumford k theory 18 1 1999 33 76 and the authors riemann roch for quotients and todd classes of simplicial toric varieties comm algebra 31 2003 3735 3752

stringy product on twisted orbifold k theory for abelian quotients in this paper we present a model to calculate the stringy product on twisted orbifold k theory of adem ruan zhang for abelian complex orbifolds in the first part we consider the non twisted case on an orbifold presented as the quotient of a manifold acted by a compact abelian lie group we give an explicit description of the obstruction bundle we explain the relation with the product defined by jarvis kaufmann kimura and via a chern character map with the chen ruan cohomology we explicitly calculate the stringy product for a weighted projective orbifold in the second part we consider orbifolds presented as the quotient of a manifold acted by a finite abelian group and twistings coming from the group cohomology we show a decomposition formula for twisted orbifold k theory that is suited to calculate the stringy product and we use this formula to calculate two examples when the group is 2 3

lattices for landau ginzburg orbifolds we consider a pair consisting of an invertible polynomial and a finite abelian group of its symmetries berglund hubsch and henningson proposed a duality between such pairs giving rise to mirror symmetry we define an orbifoldized signature for such a pair using the orbifoldized elliptic genus in the case of three variables and based on the homological mirror symmetry picture we introduce two integral lattices a transcendental and an algebraic one we show that these lattices have the same rank and that the signature of the transcendental one is the orbifoldized signature finally we give some evidence that these lattices are interchanged under the duality of pairs

delocalized chern character for stringy orbifold k theory in this paper we define a stringy product on k orb x c the orbifold k theory of any almost complex presentable orbifold x we establish that under this stringy product the delocali zed chern character chdeloc k x c h cr x after a canonical modification is a ring isomorphism here h cr x is the chen ruan cohomology of x the proof relies on an intrinsic description of the obstruc tion bundles in the construction of the chen ruan product as an application we investigate this stringy product on the equivariant k theory k g g of a finite group g with the conjugation action it turns out that the stringy pr oduct is different from the pontryagin product the latter is also called the fusion pro duct in string theory

weighted blowup correspondence of orbifold gromov witten invariants and applications let mathsf x be a compact symplectic orbifold groupoid with mathsf s being a compact symplectic sub orbifold groupoid and underline mathsf x mathfrak a be the weight mathfrak a blowup of mathsf x along mathsf s with mathsf z being the exceptional divisor we show that there is a weighted blowup correspondence between some certain absolute orbifold gromov witten invariants of mathsf x relative to mathsf s and some certain relative orbifold gromov witten invariants of the pair underline mathsf x mathfrak a mathsf z as an application we prove that the symplectic uniruledness of symplectic orbifold groupoids is a weighted blowup invariant

the quantum orbifold cohomology of weighted projective spaces we calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces we generalize givental s heuristic argument which relates small quantum cohomology to s1 equivariant floer cohomology of loop space to weighted projective spaces and use this to conjecture an explicit formula for the small j function a generating function for certain genus zero gromov witten invariants we prove this conjecture using a method due to bertram this provides the first non trivial example of a family of orbifolds of arbitrary dimension for which the small quantum orbifold cohomology is known in addition we obtain formulas for the small j functions of weighted projective complete intersections satisfying a combinatorial condition this condition naturally singles out the class of orbifolds with terminal singularities

good points and constructive resolution of singluarities in this paper we present a new algorithm of resolution of singularities over fields of characteristic zero making use of invariants that come from abhyankar s good point theory abl we also prove new properties on constructive or algorithmic desingularization let us explain what we mean by an algorithm of resolution consider a pair x w where w is a regular variety over a base field k of characteristic zero not necessarily irreducible i e w smooth over k and xc w is a closed non empty subscheme call c the class of all such pairs over different base fields k natural maps i x w1 x w arise within this class for instance if w1 w is a smooth map over a fixed field k or if w1 w arises from an arbitrary change of base field fix now a totally ordered set i and suppose assigned for each pair 7 x w of u a function p x i which is upper semi continuous and takes only finitely many values say 1 c r c i let max bp be the biggest ai and set

