isogeometric variational multiscale modeling of wall bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes abstract in this work we combine i nurbs based isogeometric analysis ii residual driven turbulence modeling and iii weak imposition of no slip and no penetration dirichlet boundary conditions on unstretched meshes to compute wall bounded turbulent flows while the first two ingredients were shown to be successful for turbulence computations at medium to high reynolds number i akkerman y bazilevs v m calo t j r hughes s hulshoff the role of continuity in residual based variational multiscale modeling of turbulence comput mech 41 2008 371 378 y bazilevs v m calo j a cottrell t j r hughes a reali g scovazzi variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows comput methods appl mech engrg 197 2007 173 201 it is the weak imposition of no slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher reynolds number y bazilevs t j r hughes weak imposition of dirichlet boundary conditions in fluid mechanics comput fluids 36 2007 12 26 y bazilevs c michler v m calo t j r hughes weak dirichlet boundary conditions for wall bounded turbulent flows comput methods appl mech engrg 196 2007 4853 4862 these three ingredients form a basis of a possible practical strategy for computing engineering flows somewhere between rans and les in complexity we demonstrate this by solving two challenging incompressible turbulent benchmark problems channel flow at friction velocity reynolds number 2003 and flow in a planar asymmetric diffuser we observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data this lends some credence to the proposed approach which we believe may become a viable engineering tool

a unifying study between modal like operators topologies and fuzzy sets the paper presents the essential connections between modal like operators topologies and fuzzy sets we show for example that each fuzzy set determines a preorder and an alexandrov topology and that similar correspondences hold also for the other direction further a category for preorder based fuzzy sets is defined and it is shown that its equivalent subcategory of representatives is isomorphic to the categories of preordered sets and alexandrov spaces moreover joins meets and complements for the objects in this category of representatives are determined this suggests how to define for fuzzy subsets of a certain universe the lattice operations in a canonical way

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

quantifying the effects of fast acting compression on the envelope of speech fast acting compression has several effects on the envelope of speech signals especially when a target and a background are mixed together three measures of the envelope are described which can be used to quantify these changes 1 within signal modulation correlation or coherence the degree of correlation or coherence of the envelope on a db scale of a single source across different frequency regions which is reduced by fast acting compression 2 fidelity of envelope shape the degree to which the envelope shape of the target speech in different frequency channels is preserved following compression and 3 across signal modulation correlation or coherence asmc the extent to which the target and background acquire a common component of modulation when they are compressed together which becomes greater in absolute value more negative when the target and background are compressed together values of these measures are presented and compared with intelligibility scores obtained using stimuli processed with a noise vocoder so as to preserve mainly envelope cues in a limited number of frequency channels the results suggest that the dominant factor affecting intelligibility is asmc

alternative characterizations for the representation of families of sets by fuzzy sets we investigate the representation of a given family of sets by a fuzzy set in such a way that the level sets of the fuzzy set are precisely the given sets this concept of representation is widely used in the literature for the classification and study of fuzzy structures on the same underlying set negoita and ralescu obtained two theorems both giving necessary and sufficient conditions one called the representation theorem and the second called the generalized representation theorem our aim in this paper is to take a closer look at both theorems hence establishing some equivalent forms and several constructive remarks including some directions for future investigations

effects of spectro temporal modulation changes produced by multi channel compression on intelligibility in a competing speech task these experiments are concerned with the intelligibility of target speech in the presence of a background talker using a noise vocoder stone and moore j acoust soc am 114 1023 1034 2003 showed that single channel fast acting compression degraded intelligibility but slow compression did not stone and moore j acoust soc am 116 2311 2323 2004 showed that intelligibility was lower when fast single channel compression was applied to the target and background after mixing rather than before and suggested that this was partly due to compression after mixing introducing comodulation between the target and background talkers experiment 1 here showed a similar effect for multi channel compression in experiment 2 intelligibility was measured as a function of the speed of multi channel compression applied after mixing for both eight and 12 channel vocoders with one compressor per channel intelligibility decreased as compression speed increased for the eight channel vocoder a compresso

a hierarchical approach to adaptive local refinement in isogeometric analysis abstract adaptive local refinement is one of the key issues in isogeometric analysis in this article we present an adaptive local refinement technique for isogeometric analysis based on extensions of hierarchical b splines we investigate the theoretical properties of the spline space to ensure fundamental properties like linear independence and partition of unity furthermore we use concepts well established in finite element analysis to fully integrate hierarchical spline spaces into the isogeometric setting this also allows us to access a posteriori error estimation techniques numerical results for several different examples are given and they turn out to be very promising

