on the structure of the cone of positive operators abstract if k 1 is a proper cone in r n 1 and k 2 is a proper cone in r n 2 then as is well known the set k 1 k 2 which consists of all n 2 x n 1 real matrices which take k 1 into k 2 forms a proper cone in the space r n 2 n 1 in this paper a study of this cone is made with particular emphasis on its faces and duality operator a face of k 1 k 2 is called simple if it is composed of all matrices in k 1 k 2 which take some fixed face of k 1 into some fixed face of k 2 maximal faces of k 1 k 2 are characterized as a particular kind of simple faces relations between the duality operator of k 1 k 2 and those of k 1 and k 2 are obtained among many other results it is proved that d k 1 k 2 the duality operator of k 1 k 2 is injective if and only if d k 2 is injective and each face of k 1 k 2 is an intersection of simple faces two open questions are posed

maximal exponents of polyhedral cones iii article history received 31 may 2009 available online 14 november 2009 submitted by j bastero

the perron generalized eigenspace and the spectral cone of a cone preserving map a unified treatment is offered to reprove known results on the following four highlights of the combinatorial spectral theory of nonnegative matrices or to extend or partly extend the results to the setting of a linear map preserving a polyhedral proper or proper cone the preferred basis theorem equivalent conditions for equality of the graph theoretic level characteristic and the spectral height characteristic the majorization relation between the two characteristics and the relation between the combinatorial properties of a nonnegative matrix and the positivity of the individual entries in its principal components this is achieved by employing the new concept of spectral cone of a cone preserving map and combining the cone theoretic methods developed in our previous papers on the geometric spectral theory of cone preserving maps with the algebraic analytic method introduced by hartwig neumann and rose and further exploited by neumann and schneider for nonnegative matrices

on the semiring of cone preserving maps abstract if k is a proper cone in r n then the cone of all linear operators that preserve k denoted by k forms a semiring under usual operator addition and multiplication recently j g horne examined the ideals of this semiring he proved that if k 1 k 2 are polyhedral cones such that k 1 and k 2 are isomorphic as semirings then k 1 and k 2 are linearly isomorphic the study of this semiring is continued in this paper in sec 3 ideals of k which are also faces are characterized in sec 4 it is shown that k has a unique minimal two sided ideal namely the dual cone of k where k is the dual cone of k extending horne s result it is also proved that the cone k is characterized by this unique minimal two sided ideal of k the set of all faces of k inherits a quotient semiring structure from k properties of this face semiring are given in sec 5 in particular it is proved that this face semiring admits no nontrivial congruence relation iff the duality operator of k is injective in sec 6 the maximal one sided and two sided ideals of k are identified in sec 8 it is shown that k never satisfies the ascending chain condition on principal one sided ideals some partial results on the question of topological closedness of principal one sided ideals of k are also given

spectral orders and isotone functionals it is shown that the spectral orders in lp are induced by some cones the result provides sufficient conditions of the schur ostrowski type for isotonicity of differentiable functionals w r t the orders 0 elsevier science inc 1997

temporal integration and compression near absolute threshold in normal and impaired ears the decrease in absolute threshold with increasing stimulus duration often referred to as temporal integration is greater for listeners with normal hearing than for listeners with sensorineural hearing loss it has been suggested that the difference is related to reduced basilar membrane bm compression in the impaired group the present experiment tested this hypothesis by comparing temporal integration and bm compression in normal and impaired ears at low levels absolute thresholds were measured for 4 24 and 44 ms pure tone signals with frequencies f s of 2 and 4 khz the difference between the absolute thresholds for the 4 and 24 ms signals was used as a measure of temporal integration compression near threshold was estimated by measuring the level of a 100 ms off frequency 0 45f s pure tone forward masker required to mask a 44 ms pure tone signal presented at sensation levels of 5 and 10 db there was a significant negative correlation between amount of temporal integration and absolute threshold however there was no correlation between absolute threshold and compression at low levels both normal and impaired ears showed a nearly linear response the results suggest that the differences in integration between normal and impaired ears cannot be explained by differences in bm compression

interpolation between non commutative bmo and non commutative lp spaces we prove that for 1 p q the analogue of the classical result bmo lp pq lq holds in the setting of a finite von neumann algebra m equipped with an increasing filtration mn n 1 of von neumann subalgebras we also obtain the corresponding results for the real method of interpolation we discuss the appropriate operator space matrix norms and show that these interpolation results hold in the category of operator spaces

