supersymmetry and singular perturbations abstract first it is shown in an abstract framework that supersymmetric quantum theory may give rise to very singular perturbations which make perturbation theories invalid then the abstract results are applied to a model of 1 dimensional supersymmetric quantum mechanics witten s model to obtain some families of singular hamiltonians some concrete examples which reveal their singularness are discussed in detail

relative index theorems and supersymmetric scattering theory we discuss supersymmetric scattering theory and employ krein s theory of spectral shift functions to investigate supersymmetric scattering systems this is the basis for the derivation of relative index theorems on some classes of open manifolds as an example we discuss the de rham complex for obstacles in n and asymptotically flat manifolds it is shown that the absolute or relative euler characteristic of an obstacle in n may be obtained from scattering data for the laplace operator on forms with absolute or relative boundary conditions respectively in the case of asymptotically flat manifolds we obtain the chern gauss bonnet theorem for thel2 euler characteristic

on the toda and kac van moerbeke systems given a solution of the toda lattice we explicitly construct a solution of the kac van moerbeke system related to each other by a miura type transformation as an illustration of our method we derive the n soliton solutions of the kac van moerbeke lattice

positive configurations of flags in a building and limits of positive representations parreau compactified the hitchin component of a closed surface s of negative euler characteristic in such a way that a boundary point corresponds to the projectivized length spectrum of an action of pi 1 s on an mathbb r euclidean building in this paper we use the positivity properties of hitchin representations introduced by fock and goncharov to explicitly describe the geometry of a preferred collection of apartments in the limiting building

commutation methods applied to the mkdv equation an explicit construction of solutions of the modified korteweg de vries equation given a solution of the ordinary korteweg de vries equation is provided our theory is based on commutation methods i e n 1 supersymmetry underlying miura s transformation that links solutions of the two evolution equations

min max attribute object bireducts on unifying models of reducts in rough set theory abstract a decision table describes a finite set of objects ob by using a finite set of condition attributes c and a finite set of decision attributes d pawlak defines attribute reducts by considering the entire decision table as a generalization we introduce the notion of min max attribute object bireducts of a sub table restricted by a pair b x of a subset of condition attributes b and a subset of objects x a pair r z is a min max attribute object bireduct of b x if and only if r is a minimal subset of b such that r and b make the same correct decisions for objects in x and z is a maximal subset of x for which b can make the correct decisions we propose the notion of the decidability of objects and introduce the decidable region of a set of objects as a generalization of the positive region of the set we define and interpret a min max attribute object bireduct based on the decidable region min max attribute object bireducts offer a general model and existing models of attribute reducts are special cases the results lead to a unified framework for studying four types of attribute reducts

relative reducts in consistent and inconsistent decision tables of the pawlak rough set model a relative reduct can be considered as a minimum set of attributes that preserves a certain classification property this paper investigates three different classification properties and suggests three distinct definitions accordingly in the pawlak rough set model while the three definitions yield the same set of relative reducts in consistent decision tables they may result in different sets in inconsistent tables relative reduct construction can be carried out based on a discernibility matrix the study explicitly stresses a fact that the definition of a discernibility matrix should be tied to a certain property regarding the three classification properties we can define three distinct definitions accordingly based on the common structure of the specific definitions of relative reducts and discernibility matrices general definitions of relative reducts and discernibility matrices are suggested

anosov flows surface groups and curves in projective space note that in 10 w goldman gives a complete description of these connected components in the case of finite covers of psl 2 r in the case of psl 2 r two homeomorphic components called teichmuller spaces play a central role these two components are well known to be homeomorphic to a ball of dimension 6g 6 n hitchin generalises this situation to psl n r indeed one of these components when n is odd and two when n is even has a very simple topology let us define an n fuchsian representation to be a representation which can be written as 0 where 0 is a cocompact representation with values in psl 2 r and is the irreducible representation of psl 2 r in psl n r we denote by reph 1 s psl n r a connected component that contains fuchsian representations and call it a hitchin component in fact when n is odd there is one hitchin component and when n is even two isomorphic ones n hitchin proves in 17