on the uniqueness of bivariant chern class and bivariant riemann roch transformations the existence of bivariant chern classes was conjectured by w fulton and r macpherson and proved by j p brasselet for cellular morphisms of analytic varieties however its uniqueness has been unsolved since then in this paper we show that restricted to morphisms whose target varieties are possibly singular but rational homology manifolds such as orbifolds the bivariant chern classes with rational coefficients are uniquely determined we also discuss some related results and problems

duality theorems for etale gerbes on orbifolds abstract let g be a finite group and y a g gerbe over an orbifold b a disconnected orbifold y and a flat u 1 gerbe c on y is canonically constructed from y motivated by a proposal in physics we study a mathematical duality between the geometry of the g gerbe y and the geometry of y twisted by c we prove several results verifying this duality in the contexts of non commutative geometry and symplectic topology in particular we prove that the category of sheaves on y is equivalent to the category of c twisted sheaves on y when y is symplectic we show by a combination of techniques from non commutative geometry and symplectic topology that the chen ruan orbifold cohomology of y is isomorphic to the c twisted orbifold cohomology of y as graded algebras

tautological classes on the moduli spaces of stable maps to p r via torus actions we present a localization proof of the fact that the cohomology of the moduli spaces of genus zero stable maps to projective spaces is entirely tautological in addition we obtain a description of a bialynicki birula decomposition of the stack of stable maps in the context of gathmann s moduli spaces of maps with prescribed contact order to a fixed hyperplane we show that the decomposition is filterable

non commutative mori contractions and p1 bundles abstract we give a method for constructing maps from a non commutative scheme to a commutative projective curve with the aid of artin zhang s abstract hilbert schemes this is used to construct analogues of the extremal contraction of a k negative curve with self intersection zero on a smooth projective surface this result will hopefully be useful in studying artin s conjecture on the birational classification of non commutative surfaces as a non trivial example of the theory developed we look at non commutative ruled surfaces and more generally at non commutative p 1 bundles we show in particular that non commutative p 1 bundles are smooth have well behaved hilbert schemes and we compute its serre functor we then show that non commutative ruled surfaces give examples of the aforementioned non commutative mori contractions

symmetric products of a semistable degeneration of surfaces we explicitly construct a v normal crossing gorenstein canonical model of the relative symmetric products of a local semistable degeneration of surfaces without a triple point by means of toric geometry using this model we calculate the stringy e polynomial of the relative symmetric product we also construct a minimal model of degeneration of hilbert schemes explicitly

cohomology theory in birational geometry this is a continuation of 9 where it was shown that k equivalent complex projective manifolds have the same betti numbers by using the theory of p adic integrals and deligne s solution to the weil conjecture the aim of this note is to show that with a little more book keeping work namely by applying faltings p adic hodge theory our p adic method also leads to the equivalence of hodge numbers a result which was previously known via motivic integration

a shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters author s vrugt ja gupta hv bouten w sorooshian s abstract markov chain monte carlo mcmc methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models however mcmc methods require the a priori definition of a proposal or sampling distribution which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the markov chain and its rate of convergence in this paper we present an mcmc sampler entitled the shuffled complex evolution metropolis algorithm scem ua which is well suited to infer the posterior distribution of hydrologic model parameters the scem ua algorithm is a modified version of the original sce ua global optimization algorithm developed by duan et al 1992 the scem ua algorithm operates by merging the strengths of the metropolis algorithm controlled random search competitive evolution and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution three case studies demonstrate that the adaptive capability of the scem ua algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional metropolis hastings samplers

motivic zeta functions on q gorenstein varieties abstract we study motivic zeta functions for q divisors in a q gorenstein variety by using a toric partial resolution of singularities we reduce this study to the local case of two normal crossing divisors where the ambient space is an abelian quotient singularity for the latter we provide a closed formula which is worked out directly on the quotient singular variety as a first application we provide a family of surface singularities where the use of weighted blow ups reduces the set of candidate poles drastically we also present an example of a quotient singularity under the action of a nonabelian group from which we compute some invariants of motivic nature after constructing a q resolution

dimensions of jet schemes of log singularities we characterize kawamata log terminal singularities and log canonical singularities by dimensions of jet schemes our main result is theorem 2 4