spectral and temporal integration of brief tones both spectral and temporal integration of tones have been explored in detail but integration of tones varying across both dimensions has received little attention this study explores temporal integration of tone pulses that vary over a range of frequencies baseline thresholds were obtained for both spectral and temporal integration with the same signals and compared with prior research the signals were then varied on both dimensions in several ways with equivalent spectral and temporal step sizes different spectral and temporal step sizes and a random pattern of frequency presentation the data were also analyzed by spectral step size temporal step size frequency range direction and slope of frequency change and predictability the spectral and temporal integration conditions showed that the current procedures and signals yielded the same improvement in detection thresholds as prior studies the spectrotemporal integration conditions showed the improvement for overall detection of the signals to be limited by spectral integration with improvement related primarily to the number of tones regardless of timing and frequency surprisingly trial by trial random presentation of signal frequencies did not negatively influence detection these results support the multiple looks hypothesis viemeister n f and wakefield g h 1991 temporal integration and multiple looks j acoust soc am 90 858 865 as applied to spectrotemporal integration

dixmier traces and extrapolation description of noncommutative lorentz spaces we study the connections between dixmier traces functions and traces of heat semigroups beyond the dual of the macaev ideal and in the general context of semifinite von neumann algebras we show that the correct framework for this investigation is that of operator lorentz spaces possessing an extrapolation description we demonstrate the applicability of our results to hormander weyl pseudo differential calculus on rn in this context we prove that the dixmier trace of a pseudo differential operator coincides with the dixmier integral of its symbol

on the positive output controllability of linear time invariant systems this paper considers the output controllability of autonomous linear control systems that are subject to non negative input constraints based on the evaluation of the geometric properties of the system necessary and sufficient conditions are proposed for the positive output controllability of continuous linear time invariant systems to aid in the practical evaluation of positive output controllability additional sufficient conditions are derived for which efficient numerical techniques exist these conditions are evaluated over a set of numerical examples which support the theoretical results

order intervals of matrices abstract some basic results for order intervals on ordered topological vector spaces are given then characterizations of order intervals where the partial orders are induced by the pointed matrix cones psd in h n and o n in r n and the pointed cones of linear transformations on matrices psd and cp among others in hp together with some seminorms and norms which they generate are given

ando s inequality for uniform submajorization abstract we discuss ando s inequality involving operator monotone functions and demonstrate that a natural strengthening of ando s result to uniform submajorization holds if and only if the operator monotone function has a very simple rational form

a contractive version of a schur horn theorem in ii1 factors we prove a contractive version of the schur horn theorem for submajorization in ii1 factors that complements some previous results on the schur horn theorem within this context we obtain a reformulation of a conjecture of arveson and kadison regarding a strong version of the schur horn theorem in ii1 factors in terms of submajorization and contractive orbits of positive operators

convex hulls of unitary orbits of normal elements in c algebras with tracial rank zero abstract let a be a unital separable simple c algebra with tracial rank zero and let x y a be two normal elements we show that x is in the closure of the convex hull of the unitary orbit of y if and only if there exists a sequence of unital completely positive linear maps n from a to a such that the sequence n y converges to x in norm and also approximately preserves the trace values a purely measure theoretical description for normal elements in the closure of the convex hull of unitary orbit of y is also given in the case that a has a unique tracial state some classical results about the closure of the convex hull of the unitary orbits in von neumann algebras are proved to hold in the c algebraic setting

multiplicative versions of klyachko s theorem in finite factors abstract let a and b be invertible positive elements in a ii 1 factor a and let s be the singular number on a we prove that exp k log s ab d s exp i log s a d s exp j log s b d s where i j k is an analogue of klyachko s list in this paper this family i j k must satisfy some hypotheses which are specific to operators a and b but we show that our family of inequalities includes the weak gelfand naimark inequality for all positive operators a and b

on the cone of positive semidefinite matrices abstract a survey of some general properties of the cone of positive semidefinite matrices its faces two isometric isomorphisms and linear transformations on it is given

baer semirings and baer semirings of cone preserving maps abstract the study of k the semiring of matrices which leave invariant the proper cone k is continued in this paper the definitions of baer rings and baer rings are extended to semirings at least in the case of k results that relate the concepts of right left annihilators right left facial ideals and p exposed or o p exposed faces are given proper cones k for which k is a right left baer semiring or a baer semiring are characterized in particular it is shown that k is a baer semiring if and only if k is a perfect cone the set of projections in k is investigated and its lattice structure is analyzed the concepts of equivalence of idempotents and equivalence of projections in k are introduced and examined

the dixmier trace and asymptotics of zeta functions abstract we obtain general theorems which enable the calculation of the dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup we prove our results in a general semi finite von neumann algebra we find for p 1 that the asymptotics of the zeta function determines an ideal strictly larger than l p on which the dixmier trace may be defined we also establish stronger versions of other results on dixmier traces and zeta functions