isogeometric analysis using polynomial splines over hierarchical t meshes for two dimensional elastic solids isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries one of the major drawbacks of nurbs based isogeometric finite elements is the inefficiency of local refinement in this study we present an alternative to nurbs based isogeometric analysis that allows for local refinement the idea is based on polynomial splines and exploits the flexibility of t meshes for local refinement the shape functions satisfy important properties such as non negativity local support and partition of unity several numerical examples are used to demonstrate the reliability of the present method

isogeometric divergence conforming variational multiscale formulation of incompressible turbulent flows a new residual based variational multiscale rbvms formulation for incompressible turbulent flows is proposed that is suitable for discretization using divergence conforming b splines the proposed methodology results in a pointwise satisfaction of the zero divergence constraint on the discrete velocity field the velocity fine scales are residual driven and constructed in a manner that is consistent with the divergence free constraint on the discrete velocity solution the resulting formulation is tested on laminar and turbulent flow benchmark problems showing excellent stability and accuracy characteristics in both regimes

on an application of fuzzy relations in biogeography abstract starting from a quasi ordering relation on a set by a well known construction an equivalence relation could be made as well as an ordering relation on the quotient set in this paper we give a similar fuzzy construction with lattice valued fuzzy relations if is a crisp correspondence from set a to set b then a quasi ordering relation on the set b could be defined in the following way x y if and only if z a z x z y in this paper an analogous fuzzy construction is given for a special type of fuzzy correspondences which appear in biogeography from this correspondence a quasi ordering relation is obtained as well as the corresponding fuzzy similarity relation and fuzzy ordering relation on the set of similarity classes this construction was developed to be applied in solving some problems of determining connections of different biogeographical areas according to recorded species here those results have been applied to determine connections of biogeographical territories in the balkan peninsula according to different species of genus cheilosia meigen 1822 and related genera diptera syrphidae hover flies

on p fuzzy correspondences and generalized associativity abstract a p fuzzy correspondence is a mapping a a 1 a 2 a n p where a1 a2 an are nonempty sets and p a partially ordered set in this paper we give necessary and sufficient conditions under which a family of ordinary correspondences on sets a1 a2 an is a family of levels of a p fuzzy correspondence a g groupoid is a quadruple s1 s2 s3 a where s1 s2 s3 are sets and a mapping a s1 s2 s3 we consider a type of p fuzzy correspondences as a generalization of a notion of g groupoids called pg fuzzy correspondences that is a pg fuzzy correspondence is a mapping a a 1 a 2 a 3 p where all sets a1 a2 an and p are partially ordered here we deal with binary pg fuzzy correspondences we give a general solution of the functional equation of generalized associativity a x b y z c d x y z where a b c and d are binary pg fuzzy correspondences in particular if a b c and d are semilattices which are solutions of the considered equation then it turns out that they are equal i e a b c d

existence and uniqueness of fuzzy ideals let r be a commutative ring the idea of identifying a fuzzy ideal of r with its corresponding chain of level ideals and its range of values although widely used in the literature for the study of fuzzy ideals has never been investigated in a general setting before we investigate in this paper the more general problem of characterization of all those fuzzy ideals that can be identified with a given arbitrary family c of subsets of r together with a given arbitrary subset s of 0 1 necessary and sufficient conditions for the existence and uniqueness of such fuzzy ideals are established in particular we obtain that uniqueness always holds true for artinian rings moreover examples are presented to further support our results and shed more light on the above mentioned problem of identification we finish by raising a natural question that is left as an open problem for further investigation

relational valued fuzzy sets abstract a generalization of the notion of a fuzzy set is given an r fuzzy set a is a mapping from a set a into the relational system s where is a binary relation on s necessary and sufficient conditions for a unique decomposition and synthesis of an r fuzzy set into the family of ordinary subsets p cuts are given as a consequence it is possible to obtain a fuzzy set as a synthesis of any collection of characteristics functions on a nonvoid set which was impossible in classical fuzzy set theory as a contribution to coding theory a possibility to express any binary block code syntheticly by a single fuzzy set is obtained note that up to now only some classes of binary codes have been characterized by fuzzy sets suitable examples bcd and a linear code are given at the end of the paper together with necessary and sufficient conditions under which an r valued fuzzy set corresponds to a linear code

