comparison between two analytic torsions on orbifolds in this paper we establish an equality between the analytic torsion introduced by dar math z 194 2 193 216 1987 and the orbifold analytic torsion defined by ma trans am math soc 357 6 2205 2233 2005 on an even dimensional manifold with isolated conical singularities which in addition has an orbifold structure we assume the orbifold flat vector bundle is an honest vector bundle although the metric on the flat bundle may not be flat

stratifiable maps and topological invariants let x and y be spaces and f x y be a map between them then a large family of problems in topology and geometry involve the attempt to relate the invariants of x and y via f this attempt has been successful often for the case x and y manifolds and f the projection of a fibre bundle for many types of important invariants for example the result of chernhirzebruch serre chs asserts that for y simply connected the signature of x is the product of the signatures of y and of the fibre f 1 y in this paper we undertake the study of maps in which the fiber may vary from point to point the spaces x and y will be any whitney stratified spaces with even codimension strata e g algebraic varieties and f will be a stratified map this means essentially that for v a component of a stratum of y thus v is an open manifold f 1v is a union of strata of x and the restriction of f to f71v is a locally trivial fibre bundle for example subanalytic maps of subanalytic sets can be stratified with respect to whitney

choquet integral with respect to łukasiewicz filters and its modifications in many decision problems a set of actions is evaluated with respect to a set of points of view called criteria this paper follows two aims first to compare the so called level dependent choquet integral introduced recently by greco et al with another transformation of choquet integral proposed by havranova and kalina the other aim of this paper is to look for an appropriate utility function in a given setting we illustrate our approach on a practical example utilizing the level dependent choquet integral

complex geometry and the asymptotics of harish chandra modules for real reductive lie groups i let g be a connected semisimple real matrix group it is now apparent that the representation theory of g is intimately connected with the complex geometry of the flag variety 9 by studying appropriate orbit structures on 9 we are naturally led to representation theory in the category of harish chandra modules x or the representation theory of category 9 the jacquet functor j f 9 has proved a useful tool in converting yfw problems into 9 problems which are often more tractable in this paper we advance the philosophy that the complex geometry of 9 associated to yf and 9 interacts in a natural way with the functor j leading to deep new information on the structure of jacquet modules this in turn gives new insight into the structure of certain nilpotent cohomology groups associated to harish chandra modules our techniques are based upon many of the ideas present in the proof of the kazhdan lusztig conjectures and bernstein s proof of the jantzen conjecture

the topological trace formula the topological trace formula is a computation of the lefschetz number of a hecke correspondence c acting on the weighted cohomology groups defined in ghm of a locally symmetric space x it expresses this lefschetz number as a sum of contributions from fixed point components of c on the reductive borel serre compactifi cation of x the proof uses the lefschetz fixed point formula of gm2

hodge cohomology of gravitational instantons we study the space of l2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type these metrics generalize the geometric structures at infinity of several different well known classes of metrics including asymptotically locally euclidean manifolds the known types of gravitational instantons and also poincare metrics on q rank 1 ends of locally symmetric spaces and on the complements of smooth divisors in kahler manifolds the answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold the l2 signature formula implied by our result is closely related to the one proved by dai 25 and more generally by vaillant 67 and identifies dai s invariant directly in terms of intersection cohomology of differing perversities this work is also closely related to a recent paper of carron 12 and the forthcoming paper of cheeger and dai 17 we apply our results to a number of examples gravitational instantons among them arising in predictions about l2 harmonic forms in duality theories in string theory

singular chain intersection homology for traditional and super perversities we introduce a singular chain intersection homology theory which generalizes that of king and which agrees with the deligne sheaf intersection homology of goresky and macpherson on any topological stratified pseudomanifold compact or not with constant or local coecients and with traditional perversities or superperversities those satisfying p 2 0 for the case p 2 1 these latter perversitie were introduced by cappell and shaneson and play a key role in their superduality theorem for embeddings we further describe the sheafification of this singular chain complex and its adaptability to broader classes of stratified spaces 2000 mathematics subject classification primary 55n33 secondary 32s60 57n80