calibration of rainfall runoff models application of global optimization to the sacramento soil moisture accounting model conceptual rainfall runoff models are difficult to calibrate by means of automatic methods one major reason for this is the inability of conventional procedures to locate the globally optimal set of parameters this paper investigates the consistency with which two global optimization methods the shuffled complex evolution sce ua method developed by the authors and the multistart simplex msx method are able to find the optimal parameter set during calibration of the sacramento soil moisture accounting model sac sma of the national weather service river forecast system nwsrfs in the first phase of this study error free synthetic data are used to conduct a comparative evaluation of the algorithms under ideal conditions in 10 independent trials of each algorithm in which 13 parameters of the sac sma model were optimized simultaneously the sce ua method achieved a 100 success rate in locating the precise global optimum i e the true parameter values while the msx method failed in all trials even with more than twice the number of function evaluations in the second phase historical data from the leaf river watershed are used to conduct a comparative evaluation of the algorithms under real conditions using two different estimation criteria drms and hmle the sce ua algorithm obtained consistently lower function values and more closely grouped parameter estimates while using one third fewer function evaluations than the msx algorithm

germs of arcs on singular algebraic varieties and motivic integration we study the scheme of formal arcs on a singular algebraic variety and its images under truncations we prove a rationality result for the poincare series of these images which is an analogue of the rationality of the poincare series associated to p adic points on a p adic variety the main tools which are used are semi algebraic geometry in spaces of power series and motivic integration a notion introduced by m kontsevich in particular we develop the theory of motivic integration for semi algebraic sets of formal arcs on singular algebraic varieties we prove a change of variable formula for birational morphisms and we prove a geometric analogue of a result of oesterle

mirror symmetry for moduli spaces of higgs bundles via p adic integration we prove the topological mirror symmetry conjecture by hausel thaddeus for smooth moduli spaces of higgs bundles of type sl n and pgl n more precisely we establish an equality of stringy hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties our proof utilises p adic integration relative to the fibres and interprets canonical gerbes present on these moduli spaces as characters on the hitchin fibres using tate duality furthermore we prove for d prime to n that the number of rank n higgs bundles of degree d over a fixed curve defined over a finite field is independent of d this proves a conjecture by mozgovoy schiffmann in the coprime case

a new equivariant cohomology ring in this paper motivated by chen ruan s stringy orbifold theory on almost complex orbifolds we construct a new equivariant cohomology ring mathscr h g x for an equivariant almost complex pair x g where x is a compact connected almost complex manifold g is a connected compact lie group which acts on x and preserves the almost complex structure

multiobjective calibration with pareto preference ordering an application to rainfall runoff model calibration 1 automatic calibration routines for hydrologic models with multiple objective capabilities are becoming increasingly popular due to advances in computational power population based optimization techniques and the recognition that a single performance measure such as the root mean square error is no longer sufficient to characterize the complex behavior of the catchment however as more objective functions are included in the calibration the number of pareto optimal solutions as well as the number of near pareto optimal parameter sets increases the calibration problem quickly becomes a decision making problem in the practical sense users of automatic calibration routines have to face the task of selecting a set of suitable model parameters from the numerous pareto optimal sets a new method of automatic calibration is proposed which combines an effective optimization routine based on multiobjective genetic algorithms and pareto preference ordering in this case pareto optimal points that are also pareto optimal in different subspace combinations of the objective functions space are preferred the proposed method is used to calibrate the mike11 nam rainfall runoff model for a danish catchment the results indicated that the method is able to sieve through the numerous pareto optimal solutions and select a small number of preferred solutions this is extremely useful to modelers who typically are required to provide the best estimated parameter sets with good overall model performance

the resolution property for schemes and stacks we prove the equivalence of two fundamental properties of algebraic stacks being a quotient stack in a strong sense and the resolution property which says that every coherent sheaf is a quotient of some vector bundle moreover we prove these properties in the important special case of orbifolds whose associated algebraic space is a scheme mathematics subject classification primary 14a20 secondary 14l30

moduli stacks of serre stable representations in tilting theory abstract we introduce a new moduli stack called the serre stable moduli stack which corresponds to studying families of point objects in an abelian category with a serre functor this allows us in particular to re interpret the classical derived equivalence between most concealed canonical algebras and weighted projective lines by showing they are induced by the universal sheaf on the serre stable moduli stack we explain why the method works by showing that the serre stable moduli stack is the tautological moduli problem that allows one to recover certain nice stacks such as weighted projective lines from their moduli of sheaves as a result this new stack should be of interest in both representation theory and algebraic geometry