explicit construction of solutions of the modified kadomtsev petviashvili equation abstract given a solution of the kadomtsev petviashvili equation we explicitly construct a solution of the modified kadomtsev petviashvili equation related to one another by a generalized miura transformation the construction is modeled after a previous treatment of the modified korteweg de vries case as an illustration of our method we derive the soliton solutions of the modified kadomtsev petviashvili equation

local rigidity of discrete groups acting on complex hyperbolic space the superrigidity theorem of margulis see zimmer 17 classifies finite dimensional representations of lattices in semi simple lie groups of real rank strictly larger than 1 it is a fundamental problem to obtain the classification of finite dimensional representations of lattices in rank i semi simple lie groups that this problem will be considerably harder than the previous one is suggested by the existence of continuous families of inequivalent representations or in other words the existence of non trivial deformations in johnson millson 6 and kourouniotis 8 such deformations were constructed for certain representations of lattices in so n 1 based on a construction of thurston called bending the deformation space of the representation of a lattice f so n 1 obtained by restricting an inclusion so n 1 so n l 1 to f is of particular interest if n 2 the space of infinitesimal deformations is hi f r 1 where f acts on r 1 by the restriction of the standard action of so n 1 the space of infinitesimal deformations is non zero for the standard arithmetic examples and the main point of the papers cited above was to establish that some of these infinitesimal deformations are integrable in 6 it is also shown that some are not in this paper we study the complex analogue of the above example we let f be a cocompact torsion free lattice in su n 1 and consider the deformation space of the representation of f obtained by restricting an inclusion su n 1 su n i 1 if n l the space of infinitesimal deformations is h f r h f c 1 in the first summand f acts trivially and the infinitesimal deformations are tangent to the obvious deformations obtained by deforming f in u n 1 by a curve of homomorphisms into the center of u n 1 observe that the above inclusion factors as su n 1 u n 1 su n i 1 in the second summand f acts by the restriction of the standard action of su n 1 this summand is non zero for the standard arithmetic examples

attribute reduction based on evidence theory in incomplete decision systems attribute reduction is a basic issue in knowledge representation and data mining this paper deals with attribute reduction in incomplete information systems and incomplete decision systems based on dempster shafer theory of evidence the concepts of plausibility reduct and belief reduct in incomplete information systems as well as relative plausibility reduct and relative belief reduct in incomplete decision systems are introduced it is shown that in an incomplete information system an attribute set is a belief reduct if and only if it is a classical reduct and a plausibility consistent set must be a classical consistent set in a consistent incomplete decision system the concepts of relative reduct relative plausibility reduct and relative belief reduct are all equivalent in an inconsistent incomplete decision system an attribute set is a relative plausibility reduct if and only if it is a relative reduct a plausibility consistent set must be a belief consistent set and a belief consistent set is not a plausibility consistent set in general

constructing solutions of the mkdv equation abstract using commutation methods i e n 1 supersymmetry underlying miura s transformation an explicit construction of solutions of the modified korteweg de vries equation given a solution of the ordinary korteweg de vries equation is provided

deformation spaces associated to compact hyperbolic manifolds in this paper we take a first step toward understanding representations of cocompact lattices in so n 1 into arbitrary lie groups by studying the deformations of rational representations see proposition 5 1 for a rather general existence result this proposition has a number of algebraic applications for example we remark that such deformations show that the margulis super rigidity theorem see 30 cannot be extended to the rank 1 case we remark also that if so n 1 is one of the standard arithmetic examples described in section 7 then has a faithful representation in so n 1 the galois conjugate of the uniformization representation and proposition 5 1 may be used to deform the direct sum of and the trivial representation in so n 2 thereby constructing non trivial families of irreducible orthogonal representations of however most of this paper is devoted to studying certain spaces of representations which are of interest in differential geometry in a sense which we now explain

a fuzzy rough set approach for incremental feature selection on hybrid information systems in real applications there may exist many kinds of data e g boolean categorical real valued and set valued data and missing data in an information system which is called as a hybrid information system his a new hybrid distance hd in his is developed based on the value difference metric and a novel fuzzy rough set is constructed by combining the hd distance and the gaussian kernel considering the information systems often vary with time the updating mechanisms for attribute reduction feature selection are analyzed with the variation of the attribute set fuzzy rough set approaches for incremental feature selection on his are presented then two corresponding incremental algorithms are proposed respectively finally extensive experiments on eight datasets from uci and an artificial dataset show that the incremental approaches significantly outperform non incremental approaches with feature selection in the computational time

