shifted simplicial complexes are laplacian integral we show that the combinatorial laplace operators associated to the boundary maps in a shifted simplicial complex have all integer spectra we give a simple combinatorial interpretation for the spectra in terms of vertex degree sequences generalizing a theorem of merris for graphs we also conjecture a majorization inequality for the spectra of these laplace operators in an arbitrary simplicial complex with equality achieved if and only if the complex is shifted this generalizes a conjecture of grone and merris for graphs

a simplified algorithm for the second order sound fields an analytical description for the second order field of the sum difference frequency and second harmonic components is derived this treatment is based on the fact that an arbitrary axially symmetric beam can be expressed as the linear superposition of a set of gaussian beams j j wen and m a breazeale j acoust soc am 83 1752 1756 1988 so that the three dimensional integral for the second order components is typically expressed as a combination of a set of interaction terms of the gaussian beams correspondingly the evaluation of the field distribution is reduced to the summation of exponential integral functions from some examples the present approach provides the results for the second order field which are in good agreement with those obtained directly by numerical integration

non paraxial model for a parametric acoustic array this study is concerned with parametric radiation from an arbitrary axisymmetric planar source with a special focus on low frequency difference frequency fields as a model equation accounting for nonlinearity diffraction and dissipation the westervelt equation is used the difference frequency field patterns are calculated in the quasi linear approximation by the method of successive approximations a multi layer integral for calculation of the acoustic field is reduced to a three dimensional one by employing an approximate analytical description of the primary field with the use of a multi gaussian beam expansion this integral is subsequently reduced in the paraxial approximation to a one dimensional form which has previously been published in literature and which represents a means for fast calculations of secondary acoustic fields the three dimensional integral is calculated numerically and the numerical results predict nonzero amplitude of the low frequency field in the vicinity of the source which is an effect that cannot be correctly encompassed in the paraxial approximation

subspace arrangements over finite fields cohomological and enumerative aspects abstract the enumeration of points on or off the union of some linear or affine subspaces over a finite field is dealt with in combinatorics via the characteristic polynomial and in algebraic geometry via the zeta function we discuss the basic relations between these two points of view counting points is also related to the l adic cohomology of the arrangement as a variety we describe the eigenvalues of the frobenius map acting on this cohomology which corresponds to a finer decomposition of the zeta function the l adic cohomology groups and their decomposition into eigenspaces are shown to be fully determined by combinatorial data finally it is shown that the zeta function is determined by the topology of the corresponding complex variety in some important cases

combinatorial decompositions of a class of rings in this paper we introduce some combinatorial methods for the study of graded rings and use these methods to analyze a class of rings that are of importance in combinatorics our methods are based on a unique representation theorem which is shown section 2 to hold for any graded algebra and which in a sense is an extension of the direct sum decomposition for cohen macaulay algebras this unique representation is reminiscent of a similar result obtained by rees 20 both results yield a decomposition of the algebra however our result differs from that of rees in that it carries more information about the algebra our main results are concerned with a class of rings see section 3 for the definition associated to simplicial complexes there are several natural operations that can be performed on simplicial complexes to obtain new complexes which in turn have an interpretation for the corresponding rings we show sections 4 5 and 6 that our basic decompositions can be transferred during these operations from the original rings to the newly constructed ones the operations studied here are the chain transform or barycentric subdivision section 4 rank selection both for partially ordered sets and for simplicial complexes section s and localization section 6 as we develop these tools we give some applications in section 5 we give a new topological characterization of the cohen macaulay property for partially ordered sets an immediate consequence of which is the rankselection theorem baclawski 2 this characterization is closely related to those obtained by garsia in 14

a categorification of biclosed sets of strings abstract we consider a closure space known as biclosed sets of strings of a gentle algebra of finite representation type palu pilaud and plamondon proved that the collection of all biclosed sets of strings forms a lattice and moreover that this lattice is congruence uniform many interesting examples of finite congruence uniform lattices may be represented as the lattice of torsion classes of an associative algebra we introduce a generalization the lattice of torsion shadows and we prove that the lattice of biclosed sets of strings is isomorphic to a lattice of torsion shadows when every indecomposable module over the gentle algebra is a brick finite congruence uniform lattices admit an alternate partial order known as the core label order in many cases the core label order of a congruence uniform lattice is isomorphic to a lattice of wide subcategories of an associative algebra analogous to torsion shadows we introduce wide shadows and prove that the core label order of the lattice of biclosed sets is isomorphic to a lattice of wide shadows

a broad class of shellable lattices abstract we introduce a new class of lattices the modernistic lattices and their duals the comodernistic lattices we show that every modernistic or comodernistic lattice has shellable order complex we go on to exhibit a large number of examples of co modernistic lattices we show comodernism for two main families of lattices that were not previously known to be shellable the order congruence lattices of finite posets and a weighted generalization of the k equal partition lattices we also exhibit many examples of co modernistic lattices that were already known to be shellable to begin with the definition of modernistic is a common weakening of the definitions of semimodular and supersolvable we thus obtain a unified proof that lattices in these classes are shellable subgroup lattices of solvable groups form another family of comodernistic lattices that were already proven to be shellable we show not only that subgroup lattices of solvable groups are comodernistic but that solvability of a group is equivalent to the comodernistic property on its subgroup lattice indeed the definition of comodernistic exactly requires on every interval a lattice theoretic analogue of the composition series in a solvable group thus the relation between comodernistic lattices and solvable groups resembles in several respects that between supersolvable lattices and supersolvable groups

