evidence for two discrete sources of 2f1 f2 distortion product otoacoustic emission in rabbit i differential dependence on stimulus parameters the results of studies of the physiological vulnerability of distortion product otoacoustic emissions dpoaes suggest that the dpoae at 2f1 f2 in vertebrate ears is generated by more than one source the principal aims of the present study were to provide independent evidence for the existence of more than one dpoae source and to determine the contributions of each to the ear canal 2f1 f2 signal to accomplish these aims specific stimulus parameters were separately and systematically varied to provide detailed parametric information regarding 2f1 f2 dpoae amplitude and phase in normal ears of awake rabbits the findings indicate that two discrete sources demonstrating differential dependence on stimulus parameters dominate the generation of the 2f1 f2 dpoae one source of distortion is dominant above 60 70 db spl at moderate primary frequency separations and at all stimulus levels when the primary tones are closely spaced the other source is dominant below 60 70 db spl at moderate primary frequency

some koszul rings from geometry abstract we give examples of koszul rings that arise naturally in algebraic geometry in the first part we prove a general result on koszul property associated to an ample line bundle on a projective variety specifically we show how koszul property of multiples of a base point free ample line bundle depends on its castelnuovo mumford regularity in the second part we give examples of koszul rings that come from adjoint line bundles on minimal irregular surfaces of general type

the equation of complex monge ampere type and stability of solutions we prove that in a family of plurisubharmonic functions with monge ampere measures bounded from above by such a measure of one function weak convergence is equivalent to convergence in capacity we also show a very general statement on the existence of solutions of the complex monge ampere type equation

on the cegrell classes the cegrell classes with zero boundary data are defined by certain decreasing approximating sequences of functions with different properties depending on the class in question it is different for cegrell classes which are given by a continuous function f these classes are defined by an inequality it is proved in this article that it is possible to define the cegrell classes which are given by f in a similar manner as those classes with zero boundary data an existence result for the dirichlet problem for certain singular measures is proved the article ends with three applications results connected to convergence in capacity subextension of plurisubharmonic functions and integrability are proved

frequency responses of two and three tone distortion product otoacoustic emissions in mongolian gerbils the frequency responses of distortion product otoacoustic emission dpoaes were investigated in adult mongolian gerbils the main goal was to investigate in this species the extent to which dpoae measurements might be useful in estimating cochlear frequency tuning characteristics specifically this study investigated the parameter space for generation of dpoaes to determine those regions if any where the emission responses gave simple frequency responses i e responses similar in form to typical neural responses at the same time it was desired to determine in this species the existence extent and nature of the more complex three tone emission frequency responses as observed in some other species e g martin et al hearing res 136 105 123 1999 in the present work two tone frequency response curves f2 f1 ratio functions were obtained by varying the lower frequency f1 while holding the f2 frequency and both amplitudes l1 l2 constant only for frequencies f2 near 8 khz did the re

equicontinuity of families of plurisubharmonic functions with bounds on their monge ampere masses it is proved that families of solutions of the complex monge ampere equation with fixed boundary values and certain bounds on the right hand side are equicontinuous

weak convergence of currents we give certain condictions to guarantee weak convergence u kt k rightarrow ut where u k u are plurisubharmonic functions and t k t are positive closed currents as applications we obtain that convergence in capacity of plurisubharmonic functions u k implies weak convergence of the complex monge amp ere measures dd cu k n if all of the plurisubharmonic functions u k are bounded below by one of some sorts of plurisubharmonic functions

schur weyl quasi duality and co triangular hopf quasigroups schur weyl duality relates the representation theories of general linear and symmetric groups in defining characteristic and plays a central role in many parts of algebraic lie theory in this paper we will introduce the notion of schur weyl quasi duality and study it for this generally we consider a braided vector space v c and its braided lie algebra endk v then we can construct its braided enveloping algebra u endk v which is a connected braided c cocommutative hopf algebra let h be a triangular hopf quasigroup with bijective antipode and b be a cotriangular hopf quasigroup with bijective antipode let v be any finite dimensional vector space in the category lq h r b of generalized long quasimodules we show that u endkv h b ksn v n is a schur weyl quasi duality under suitable conditions

graded decomposition numbers for the blob algebra abstract we give a closed formula for the graded decomposition numbers of the blob algebra over a field of characteristic zero at a root of unity

viscosity solutions to degenerate complex monge ampere equations we develop an alternative approach to degenerate complex monge ampere equations on compact kahler manifolds based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theoretic ones we generalize to the kahler case a theorem due to dinew and zhang in the projective case to the effect that their pluripotential solutions constructed previously by the authors are continuous