rough set concept analysis based on ideas from formal concept analysis this paper interprets the notions of rs definable concepts i e rough set definable concepts and the boolean algebra of rs definable concepts we explicitly represent a rs definable concept as a pair of an extension and an intension where the extension is a set of objects and the intension is a family of sets of attribute value pairs called avp sets an object in the extension satisfies at least one avp set in the intension and each avp set in the intension is satisfied by only objects in the extension the two directional connections produce an atomic boolean algebra of rs definable concepts corresponding to the lattice of formal concepts in formal concept analysis the boolean algebra of rs definable concepts is used to define and interpret a subset of objects through a pair of lower and upper approximations the new formulation emphasizes on an in depth conceptual understanding of rough set concept analysis

asymptotics of higgs bundles in the hitchin component in this paper we pursue a more geometric approach to compactification of the hitchin component our main motivation is wolf s harmonic map interpretation of thurston s compactification of teichmuller space with measured foliations using hitchin s parameterization of the hitchin component by holomorphic differentials we study asymptotics of certain rays of representations more precisely along these rays we solve the hitchin equations asymptotically and use the solution to study the asymptotics of the parallel transport operator of the associated flat connection the asymptotics of the corresponding family of equivariant harmonic maps to the symmetric space sl n r so n r proves a conjecture of katzarkov noll pandit and simpson 17 on the hitchin wkb problem in our setting

matrix korteweg de vries and modified korteweg de vries hierarchies noncommutative soliton solutions the present work continues work on kdv type hierarchies presented by s carillo and c schiebold noncommutative korteweg de vries and modified korteweg de vries hierarchies via recursion methods j math phys 50 073510 2009 10 1063 1 3155080 general solution formulas for the kdv and mkdv hierarchies are derived by means of banach space techniques both in the scalar and matrix case a detailed analysis is given of solitons breathers their countable superpositions as well as of multisoliton solutions for the matrix hierarchies

class specific attribute reducts in rough set theory abstract the concept of attribute reducts plays a fundamental role in rough set analysis there are at least two possibilities to define an attribute reduct a classification based or global attribute reduct is a minimal subset of condition attributes that preserves the positive region of the decision classification namely the positive regions of all decision classes in a decision table a class specific class dependent or local attribute reduct is a minimal subset of condition attributes that preserves the positive region of a particular decision class while a classification based reduct may not work equally well for every decision class a class specific attribute reduct is optimally tailored to a particular decision class however studies in rough set theory are dominated by classification based reducts there is very limited investigation on class specific reducts an objective of this paper is to draw attention to class specific reducts we systematically compare the two types of reducts and investigate their relationships with respect to both individual reducts and families of all reducts it is possible to derive a class specific reduct from a classification based reduct and to derive a classification based reduct from a family of class specific reducts the families of all class specific reducts provide a pair of lower and upper bounds of the family of all classification based reducts based on a three way classification of attributes into the pair wise disjoint sets of core marginal and nonuseful attributes we examine relationships between the corresponding classes of classification based and class specific attributes the union of the sets of class specific core attributes is the set of classification based core attributes it is only possible to obtain an upper bound for the set of classification based marginal attributes and a lower bound for the set of classification based nonuseful attributes from the family of the class specific corresponding sets of attributes

decision region distribution preservation reduction in decision theoretic rough set model abstract in the pawlak rough set model the positive region the boundary region and the non negative region are monotonic with respect to the set inclusion of attributes however the monotonicity property of the decision regions positive region boundary region or non negative region with respect to the set inclusion of attributes does not hold in the decision theoretic rough set model therefore the decision regions may be changed after attribute reduction based on quantitative preservation or qualitative preservation of decision regions this effect is observed partly because three decision regions are defined by introducing the probabilistic threshold values in addition heuristic reduction algorithms based on decision regions may find super reducts because of the non monotonicity of decision regions to address the above issues this paper proposes solutions to the attribute reduction problem based on decision region preservation in the decision theoretic rough set model first the positive region distribution preservation reduct the boundary region distribution preservation reduct and the negative region distribution preservation reduct are introduced into the decision theoretic rough set model second three new monotonic measures are constructed by considering variants of the conditional information entropy from which we can obtain the heuristic reduction algorithms the results of the experimental analysis validate the monotonicity of new measures and verify the effectiveness of decision region distribution preservation reducts