fuzzy choquet integration of homogeneous possibility and probability distributions the fuzzy integral fi is an extremely flexible and powerful tool for data and information aggregation the fi is parametrized by the fuzzy measure fm a normal and monotone capacity based on the selection of fm the fi produces different aggregation operators in recent years a number of fi extensions have been put forth relative to different types of uncertain information e g real interval and set valued under various constraints herein we study the applicability and behavior of different extensions of the fuzzy choquet integral for fusing homogeneous possibility and probability distributions this analysis is of great utility in terms of understanding what extensions and under what conditions it is possible to aggregate and maintain homogeneity within uncertain information we show that two extensions gfi and ndfi can aggregate both probability and possibility distributions while these extensions do not always maintain homogeneity they do under certain conditions last while we specifically focus on the aggregation of homogeneous uncertain information the propositions put forth also shed light into heterogeneous information aggregation via the gfi and the ndfi

low sidelobe limited diffraction beams in the nonlinear regime in linear propagation sidelobe levels of bessel limited diffraction beams are only about 8 db down relative to the mainlobe in the nonlinear regime these beams will have a region near the source where the side lobe level of the second harmonic is 16 db down but this region has usually been considered to be so small that it is of little practical interest in this paper it is shown that when there are only 1 to 3 sidelobes in a finite aperture bessel beam the second harmonic field will have low sidelobes for distances up to half of the depth of field this result is backed up by simulations in a medium with absorption previous theory has shown that the sidelobes of the bessel beam will also be reduced but only for absorption that was too high to be of practical use simulations presented here show that for breast tissue which only has about 10 of the absorption of previous criteria one will still get sidelobes which are comparable to that of a rectangular aperture even when the sidelobes would be high in a non absorbing medium

an iterative method for the computation of nonlinear wide angle pulsed acoustic fields of medical diagnostic transducers the development and optimization of medical ultrasound transducers and imaging modalities require a computational method that accurately predicts the nonlinear acoustic pressure field a prospective method should provide the wide angle pulsed field emitted by an arbitrary planar source distribution and propagating in a three dimensional large scale domain holding a nonlinear acoustic medium in this paper a method is presented that is free of any assumed wavefield directionality the nonlinear acoustic wave equation is solved by treating the nonlinear term as a contrast source this formulation leads to an iterative scheme that involves the repetitive solution of a linear wave problem through green s function method it is shown that accurate field predictions may be obtained within a few iterations moreover by employing a dedicated numerical convolution technique the method allows for a discretization down to two points per wavelength or period of the highest frequency of interest the performance of the method is evaluated through a number of nonlinear field predictions for pulsed transducers with various geometries the results demonstrate the directional independence of the method moreover comparison with results from several existing methods shows that the method accurately predicts the nonlinear field for weak to moderate nonlinearity

second harmonic generation of practical bessel beams a fast gaussian expansion approach is used to investigate fundamental and second harmonic generation in practical bessel beams of finite aperture the analysis is based on the integral solutions of the kzk equation under the quasilinear approximation the influence of the medium s attenuation on the beam profile is considered analysis results show that the absorption parameter has a significant effect on the far field beam profile of the second harmonic under certain circumstances the second harmonic of a practical bessel beam still has the main properties of an ideal bessel beam of infinite aperture when it propagates within its depth of field

nearfield of a large acoustic transducer part i linear radiation results are reported of an investigation of the nearfield of a large circular transducer 182 cm diameter and composed of 364 smaller elements operating in water at 11 16 khz and with parametric generated difference frequencies in the range 0 5 5 khz linear radiation is considered in this paper part i whereas parametric radiation is discussed in a related paper part ii amplitude and phase are measured at various distances and compared with calculations based on a simplified integral representation of the field obtained by naze tjo tta and tjo tta j acoust soc am 68 334 339 1980 as a solution of the parabolic approximation of the helmholtz equation comparison is also made with an exact on axis calculation the main results are 1 the transducer radiates as a piston with a uniform velocity distribution 2 the integral solution represents an adequate description of the observed sound field it provides a simple method to obtain general properties of the field as well as numerical results by computing a simple line integral 3 within the same approximation scheme formulas are presented for the case of axial symmetry from which the field of an amplitude or phase shaded source can be calculated from a simple line integral 4 from this it is further shown how the farfield amplitude and phase can be calculated readily from the nearfield measurements

a characterization of solvability for finite groups in terms of their frame abstract the frame of a group is the poset of conjugacy classes of all its proper subgroups in this paper we will prove that a finite group is solvable if and only if every collection of maximal elements of its frame has a well defined meet and the poset consisting of all such meets including the meet of the empty set is a modular lattice