subsolution theorem and the dirichlet problem for the quaternionic monge ampere equation in this paper we obtain the existence of solution to the dirichlet problem for quaternionic monge ampere equation after showing a stability theorem we prove the subsolution theorem for quaternionic monge ampere equation by combining our stability theorem and kolodziej s approach for the complex case

on the dirichlet problem for the complex monge ampere operator on considere le probleme de dirichlet pour l equation de monge ampere complexe sur un ouvert borne de c n

milnor moore categories and monadic decomposition abstract in this paper monoidal hom lie algebras lie color algebras lie superalgebras and other type of generalized lie algebras are recovered by means of an iterated construction known as monadic decomposition of functors which is based on eilenberg moore categories to this aim we introduce the notion of milnor moore category as a monoidal category for which a milnor moore type theorem holds we also show how to lift the property of being a milnor moore category whenever a suitable monoidal functor is given and we apply this technique to provide examples

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

nonlinear interactions that could explain distortion product interference response areas suppression and or enhancement of third and fifth order distortion products by a third tone that can have a frequency more than an octave above and a level more than 40 db below the primary tones have recently been measured by martin et al hear res 136 105 123 1999 contours of iso suppression and iso enhancement that are plotted as a function of third tone frequency and level are called interference response areas after ruling out order aliasing two possible mechanisms for this effect have been developed a harmonic mechanism and a catalyst mechanism the harmonic mechanism produces distortion products by mixing a harmonic of one of the primary tones with the other primary tone the catalyst mechanism produces distortion products by mixing one or more intermediate distortion products that are produced by the third tone with one or more of the input tones the harmonic mechanism does not need a third tone and the catalyst mechanism does because the basilar membrane frequency response is predic

weak solutions to degenerate complex monge ampere flows i the authors apply the method of viscosity solutions to the parabolic version of the complex monge amp ere equation in a strictly pseudoconvex domain omega that is exp partial t varphi t f t z varphi t mu z dd c varphi t n 0 text in 0 t times omega with f continuous and nondecreasing in the last variable mu a bounded continuous nonnegative volume form and varphi t varphi t cdot the unknown function first they review the results of carandall ishii lions and others in classical pde viscosity theory then the following results are shown any bounded subsolution is plurisubharmonic on space slices the parabolic comparison principle is valid under certain assumptions on the initial data satisfied when mu 0 the solution of the cauchy dirichlet problem exists for all time and it is an upper envelope of all subsolutions finally with the same assumptions and f independent of time varphi t converges to the solution of the related elliptic equation as t to infty

sur l existence de solutionsc 1 1 n c 1 1 etc 2 radiales pour des quations de type monge ampre complexe dans la boule unit de n on considere dans la boule unite de c n le probleme de dirichlet pour une equation non lineaire de type monge ampere on demontre l existence d une solution radiale

the space of poincare type kahler metrics on the complement of a divisor consider a divisor d with simple normal crossings in a compact kahler manifold x it has been known since the work by g tian and s t yau that if k d is ample there exists on x d a unique kahler einstein metric with cusp singularities along the divisor implying completeness and finite volume we show in this article that a kahler metric in an arbitrary class with constant scalar curvature and singularities analogous to that constructed by tian and yau is unique in this class when k d is ample this we do by generalizing chen s construction of approximate geodesics in the space of kahler metrics and proving an approximate version of the calabiyau theorem both independently of the ampleness of k d

braided version of shirshov witt theorem the shirshov witt theorem claims that every subalgebra of a free lie algebra is free in character istic zero this theorem can be restated in terms of a free associative algebra every hopf subalgebra of a free algebra kxiwith the coproduct xi xi 1 1 xi is free and it is freely generated by primitive elements our aim is to extend this result to free algebras with a braided coproduct as far as possible by means of p m cohn theory we show that if a subalgebra is a right categorical right coideal then it is free we consider more thoroughly involutive braidings 2 id over a field of zero characteristic in this case every braided hopf subalgebra is generated by primitive elements moreover the space of all primitive elements forms a free lie algebra in the context of this re sult we discuss the situation that arises around the problem of embedding of a lie algebra in its associative universal enveloping algebra 2005 elsevier inc all rights reserved

a comparison principle for the complex monge ampere operator in cegrell s classes and applications in this article we will first prove a result about the convergence in capacity next we will obtain a general decomposition theorem for complex monge ampere measures which will be used to prove a c