local attribute reductions for decision tables abstract attribute reduction is among the most important areas of research in rough sets this paper investigates the types of local attribute reduction for decision tables we propose the concepts of lth decision class lower approximation reduction lth decision class reduction and lth decision class reduction for decision tables and provide their corresponding reduction algorithms via discernibility matrices we also establish the relationship between positive region reduction and the lth decision class reduction and report a case study using the university of california irvine dataset to verify the theoretical results

local reduction of decision system with fuzzy rough sets one important and valuable topic in fuzzy rough sets is attribute reduction of decision system the existing attribute reductions with fuzzy rough sets consider all decision classes together and cannot identify key conditional attributes explicitly for special decision class in this paper we introduce the concept of local reduction with fuzzy rough sets for decision system the local reduction can identify key conditional attribute and offer a minimal description for every single decision class approach of discernibility matrix is employed to investigate the structure of local reduction at last several experiments are performed to show that the idea of local reduction is feasible and valid

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

large time behavior of the lp norm of schrodinger semigroups abstract letv 0 v c0 rv with v 3 be such that h 1 2 v 0 but for any e 0 1 2 1 e v is not positive we determine the exact rate of divergence of the norm of e th as a map from l to l a number of related problems are discussed

neighbor inconsistent pair selection for attribute reduction by rough set approach rough set theory as one of the most useful soft computing methods dealing with vague and uncertain information has been successfully applied to many fields and one of its main applications is to perform attribute reduction although many heuristic attribute reduction algorithms have been proposed within the framework of the rough set theory these methods are still computationally time consuming in order to overcome this deficit we propose in this paper two quick feature selection algorithms based on the neighbor inconsistent pair which can reduce the time consumed in finding a reduct at first we propose several concepts regarding simplified decision table u prime and neighbor inconsistent pairs based on neighbor inconsistent pairs we constructed two new attribute significance measures furthermore we put forward two new attribute reduction algorithms based on quick neighbor inconsistent pairs the key characteristic of the presented algorithms is that they only need to calculate u prime r once under the process of selecting the best attribute from attribute sets c r while most existing algorithms need to calculate partition of u prime for c r times in addition the proposed algorithms need only to deal with the equivalent classes in u prime r that contain at least one neighbor inconsistent pair while most existing algorithms need to consider all objects in u prime the experimental results show that the proposed algorithms are feasible and efficient

structure of positive solutions to δ v u 0 in rn on etudie la structure de toutes les solutions positives d une equation de schrodinger stationnaire ou le potentiel v est suppose etre une fonction a valeur reelle appartenant a l p loc r n avec p n 2 pour n 2 et p 1 pour n 1 on considere une formule de representation explicite pour des solutions positives leurs asymptotes a l infini et le probleme de dirichlet avec une condition aux limites a l infini

feature selection for monotonic classification monotonic classification is a kind of special task in machine learning and pattern recognition monotonicity constraints between features and decision should be taken into account in these tasks however most existing techniques are not able to discover and represent the ordinal structures in monotonic datasets thus they are inapplicable to monotonic classification feature selection has been proven effective in improving classification performance and avoiding overfitting to the best of our knowledge no technique has been specially designed to select features in monotonic classification until now in this paper we introduce a function which is called rank mutual information to evaluate monotonic consistency between features and decision in monotonic tasks this function combines the advantages of dominance rough sets in reflecting ordinal structures and mutual information in terms of robustness then rank mutual information is integrated with the search strategy of min redundancy and max relevance to compute optimal subsets of features a collection of numerical experiments are given to show the effectiveness of the proposed technique