structure of the loday ronco hopf algebra of trees abstract loday and ronco defined an interesting hopf algebra structure on the linear span of the set of planar binary trees they showed that the inclusion of the hopf algebra of non commutative symmetric functions in the malvenuto reutenauer hopf algebra of permutations factors through their hopf algebra of trees and these maps correspond to natural maps from the weak order on the symmetric group to the tamari order on planar binary trees to the boolean algebra we further study the structure of this hopf algebra of trees using a new basis for it we describe the product coproduct and antipode in terms of this basis and use these results to elucidate its hopf algebraic structure in the dual basis for the graded dual hopf algebra our formula for the coproduct gives an explicit isomorphism with a free associative algebra we also obtain a transparent proof of its isomorphism with the non commutative connes kreimer hopf algebra of foissy and show that this algebra is related to non commutative symmetric functions as the commutative connes kreimer hopf algebra is related to symmetric functions

unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation various numerical algorithms have been developed to solve the khokhlov kuznetsov zabolotskaya kzk parabolic nonlinear wave equation in this work a generalized time domain numerical algorithm is proposed to solve the diffraction term of the kzk equation this algorithm solves the transverse laplacian operator of the kzk equation in three dimensional 3d cartesian coordinates using a finite difference method based on the five point implicit backward finite difference and the five point crank nicolson finite difference discretization techniques this leads to a more uniform discretization of the laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term in addition a new empirical algorithm based on the lu decomposition technique is proposed to solve the system of linear equations obtained from this discretization the proposed empirical algorithm improves the calculation speed and memory usage while the order of computational complexity remains linear in calculation of the diffraction term in the kzk equation for evaluating the accuracy of the proposed algorithm two previously published algorithms are used as comparison references the conventional 2d texas code and its generalization for 3d geometries the results show that the accuracy efficiency performance of the proposed algorithm is comparable with the established time domain methods

minimum classification error training for choquet integrals with applications to landmine detection a novel algorithm for discriminative training of choquet integral based fusion operators is described fusion is performed by choquet integration of classifier outputs with respect to fuzzy measures the fusion operators are determined by the parameters of fuzzy measures these parameters are found by minimizing a minimum classification error mce objective function the minimization is performed with respect to a special class of measures the sugeno lambda measures an analytic expression is derived for the gradient of the choquet integral with respect to the sugeno lambda measure the new algorithm is applied to a landmine detection problem and compared to previous techniques

extension of the fuzzy integral for general fuzzy set valued information the fuzzy integral fi is an extremely flexible aggregation operator it is used in numerous applications such as image processing multicriteria decision making skeletal age at death estimation and multisource e g feature algorithm sensor and confidence fusion to date a few works have appeared on the topic of generalizing sugeno s original real valued integrand and fuzzy measure fm for the case of higher order uncertain information both integrand and measure for the most part these extensions are motivated by and are consistent with zadeh s extension principle ep namely existing extensions focus on fuzzy number fn i e convex and normal fuzzy set fs valued integrands herein we put forth a new definition called the generalized fi gfi and efficient algorithm for calculation for fs valued integrands in addition we compare the gfi numerically and theoretically with our non ep based fi extension called the nondirect fi ndfi examples are investigated in the areas of skeletal age at death estimation in forensic anthropology and multisource fusion these applications help demonstrate the need and benefit of the proposed work in particular we show there is not one supreme technique instead multiple extensions are of benefit in different contexts and applications

topology of order complexes of intervals in subgroup lattices abstract we conjecture that the order complex of an open interval in the subgroup lattice of a finite group has the homotopy type of a wedge of spheres and prove that if h g is a minimal counterexample to this conjecture then either g is almost simple or g hn where n is the unique minimal normal subgroup of g n is non abelian and h n 1

nonlinear effects in the farfield of a directive sound source nonlinear propagation of a periodic sound beam in a dissipative fluid is considered using fourier series expansion and numerical methods to solve the governing equation of motion in the parabolic approximation the nearfield was considered in a previous paper aanonsen et al j acoust soc am 75 749 768 1984 the analysis is now extended to the farfield numerical and asymptotic results are derived and used to explain the development of the fundamental and harmonic components from the nearfield into the farfield a discussion is also given of some earlier models for the farfield of directional waves emphasis is put on the importance of imposing the proper matching conditions between the nearfield solution and the spherical solution in the farfield in order to obtain a good approximation propagation and saturation curves are calculated as well as beam patterns for various harmonic components the results are compared with available experimental observations nonlinear effects although generated

a gaussian finite element method for description of sound diffraction a new method for solving diffraction problems is presented it is based on the use of gaussian diffraction theory comparison of the gaussian beam expansion and fourier series expansion reveals that the gaussian expansion is a more general and more powerful technique the new method combines the gaussian beam superposition technique wen and breazeale j acoust soc am 83 1752 1756 1988 and the numerical finite element solution to the parabolic equation huang j acoust soc am 84 1405 1413 1988 the new method is capable of solving for the sound field even in an inhomogeneous medium or in the presence of reflection as shown by computer modeling the source may be a gaussian source or a distributed source calculated results are compared with experimental results in a laboratory water tank