vector t norms with applications some basic t norms defined on 0 1 are well known in many study areas and applications however more general extension of them into vector forms can be used in a lot of new decision making realms in this study we first define preference vector on a linearly ordered set which includes different special vectors that are mathematically equivalent but with different application backgrounds and practical meanings as a reasoning rule we provide a merging method for more than two preference vectors to be aggregated into a finally resultant preference vector the merging method is based on a special vector value function which can be seen as a reasonable counterpart of product t norm f x y xy x and y belong to 0 1 in addition we use bilinear frame to define corresponding four types of basic bilinear vector t norms which are just counterparts of basic t norms from many aspects mathematically preference vectors are related to decreasing matrices and we find the general entry relation for the decreasing matrices by which we prove that a decreasing matrix is commutative and closed under matrix multiplication thus we finally present the definition of preference multiplication commutative monoid which is equivalent to product bilinear vector t norm we also show illustrative examples and applications of some results

the application of multiwavelet filterbanks to image processing multiwavelets are a new addition to the body of wavelet theory realizable as matrix valued filterbanks leading to wavelet bases multiwavelets offer simultaneous orthogonality symmetry and short support which is not possible with scalar two channel wavelet systems after reviewing this theory we examine the use of multiwavelets in a filterbank setting for discrete time signal and image processing multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank we describe two methods repeated row and approximation deapproximation for obtaining such a vector input stream from a one dimensional 1 d signal algorithms for symmetric extension of signals at boundaries are then developed and naturally integrated with approximation based preprocessing we describe an additional algorithm for multiwavelet processing of two dimensional 2 d signals two rows at a time and develop a new family of multiwavelets the constrained pairs that is well suited to this approach this suite of novel techniques is then applied to two basic signal processing problems denoising via wavelet shrinkage and data compression after developing the approach via model problems in one dimension we apply multiwavelet processing to images frequently obtaining performance superior to the comparable scalar wavelet transform

smoothing q convex functions in the singular case definition 1 let f2 be a complex space f 2 r a continuous function and q 1 an integer then a q is called q convex in the c sense if for each point p c f2 there is a local coordinate patch u on 62 with a holomorphic embedding z u t for some open set u c c n and a c strongly q convex function on v such that 1u o i b 0 is called q convex with corners if for each p c f2 there is an open neighborhood u c f2 and on u finitely many q convex functions in the c sense q1 q such that qi u max 01 qz

owa generation function and some adjustment methods for owa operators with application we propose the concept of ordered weighted averaging owa generation function with some properties illustrative examples and usages a number of new properties of owa operators and relations between some well known owa operators are proposed and proved using owa generation functions we discuss some orness andness adjustment methods for a predetermined owa operator a practical application about investment prediction problem is given with detailed illustration and analysis which can show the advantages of the adjustment methods proposed in this paper in particular the concept consistent adjustment matrix is proposed and the interests and advantages of it can be shown by its special properties

simplicial differential forms with poles shadow forms consider a simplicial complex k whitney associated to each simplicial cochain 4 a differential form v 4 on k whitney s map v from simplicial cochains to differential forms is a map of cochain complexes which induces the derham isomorphism we call the forms v 4 whitney forms they have been useful in several contexts most notably integral geometry and rational homotopy theory in this paper we introduce a generalization of whitney forms called shadow forms we associate to certain simplicial chains g with respect to the first derived subdivision k of k a shadow form w on k let us illustrate the construction of shadow forms when k is a single n simplex which we now denote by a in this case w g is defined for k simplices g of ax which do not lie in the boundary of a or for linear combinations of these for example if a is the 2 simplex then either of the 1 simplices or 2 pictured below has an associated shadow form

the boden hu conjecture holds precisely up to rank 8 we consider moduli schemes of vector bundles over a smooth projective curve endowed with parabolic structures over a marked point boden and hu observed that a slight variation of the weights leads to a desingularisation of the moduli scheme and they conjectured that one can always obtain a small resolution this way the present text proves this conjecture in some cases including all bundles of rank up to eight and gives counterexamples in all other cases in particular in every rank beyond eight the main tool is a generalisation of ext groups involving more than two quasiparabolic bundles

lefschetz duality for intersection co homology we prove the lefschetz duality for intersection co homology in the framework of pesudomanifolds we work with general perversities and without restriction on the coefficient ring