lattice of partially ordered fuzzy subalgebras abstract fuzzy subalgebras are defined to be mappings from an algebra to a poset which can be a lattice and also the interval 0 1 so that every level subset is an ordinary subalgebra every fuzzy subalgebra has a canonical representation a mapping from the algebra to the poset of levels necessary and sufficient conditions under which a fuzzy subalgebra can be explicitly described by a suitable formula in lattice theoretic terms are given classes of algebras for which the poset of fuzzy subalgebras is a lattice are characterized

superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis abstract in this article we address adaptive methods for isogeometric analysis based on local refinement guided by recovery based a posteriori error estimates isogeometric analysis was introduced a decade ago and an impressive progress has been made related to many aspects of numerical methods and advanced applications however related to adaptive mesh refinement guided by a posteriori error estimators rather few attempts are pursued besides the use of classical residual based error estimators in this article we explore a feature common for isogeometric analysis iga namely the use of structured tensorial meshes that facilitates superconvergence behavior of the gradient in the galerkin discretization by utilizing the concept of structured mesh refinement using lr b splines our aim is to facilitate superconvergence behavior for locally refined meshes as well superconvergence behavior matches well with the use of recovery based a posteriori estimator in the superconvergent patch recovery spr procedure however to our knowledge so far the spr procedure has not been exploited in the iga community we start out by addressing the existence of derivative superconvergent points in the computed finite element solution based on b splines and lr b splines for an elliptic model problem 1d and 2d poisson then we present some recovery procedures for improving the derivatives or gradient of the isogeometric finite element solution where the spr procedure will be the main focus in particular we show that our spr procedure for the improvement of derivatives fulfills the desired consistency criteria at the end we develop a posteriori error estimator where the improved gradient obtained from the proposed recovery procedures is used numerical results are presented to illustrate the efficiency of using spr procedure for the improvement of derivatives or gradient of computed solution in isogeometric analysis then the proposed a posteriori error estimator based adaptive refinement methodology is tested to solve smooth and non smooth elliptic benchmark problems the focus is put on whether optimal convergence rates are obtained in the computed solution or not as well as the effectivity index of the proposed error estimators

a subdivision based implementation of the hierarchical b spline finite element method abstract a novel technique is presented to facilitate the implementation of hierarchical b splines and their interfacing with conventional finite element implementations the discrete interpretation of the two scale relation as common in subdivision schemes is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b spline basis the subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same level basis functions their subsequent multiplication with subdivision matrices projects them during the assembly stage to the correct levels of the hierarchical b spline basis the proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one two and three space dimensions

an isogeometric design through analysis methodology based on adaptive hierarchical refinement of nurbs immersed boundary methods and t spline cad surfaces we explore hierarchical refinement of nurbs as a basis for adaptive isogeometric and immersed boundary analysis we use the principle of b spline subdivision to derive a local refinement procedure which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions we test hierarchical refinement of nurbs for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases using the b spline version of the finite cell method we illustrate the potential of immersed boundary methods as a seamless isogeometric design through analysis procedure for complex engineering parts defined by t spline cad surfaces specifically a ship propeller and an automobile wheel we show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features

on an equivalence of fuzzy subgroups ii this paper forms a sequel to the paper on an equivalence of fuzzy subgroups i here we determine the number of distinct equivalence classes of fuzzy subgroups of g z p 1 z p n where p 1 p 2 p n are distinct primes we introduce the notion of a keychain of a chain of length n 1 and index of a keychain in order to determine the number of fuzzy subgroups of g we achieve this by using induction on the index of a keychain

non standard cut classification of fuzzy sets abstract several important non standard cut sets of lattice valued fuzzy sets are investigated these are strong cuts not less and neither less nor equal cuts in each case it is proved that collection of all cuts of any lattice valued fuzzy set form a complete lattice under inclusion decomposition theorem representation by cuts is proved for neither less nor equal cuts necessary and sufficient conditions under which two lattice valued fuzzy sets with the same domain have equal families of corresponding cut sets are given

an isogeometric analysis approach to gradient damage models continuum damage formulations are commonly used for the simulation of diffuse fracture processes implicit gradient damage models are employed to avoid the spurious mesh dependencies associated with local continuum damage models the c 0 continuity of traditional finite elements has hindered the study of higher order gradient damage approximations in this contribution we use isogeometric finite elements which allow for the construction of higher order continuous basis functions on complex domains we study the suitability of isogeometric finite elements for the discretization of higher order gradient damage approximations

isogeometric analysis using lr b splines abstract the recently proposed locally refined b splines denoted lr b splines by dokken et al 2013 6 may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis in this paper we propose local refinement strategies for adaptive isogeometric analysis using lr b splines and investigate its performance by doing numerical tests on well known benchmark cases the theory behind lr b spline is not presented in full details but the main conceptual ingredients are explained and illustrated by a number of examples