linear decision trees subspace arrangements and mobius functions let p be a set in rn given a point x we want to test if x e p our model of computation is a linear decision tree a rooted ternary tree t where with each interior node v is associated a linear function lv x l j ajxj b and the three edges connecting v to its descendants are labelled starting from the root we move down the tree at each internal node v we check whether iv x 0 and follow the appropriately labelled edge leaves are labelled yes and no and arriving at a leaf we read off the answer to the question is x e p linear decision trees are sometimes surprisingly powerful devices we mention here the result that some np complete problems like the knapsack problem have polynomial depth linear decision trees mh lower bound results on the size or depth of linear decision trees usually depend on counting the number of connected components of p or r n p this method was introduced by dobkin and lipton dl and further developed by steele and yao sy ben or bo and others in this paper we describe topological methods that can be applied to obtain lower bounds also if these sets are connected the basic idea of this paper was first explored in bly the euler characteristic of p or r n p was used to estimate the number of leaves in a linear decision tree for p here we improve and extend the topological methods of bly in particular we show that the euler characteristic can be replaced by the sum of the betti numbers of r n p in bl y the method was applied to the case when p is a subspace arrangement i e a union of a finite number of affine subspaces the euler characteristic of the union is essentially the mobius function of the intersection lattice of these subspaces in this paper using a formula of goresky and macpherson gm we work with the betti numbers of the complement of this union and thereby obtain better bounds the motivating problem in bly was the k equal problem given n real numbers xl xn decide if some k of them are equal it was shown that ev ry linear decision tree for the k equal problem has size at least 2njk 0 n and consequently depth at least q nlog 2njk which is best possible we

how to compute the stanley depth of a monomial ideal abstract let j i be monomial ideals we show that the stanley depth of i j can be computed in a finite number of steps we also introduce the fdepth of a monomial ideal which is defined in terms of prime filtrations and show that it can also be computed in a finite number of steps in both cases it is shown that these invariants can be determined by considering partitions of suitable finite posets into intervals

why the characteristic polynomial factors we survey three methods for proving that the characteristic polynomial of a finite ranked lattice factors over the nonnegative integers and indicate how they have evolved recently the first technique uses geometric ideas and is is based on zaslavsky s theory of signed graphs the second approach is algebraic and employs results of saito and terao about free hyperplane arrangements finally we consider a purely combinatorial theorem of stanley about supersolvable lattices and its generalizations

generalized lebesgue integrals of fuzzy complex valued functions in this paper on the basis of the theory of fuzzy complex numbers introduced by buckley we define fuzzy complex valued measurable functions fuzzy complex valued fuzzy measures and corresponding generalized lebesgue integrals of the fuzzy complex valued functions furthermore some basic properties and convergence theorems with respect to this kind of lebesgue integrals will be discussed

on borel fixed ideals generated in one degree abstract we construct a shellable polytopal cell complex that supports a minimal free resolution of a borel fixed ideal which is borel generated by just one monomial in s k x 1 x 2 x n this includes the case of powers of the homogeneous maximal ideal x 1 x 2 x n as a special case in our most general result we prove that for any borel fixed ideal i generated in one degree there exists a polytopal cell complex that supports a minimal free resolution of i

fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices this paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set it also presents basic ideas on fuzzy integrals defined using these fuzzy measures definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers several useful properties of fuzzy measures and fuzzy integrals are stated and proved definitions presented in this paper and its results will be employed in subsequent papers on generalized quantifiers defined using this type of fuzzy integral

characteristic polynomials of subspace arrangements and finite fields let a be any subspace arrangement in rndefined over the integers and let fqdenote the finite field withqelements letqbe a large prime we prove that the characteristic polynomial a q of a counts the number of points in fnqthat do not lie in any of the subspaces ofa viewed as subsets of fnq this observation which generalizes a theorem of blass and sagan about subarrangements of the bnarrangement reduces the computation of a q to a counting problem and provides an explanation for the wealth of combinatorial results discovered in the theory of hyperplane arrangements in recent years the basic idea has its origins in the work of crapo and rota 1970 we find new classes of hyperplane arrangements whose characteristic polynomials have simple form and very often factor completely over the nonnegative integers

generalized quotients in coxeter groups for w s a coxeter group we study sets of the form w v w e w i l wv 1 w i v for all v e v where v c w such sets w v here called generalized quotients are shown to have much of the rich combinatorial structure under bruhat order that has previously been known only for the case when v c s i e for minimal coset representatives modulo a parabolic subgroup we show that bruhat intervals in w v for general v c w are lexicographically shellable the mobius function on w v under bruhat order takes values in 1 0 1 for finite groups w generalized quotients are the same thing as lower intervals in the weak order this is however in general not true connections with the weak order are explored and it is shown that w v is always a complete meet semilattice and a convex order ideal as a subset of w under weak order descent classes di w e w il1 ws 1 w xt s e i for all s e s i c s are also analyzed using generalized quotients it is shown that each descent class as a poset under bruhat order or weak order is isomorphic to a generalized quotient under the corresponding ordering the latter half of the paper is devoted to the symmetric group and to the study of some specific examples of generalized quotients which arise in combinatorics for instance the set of standard young tableaux of a fixed shape or the set of linear extensions of a rooted forest suitably interpreted form generalized quotients we prove a factorization result for the quotients that come from rooted forests which shows that algebraically these quotients behave as a system of minimal coset representatives of a subset which is in general not a subgroup we also study the rank generating function for certain quotients in the symmetric group