geometry of homogeneous convex cones duality mapping and optimal self concordant barriers we study homogeneous convex cones we first characterize the extreme rays of such cones in the context of their primal construction due to vinberg and also in the context of their dual construction due to rothaus then using these results we prove that every homogeneous cone is facially exposed we provide an alternative proof of a result of guler and tunc el that the siegel rank of a symmetric cone is equal to its caratheodory number our proof does not use the jordan von neumann wigner characterization of the symmetric cones but it easily follows from the primal construction of the homogeneous cones and our results on the geometry of homogeneous cones in primal and dual forms we study optimal self concordant barriers in this context we briefly discuss the duality mapping in the context of automorphisms of convex cones and prove using numerical integration that the duality mapping is not an involution on certain self dual cones

a study of projectionally exposed cones abstract in view of possible applications to abstract convex programs barker laidacker and poole have made an initial study of p exposed cones and o p exposed cones by restricting their attention to closed pointed cones a study of these cones is continued in this paper sufficient conditions for a face of a proper cone to be a p exposed or an o p exposed face are established characterizations of o p exposed cones among polyhedral cones are also obtained the relation between exposedness and p exposedness of faces of a general cone is examined as one consequence a question posed by iochum is answered in the finite dimensional case that is there is no finite dimensional semiregular self dual cones which are not regular also a conjecture posed by barker and thompson on p exposed faces of p n that the cone of all real polynomials of degree n which are nonnegative on the closed interval 0 1 is settled

closed convex hulls of unitary orbits in c algebras of real rank zero abstract in this paper we study closed convex hulls of unitary orbits in various c algebras for unital c algebras with real rank zero and a faithful tracial state determining equivalence of projections a notion of majorization describes the closed convex hulls of unitary orbits for self adjoint operators other notions of majorization are examined in these c algebras combining these ideas with the dixmier property we demonstrate unital infinite dimensional c algebras of real rank zero and strict comparison of projections with respect to a faithful tracial state must be simple and have a unique tracial state also closed convex hulls of unitary orbits of self adjoint operators are fully described in unital simple purely infinite c algebras

on the completely positive and positive semidefinite preserving cones abstract the cone cp n q of completely positive linear transformations from m n c m n to m q is shown to be isometrically isomorphic to p nq the cone of nq by nq positive semidefinite matrices generalizations of scalar and matrix results to cp n q hp n q l m n m q where hp n q represents the hermitian preserving linear transformations are discussed relationships among the completely positives the set of positive semidefinite preservers p n and its dual m n are given left and right facial ideals of cp are characterized properties of the joint angular field of values of a finite sequence of hermitian matrices h 1 h m are studied leading to a characterization of p q p n

representability of convex sets by analytical linear inequality systems the solution sets of analytical linear inequality systems posed in the euclidean space form a transition class between the polyhedral convex sets and the closed convex sets which are representable by means of linear continuous systems the constraint systems of many semi infinite programming problems are analytical and their feasible sets retain geometric properties of the polyhedral sets which are useful in the numerical treatment of such kind of optimization problems the euclidean closed n dimensional balls admit analytical representation if and only if n 3 this paper solves in a negative way the analytical representation problem for a wide class of n dimensional convex sets with n 3 which includes quasi polyhedral sets and smooth convex bodies

multivariable schur horn theorems fil massey pedro gustavo universidad nacional de la plata facultad de ciencias exactas departamento de matematicas argentina consejo nacional de investigaciones cientificas y tecnicas oficina de coordinacion administrativa saavedra 15 instituto argentino de matematica alberto calderon argentina

theory of cones abstract this survey deals with the aspects of archimedian partially ordered finite dimensional real vector spaces and order preserving linear maps which do not involve spectral theory the first section sketches some of the background of entrywise nonnegative matrices and of systems of inequalities which motivate much of the current investigations the study of inequalities resulted in the definition of a polyhedral cone k and its face lattice f k in section ii a the face lattice of a not necessarily polyhedral cone k in a vector space v is investigated in particular the interplay between the lattice properties of f k and geometric properties of k is emphasized section ii b turns to the cones k in the space of linear maps on v recall that k is the cone of all order preserving linear maps of particular interest are the algebraic structure of k as a semiring and the nature of the group aut k of nonsingular elements a k for which a 1 k as well in a short final section the cone p n of n n positive semidefinite matrices is discussed a characterization of the set of completely positive linear maps is stated the proofs will appear in a forthcoming paper

an extension of inequalities by ando abstract we give variations on ando s result comparing f b f a and f b a with respect to unitarily invariant norms on matrices