witt spaces a geometric cycle theory for ko homology at odd primes introduction this paper studies a class of stratified piecewiselinear pseudomanifolds which we call witt spaces characterized by natural local intersection homology conditions 11 we compute the cobordism groups by introducing an invariant taking values in the witt group of symmetric bilinear forms over the rationals w q these pseudomanifolds solve a problem posed by d sullivan 25 to construct a class of p l cycles with signature which represent the connected version of ko homology at odd primes ko 0d z 1 2 the result was one of the first applications of the intersection homology theory of goresky and macpherson 11 specifically the rational intersection homology groups of witt spaces satisfy a poincare duality theorem to each witt space x we associate a p l invariant w x with values in w q this invariant generalizes the signature of manifolds and satisfies cobordism invariance additivity and a product formula adapting classical surgery spherical modification to this setting we prove that w x determines the cobordism class of x and obtain an explicit description of the witt cobordism groups the only nontrivial groups occur in dimensions 4k and for k 0 they are w q sullivan 25 27 has shown that a class of p l pseudomanifolds equipped with such an invariant possesses canonical orientations in ko 0 z 1 2 the orientations induce a natural transformation it of homology theories from witt space bordism to ko 0 z 1 2 the structure of w q is known 14 and we conclude that it is an equivalence at odd primes in this paper we study the cobordism theory of a class of stratified p l pseudomanifolds by means of the recent intersection homology theory of goresky and macpherson 11 goresky and macpherson were interested in finding a class of spaces with cobordism invariant signature for the purpose of extending the hirzebruch l class to the setting of manifolds with

on the topology of birational minimal models in the study of higher dimensional algebraic geometry an important reduction step is to study certain good birational models of a given algebraic manifold this leads to the famous minimal model program initiated by mori the search for birational models with numerically effective canonical divisors and with at most terminal singularities the existence problem is still completely open in dimensions bigger than three but even worse in contrast to the two dimensional case the minimal model is not unique in higher dimensions it is then an important question to see what kind of invariants are shared by all the birationally equivalent minimal models and more generally to see what kind of invariants are preserved under certain elementary birational transformations in this paper some results in this direction are given theorem a let f x x be a birational map between two smooth complex projective varieties such that the canonical bundles are numerically effective along the exceptional loci then x and x have the same betti numbers in particular birational smooth minimal models have the same betti numbers

smart 2017 second conference on subdivision geometric and algebraic methods isogeometric analysis and refinability in italy abstract this introductory paper provides an overview of a selection of contributions presented at the 2nd international conference on subdivision geometric and algebraic methods isogeometric analysis and refinability in italy smart2017 gaeta september 17 21 2017 the smart2017 special issue is also an opportunity to honor the memory of laura gori who was one of the proposers of this conference series

generalizations of owa operators owa operators can be seen as symmetrized weighted arithmetic means as choquet integrals with respect to symmetric measures or as comonotone additive functionals following these three different looks on owas we discuss several already known generalizations of owa operators including gowa iowa oma operators as well as we propose new types of such generalizations

interval sugeno integral with preference sugeno integral is based on fuzzy integral inference and widely used in applications such as decision making and computational intelligence when concerned inputs are intervals directly using sugeno integral to respectively aggregate the lower bounds and upper bounds of those intervals has limitations and does not embody fuzzy integral inference this study analyzes the fuzzy integral inference in interval environment defines some more suitable orderings on the set of all intervals in 0 1 i e the congruent lambda ordering and then proposes the interval sugeno integral with preference the novel aggregation technique proposed in this study proves to better embody fuzzy integral inference when performing sugeno integral

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

intersection cohomology of quotients of nonsingular varieties let m p be a nonsingular projective variety acted on by a connected complex reductive group g kc via a homomorphism g gl n 1 which is the complexification of a homomorphism k u n 1 geometric invariant theory git gives us a recipe to form a quotient m m g of the set of semistable points and many interesting spaces in algebraic geometry are constructed in this manner mfk94 but often this quotient is singular and hence intersection cohomology with middle perversity is an important topological invariant the purpose of this paper is to present a way to compute the middle perversity intersection cohomology of the singular quotients the choice of an embedding m p provides us with a moment map for the k action and the morse stratification of m with respect to its norm square is kequivariantly perfect with the unique open dense stratum m kir84 hence one can compute the betti numbers for the equivariant cohomology h k m as well as the cup product at least in principle see also kir92 when g acts locally freely on m we get an orbifold m g m g and h k m h m g ih m g