nonlinear effects in focused sound fields focused finite amplitude sound fields are investigated with numerical solutions of the khokhlov zabolotskaya kuznetsov kzk equation the numerical solution is based on the algorithm developed by aanonsen et al j acoust soc am 75 749 768 1984 who used a fourier series expansion of the sound pressure to reduce the kzk equation to a set of coupled parabolic equations the basic algorithm has been modified by introducing a coordinate system that follows the convergent geometry of focused sound fields in this way more efficient numerical evaluation of the detailed field structure within the focal region is achieved arbitrary axisymmetric sources can be modeled here circular sources having linear focusing gains of order 50 will be considered the calculated time waveforms propagation curves and beam patterns illustrate clearly the combined effects of nonlinearity diffraction and absorption on finite amplitude sound that passes through a focal region among the new results are power curves

eigenspace arrangements of reflection groups the lattice of intersections of reflecting hyperplanes of a complex reflection group w may be considered as the poset of 1 eigenspaces of the elements of w in this paper we replace 1 with an arbitrary eigenvalue and study the topology and homology representation of the resulting poset after posing the main question of whether this poset is shellable we show that all its upper intervals are geometric lattices and then answer the question in the affirmative for the infinite family g m p n of complex reflection groups and the first 31 of the 34 exceptional groups by constructing cl shellings in addition we completely determine when these eigenspaces of w form a k 1 resp free arrangement for the symmetric group we also extend the combinatorial model available for its intersection lattice to all other eigenvalues by introducing balanced partition posets presented as particular upper order ideals of dowling lattices study the representation afforded by the top co homology group and give a simple map to the posets of pointed d divisible partitions 1 main question and results let v denote an n dimensional c vector space a reflection in v is any nonidentity element r in gl v of finite order that fixes some hyperplane hr and a finite subgroup w of gl v is called a reflection group if it is generated by reflections example the action of the symmetric group sn on n 1 2 n gives rise to a faithful action on c via ei e i where e1 e2 en denote the standard basis vectors since the transpositions act as reflections and generate the group this representation realizes sn as a reflection group in gl c we shall refer to it as the defining representation for an element g w and root of unity let v g denote the eigenspace of g in v define e w to be the w poset partially ordered set of all such eigenspaces v g g w ordered by reverse inclusion with w action given by h v g v hgh the eigenvalue 1 gives the lattice lw of intersections of reflecting hyperplanes for w see 29 lemma 4 4 the minimal elements of e w i e the inclusion maximal eigenspaces forw are the focus of springer s theory of regular elements 35 and each has dimension equal to the number a d of degrees d1 d2 dn of w that are divisible by d the order of see proposition 3 7 below when w is crystallographic the poset e w itself appears in broue malle and michel s sylow theory 8 2010 mathematics subject classification primary 20f55 05e10 05e18 55p20 14n20

shellable nonpure complexes and posets ii this is a direct continuation of shellable nonpure complexes and posets i which appeared in transactions of the american mathematical society 348 1996 1299 1327 8 interval generated lattices and dominance order in this section and the following one we will continue exemplifying the applicability of lexicographic shellability to nonpure posets let f i1 i2 in be a family of intervals of integers by which is meant sets of the form a b a a 1 b a b we assume that there are no containments among these intervals and that they are ordered so that their left and right endpoints are increasing let l f be the lattice of all sets that are unions of subfamilies of f ordered by inclusion such interval generated lattices l f were introduced and studied by greene g define an edge labeling of l f as follows if a b is a covering and a max b a then a b a if a 1 a and a is the left endpoint of some i f

modeling of nonlinear ultrasound propagation in tissue from array transducers a computationally efficient model capable of simulating finite amplitude ultrasound beam propagation in water and in tissue from phased linear arrays and other transducers of arbitrary quasiplanar geometry is described it is based on a second order operator splitting approach tavakkoli et al j acoust soc am 104 2061 2072 1998 with a fractional step marching scheme whereby the effects of diffraction attenuation and nonlinearity can be computed independently over incremental steps this approach is an extension to that of christopher and parker j acoust soc am 90 507 521 90 488 499 1991 wherein linear and nonlinear effects are propagated separately over incremental steps and the computation of the diffractive substeps are based on an angular spectrum technique with a modified sampling scheme for accurate and efficient implementation of diffractive propagation from nonradially symmetric sources results of the model are compared with published data predicted field profiles for nonlinear propagation in tissue from realistic array transducers using the pulse inversion method are presented

supplementary notes on the gaussian beam expansion the letter provides alternatively a simple way of computing the fresnel field integral a further extension to the gaussian beam expansion the zeroth order bessel function of the first kind is expanded into an approximate sum of gaussian functions the field integral is then expressible in terms of these simple functions the approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics as examples the calculation results for the uniform and the simply supported piston sources are presented in a good agreement with those evaluated by numerical integration