a new selection metric for multiobjective hydrologic model calibration a novel selection metric called convex hull contribution chc is introduced for solving multiobjective mo optimization problems with pareto fronts that can be accurately approximated by a convex curve the hydrologic model calibration literature shows that many biobjective calibration problems with a proper setup result in such pareto fronts the chc selection approach identifies a subset of archived nondominated solutions whose map in the objective space forms convex approximation of the pareto front the optimization algorithm can sample solely from these solutions to more accurately approximate the convex shape of the pareto front it is empirically demonstrated that chc improves the performance of pareto archived dynamically dimensioned search pa dds when solving mo problems with convex pareto fronts this conclusion is based on the results of several benchmark mathematical problems and several hydrologic model calibration problems with two or three objective functions the impact of chc on pa dds performance is most evident when the computational budget is somewhat limited it is also demonstrated that 1 000 solution evaluations limited budget in this study is sufficient for pa dds with chc based selection to achieve very high quality calibration results relative to the results achieved after 10 000 solution evaluations

variable weighted synthesis inference method for fuzzy reasoning and fuzzy systems a new fuzzy inference method called a vwsi variable weighted synthesis inference method is presented by applying the principle of variable weighted synthesis in factor spaces theory to fuzzy inference the analysis for response abilities of fuzzy systems constructed by vwsi algorithms indicates that such fuzzy systems have a characteristic of interpolation approximations to unknown functions the fuzzy systems constructed by commonly used fuzzy inference algorithms are equivalent to some special fuzzy systems constructed by vwsi algorithms a simulation experiment shows the advantage of vwsi method

the integral orbifold chow ring of toric deligne mumford stacks in this paper we study the integral chow ring of toric deligne mumford stacks we prove that the integral chow ring of a semi projective toric deligne mumford stack is isomorphic to the stanley reisner ring of the associated stacky fan the integral orbifold chow ring is also computed our results are illustrated with several examples

orbifold cohomology for global quotients let x be an orbifold that is a global quotient of a manifold y by a finite group g we construct a noncommutative ring h sp ast y g with a g action such that h sp y g sp g is the orbifold cohomology ring of x defined by w chen and y ruan cr when y s sp n with s a surface with trivial canonical class and g mathfrak s sb n we prove that a small modification of the orbifold cohomology of x is naturally isomorphic to the cohomology ring of the hilbert scheme s sp n computed by m lehn and c sorger ls2

a relation between the parabolic chern characters of the de rham bundles in this paper we consider the weight i de rham gauss manin bundles on a smooth variety arising from a smooth projective morphism f x u longrightarrow u for i geq 0 we associate to each weight i de rham bundle a certain parabolic bundle on s and consider their parabolic chern characters in the rational chow groups for a good compactification s of u we show the triviality of the alternating sum of these parabolic bundles in the positive degree rational chow groups this removes the hypothesis of semistable reduction in the original result of this kind due to esnault and viehweg

gromov witten theory of deligne mumford stacks given a smooth complex deligne mumford stack cal x with a projective coarse moduli space we introduce gromov witten invariants of cal x and prove some of their basic properties including the wdvv equation

canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant this article contains an elementary constructive proof of resolution of singularities in characteristic zero our proof applies in particular to schemes of finite type and to analytic spaces so we recover the great theorems of hironaka we introduce a discrete local invariant rm inv x a whose maximum locus determines a smooth centre of blowing up leading to desingularization to define rm inv x we need only to work with a category of local ringed spaces x x cal o x satisfying certain natural conditions if a in x then rm inv x a depends only on widehat cal o x a more generally rm inv x is defined inductively after any sequence of blowings up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of rm inv x cdot the paper is self contained and includes detailed examples one of our goals is that the reader understand the desingularization theorem rather than simply know it is true

a new cohomology theory of orbifold based on the orbifold string theory model in physics we construct a new cohomology ring for any almost complex orbifold the key theorem is the associativity of this new ring some examples are computed