algebraic aspects of the quantum yang baxter equation in this paper we examine a variety of algebraic contexts in which the quantum yang baxter equation arises and derive methods for generating new solutions from given ones the solutions we describe are encoded in objects which have a module and a comodule structure over a bialgebra our work here is based in part on the ideas of dr1 dr2 suppose that r m m m m is a solution to the quantum yang baxter equation where m is a finite dimensional vector space over a field k in dr2 it was shown that r can be derived from a left h module structure and a right h comodule structure on m for some bialgebra h over k also see yet maj1 maj2 frt2 the module and comodule structure satisfy a natural compatibility condition m together with these structures is called a left quantum yang baxter h module every left quantum yang baxter module gives rise to a solution to the quantum yang baxter equation in a natural way we study the category hyb of left quantum yang baxter h modules and show that many of the familiar constructions in the module category hm can be made in hyb through these constructions solutions to the quantum yang baxter equation can be combined in various ways to generate new ones we place particular emphasis on the tensor product of objects of hyb and ways in which the tensor algebra t m of an object m of hyb can be viewed as an object of hyb using the tensor algebra we are able to extend certain solutions when dim m 2 to the quantum plane we turn the tensor algebra t m of an object m of hyb into an object of hyb by giving it a module algebra and a comodule algebra structure module algebra and comodule algebra structures play a very important role in this paper in section 9 we develop a calculus for uq sl2 starting with a right k slq 2 comodule algebra structure on the quantum plane k x y q where k slq 2 is the coordinate ring of quantum slq 2 over k this calculus has been described in other ways m s sud the right comodule algebra structure on k x y q accounts for the left uq sl2 module algebra structure on k x y q described in m s we show how the basic irreducible representations of tak follow by the calculus a module algebra action or comodule algebra action is a natural vehicle for extending structure on a submodule or subcomodule respectively to the subalgebra it generates the calculus and the solutions to the quantum yang baxter equation we describe in this paper are determined in this manner on small structures two dimensional in this case we believe that many more results will follow from this circle of ideas in section 2 we discuss basic aspects of coalgebra and bialgebras used in the sequel a good general reference for this is sweedler s book sb on hopf algebras in section 3 we review the quantum yang baxter equation in connection with quantum yang baxter modules the a r construction of faddeev reshetikhin and takhtajan frt is considered in this light and examined in detail in when r arises from two commuting operators even though this particular r is rather simple the algebra structure of a r is surprisingly complex using the scratchpad computer algebra system we determine the algebra structure of a r in an interesting specific case showing that our particular example has a finite non commutative groeb

distortion product otoacoustic emission 2 f1 f2 amplitude as a function of f2 f1 frequency ratio and primary tone level separation in human adults and neonates distortion product otoacoustic emission dpoae 2 f1 f2 amplitude is dependent upon both the frequency ratio and level separation of the eliciting primary tones in adults it has been established that on average a f2 f1 ratio of 1 22 is optimal for evoking the most robust dpoae dpoae amplitude is systematically reduced when f2 f1 ratio is either increased or decreased thus forming a bandpass function harris et al 1989 the frequency ratio function dpoae amplitude f2 f1 ratio is thought to reflect the filtering properties of the cochlea allen and fahey 1993 brown et al 1993 primary tone level separation also influences dpoae amplitude with a 10 to 15 db level difference between the primary tones l1 l2 typically generating largest amplitude in adults equivalent studies have not been conducted in neonates the present study evoked the 2 f1 f2 dpoae in adults term and premature neonates to define the optimal f2 f1 ratio and l1 l2 level separation and to investigate the filtering prope

the behavior of the acoustic distortion product 2f1 f2 from the human ear and its relation to auditory sensitivity the acoustic intermodulation distortion product 2f1 f2 adp was measured in human subjects to investigate 1 the dependence of adp level on stimulus parameters and 2 the relationship between adp level and auditory sensitivity the frequency ratio f2 f1 at which adp level is maximal varies only slightly across frequency and subjects the average optimal ratio is 1 225 beyond the maximum the adp level declines with increasing f2 f1 ratio at rates of up to 250 db oct as the level of one stimulus is increased relative to the other the adp grows saturates and in most cases shows a bendover maximum distortion is generated when l 1 exceeds l 2 growth rate and saturation point are dependent on which stimulus is incremented and on the level of the stationary stimulus with optimal stimulus parameters levels below 60 db spl l 1 greater than l 2 by 15 db f2 f1 1 225 adp levels are commonly 30 db below l 2 patterns of adp level across frequency vary between subjects but are repeatable within each subject as the frequency of one or both of the stimuli is varied changes in adp level exhibit a broadly featured pattern with a fine structure superimposed upon it this fine structure was compared with the features in the stimulus frequency emission spectrum in one subject with appropriate stimulus parameters half of our subjects show a statistically significant correlation across frequency between adp level and auditory sensitivity at the corresponding f1 frequency our results suggest that with low levels of stimulation adp measurements could form the basis of an objective measure of cochlear function in human subjects