some extensions of the gaussian beam expansion radiation fields of the rectangular and the elliptical transducer a straightforward extension of gaussian beam expansion is presented for calculation of the fresnel field integral j j wen and m a breazeale j acoust soc am 83 1752 1756 1988 the source distribution function is expanded into the superposition of a series of two dimensional gaussian functions the corresponding radiation field is expressed as the superposition of these two dimensional gaussian beams and is then reduced to the computation of these simple functions this treatment overcomes the limit that the shape of source is of circular axial symmetry the numerical examples are presented for the field of the uniform elliptical and the rectangular piston transducers and agree well with the results given by complicated computation

group actions on arrangements of linear subspaces and applications to configuration spaces for an arrangement of linear subspaces in ri that is invariant under a finite subgroup of the general linear group gin ir we develop a formula for the g module structure of the cohomology of the complement m a our formula specializes to the well known goresky macpherson theorem in case g 1 but for g 1 the formula shows that the g module structure of the complement is not a combinatorial invariant as an application we are able to describe the free part of the cohomology of the quotient space ma4ig our motivating examples are arrangements in cn that are invariant under the action of sn by permuting coordinates a particular case is the k equal arrangement first studied by bj6rner lovasz and yao motivated by questions in complexity theory in these cases ma4 and ma sn are spaces of ordered and unordered point configurations in cn many of whose properties are reduced by our formulas to combinatorial questions in partition lattices more generally we treat point configurations in rd and provide explicit results for the k equal and the k divisible cases

free resolutions of lex ideals over a koszul toric ring in this paper we study the minimal free resolution of lex ideals over a koszul toric ring in particular we study in which toric ring r all lex ideals are componentwise linear we give a certain necessity and sufficiency condition for this property and show that lex ideals in a strongly koszul toric ring are componentwise linear in addition it is shown that in the toric ring arising from the segre product p p every hilbert function of a graded ideal is attained by a lex ideal and that lex ideals have the greatest graded betti numbers among all ideals having the same hilbert function

fuzzy integral equations abstract we introduce a definition of the integral of a fuzzy valued function that is only slightly different from the usual one yet that is more intuitive and that can be applied to a larger class of functions we show that our definition is equivalent to the extension principle for functions of this class we then apply integration theory of fuzzy valued functions to integral equations we define a measure of the fuzziness of a fuzzy valued function and show that using this measure we can view the integration of fuzzy functions as a fuzzy linear transformation from a certain subspace of fuzzy valued functions to the space of fuzzy numbers we then show how this can be used to study fredholm integral equations of the second kind

notes on the gaussian beam expansion a powerful gaussian beam expansion technique j j wen and m a breazeale j acoust soc am 83 1752 1756 1988 is widely used in calculating the fresnel field integral a basic ideal of this treatment is to expand the source distribution function into the superposition of a series of gaussian functions the evaluation of the radiation field is then greatly simplified as a supplement this paper presents a simple approach to determine the expansion coefficients for the sound source the results for the ultrasonic field radiated by piston transducers are typically given in a fairly good agreement with those calculated by numerical integration and breazeale s the limits of the present method are also discussed

a simple calculation approach for the second harmonic sound field generated by an arbitrary axial symmetric source in a linear approximation an arbitrary axial symmetric source can be expressed as the linear superposition of a set of gaussian sources and the corresponding radiated sound field can be represented as the superposition of this set of gaussian beams the analysis is extended to the second harmonic generation due to nonlinear effects under a quasilinear approximation then the second harmonic sound field could be considered as a sum of self and cross interaction terms produced by a series of gaussian beams therefore the calculation of the second harmonic sound field of an axial symmetric source can be reduced to a simple linear combination of a set of exponential integral functions instead of a complicated triple integral in order to verify this calculation approach the second harmonic generation of a focused and a simple piston source is examined and the result is in good agreement with that in earlier paper by complicated computation

a review of methods for capacity identification in choquet integral based multi attribute utility theory applications of the kappalab r package the application of multi attribute utility theory whose aggregation process is based on the choquet integral requires the prior identification of a capacity the main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed all the reviewed methods have been implemented within the kappalab r package their application is illustrated on a detailed example

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

algebraic study on cameron walker graphs abstract let g be a finite simple graph on n and i g s the edge ideal of g where s k x 1 x n is the polynomial ring over a field k let m g denote the maximum size of matchings of g and i m g that of induced matchings of g it is known that i m g reg s i g m g where reg s i g is the castelnuovo mumford regularity of s i g cameron and walker succeeded in classifying the finite connected simple graphs g with i m g m g we say that a finite connected simple graph g is a cameron walker graph if i m g m g and if g is neither a star nor a star triangle in the present paper we study cameron walker graphs from a viewpoint of commutative algebra first we prove that a cameron walker graph g is unmixed if and only if g is cohen macaulay and classify all cohen macaulay cameron walker graphs second we prove that there is no gorenstein cameron walker graph finally we prove that every cameron walker graph is sequentially cohen macaulay