the role of bezier extraction in adaptive isogeometric analysis local refinement and hierarchical refinement summary we present two adaptive refinement techniques namely adaptive local refinement and adaptive hierarchical refinement for isogeometric analysis an element wise point of view is adopted exploiting bezier extraction which facilitates the implementation of adaptive refinement in isogeometric analysis locally refined t splines lr t splines and hierarchical t splines are employed for the description of the geometry as well as for the approximation of the solution space in the analysis the refinement is carried out with the aid of a subdivision operator which is computed by again exploiting the bezier extraction operator the concept and algorithm of an element based adaptive isogeometric analysis are illustrated numerical examples are given to examine the accuracy the convergence and the condition number this article is protected by copyright all rights reserved

a note on cut worthiness of recognizable tree series the topic of this short note is tree series over semirings with partially ordered carrier set thus tree series become poset valued fuzzy sets starting with a collection of recognizable tree languages we construct a tree series recognizable over any semiring such that the carrier set is a poset generated by the collection in the framework of fuzzy structures the starting collection becomes a subset of the collection of the corresponding cut sets under some stricter conditions it is even equal to this collection we also partially solve an open problem which was posed in borchardt et al cut sets as recognizable tree languages fuzzy sets and systems 157 2006 1560 1571 namely we show that if f is a given tree series over a partially ordered locally finite semiring a then f is recognizable if and only if there are finitely many cut sets of f and every cut set is a recognizable tree language

a new representation theorem of l subsets abstract in the paper the implication and tensor operations of strong l nested systems are found and further we show that the family of all strong l nested systems on a universal set forms a complete girard residuated lattice provided the underlying complete residuated lattice is girard finally an isomorphism of complete girard residuated lattices between the family of all strong l nested systems and the l power set for any fixed universal set is established and thus a new representation theorem of l subsets is obtained

on the completeness of hierarchical tensor product b splines abstract given a grid in r d consisting of d bi infinite sequences of hyperplanes possibly with multiplicities orthogonal to the d axes of the coordinate system we consider the spaces of tensor product spline functions of a given degree on a multi cell domain such a domain consists of finite set of cells which are defined by the grid a piecewise polynomial function belongs to the spline space if its polynomial pieces on adjacent cells have a contact according to the multiplicity of the hyperplanes in the grid we prove that the connected components of the associated set of tensor product b splines whose support intersects the multi cell domain form a basis of this spline space more precisely if the intersection of the support of a tensor product b spline with the multi cell domain consists of several connected components then each of these components contributes one basis function in order to establish the connection to earlier results we also present further details relating to the three dimensional case with single knots only a hierarchical b spline basis is defined by specifying nested hierarchies of spline spaces and multi cell domains we adapt the techniques from giannelli and juttler 2013 to the more general setting and prove the completeness of this basis in the sense that its span contains all piecewise polynomial functions on the hierarchical grid with the smoothness specified by the grid and the degrees under certain assumptions on the domain hierarchy finally we introduce a decoupled version of the hierarchical spline basis that allows to relax the assumptions on the domain hierarchy in certain situations such as quadratic tensor product splines the decoupled basis provides the completeness property for any choice of the domain hierarchy

representing ordered structures by fuzzy sets an overview we present a survey on representations of ordered structures by fuzzy sets any poset satisfying some finiteness condition semilattice lattice belonging to a special class e g distributive noetherian complete and others can be represented by a single function i e by a fuzzy set its domain and co domain are particular subsets of the same structure and consist of irreducible elements the representation is minimal in the sense that another representation could not be obtained by replacing the domain of the former by its proper subset by this approach the structure itself is uniquely represented by the collection of cuts ordered dually to inclusion

poset valued convexities we analyze cut properties of lattice and poset valued functions fuzzy sets of n dimensional real variable with respect to convexity in the lattice valued case convexity of a fuzzy set is equivalent with the convexity of its standard cuts dealing with non standard cuts we show that unless the space of the values is a chain such statement in general does not hold we present analogue results in the more general setting of poset valued functions we also prove that there exist lattice and poset valued functions whose cuts are precisely the convex sets of particular families our work is motivated by possible applications of convex functions e g in image processing