maximal exponents of polyhedral cones i abstract let k be a proper i e closed pointed full convex cone in r n an n n matrix a is said to be k primitive if there exists a positive integer k such that a k k 0 int k the least such k is referred to as the exponent of a and is denoted by a for a polyhedral cone k the maximum value of a taken over all k primitive matrices a is called the exponent of k and is denoted by k it is proved that if k is an n dimensional polyhedral cone with m extreme rays then for any k primitive matrix a a m a 1 m 1 1 where m a denotes the degree of the minimal polynomial of a and the equality holds only if the digraph e p a k associated with a as a cone preserving map is equal to the unique up to isomorphism usual digraph associated with an m m primitive matrix whose exponent attains wielandt s classical sharp bound as a consequence for any n dimensional polyhedral cone k with m extreme rays k n 1 m 1 1 our work answers in the affirmative a conjecture posed by steve kirkland about an upper bound of k for a polyhedral cone k with a given number of extreme rays

auditory temporal integration and the power function model the auditory temporal integration function was studied with the objective of improving both its quantitative description and the specification of its principle independent variable stimulus duration in sec i temporal integration data from 20 studies were subjected to uniform analyses using standardized definitions of duration and two models of temporal integration analyses revealed that these data were best described by a power function model used in conjunction with a definition of duration termed assigned duration that de emphasized the rise fall portions of the stimuli there was a strong effect of stimulus frequency and in general the slope of the temporal integration function was less than 10 db per decade of duration i e a power function exponent less than 1 0 in sec ii an experimental study was performed to further evaluate the models and definitions detection thresholds were measured in 11 normal hearing human subjects using a total of 24 single burst and multiple burst acoustic stimuli of 3 125 khz the issues addressed are the quantitative description of the temporal integration function the definition of stimulus duration the similarity of the integration processes for single burst and multiple burst stimuli and the contribution of rise fall time to the integration process a power function in conjunction with the assigned duration definition was again most effective in describing the data single and multiple burst stimuli both seemed to be integrated by the same central mechanism with data for each type of stimulus being described by a power function exponent of approximately 0 6 at 3 125 khz it was concluded that the contribution of the rise fall portions of the stimuli can be factored out from the rest of the temporal integration process in sec iii the conclusions that emerged from the review of published work and the present experimental work suggested that auditory temporal integration is best described by a power function in conjunction with the assigned duration definition the exponent for the power function is typically less than 1 0 and varies with frequency and hearing level second a means of empirically assaying the contribution of the rise fall portions of the stimuli is presented and evaluated finally properties of a central auditory integrator are hypothesized abstract truncated at 250 words

automatic continuity of orthogonality preservers on a non commutative lp τ space abstract elements a and b of a non commutative l p space associated to a von neumann algebra n equipped with a normal semifinite faithful trace are called orthogonal if l a l b r a r b 0 where l x and r x denote the left and right support projections of x a linear map t from l p n to a normed space y is said to be orthogonality to p orthogonality preserving if t a t b p a p b p whenever a and b are orthogonal in this paper we prove that an orthogonality to p orthogonality preserving linear bijection from l p n 1 p p 2 to a banach space x is automatically continuous whenever n is a separably acting von neumann algebra if n is a semifinite factor not of type i 2 we establish that every orthogonality to p orthogonality preserving linear mapping t l p n x is continuous and invertible whenever t 0 furthermore there exists a positive constant c p 1 p p 2 so that t t 1 c p 2 for every non zero orthogonality to p orthogonality preserving linear mapping t l p n x for p 1 this inequality holds with c p 1 that is t is a multiple of an isometry

multiplication operators on non commutative spaces abstract boundedness and compactness properties of multiplication operators on quantum non commutative function spaces are investigated for endomorphic multiplication operators these properties can be characterized in the setting of quantum symmetric spaces for non endomorphic multiplication operators these properties can be completely characterized in the setting of quantum l p spaces and a partial solution obtained in the more general setting of quantum orlicz spaces

state convertibility in the von neumann algebra framework we establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi finite von neumann algebras namely we establish a generalisation to this setting of nielsen s theorem on the convertibility of quantum states under local operations and classical communication locc schemes along the way we introduce an appropriate generalisation of locc operations and connect the resulting notion of approximate convertibility to the theory of singular numbers and majorisation in von neumann algebras as an application of our result in the setting of mathrm ii 1 factors we show that the entropy of the singular value distribution relative to the unique tracial state is an entanglement monotone in the sense of vidal thus yielding a new way to quantify entanglement in that context building on previous work in the infinite dimensional setting we show that trace vectors play the role of maximally entangled states for general mathrm ii 1 factors examples are drawn from infinite spin chains quasi free representations of the car and discretised versions of the ccr