the decomposition theorem perverse sheaves and the topology of algebraic maps we give a motivated introduction to the theory of perverse sheaves culminating in the decomposition theorem of beilinson bernstein deligne and gabber a goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties while most proofs are omitted we discuss several approaches to the decomposition theorem indicate some important applications and examples

local structures on stratified spaces abstract we develop a theory of conically smooth stratified spaces and their smooth moduli including a notion of classifying maps for tangential structures we characterize continuous space valued sheaves on these conically smooth stratified spaces in terms of tangential data and we similarly characterize 1 excisive invariants of stratified spaces these results are based on the existence of open handlebody decompositions for conically smooth stratified spaces an inverse function theorem a tubular neighborhood theorem an isotopy extension theorem and functorial resolutions of singularities to smooth manifolds with corners

generalizing the migrativity of continuous t norms this paper generalizes the migrativity of triangular norms t norms for short precisely we find those continuous t norms t which satisfy t l 1x l 2y email protected 3t x y where l email protected 0 1 i 1 2 3 are given it is worth pointing out that this paper provides a new characterization of the product t norm

on the reductive borel serre compactification l p cohomology of arithmetic groups for large p the l 2 cohomology of an arithmetic quotient of an hermitian symmetric space i e of a locally symmetric variety is known to have the topological interpretation as the intersection homology of its baily borel satake compactification in this article we observe that even without the hermitian hypothesis the l p cohomology of an arithmetic quotient for p finite and sufficiently large is isomorphic to the ordinary cohomology of its reductive borel serre compactification we use this to generalize a theorem of mumford concerning homogeneous vector bundles their invariant chern forms and the canonical extensions of the bundles here though we are referring to canonical extensions to the reductive borel serre compactification of any arithmetic quotient to achieve that we give a systematic discussion of vector bundles and chern classes on stratified spaces

improved minimax disparity model for obtaining owa operator weights the determination of weights vector is one of the key issues in the theory of ordered weighted averaging owa operators for this reason many weight generating models have been proposed in the literature the main purpose of this note is to point out that the improved minimax disparity model which is suggested by emrouznejad and amin 2010 has infinite solutions as a consequence this model is not reliable

cup and cap products in intersection co homology abstract we construct cup and cap products in intersection co homology with field coefficients the existence of the cap product allows us to give a new proof of poincare duality in intersection co homology which is similar in spirit to the usual proof for ordinary co homology of manifolds

analytic cohomology groups in top degrees of zariski open sets in mathbb p n we show that if a is a closed analytic subset of mathbb p n of pure codimension q then h i mathbb p n setminus a mathcal f are finite dimensional for every coherent algebraic sheaf mathcal f and every i geq n left frac n 1 q right if n 1 geq 2q rm we show that h n 2 mathbb p n setminus a mathcal f 0

eliciting different lattice dominance points to evaluate distribution information finding the maximum and minimum values of a given collection of real inputs is critical in many decision making and evaluation models in often encountered evaluation problems where information is collected based on survey or statistics and embodied by a collection of normalized distributions on lattice we cannot directly obtain the corresponding concept of maximum and minimum to process such situations and related evaluation problem we first define the distributions poset on a given lattice structure and then propose the concept of lattice dominance points which can sometimes be seen as a type generalized maximum points often there may be infinite dominance points to choose from in order to find some more suitable ones according with our intuition and with mathematical completeness we propose an optimization method and distribution t conorm methods to elicit lattice dominances based on given collection of normalized distributions the distribution and bilinear distribution t conorms examples are well defined and some related properties are proposed with strict proofs in addition a commonly used evaluation model is proposed with results for comparing differently elicited lattice dominance points

becker gottlieb transfer in etale homotopy introduction in this paper we establish a version of the beckergottlieb transfer in the context of etale homotopy the transfer map we obtain generalises the becker gottlieb transfer to smooth quasi projective varieties over any algebraically closed field of arbitrary characteristic we next recall the becker gottlieb transfer in topology for fiber bundles with compact fiber see b g 3 p 107 let

an extension of a theorem by cheeger and muller to spaces with isolated conical singularities the aim of this article is to extend a theorem by cheeger and muller to spaces with isolated conical singularities by generalizing the proof of bismut and zhang to the singular setting the main tools in this approach are the witten deformation and local index techniques