semi calabi yau orbifolds and mirror pairs abstract we generalize the cohomological mirror duality of borcea and voisin in any dimension and for any number of factors our proof applies to all examples which can be constructed through berglund hubsch duality our method is a variant of the so called landau ginzburg calabi yau correspondence of calabi yau orbifolds with an involution that does not preserve the volume form we deduce a version of mirror duality for the fixed loci of the involution which are beyond the calabi yau category and feature hypersurfaces of general type

twisted orbifold k theory we use equivariant methods to define and study the orbifold k theory of an orbifold x adapting techniques from equivariant k theory we construct a chern character and exhibit a multiplicative decomposition for k orb x in particular showing that it is additively isomorphic to the orbifold cohomology of x a number of examples are provided we then use the theory of projective representations to define the notion of twisted orbifold k theory in the presence of discrete torsion an explicit expression for this is obtained in the case of a global quotient

higher algebraic k theory for actions of diagonalizable groups we study the k theory of actions of diagonalizable group schemes on noetherian regular separated algebraic spaces our main result shows how to reconstruct the k theory ring of such an action from the k theory rings of the loci where the stabilizers have constant dimension we apply this to the calculation of the equivariant k theory of toric varieties and give conditions under which the merkurjev spectral sequence degenerates so that the equivariant k theory ring determines the ordinary k theory ring we also prove a very refined localization theorem for actions of this type

chern classes of deligne mumford stacks and their coarse moduli spaces let x be a complex projective algebraic variety with gorenstein quotient singularities and mathcal x a smooth deligne mumford stack having x as its coarse moduli space we show that the csm class c sm x coincides with the pushforward to x of the total chern class c t i mathcal x of the inertia stack i mathcal x we also show that the stringy chern class c str x of x whenever it is defined coincides with the pushforward to x of the total chern class c t ii mathcal x of the double inertia stack ii mathcal x some consequences concerning stringy orbifold hodge numbers are deduced

mori dream stacks we propose a generalisation of mori dream spaces to stacks we show that this notion is preserved under root constructions and taking abelian gerbes unlike the case of mori dream spaces such a stack is not always given as a quotient of the spectrum of its cox ring by the picard group we give a criterion when this is true in terms of mori dream spaces and root constructions finally we compare this notion with that of smooth toric deligne mumford stacks

weighted ehrhart theory and orbifold cohomology we introduce the notion of a weighted d vector of a lattice polytope although the definition is motivated by motivic integration we study weighted d vectors from a combinatorial perspective we present a version of ehrhart reciprocity and prove a change of variables formula we deduce a new geometric interpretation of the coefficients of the ehrhart d vector more specifically they are sums of dimensions of orbifold cohomology groups of a toric stack

a virtual fundamental class construction for the moduli space of c n equivariant morphisms abstract let x be a smooth projective variety with the action of c n the article describes the moduli space of c n equivariant morphisms from stable toric varieties into x as the inverse limit of the git quotients of x and their flips when these spaces are enhanced with a naturally associated deligne mumford stack structure this description is used for constructing a class in the chow group of the moduli space of dimension dim x n which is invariant under equivariant deformations of x

on the use of spatial regularization strategies to improve calibration of distributed watershed models 1 hydrologic models require the specification of unknown model parameters via calibration to historical input output data for spatially distributed models the large number of unknowns makes the calibration problem poorly conditioned spatial regularization can help to stabilize the problem by facilitating inclusion of additional information while a common regularization approach is to apply a scalar multiplier to the prior estimate of each parameter field this can cause problems by simultaneously changing both the mean and the variance of the distribution this paper explores a multiple criteria regularization approach that facilitates adjustment of the mean variance and shape of the parameter distribution using prior information to constrain the problem while providing sufficient degrees of freedom to enable model performance improvements we also test simple squashing functions to help in maintaining conceptually reasonable parameter values throughout the spatial domain we apply the method to three basins in the context of the distributed model intercomparison project dmip2 obtaining considerable performance improvements at the basin outlet however the prior parameter estimates are found to give much better performance at the interior points treated as ungauged suggesting that the spatial information has not been properly exploited the results also suggest that basin outlet hydrographs may not be particularly sensitive to spatial parameter variability and that an overall basin mean value may be sufficient for flow forecasting at the outlet although not at the interior points we discuss weaknesses in our study approach and suggest diagnostically more powerful strategies to be pursued