rings with lexicographic straightening law the concept of a straightening law as a means of analyzing the structure of particular commutative algebras has appeared independently in the work of a number of authors the purpose of this paper is to introduce a systematic theory of algebras endowed with a structure of a lexicographic straightening law based on a partially ordered set or lexicographic ring for short much of the work in the literature dealing with such rings fits quite naturally in the context of our theory and we sketch some of this work moreover some of our later results in particular the betti number bound in section 6 may actually be new results even for the special cases of the known examples of lexicographic rings the concept of a lexicographic ring as an interesting area of study was suggested to this author by deconcini who conjectured that a lexicographic ring is cohen macaulay if the underlying partially ordered set is so we prove this result in two different ways it has recently come to our attention that this conjecture has also been proved by deconcini et al 131 using deformation theory methods the results of this paper are arranged in two parts the first part consisting of sections 2 through 4 is more elementary and uses the technique of combinatorial decompositions as developed by garsia and this author the second part sections 6 and 7 requires some knowledge of homological algebra methods in ring theory the intermediate section 5 discusses some of the known examples of lexicographic rings in this section we also sketch some of the ways that our theory may be extended to more general contexts the main result of the first part is the transfer theorem 4 3 which enables one to transfer combinatorial decompositions from the underlying partially ordered set or more precisely from the corresponding stanley reisner ring to the lexicographic ring as a result those concepts that are expressible in terms of combinatorial decompositions are also

acoustic bullets transient bessel beams generated by planar apertures acoustic bullets are defined to be waves which maintain their peak amplitude and or general shape as they propagate in free space a general theoretical approach is presented to investigate the space time properties of a new class of acoustic bullets which are defined here as acoustic transient bessel beams the approach encompasses both baseband and modulated carrier signal wave fields closed form space time expressions are developed using fourier and hilbert transform methods for several special cases of transient bessel beams the space time source distributions for generating such wave fields from planar apertures are developed from the free space wave fields via the use of the rayleigh surface integral solution for time dependent fields finally numerical results are presented to illustrate the general space time characteristics of the acoustic transient bessel beams

a simplified algorithm for second order sound beams with arbitrary source distribution and geometry l an earlier investigation j acoust soc am 108 2759 2764 2000 of the simplified algorithm for the second order sound fields with circular axial symmetry is extended to a more general case of the sound sources with an arbitrary distribution this extension is based on the fact that the source function is expanded into the sum of a series of two dimensional gaussian ones the two and five dimensional integral expressions for the primary and second order fields are respectively reduced in terms of gaussian functions and simple one dimensional integrals numerical calculations are then greatly simplified

fuzzy valued fuzzy measures and generalized fuzzy integrals in this paper the concept of fuzzy valued fuzzy measures is introduced at first and then based on the generalized fuzzy integral given by wu et al fuzzy sets and systems 57 1993 219 the generalized fuzzy integral of fuzzy valued functions with respect to fuzzy valued fuzzy measures is defined and the properties and convergence theorems are given all these are extensions of the sugeno theory of fuzzy integrals and its applications ph d thesis tokyo institute of technology 1974 and wu et al 1993 theory

a hybrid approach for image recognition combining type 2 fuzzy logic modular neural networks and the sugeno integral in this paper a hybrid approach for image recognition combining type 2 fuzzy logic modular neural networks and the sugeno integral is described interval type 2 fuzzy inference systems are used to perform edge detection and to calculate fuzzy densities for the decision process a type 2 fuzzy system is used for edge detection which is a pre processing applied to the training data for better use in the neural networks another type 2 fuzzy system calculates the fuzzy densities necessary for the sugeno integral which is used to integrate results of the neural network modules in this case fuzzy logic is shown to be a good methodology to improve the results of a neural system facilitating the representation of the human perception a comparative study is also made to verify that the proposed approach is better than existing approaches and improves the performance over type 1 fuzzy logic

generalized fuzzy integrals of set valued functions in this paper based on wu s generalized fuzzy integrals of point valued function c wu et al fuzzy sets and systems 70 1995 75 a theory of generalized fuzzy integrals of fuzzy valued functions will be investigated it includes definitions properties and various kinds of convergence theorems these are extensions of results in c wu et al fuzzy sets and systems 70 1995 75 d zhang and z wang fuzzy sets and systems 54 1993 63

euler flag enumeration of whitney stratified spaces abstract the flag vector contains all the face incidence data of a polytope and in the poset setting the chain enumerative data it is a classical result due to bayer and klapper that for face lattices of polytopes and more generally eulerian graded posets the flag vector can be written as a c d index a non commutative polynomial which removes all the linear redundancies among the flag vector entries this result holds for regular cw complexes we relax the regularity condition to show the c d index exists for whitney stratified manifolds by extending the notion of a graded poset to that of a quasi graded poset this is a poset endowed with an order preserving rank function and a weighted zeta function this allows us to generalize the classical notion of eulerianness and obtain a c d index in the quasi graded poset arena we also extend the semi suspension operation to that of embedding a complex in the boundary of a higher dimensional ball and study the simplicial shelling components