t norm based cuts of intuitionistic fuzzy sets abstract we consider the system of intuitionistic fuzzy sets if sets in a universe x and study the cuts of an if set suppose a left continuous triangular norm is given the t norm based cut level set of an if set is defined in a way that binds the membership and nonmembership functions via the triangular norm this is an extension of usual cuts of if sets we show that the system of these cuts fulfils analogical properties as usual systems of cuts however it is not possible to reconstruct an if set from the system of t norm based cuts

on the uniqueness of l fuzzy sets in the representation of families of sets abstract this paper deals with the uniqueness of l fuzzy sets in the representation of a given family of subsets of a nonempty set it first shows a formula of the number of l fuzzy sets whose collection of cuts coincides with a given family of subsets of a nonempty set and then provides a necessary and sufficient condition under which such l fuzzy set is unique

the extension principle and a decomposition of fuzzy sets we give an algorithm to decompose a fuzzy interval u using this decomposition and the multilinearization of a univariate function f we obtain an approximation of the fuzzy interval where is obtained from f by applying the extension principle we provide approximation bounds some numeric illustration is provided

fast divergence conforming reduced basis methods for steady navier stokes flow abstract reduced basis methods rb methods or rbms form one of the most promising techniques to deliver numerical solutions of parametrized pdes in real time with reasonable accuracy for incompressible flow problems rbms based on lbb stable velocity pressure spaces do not generally inherit the stability of the underlying high fidelity model and instead additional stabilization techniques must be introduced one way of bypassing the loss of lbb stability in the rbm is to inflate the velocity space with supremizer modes this however deteriorates the performance of the rbm in the performance critical online stage as additional dofs must be introduced to retain stability while these dofs do not effectively contribute to accuracy of the rb approximation in this work we consider a velocity only rb approximation exploiting a solenoidal velocity basis the solenoidal reduced basis emerges directly from the high fidelity velocity solutions in the offline stage by means of piola transforms the solenoidality of the velocity space is retained under geometric transformations making the proposed rb method suitable also for the investigation of geometric parameters to ensure exact solenoidality of the high fidelity velocity solutions that constitute the rb we consider approximations based on divergence conforming compatible b splines we show that the velocity only rb method leads to a significant improvement in computational efficiency in the online stage and that the pressure solution can be recovered a posteriori at negligible extra cost we illustrate the solenoidal rb approach by modeling steady two dimensional navier stokes flow around a naca0015 airfoil at various angles of attack

an unfitted hp adaptive finite element method based on hierarchical b splines for interface problems of complex geometry generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries the paper at hand introduces a b spline finite element method which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement which adds several levels of local basis functions in the close vicinity of interfaces but unfitted to their exact location so that a simple regular grid of knot span elements can be maintained numerical experiments show that an hp refinement strategy which simultaneously increases the polynomial degree of the b spline basis and the levels of refinement around interfaces achieves exponential rates of convergence despite the presence of discontinuities it is also demonstrated that the hierarchical b spline fem can be used to transfer the recently introduced finite cell concept to geometrically nonlinear problems its computational performance imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one two and three dimensions and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite

a generalization of the representation theorem abstract we generalize the representation theorem for fuzzy sets more specifically we give necessary and sufficient conditions for a family of sets to represent a permutation of the levels of some fuzzy set

algebraic fuzzy systems abstract a general theory of algebraic fuzzy systems is developed by introducing the notion of a fuzzy l subset corresponding to a set l of subsets of a nonempty set x assuming truth values in a complete brouwerian lattice it is observed that the set fl of all fuzzy l subsets of x is a closure algebraic closure fuzzy set system if and only if l is a closure algebraic closure set system on x a fuzzy l subset generated by a fuzzy subset is described modularity and distributivity of the complete lattices l and fl are discussed a method to construct fuzzy l subsets from certain family of members of l is established certain applications of the general theory are mentioned

cuts of poset valued functions in the framework of residuated maps abstract we analyze cuts of poset valued functions relating them to residuated mappings dealing with the lattice valued case we prove that a function x l induces a residuated map f l p x whose values are the cuts of and we describe the corresponding residual conversely it turns out that every residuated map f from l to the power set of x determines a lattice valued function x l whose cuts coincide with the values of f for general poset valued functions we give conditions under which the map sending an element of a poset to the corresponding cut is quasi residuated and then conditions under which it is also residuated we prove that without additional conditions the map analogue to the residual is a partial function hence we get particular weakly residuated maps which on the power set of the domain generate centralized systems instead of closures we show that the main properties of residuated maps are preserved in this generalized case we apply these results to the canonical representation of poset valued and lattice valued functions using the corresponding closures and centralized systems