the gardner equation and the l 2 stability of the n soliton solution of the korteweg de vries equation multi soliton solutions of the korteweg de vries equation kdv are shown to be globally l2 stable and asymptotically stable in the sense of martel and merle the proof is surprisingly simple and combines the gardner transform which links the gardner and kdv equations together with the martel merle tsai and martel merle recent results on stability and asymptotic stability in the energy space applied this time to the gardner equation as a by product the results of maddocks sachs and merle vega are improved in several directions

compactification d espaces de representations de groupes de type fini let be a finitely generated group and g be a noncompact semisimple connected real lie group with finite center we consider the space fancyscript x gamma g of conjugacy classes of semisimple representations of into g which is the maximal hausdorff quotient of rm hom gamma g g we define the translation vector of g in g with value in a weyl chamber as a natural refinement of the translation length of g in the symmetric space associated with g we construct a compactification of fancyscript x gamma g induced by the marked translation vector spectrum generalizing thurston s compactification of the teichmuller space we show that the boundary points are projectivized marked translation vector spectra of actions of on affine buildings with no global fixed point an analoguous result holds for any reductive group g over a local field

attribute selection with fuzzy decision reducts rough set theory provides a methodology for data analysis based on the approximation of concepts in information systems it revolves around the notion of discernibility the ability to distinguish between objects based on their attribute values it allows to infer data dependencies that are useful in the fields of feature selection and decision model construction in many cases however it is more natural and more effective to consider a gradual notion of discernibility therefore within the context of fuzzy rough set theory we present a generalization of the classical rough set framework for data based attribute selection and reduction using fuzzy tolerance relations the paper unifies existing work in this direction and introduces the concept of fuzzy decision reducts dependent on an increasing attribute subset measure experimental results demonstrate the potential of fuzzy decision reducts to discover shorter attribute subsets leading to decision models with a better coverage and with comparable or even higher accuracy

large scale multimodality attribute reduction with multi kernel fuzzy rough sets in complex pattern recognition tasks objects are typically characterized by means of multimodality attributes including categorical numerical text image audio and even videos in these cases data are usually high dimensional structurally complex and granular those attributes exhibit some redundancy and irrelevant information the evaluation selection and combination of multimodality attributes pose great challenges to traditional classification algorithms multikernel learning handles multimodality attributes by using different kernels to extract information coming from different attributes however it cannot consider the aspects fuzziness in fuzzy classification fuzzy rough sets emerge as a powerful vehicle to handle fuzzy and uncertain attribute reduction in this paper we design a framework of multimodality attribute reduction based on multikernel fuzzy rough sets first a combination of kernels based on set theory is defined to extract fuzzy similarity for fuzzy classification with multimodality attributes then a model of multikernel fuzzy rough sets is constructed finally we design an efficient attribute reduction algorithm for large scale multimodality fuzzy classification based on the proposed model experimental results demonstrate the effectiveness of the proposed model and the corresponding algorithm

on critical and subcritical sturm liouville operators we study critical and subcritical sturm liouville operators k 1 ddx p ddx v in l2 a b k dx a b r defined as friedrichs extensions under most general conditions on k p and v in particular we prove the equivalence of the notions of criticality as introduced by simon and murata for an important class of potentials v

approaches to knowledge reduction based on variable precision rough set model this paper deals with approaches to knowledge reduction based on variable precision rough set model the concepts of lower distribution reduct and upper distribution reduct based on variable precision rough sets vprs are first introduced their equivalent definitions are then given and the relationships among lower and upper distribution reducts and alternative types of knowledge reduction in inconsistent systems are investigated it is proved that for some special thresholds lower distribution reduct is equivalent to the maximum distribution reduct whereas upper distribution reduct is equivalent to the possible reduct the judgement theorems and discernibility matrices associated with the lower and upper distribution reducts are also established from which we can obtain the approaches to knowledge reduction in vprs

conjugacy classes of n tuples in lie algebras and algebraic groups let g be a reductive algebraic group over an algebraically closed field f of characteristic zero and let l g be the lie algebra of g then g acts on g by inner automorphisms and it acts on l g by the adjoint representation by taking the diagonal actions we get actions of g on the spaces of n tuples g n and l g in this paper we will prove a number of geometric properties of the orbits of g on these spaces of n tuples