on the connection of facially exposed and nice cones abstract a closed convex cone k in a finite dimensional euclidean space is called nice if the set k f is closed for all f faces of k where k is the dual cone of k and f is the orthogonal complement of the linear span of f the niceness property plays a role in the facial reduction algorithm of borwein and wolkowicz and the question of whether the linear image of the dual of a nice cone is closed also has a simple answer we prove several characterizations of nice cones and show a strong connection with facial exposedness we prove that a nice cone must be facially exposed conversely facial exposedness with an added condition implies niceness we conjecture that nice and facially exposed cones are actually the same and give supporting evidence

differentiation of operator functions in non commutative lp spaces the principal results in this paper are concerned with the description of differentiable operator functions in the non commutative lp spaces 1 p associated with semifinite von neumann algebras for example it is established that if f r r is a lipschitz function then the operator function f is g teaux differentiable in l2 m for any semifinite von neumann algebra m if and only if it has a continuous derivative furthermore if f r r has a continuous derivative which is of bounded variation then the operator function f is g teaux differentiable in any lp m 1 p

on the invariant faces associated with a cone preserving map for an n n nonnegative matrix p an isomorphism is obtained between the lattice of initial subsets of 1 n for p and the lattice of p invariant faces of the nonnegative orthant r motivated by this isomorphism we generalize some of the known combinatorial spectral results on a nonnegative matrix that are given in terms of its classes to results for a cone preserving map on a polyhedral cone formulated in terms of its invariant faces in particular we obtain the following extension of the famous rothblum index theorem for a nonnegative matrix if a leaves invariant a polyhedral cone k then for each distinguished eigenvalue ofa fork there is a chain of m distinct a invariant join irreducible faces of k each containing in its relative interior a generalized eigenvector of a corresponding to referred to as semi distinguished a invariant faces associated with where m is the maximal order of distinguished generalized eigenvectors of a corresponding to but there is no such chain with more than m members we introduce the important new concepts of semi distinguished a invariant faces and of spectral pairs of faces associated with a cone preserving map and obtain several properties of a cone preserving map that mostly involve these two concepts when the underlying cone is polyhedral perfect or strictly convex and or smooth or is the cone of all real polynomials of degree not exceeding n that are nonnegative on a closed interval plentiful illustrative examples are provided some open problems are posed at the end 1991 mathematics subject classification primary 15a48 secondary 47b65 47a25 46b42

exposed faces and duality for symmetric and unitarily invariant norms abstract let be a unitarily invariant norm on the space of real or complex n m matrices and g the associated symmetric gauge function thus a g s a where s a is the decreasing sequence of singular values of a denote by b and bg the closed unit balls of and g in a previous paper we showed a close relationship between the faces of b and those of bg in particular to each face of b we associated a standard face of bg and we used this association to completely describe the matrices that are members of an individual face of in the present paper we consider the duality operator that transforms each exposed face of b into an exposed face of the unit ball of s dual and the duality operator that does the same with exposed faces of bg we show that these two operators are very nicely related among other results we prove the following given an exposed face e of b the standard face associated with the dual of e is precisely the dual of the standard face of bg associated with e e is an exposed face of b if and only if its associated standard face is an exposed face of bg as a by product we completely determine the subdifferential of in terms of the subdifferential of g and we completely characterize the matrices that are dual to a given matrix a with respect to

commutator estimates in w algebras abstract let m be a w algebra and let ls m be the algebra of all locally measurable operators affiliated with m it is shown that for any self adjoint element a ls m there exists a self adjoint element c 0 from the center of ls m such that for any e 0 there exists a unitary element u e from m satisfying a u e 1 e a c 0 a corollary of this result is that for any derivation on m with the range in a not necessarily norm closed ideal i m the derivation is inner that is a a and a i similar results are also obtained for inner derivations on ls m

optimal bounds on the positivity of a matrix from a few moments in many contexts one encounters hermitian operators m on a hilbert space whose dimension is so large that it is impossible to write down all matrix entries in an orthonormal basis how does one determine whether such m is positive semidefinite here we approach this problem by deriving asymptotically optimal bounds to the distance to the positive semidefinite cone in schatten p norm for all integer p in 1 infty assuming that we know the moments mathbf tr m k up to a certain order k 1 ldots m we then provide three methods to compute these bounds and relaxations thereof the sos polynomial method a semidefinite program the handelman method a linear program relaxation and the chebyshev method a relaxation not involving any optimization we investigate the analytical and numerical performance of these methods and present a number of example computations partly motivated by applications to tensor networks and to the theory of free spectrahedra

isomorphic classification of lp q spaces abstract we prove that for all 1 p q p q p 1 p 2 and p 2 q 2 the banach space l p q does not isomorphically embed into the space l p q 0 1 we also prove under the same conditions that the space l p q 0 does not isomorphically embed into the space l p q 0 1 l p q