isogeometric divergence conforming b splines for the unsteady navier stokes equations divergence conforming b splines are developed for application to the incompressible navier stokes equations on geometrically mapped domains these enable smooth pointwise divergence free solutions and thus satisfy mass conservation in the strongest possible sense semi discrete methods based on divergence conforming b splines are shown to conserve linear and angular momentum and satisfy balance laws for energy vorticity enstrophy and helicity these are geometric structure preserving quantities and numerical simulations that are sensitive to them are shown to be qualitatively correct and quantitatively accurate the methods developed are anticipated to open new doors to the practical calculation of complex flows and to studies of their physical behavior

the effect of amplitude comodulation on extracting sentences from noise evidence from a variety of contexts while signal to noise ratios range from about 50 90 db in laboratory experiments measurements of speech levels in most natural environments show much poorer listening conditions for example teder hear instrum 11 32 33 1990 measured signal to noise ratios ranged from a high of 13 db in a carpeted office to low of 1 db in a 1986 chevy nova traveling at 55 mph these numbers indicate an immense difference between speech signals presented to listeners in laboratory experiments as opposed to the real world environment although speech intelligibility has been well studied in noise there has been little study of the acoustic characteristics of speech that allow the message to be separated from the background noise one characteristic of voiced speech that shows great promise in this regard is amplitude comodulation in the present research amplitude comodulated tone analog sentences carrell and opie percept psychophys 52 437 445 1989 were presented with simultaneous white noise and multispeaker babble at 0 5 and 10 db signal to noise ratios it was found that the beneficial effect of amplitude comodulation was greater at the lower signal to noise ratios

fuzzy groups and collections of subgroups abstract the aim of the paper is to investigate fuzzy subgroups of a group from a general point of view using collections of ordinary subgroups fuzzy subgroups are taken to be special mappings from a group to a partially ordered set which can also be a lattice and particularly the unit interval 0 1 as it is known every fuzzy subgroup uniquely determines a poset of level subgroups of the same group properties of that poset are investigated on the other hand it is proved that every collection of subgroups can be used for the construction of a suitable fuzzy subgroup of a group for that purpose particular fuzzy completions of collections of subsets are introduced it turns out that fuzzy subgroup is an intrinsic notion expressible in terms of collections of subgroups under set theoretic relations and operations

representation of lattices by fuzzy sets abstract we prove that every lattice l of finite length can be represented by a fuzzy set on the collection x of meet irreducible elements of l a decomposition of this fuzzy set gives a family of isotone functions from x to 2 0 1 the lattice of which is isomorphic to l more generally conditions under which any collection of isotone functions from a finite set into 2 corresponds to a decomposition of a fuzzy set are given as a consequence the representation theorem for a finite distributive lattice by the lattice of all isotone functions is obtained the collection of all lattices characterized by the same fuzzy set turns out to be a lattice with the above mentioned distributive lattice as the greatest element

optimal quadrature for univariate and tensor product splines abstract numerical integration is a core subroutine in many engineering applications including the finite element method fem isogeometric analysis is a fem technology that uses smooth b spline and nurbs basis functions traditionally gaussian quadrature was used for numerical integration but this yields suboptimal performance this is attributed to the fact that gaussian quadrature rules do not take inter element smoothness of the spline basis into account resulting in over integration the equations for exact quadrature are well known but prove notoriously hard to solve due to their nonlinear nature these generalized gauss rules were first introduced in hughes et al 2010 in the context of isogeometric analysis where newton iteration was utilized to study and tabulate several cases later homotopy continuation barto and calo 2015 was used as an alternative strategy for finding these rules in this paper we describe an algorithm to generalize on both of these techniques it is optimal in the sense that it will integrate a space of dimension n using no more than n 1 2 quadrature points the algorithm works on arbitrary nonuniform knot vectors of any polynomial degree and continuity and is demonstrated on polynomial orders up to 15 it extends to 2d and 3d integrals by tensor product

homomorphisms of poset valued algebras the notion of a homomorphism for fuzzy algebraic structures having arbitrary possibly different partially ordered sets or lattices as co domains is introduced basic properties of homomorphisms embeddings and isomorphisms are investigated and fundamental homomorphism and isomorphism theorems are proved

preferential normal fuzzy subgroups in this paper we consider the notion of normality on preferential fuzzy subgroups of a finite group g and define the associated concept of a normal pinned flag we discuss the preferential equality of quotients and products of normal preferential fuzzy subgroups further normalizers of fuzzy subgroups under preferential equality are briefly dealt with examples are given to illustrate the structure of preferential normal fuzzy subgroups and normal pinned flags