poincare duality hilbert complexes and geometric applications abstract let m g be an open oriented and incomplete riemannian manifold the aim of this paper is to study the following two sequences of l 2 cohomology groups 1 h 2 m m i m g defined as the image h 2 min i m g h 2 max i m g 2 h 2 m m i m g defined as the image h 2 min i m g h 2 max i m g we show under suitable hypothesis that the first sequence is the cohomology of a hilbert complex which contains the minimal one and is contained in the maximal one in particular this leads us to prove a hodge theorem for these groups we also show that when the second sequence is finite dimensional then poincare duality holds and that with the same assumptions when dim m 4 n then we can employ h 2 m m 2 n m g in order to define an l 2 signature on m we prove several applications to the intersection cohomology of compact smoothly stratified pseudomanifolds and we get some results about the friedrichs extension i f of i

superperverse intersection cohomology stratification in dependence within its traditional range of perversity parameters intersection cohomology is a topological invariant of pseudomanifolds this is no longer true once one allows superperversities perversities with open image in new window in this case intersection cohomology may depend on the choice of the stratification by which it is defined topological invariance also does not hold if one allows stratifications with codimension one strata nonetheless both errant situations arise in important situations the former in the cappell shaneson superduality theorem and the latter in any discussion of pseudomanifold bordism we show that while full invariance of intersection cohomology under restratification does not hold in this generality it does hold up to restratifications that fix the the top stratum

intersection homology ii in 19 20 we introduced topological invariants ih x called intersection homology groups for the study of singular spaces x these groups depend on the choice of a perversity p a perversity is a function from 2 3 to the non negative integers such that both c and c 2 c are positive and increasing functions of c 2 1 the group ihr is defined for spaces x called pseudomanifolds a pseudomanifold of dimension n is a space that admits a stratification x x n x n z x n 3 x 1 x 0

local cohomology of modules of covariants abstract let g be a connected reductive algebraic group over an algebraically closed field of characteristic zero and let w u be two finite dimensional representations of g in this paper we compute the local cohomology of u sw g provided a certain relatively weak technical condition is true

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

the kashiwara conjugation and wave front sets of regular holonomic distributions on a complex manifold if a distributionu on a complex manifoldx is a solution of a regular holonomicdx module one shows that its wave front sets coincide with the characteristic variety of thedx module generated byu the proof relies essentially on a microlocal form of kashiwara s conjugation functor as a byproduct regular holonomicex modules are locally embedded into the sheaf of temperate microfunctions

the intersection cohomology of the satake compactification of mathcal a _g for g le 4 we completely determine the intersection cohomology of the satake compactifications mathcal a 2 mathrm sat mathcal a 3 mathrm sat and mathcal a 4 mathrm sat except for ih 10 mathcal a 4 mathrm sat we also determine all the ingredients appearing in the decomposition theorem applied to the map from a toroidal compactification to the satake compactification in these genera as a byproduct we obtain in addition several results about the intersection cohomology of the link bundles involved

equivariant sheaves on flag varieties we show that the borel equivariant derived category of sheaves on the flag variety of a complex reductive group is equivalent to the perfect derived category of differential graded modules over the extension algebra of the direct sum of the simple equivariant perverse sheaves this proves a conjecture of soergel and lunts in the case of flag varieties

foliated stratified spaces and a de rham complex describing intersection space cohomology the method of intersection spaces associates cell complexes depending on a perversity to certain types of stratified pseudomanifolds in such a way that poincare duality holds between the ordinary rational cohomology groups of the cell complexes associated to complementary perversities the cohomology of these intersection spaces defines a cohomology theory hi for singular spaces which is not isomorphic to intersection cohomology ih mirror symmetry tends to interchange ih and hi the theory ih can be tied to type iia string theory while hi can be tied to iib theory for pseudomanifolds with stratification depth 1 and flat link bundles the present paper provides a de rham theoretic description of the theory hi by a complex of global smooth differential forms on the top stratum we prove that the wedge product of forms introduces a perversity internal cup product on hi for every perversity flat link bundles arise for example in foliated stratified spaces and in reductive borel serre compactifications of locally symmetric spaces a precise topological definition of the notion of a stratified foliation is given