dualistic differential geometry of positive definite matrices and its applications to related problems abstract analysis on the set of positive definite matrices is involved in many engineering problems we develop a differential geometric theory of the set of positive definite matrices by means of a specific class of connections introduced into it consequently various dualistic aspects of the set are elucidated next using the theory we derive new results and interesting geometrical interpretations for matrix approximation positive definite matrix completion and linear matrix inequality problems

complementation in the face lattice of a proper cone abstract barker proved that the lattice of faces f k of a finite dimensional proper cone k is always complemented the proof however contained a gap in this paper we offer a correct proof of the result at the same time new characterizations of lattices of finite length which are section complemented or relatively complemented are found it is also proved that the lattice of exposed faces of a proper cone k is complemented finally we show that the class of proper cones with a relatively complemented face lattice is strictly contained in the class of proper cones with a dual atomistic face lattice for a few natural related questions counterexamples are given it turns out that one of our examples also answers in the negative an open problem posed recently by the second author

cross positive matrices revisited abstract for a closed pointed n dimensional convex cone k in r n let k denote the set of all n n real matrices a which as linear operators map k into itself let k denote the set of all n n matrices that are cross positive on k and l k k k the lineality space of k let r i the set of all real multiples of the n n identity matrix i then k k l k cl k k the final equality was proved in 1970 by schneider and vidyasagar who showed also that k k when k is polyhedral but not when k is a three dimensional circular cone they asked for a general characterization of those k for which the equality holds it is shown here that if n 3 and the cone k is strictly convex or smooth then k k hence for n 3 the equality fails for almost all k in the sense of baire category however the equality does hold for some nonpolyhedral k as was shown by a construction that appeared in the third author s 1977 dissertation and is explained here in more detail in 1994 it was shown by stern and wolkowicz that the weaker equality k l k k holds for all ellipsoidal as well as for all polyhedral k and they wondered whether this equality holds for all k however their equality certainly fails for all strictly convex or smooth k such that l k and it is shown here that this also includes almost all k when n 3

a maximum likelihood method for estimating thresholds in a yes no task a maximum likelihood procedure for estimating threshold values in a yes no task is presented in computer simulations of this procedure it is demonstrated that the variability of the threshold estimates is little affected by the density of the hypotheses tested for a fixed range or by serious misestimates of the slope of the psychometric functions the threshold value is also largely independent of the starting value of the signal the standard deviation of the threshold estimates appears to decrease with the square root of the number of trials with a 2 to 3 db standard deviation possible if only 12 trials are used in the threshold estimates data are presented using human listeners tested on 5 days two threshold estimates based on 12 trials were made at each of the six audiometric frequencies on each day the mean data appear sensible and the standard deviation of the measured thresholds is about 3 db using this procedure it takes less than 3 min to measure the audiogram for a single ear

generalized inverses of cone preserving maps abstract let k 1 and k 2 be solid cones in r n and r m respectively and let a be a linear operator such that ak 1 k 2 necessary and sufficient conditions for the existence of various kinds of generalized inverses of a taking k 2 into k 1 are given projections which belong to k the set of all linear operators that preserve a are studied in particular it is proved that a projection p in k is a simplicial nonnegative linear combination of its rank one operators iff im p k is a simplical cone an open question of burns fiedler and haynsworth concerning minimal generating matrices of polyhedral cones is also extended and answered affirmatively

on the duality operator of a convex cone let c be a convex set in r for each y c the cone of c at y denoted by cone y c is the cone a x y a 0 and x e c if k is a cone in r we shall denote by k its dual cone and by k the lattice of faces of k then the duality operator of k is the mapping dk k k given by dn f span f a cq k properties of the duality operator d k of a closed pointed hill cone k have been studied before in this paper we study da for a general cone k especially m relation to d o c v k where y e k our main result says that for any closed cone k in r the duality operator d k is injective surjective if and only if the duality operator d o u n is injective surjective for each vector y e k k n k in the last part of the paper we obtain some partial results on the problem of constructing a compact convex set c which contains the zero vector such that cone 0 c is equal to a given cone

majorizations and inequalities in matrix theory abstract in matrix theory majorization plays a significant role for instance majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities this survey article is intended as a review of recent results in matrix theory related to majorization

temporal integration frequency resolution and off frequency listening in normal hearing and cochlear impaired listeners temporal integration for a 1000 hz signal was determined for normal hearing and cochlear hearing impaired listeners in quiet and in masking noise of variable bandwidth critical ratio and 3 db critical band measures of frequency resolution were derived from the masking data temporal integration for the normal hearing listeners was markedly reduced in narrow band noise when contrasted with temporal integration in quiet or in wideband noise the effect of noise bandwidth on temporal integration was smaller for the hearing impaired group hearing impaired subjects showed both reduced temporal integration and reduced frequency resolution for the 200 ms signal however a direct relation between temporal integration and frequency resolution was not indicated frequency resolution for the normal hearing listeners did not differ from that of the hearing impaired listeners for the 20 ms signal it was suggested that some of the frequency resolution and temporal integration differences between normal hearing and hearing impaired listeners could be accounted for by off frequency listening