on existence of p valued fuzzy sets with a given collection of cuts a representation theorem of families of subsets by poset valued fuzzy sets is presented namely necessary and sufficient conditions are given under which for a given family of subsets f of a set x and a fixed poset p there is a fuzzy set m x p such that the collection of cuts of m coincides with f

on the similarities and differences between classical hierarchical truncated hierarchical and lr b splines abstract smooth spline functions such as b splines and nurbs are already an established technology in the field of computer aided design cad and have in recent years been given a lot of attention from the computer aided engineering cae community the advantages of local refinement are obvious for anyone working in either field and as such several approaches have been proposed among others we find the three strategies classical hierarchical b splines truncated hierarchical b splines and locally refined b splines we will in this paper present these three frameworks and highlight similarities and differences between them in particular we will look at the function space they span and the support of the basis functions we will then analyse the corresponding stiffness and mass matrices in terms of sparsity patterns and conditioning numbers we show that the basis functions in general do not span the same space and that conditioning numbers are comparable moreover we show that the weighting needed by the classical hierarchical basis to maintain partition of unity has significant implications on the conditioning numbers

from fuzzy sets to the decompositions of non rigid sets the concept of identifying a fuzzy subset of a set r with its collection of level sets and its collection of membership values plays an important role in many real life applications such identification is possible only if the fuzzy set can be recaptured this implies that uniqueness of the fuzzy set plays an important role it has been recently shown that in order to have uniqueness it is necessary and sufficient that the collection s of membership values of the fuzzy set be a rigid set with this in mind the authors went on to show that if s has the min max property then s is a rigid set and left the converse as an open problem we start this paper by constructing a counterexample that shows that rigid sets do not have to have the min max property we then take a closer look at non rigid sets by decomposing them into isomorphism invariant components and into s connected components in the hope of getting a characterization of non rigid sets which will lead to a characterization of rigid sets and hence of uniqueness of the fuzzy set we also investigate in the case of nonuniqueness the number of fuzzy sets corresponding to a collection of level sets and a collection of membership values

isogeometric methods for computational electromagnetics b spline and t spline discretizations in this paper we introduce methods for electromagnetic wave propagation based on splines and on t splines we define spline spaces which form a de rham complex and following the isogeometric paradigm we map them on domains which are piecewise spline or nurbs geometries we analyze their geometric and topological structure as related to the connectivity of the underlying mesh and we present degrees of freedom together with their physical interpretation the theory is then extended to the case of meshes with t junctions leveraging on the recent theory of t splines the use of t splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose

on the dimension of spline spaces on planar t meshes we analyze the space of bivariate functions that are piecewise polynomial of bi degree m m and of smoothness r along the interior edges of a planar t mesh we give new combinatorial lower and upper bounds for the dimension of this space by exploiting homological techniques we relate this dimension to the weight of the maximal interior segments of the t mesh defined for an ordering of these maximal interior segments we show that the lower and upper bounds coincide for high enough degrees or for hierarchical t meshes which are enough regular we give a rule of subdivision to construct hierarchical t meshes for which these lower and upper bounds coincide finally we illustrate these results by analyzing spline spaces of small degrees and smoothness

divergence conforming discretization for stokes problem on locally refined meshes using lr b splines abstract to solve the incompressible flow problems using isogeometric analysis the div compatible spline spaces were originally introduced by buffa et al 2011 and later developed by evans 2011 in this paper we extend the div compatible spline spaces with local refinement capability using locally refined lr b splines over rectangular domains we argue that the spline spaces generated on locally refined meshes will satisfy compatibility provided they span the entire function spaces as governed by mourrain 2014 dimension formula we will in this work use the structured refined lr b splines as introduced by johannessen et al 2014 further we consider these div compatible lr b spline spaces to approximate the velocity and pressure fields in mixed discretization for stokes problem and a set of standard benchmark tests are performed to show the stability efficiency and the conservation properties of the discrete velocity fields in adaptive isogeometric analysis

isogeometric analysis in electromagnetics b splines approximation abstract we introduce a new discretization scheme for maxwell equations in two space dimension inspired by the new paradigm of isogeometric analysis introduced in hughes et al 2005 16 we propose an algorithm based on the use of bivariate b splines spaces suitably adapted to electromagnetics we construct b splines spaces of variable interelement regularity on the parametric domain these spaces and their push forwards on the physical domain form a de rham diagram and we use them to solve the maxwell source and eigen problem our scheme has the following features i is adapted to treat complex geometries ii is spectral correct iii provides regular e g globally c 0 discrete solutions of maxwell equations