a fuzzy similarity inference method for fuzzy reasoning in this paper fuzzy similarity inference fsi is investigated first the axiomatic definition of the fuzzy similarity measure is introduced it is a generalization of the similarity measure some formulas are given to compute the fuzzy similarity of two fuzzy sets second a novel fuzzy reasoning called fuzzy similarity inference is proposed computational formulas for both fuzzy modus ponens fmp and fuzzy modus tollens fmt are obtained based on the theory of partial valuations fsi method is put under the framework of logic semantically furthermore the generalized problem of fsi is investigated computational formulas for a fsi fmp and a fsi fmt are obtained at last reversibility properties of fsi are proved

functorial reconstruction theorems for stacks abstract we study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes this is possible surprisingly often we show that many of the standard examples of moduli stacks are determined by their functors our methods seem to exhibit new anabelian style phenomena in the form of structures in the category of schemes that encode automorphism data in groupoids

effective and efficient algorithm for multiobjective optimization of hydrologic models 1 practical experience with the calibration of hydrologic models suggests that any single objective function no matter how carefully chosen is often inadequate to properly measure all of the characteristics of the observed data deemed to be important one strategy to circumvent this problem is to define several optimization criteria objective functions that measure different complementary aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated efficient or pareto optimal solutions in this paper we present an efficient and effective markov chain monte carlo sampler entitled the multiobjective shuffled complex evolution metropolis moscem algorithm which is capable of solving the multiobjective optimization problem for hydrologic models moscem is an improvement over the shuffled complex evolution metropolis scem ua global optimization algorithm using the concept of pareto dominance rather than direct single objective function evaluation to evolve the initial population of points toward a set of solutions stemming from a stable distribution pareto set the efficacy of the moscem ua algorithm is compared with the original mocom ua algorithm for three hydrologic modeling case studies of increasing complexity

on the conjecture of king for smooth toric deligne mumford stacks abstract we construct full strong exceptional collections of line bundles on smooth toric fano deligne mumford stacks of picard number at most two and of any picard number in dimension two it is hoped that the approach of this paper will eventually lead to the proof of the existence of such collections on all smooth toric nef fano deligne mumford stacks

stringy k theory and the chern character we construct two new g equivariant rings mathcal k x g called the stringy k theory of the g variety x and mathcal h x g called the stringy cohomology of the g variety x for any smooth projective variety x with an action of a finite group g for a smooth deligne mumford stack mathcal x we also construct a new ring mathsf k mathrm orb mathcal x called the full orbifold k theory of mathcal x we show that for a global quotient mathcal x x g the ring of g invariants k mathrm orb mathcal x of mathcal k x g is a subalgebra of mathsf k mathrm orb x g and is linearly isomorphic to the orbifold k theory of adem ruan ar and hence atiyah segal but carries a different quantum product which respects the natural group grading

motivic integration over deligne mumford stacks abstract the aim of this article is to develop the theory of motivic integration over deligne mumford stacks and to apply it to the birational geometry of deligne mumford stacks

a derham model for chen ruan cohomology ring of abelian orbifolds we present a derham model for chen ruan cohomology ring of abelian orbifolds we introduce the notion of twist factors so that formally the stringy cohomology ring can be defined without going through pseudo holomorphic orbifold curves thus our model can be viewed as the classical description of chen ruan cohomology for abelian orbifolds the model simplifies computation of chen ruan cohomology ring using our model we give a version of wall crossing formula

stringy chern classes of singular varieties motivic integration m kontsevich motivic integration lecture at orsay 1995 and macpherson s transformation r macpherson chern classes for singular varieties ann of math 100 1974 423 432 are combined in this paper to construct a theory of stringy chern classes for singular varieties these classes enjoy strong birational invariance properties and their definition encodes data coming from resolution of singularities the singularities allowed in the theory are those typical of the minimal model program examples are given by quotients of manifolds by finite groups for the latter an explicit formula is proven assuming that the canonical line bundle of the manifold descends to the quotient this gives an expression of the stringy chern class of the quotient in terms of chern schwartz macpherson classes of the fixed point set data