a noncommutative version of the john nirenberg theorem we prove a noncommutative version of the john nirenberg theorem for nontracial filtrations of von neumann algebras as an application we obtain an analogue of the classical large deviation inequality for elements of the associated bmo space

sums of commutators in non commutative banach function spaces let m be a ii factor and denote by its normal faithful semi finite trace for any rearrangement invariant kothe function space x on 0 let x m be the associated non commutative banach function space this paper is concerned with ideals in m of the form ix m m x m that are contained in lp m for some p 0 it is proved that an element t in ix m is a finite sum of commutators of the form a b with a ix m and b m if and only if the function t 1t t t d t belongs to x where t is the brown spectral measure of t and t t t is the non increasing rearrangement of the function with respect to t this extends to general banach function spaces a result obtained by kalton for quasi banach ideals of compact operators and implies that the dixmier s trace of a quasi nilpotent element in l1 m is always zero

kadec klee property for convergence in measure of noncommutative orlicz spaces abstract this paper studies the kadec klee property for convergence in measure of noncommutative orlicz spaces l m where m is the space of measurable operators and is an orlicz function we show that l m has the kadec klee property in measure if and only if the satisfies the 2 condition as a corollary the dual space and reflexivity of l m are given

on the zero pattern properties and asymptotic behavior of continuous time positive system trajectories abstract in this paper the zero pattern properties and the asymptotic evolution of the trajectories of a continuous time positive system are investigated to this end we need to introduce some new tools and to derive some new results within the broad research area of nonnegative matrix theory which enable use to explore the zero pattern and the elementary modes of the exponential of a metzler matrix specifically a normal form for the exponential of a metzler matrix is provided and the concept of echelon basis consisting of eigenvectors and generalized eigenvectors of the metzler matrix is introduced by making use of these two ingredients a detailed result about the dominant mode of each single block appearing in the normal form of the exponential matrix is provided this allows to obtain a modal decomposition of the exponential matrix emphasizing the column dominant modes as a result the zero pattern as well as the asymptotic behavior of every free state evolution depending on the zero pattern of the initial state can be easily determined

on the cone of a finite dimensional compact convex set at a point abstract four equivalent conditions for a convex cone in a euclidean space to be an f set are given our result answers in the negative a recent open problem posed by tam 5 characterizes the barrier cone of a convex set and also provides an alternative proof for the known characterizations of the inner aperture of a convex set as given by bronsted 2 and larman 3

on the closedness of the linear image of a closed convex cone when is the linear image of a closed convex cone closed we present very simple and intuitive necessary conditions that 1 unify and generalize seemingly disparate classical sufficientconditions such as polyhedrality of the cone and slater type conditions 2 are necessary and sufficient when the dual cone belongs to a class that we call nice cones nice cones subsume all cones amenable to treatment by efficient optimization algorithms for instance polyhedral semidefinite and p cones and 3 provide similarly attractive conditions for an equivalent problem the closedness of the sum of two closed convex cones

noncommutative kothe duality using techniques drawn from the classical theory of rearrangement invariant banach function spaces we develop a duality theory in the sense of kothe for symmetric banach spaces of measurable operators affiliated with a semifinite von neumann algebra equipped with a distinguished trace a principal result of the paper is the identification of the kothe dual of a given banach space of measurable operators in terms of normality

the psychophysics of absolute threshold and signal duration a probabilistic approach the absolute threshold for a tone depends on its duration longer tones have lower thresholds this effect has traditionally been explained in terms of temporal integration involving the summation of energy or perceptual information over time an alternative probabilistic explanation of the process is formulated in terms of simple equations that predict not only the time duration dependence but also the shape of the psychometric function at absolute threshold it also predicts a tight relationship between these two functions measurements made using listeners with either normal or impaired hearing show that the probabilistic equations adequately fit observed threshold duration functions and psychometric functions the mathematical formulation implies that absolute threshold can be construed as a two valued function a gain and b sensory threshold and both parameters can be estimated from threshold duration data sensorineural hearing impairment is sometimes associated with a smaller threshold duration effect and sometimes with steeper psychometric functions the equations explain why these two effects are expected to be linked the probabilistic approach has the potential to discriminate between hearing deficits involving gain reduction and those resulting from a raised sensory threshold