adaptive isogeometric analysis by local h refinement with t splines isogeometric analysis based on non uniform rational b splines nurbs as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space which renders a purely local refinement impossible this paper demonstrates how this difficulty can be overcome by using t splines instead t splines allow the introduction of so called t junctions which are related to hanging nodes in the standard fem obeying a few straightforward rules rectangular patches in the parameter space of the t splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry furthermore it is shown how state of the art a posteriori error estimation techniques can be combined with refinement by t splines numerical examples underline the potential of isogeometric analysis with t splines and give hints for further developments

completion of ordered structures by cuts of fuzzy sets an overview the aim of the paper is to present a role of fuzzy sets in the theory of ordered structures main algebraic properties of cuts of fuzzy sets are given and a completion of partially ordered sets to complete lattices is described it turns out that this completion is equivalent with the famous dedekind macneille completion but the algorithm presented here is much simpler

l fuzzy sets and codes abstract a decomposition of an l valued finite fuzzy set l is a lattice gives a family of characteristic functions which can be considered as a binary block code using a previous theorem of synthesis for fuzzy sets we give conditions under which an arbitrary block code corresponds to an l valued fuzzy set an explicit description of the hamming distance as well as of any code distance is also given all in lattice theoretic terms finally we give necessary and sufficient conditions under which a linear code corresponds to an l valued fuzzy set it turns out that in such case the lattice l has to be boolean

on a generalization of fuzzy algebras and congruences abstract partially ordered fuzzy algebras are mappings from an algebra to a partially ordered set with the property that every level subset is an ordinary subalgebra similar definitions are induced for p valued congruences and weak congruences necessary and sufficient conditions under which an arbitrary collection of subalgebras congruences enables construction of a p valued fuzzy subalgebra congruence are given any p valued weak congruence uniquely determines a p valued subalgebra of the same algebra finally any collection of subalgebras or congruences of a given algebra can be used for the construction of a relational valued fuzzy algebra or congruence this seems to be the most general way to obtain a fuzzy algebra congruence out of the collection of the ordinary subalgebras congruences

short communication lattice representations of interval valued fuzzy sets in this paper a solution of the problem of the interval valued fuzzy sets synthesis is given the codomain is considered to be a lattice of intervals the necessary and sufficient conditions for a family of subsets to be a family of cut sets of an interval valued fuzzy set are given

uniqueness in the generalized representation by fuzzy sets the concept of representation of a given family of sets by a fuzzy set in such a way that the level sets of the fuzzy set are precisely the given sets is widely used in the literature for the classification and study of fuzzy algebraic structures on the same underlying set the problem of existence of such fuzzy sets was investigated by various authors as far as we know the problem of uniqueness of such fuzzy sets was not studied before we establish among other things necessary and sufficient conditions under which uniqueness is guaranteed in the cases of complete as well as partial representations of the level sets of the fuzzy set

more on fuzzy lattices in this paper the concept of an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter in a lattice is introduced which is a generalization of the concept as given by davvaz and kazanci 2011 18 characterizations for an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter are provided different classes of lattices are characterized by the properties of these fuzzy sublattices ideals filters using the notions of a fuzzy sublattice ideal filter with thresholds characterization of a fuzzy sublattice ideal filter an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter are discussed

on a representation of posets by fuzzy sets the aim of the paper is to present an application of fuzzy sets in mathematics namely in the theory of ordered sets an algorithm for the construction of p fuzzy sets with distinct levels is given in connection with this every finite poset can be mapped by an anti isotone bijection onto the poset of levels of a suitable fuzzy set moreover it is proved that every finite partially ordered set p can be represented by the poset of levels of a particular fuzzy set defined on the collection of meet irreducible elements of p

a note on the lattice of weak l valued congruences on the group of prime order abstract weak l valued fuzzy congruences on an algebra where l is a lattice were induced in 4 in this note we give a representation theorem for one subdirect power of l by means of the lattice of l valued congruences on any cyclic group of prime order

a note on a natural equivalence relation on fuzzy power set the necessary and sufficient conditions under which two fuzzy sets with the same domain have equal families of cut sets are given consequently there is a corresponding equivalence relation on the related fuzzy power set the collection of classes under this relation can be ordered and we give a necessary and sufficient condition under which it is a lattice

generalized representation and extension a very general abstraction of a fuzzy set is presented appropriate conditions for representation and extension are presented some insight into the fundamental nature of fuzzy sets is provided