analysis and design of time variant fuzzy systems based on dynamic fuzzy inference in this paper a class of time variant fuzzy systems is designed and analyzed firstly a novel model of dynamic fuzzy inference dfi is proposed and the corresponding dfi method is obtained then the response abilities of time variant fuzzy systems constructed by the dfi method are analyzed some sufficient conditions for time variant fuzzy systems as step functions fitted functions and interpolation functions are derived furthermore a sufficient and necessary condition for time variant fuzzy systems as interpolation functions is also deduced in addition the approximation problem of time variant fuzzy systems is discussed it is proved that time variant fuzzy systems constructed by the dfi method are universal approximators to a class of nonlinear systems in addition the approximation accuracy of the corresponding time variant fuzzy systems is investigated finally a simulation experiment is provided to demonstrate how to design a time variant fuzzy system in order to approximate a given nonlinear system to a desired accuracy

contact cohomology of the projective plane we construct an associative ring which is a deformation of the quantum cohomology ring of the projective plane just as the quantum cohomology encodes the incidence characteris tic numbers of rational plane curves the contact cohomology encodes the tangency characteristic numbers 1 introduction in this paper we construct an associative ring which we call the contact cohomology ring of the projective plane we believe that an analogous construction should work for all homogeneous varieties but in our proof of associativity we rely on certain technical results from our earlier paper on characteristic numbers of rational plane curves ek98 as we formulate it in section 3 of the present paper the quantum product is actually a whole family of products parametrized by elements of the chow ring

new calabi yau orbifolds with mirror hodge diamonds abstract we prove a representation theoretic version of borisov batyrev mirror symmetry and use it to construct infinitely many new pairs of orbifolds with mirror hodge diamonds with respect to the usual hodge structure on singular complex cohomology we conjecture that the corresponding orbifold hodge diamonds are also mirror when x is the fermat quintic in p 4 and x is a sym 5 equivariant toric resolution of its mirror x we deduce that for any subgroup of the alternating group a 5 the hilbert schemes hilb x and hilb x are smooth calabi yau threefolds with explicitly computed mirror hodge diamonds

fuzzy reasoning method by optimizing the similarity of truth tables this paper presents a new fuzzy reasoning method by optimizing the similarity of truth tables os method for short its basic idea is to find a fuzzy set such that the truth tables generated by the antecedent rule and the consequent rule are as similar as possible based on this idea the principle of os method and the fuzzy reasoning with os method are given and discussed and then the os methods with certain similarity measure and several fuzzy implications are investigated finally numerical examples are analyzed to compare the proposed method with compositional rule of inference cri method

decision support for fuzzy comprehensive evaluation of urban development urban development often impacts the economic development pattern and the spacial distribution of resource allocation of a particular area urban development can be conceptualized as a multicriteria decision making problem therefore multicriteria evaluation has been used to trace the trend of urban development in this paper a fuzzy multicriteria evaluation model is developed to study the trend of urban development first a multilayer evaluation index system is presented it is used to conduct horizontal analysis on urban systems second a fuzzy multicriteria multilayer evaluation model is proposed third the detailed modeling aspects are discussed which include the fuzzy evaluation models under different evaluation rules the methods used to determine the weights of criteria and the determination of the membership grades of evaluation matrix the model has been implemented and the application results indicate that the proposed model is able to represent those important factors affecting urban development layer by layer and stage by stage

on the convergence of multiobjective evolutionary algorithms we consider the usage of evolutionary algorithms for multiobjective programming mop i e for decision problems with alternatives taken from a real valued vector space and evaluated according to a vector valued objective function selection mechanisms possibilities of temporary fitness deterioration and problems of unreachable alternatives for such multiobjective evolutionary algorithms moeas are studied theoretical properties of moeas such as stochastic convergence with probability 1 are analyzed

hom stacks and restriction of scalars fix an algebraic space s and let x and y be separated artin stacks of finite presentation over s with finite diagonals over s we define a stack homs x y classifying morphisms between x and y assume that x is proper and flat over s and assume fppf locally on s that there exists a finite finitely presented flat cover z x with z an algebraic space then we show that homs x y is an artin stack with quasi compact and separated diagonal