extreme points of the set of elements majorised by an integrable function resolution of a problem by luxemburg and of its noncommutative counterpart abstract let f be an arbitrary integrable function on a finite measure space x we characterise the extreme points of the set f of all measurable functions on x majorised by f providing a complete answer to a problem raised by w a j luxemburg in 1967 moreover we obtain a noncommutative version of this result

lipschitz continuity of the absolute value and riesz projections in symmetric operator spaces a principal result of the paper is that ifeis a symmetric banach function space on the positive half line with the fatou property then for all semifinite von neumann algebras m the absolute value mapping is lipschitz continuous on the associated symmetric operator spacee m with lipschitz constant depending only oneif and only ifehas non trivial boyd indices it follows that if m is any von neumann algebra then the absolute value map is lipschitz continuous on the corresponding haageruplp space provided 1 p

twisting non commutative lp spaces abstract the paper makes the first steps into the study of extensions twisted sums of noncommutative l p spaces regarded as banach modules over the underlying von neumann algebra m our approach combines kalton s description of extensions by centralizers these are certain maps which are in general neither linear nor bounded with a general principle due to rochberg and weiss saying that whenever one finds a given banach space y as an intermediate space in a complex interpolation scale one automatically gets a self extension 0 y x y 0 for semifinite algebras considering l p l p m as an interpolation space between m and its predual m one arrives at a certain self extension of l p that is a kind of noncommutative kalton peck space and carries a natural bimodule structure some interesting properties of these spaces are presented for general algebras including those of type iii the interpolation mechanism produces two rather than one extensions of one sided modules one of left modules and the other of right modules whether or not one may find nontrivial self extensions of bimodules in all cases is left open

weak supermajorization and families as doubly superstochastic operators on lp i abstract we present necessary and sufficient conditions that a family a a i j i j i of real numbers may be considered as a bounded linear operator on banach spaces l 1 i and l i where i is an arbitrary non empty set moreover we get that these conditions are sufficient for a family to be a bounded linear operator on l p i for each p 1 within this class of operators the notion of doubly superstochastic operator is introduced as an extension of the doubly superstochastic matrix and some of its essentially properties are presented in the second part we extend the notion of weak supermajorization relation on the banach space l p i using doubly superstochastic operators and present close relationship between this relation and superstochastic operators as generalisation well known results in the theory of majorization among others for two functions f g l 1 i we show that relations f w s g and g w s f hold if and only if there exist a permutation p such that g p f

fine structure of hearing threshold and loudness perception hearing thresholds measured with high frequency resolution show a quasiperiodic change in level called threshold fine structure or microstructure the effect of this fine structure on loudness perception over a range of stimulus levels was investigated in 12 subjects three different approaches were used individual hearing thresholds and equal loudness contours were measured in eight subjects using loudness matching paradigms in addition the loudness growth of sinusoids was observed at frequencies associated with individual minima or maxima in the hearing threshold from five subjects using a loudness matching paradigm at low levels loudness growth depended on the position of the test or reference tone frequency within the threshold fine structure the slope of loudness growth differs by 0 2 db db when an identical test tone is compared with two different reference tones i e a difference in loudness growth of 2 db per 10 db change in stimulus finally loudness growth was measured for the same f

non commutative orlicz spaces associated to a modular on τ measurable operators abstract in this paper we consider non commutative orlicz spaces as modular spaces and show that they are complete with respect to their modular we prove some convergence theorems for measurable operators and deal with uniform convexity of non commutative orlicz spaces

the cone of distance matrices abstract the geometry of the cone of euclidean distance matrices edms is analyzed using a new characterization of an edm the facial structure and the angle that edms of embedding dimension one make with the center ray are found this result follows from a complete analysis of the critical points of the distance function in frobenius norm from the matrix e consisting of zero diagonal and ones elsewhere to the edms of embedding dimension one

non commutative banach function spaces in this paper we survey some aspects of the theory of non commutative banach function spaces that is spaces of measurable operators associated with a semi finite von neumann algebra these spaces are also known as non commutative symmetric spaces the theory of such spaces emerged as a common generalization of the theory of classical commutative rearrangement invariant banach function spaces in the sense of w a j luxemburg and a c zaanen and of the theory of symmetrically normed ideals of bounded linear operators in hilbert space in the sense of i c gohberg and m g krein these two cases may be considered as the two extremes of the theory in the first case the underlying von neumann algebra is the commutative algebra l on some measure space with integration as trace in the second case the underlying von neumann algebra is b the algebra of all bounded linear operators on a hilbert space with standard trace important special cases of these non commutative spaces are the non commutative l p spaces which correspond in the commutative case with the usual l p spaces on a measure space and in the setting of symmetrically normed operator ideals they correspond to the schatten p classes mathfrak s p