dimension filtration sequential cohen macaulayness and a new polynomial invariant of graded algebras let k be a field and let a be a standard n graded k algebra using numerical information of some invariants in the primary decomposition of 0 in a namely the so called dimension filtration we ass

a new subgroup lattice characterization of finite solvable groups abstract we show that if g is a finite group then no chain of modular elements in its subgroup lattice l g is longer than a chief series also we show that if g is a nonsolvable finite group then every maximal chain in l g has length at least two more than the chief length of g thereby providing a converse of a result of j kohler our results enable us to give a new characterization of finite solvable groups involving only the combinatorics of subgroup lattices namely a finite group g is solvable if and only if l g contains a maximal chain x and a chain m consisting entirely of modular elements such that x and m have the same length

some combinatorial and algebraic properties of coxeter complexes and tits buildings a des groupes de coxeter et des groupes a bn paire sont associes certaines structures combinatoires les complexes de coxeter et les constructions de tits on etudie ces structures du point de vue des complexes de cohen macaulay et des complexes decorticables

on the shellability of the order complex of the subgroup lattice of a finite group we show that the order complex of the subgroup lattice of a finite group g is nonpure shellable if and only if g is solvable a by product of the proof that nonsolvable groups do not have shellable subgroup lattices is the determination of the homotopy types of the order complexes of the subgroup lattices of many minimal simple groups

the homology representations of the k equal partition lattice we determine the character of the action of the symmetric group on the homology of the induced subposet of the lattice of partitions of the set 1 2 nr obtained by restricting block sizes to the set 1 k k 1 a plethystic formula for the generating function of the frobenius characteristic of the representation is given we combine techniques from the theory of nonpure shellability recently developed by bj6rner and wachs with symmetric function techniques developed by sundaram for determining representations on the homology of subposets of the partition lattice

a generalization of rota s nbc theorem abstract we generalize rota s theorem characterizing the mobius function of a geometric lattice in terms of subsets of atoms containing no broken circuit and give applications to the weak bruhat order of a finite coxeter group and the tamari lattices we also give a direct proof of the fact that in the geometric case any total order of the atoms can be used simple involutions are used in both proofs finally we show how involutions can be used in similar situations specifically in a special case of rota s crosscut theorem as well as in related proofs of walker on hall s theorem and reiner on characteristic and poincare polynomials

poset fiber theorems suppose that f p q is a poset map whose fibers f 1 qless than or equal to q are sufficiently well connected our main result is a formula expressing the homotopy type of p in terms of q and the fibers several fiber theorems from the literature due to babson baclawski and quillen are obtained as consequences or special cases homology cohen macaulay and equivariant versions are given and some applications are discussed

joins ears and castelnuovo mumford regularity abstract we introduce a new class of polynomial ideals associated to a simple graph g let k e g be the polynomial ring on the edges of g and k v g the polynomial ring on the vertices of g we associate to g an ideal i x g defined as the preimage of x i 2 x j 2 i j v g k v g by the map k e g k v g which sends a variable t e associated to an edge e i j to the product x i x j of the variables associated to its vertices we show that k e g i x g is a one dimensional cohen macaulay graded ring and we relate its degree with the number of vertices and connected components of the graph we show that i x g is a binomial ideal and that with respect to a fixed monomial order its initial ideal has a generating set independent of the field k we focus on the castelnuovo mumford regularity of i x g providing the following sharp upper and lower bounds g reg i x g v g b 0 g 1 where g is the maximum vertex join number of the graph and b 0 g is the number of its connected components we show that the lower bound is attained for a bipartite graph and use this to derive a new combinatorial result on the number of even length ears of nested ear decomposition

decomposable clutters and a generalization of simon s conjecture abstract each equigenerated squarefree monomial ideal in the polynomial ring s k x 1 x n represents a family of subsets of n called a uniform clutter in this paper we introduce a class of uniform clutters called decomposable clutters whose associated ideal has linear quotients and hence linear resolution over all fields we show that chordality of these clutters guarantees the correctness of a conjecture raised by r s simon 23 on extendable shellebility of d skeletons of a simplex n for all d we then prove this conjecture for d n 3

combining uncertain information of differing modalities in this paper we consider approaches for combining separately possibilistic uncertainty probabilistic uncertainty and situations where both forms of uncertainty appear an approach to probability aggregation using rational consensus with equi weighting is developed this aggregation is analyzed with information measures as one way to assess combinations and understand the impact on uncertainty the analysis is based on combinations of bounding cases of probability distributions measures of conflict and the effect on information are developed next possibility transformations are used and illustrated by three representative possibility cases the resultant transformed probabilities are aggregated with general probability distributions and the result evaluated with information measures as before finally a general approach to combining possibility distributions directly using quality criteria is described an example is provided to illustrate the basic possibility distribution aggregation fusion developed

clusters coxeter sortable elements and noncrossing partitions we introduce coxeter sortable elements of a coxeter group for finite we give bijective proofs that coxeter sortable elements are equinumerous with clusters and with noncrossing partitions we characterize coxeter sortable elements in terms of their inversion sets and in the classical cases in terms of permutations