generalized transformed t conorm integral and multifold integral fuzzy integrals are commonly used as aggregation operators in this paper we present new composite models based on fuzzy integrals with several t conorms these models permit to further increase the computational power of the previous models basic properties of new composite models are studied in particular it is shown that for composite models the only meaningful case is when not all the t conorms are the same

on hermite vector splines and multi wavelets abstract explicit and recursive formulations are derived for the computation of refinable interpolatory hermite vector splines of arbitrary odd degree and supported on 1 1 as well as for the corresponding refinement matrix sequences it is moreover shown that a contracted and shifted version of these hermite vector splines is a minimally supported hermite spline multi wavelet with an explicitly calculated decomposition relation

hodge genera of algebraic varieties i the aim of this paper is to study the behavior of hodge theoretic intersection homology genera and their associated characteristic classes under proper morphisms of complex algebraic varieties we obtain formulae that relate parametrized families of global invariants of a complex algebraic variety x to such invariants of singularities of proper algebraic maps defined on x such formulae severely constrain both topologically and analytically the singularities of complex maps even between smooth varieties similar results were announced by the first and third author in 13 32 2007 wiley periodicals inc

euler characteristics of algebraic varieties this note studies the behavior of euler characteristics and of intersection homology euler characteristics under proper morphisms of algebraic respectively analytic varieties the methods also yield for algebraic respectively analytic varieties formulae comparing these two kinds of euler characteristics the main results are direct consequences of the calculus of constructible functions and grothendieck groups of constructible sheaves similar formulae for hodgetheoretic invariants of algebraic varieties under morphisms were announced by the first and third authors in 5 14 c 2007 wiley periodicals inc

intersection numbers of hecke cycles on hilbert modular varieties let o be the ring of integers of a totally real number field e and set g res e q gl 2 fix an ideal c 0 for each ideal m 0 let t m denote the mth hecke operator associated to the standard compact open subgroup u 0 c of g a f setting x 0 c g q g a k u 0 c where k is a certain subgroup of g r we use t m to define a hecke cycle z m ih 2 e q x 0 c x 0 c here ih denotes intersection homology we use zucker s conjecture proven by looijenga and independently by saper and stern to obtain a formula relating the intersection number z m z n to the trace of t m o t n considered as an endomorphism of the space of hilbert cusp forms on u 0 c

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

fuzzy t conorm integral with respect to fuzzy measures generalization of sugeno integral and choquet integral abstract this article discusses integrals with respect to sugeno s fuzzy measures sugeno integrals and choquet integrals with respect to general fuzzy measures are generalized in the setting of a t conorm algebraic system first t conorm integrals with respect to decomposable measures based on t conorm algebraic system are defined they are a modification of the weber integral secondly they are extended to fuzzy t conorm integrals with respect to general fuzzy measures the extension is made in the same way as the extension of the lebesgue integral to the choquet integral the class of fuzzy t conorm integrals includes choquet integrals and sugeno integrals properties of the integrals especially their representation are discussed

local contribution to the lefschetz fixed point formula for a class of self correspondencesc calledweakly hyperbolic we give a computable formula for the contribution of a fixed point component to the lefschetz number ofc the formula applies to lefschetz numbers of cohomology with coefficients in a constructible complex of sheaves such as intersection homology

cognitive integrals with its generalized and adapted forms motivated by some cognition styles this study first proposes a new type of preaggregation functions called cognitive integrals with its generalized forms rather than being affected only by selected capacity generalized cognitive integrals consider other two parameters the cognitive strength and the involved semicopula our main focus is on cognitive strength by which the integrals values will be monotonically decreasing with respect to our cognitive strength after some appropriated adaptations we later propose the concept of adapted cognitive integrals with two equivalent forms of itself not only being a type of the preaggregation functions we prove that adapted cognitive integrals are indeed one new type of aggregation functions still equipped with the two new parameters like in cognitive integrals

a little microlocal morse theory if a complex analytic function f has a stratified isolated critical point then it is known that the cohomology of the milnor fibre of f has a direct sum decomposition in terms of the normal morse data to the strata we use microlocal morse theory to obtain the same result under the weakened hypothesis that the vanishing cycles along f have isolated support we also investigate an index theoretic proof of this fact

whitney stratified chains and cochains this paper contains the technical constructions necessary for a geometric cycle definition of cohomology and homology in the context of whitney stratifications cup and cap products are interpreted as the transverse intersection of geometric cocycles and cycles