constants of coordinate differential calculi defined by yang baxter operators we investigate in details a first order differential calculus with right partial derivatives set up by a not necessarily invertible yang baxter operator the optimal algebra for this calculus has a natural structure of a braided hopf algebra and it is isomorphic to the quantum symmetric algebra the induced to the optimal algebra and to the free cover algebra calculi are right covariant they are bicovariant if and only if the related braiding is involutive by means of the p m cohn theory we show that the subalgebra of constants for the cover free differential algebra is a free algebra and an ad invariant left coideal if the given algebra is finitely generated then every differential left ideal is generated by constants a noncommutative taylor series decomposition formula is valid and the category of locally nilpotent modules over the operator algebra is semisimple with the only simple object that is isomorphic to the optimal algebra as a module we find a necessary and sufficient condition for a 1 form to be a complete differential

on cotriangular hopf algebras in an earlier paper we proved that any triangular semisimple hopf algebra over an algebraically closed field k of characteristic 0 is obtained from the group algebra k g of a finite group g by twisting its comultiplication by a twist in the sense of drinfeld in this paper we generalize this result to not necessarily finite dimensional cotriangular hopf algebras namely our main result says that a cotriangular hopf algebra a over k is obtained from a function algebra of a proalgebraic group by twisting its multiplication by a hopf 2 cocycle and possibly changing its r form by a central grouplike element of a of order 2 if and only if the trace of the squared antipode on any finite dimensional subcoalgebra of a is the dimension of this subcoalgebra the generalization like the original theorem is proved using deligne s theorem on tannakian categories we then give examples of twisted function algebras and in particular show that in the infinite dimensional case the squared antipode may not equal the identity on the other hand we show that in all of our examples the squared antipode is unipotent and conjecture it to be the case for any twisted function algebra we prove this conjecture in a large number of special cases using the quantization theory of the first author and d kazhdan

koszul duality patterns in representation theory the aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of koszul duality to repre sentation theory the paper consists of three parts relatively independent of each other the first part gives a reasonably selfcontained introduction to koszul rings and koszul duality koszul rings are certain z graded rings with particularly nice homological properties which involve a kind of duality thus to a koszul ring one associates naturally the dual koszul ring the second part is devoted to an application to representation theory of semisimple lie algebras we show license or copyright restrictions may apply to redistribution see http www ams org journal terms of use koszul duality patterns 527 that the block of the bernstein gelfand gelfand category o that corresponds to any fixed central character is governed by the koszul ring moreover the dual of that ring governs a certain subcategory of the category o again this generalizes the selfduality theorem conjectured by beilinson and ginsburg in 1986 and proved by soergel in 1990 in the third part we study certain cate gories of mixed perverse sheaves on a variety stratified by affine linear spaces we provide a general criterion for such a category to be governed by a koszul ring in the flag variety case this reduces to the setup of part two in the more general case of affine flag manifolds and affine grassmannians the criterion should yield interesting results about representations of quantum groups and affine lie algebras department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address sasha math mit edu department of mathematics the university of chicago chicago illinois 60637 e mail address ginzburg math uchicago edu max planck institut fur mathematik gottfried claren strase 26 d 53 bonn 3 germany current address mathematisches institut universitat freiburg albertstrase 23b d 79104 freiburg germany e mail address soergel sun1 mathematik uni freiburg de license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

n cohomology of simple highest weight modules on walls and purity letg p b be respectively a complex connected linear algebraic semisimple group a parabolic subgroup and a borel subgroup the first main result is the following theorem let be a pure complex ong b smooth with respect to bruhat cells then its restriction to anyp orbit is pure as well of the same weight as a consequence we are able to compute then cohomology of simple highest weight modules on walls

formal groups and unipotent affine groups in non categorical symmetry abstract as is well known in characteristic zero the lie algebra functor gives two category equivalences one from the formal groups to the finite dimensional lie algebras and the other from the unipotent algebraic affine groups to the finite dimensional nilpotent lie algebras we prove these category equivalences in a quite generalized framework proposed by gurevich d i gurevich the yang baxter equation and generalization of formal lie theory soviet math dokl 33 1986 758 762 and later by takeuchi m takeuchi survey of braided hopf algebras in n andruskiewitsch et al eds new trends in hopf algebra theory in contemp math vol 267 amer math soc providence ri 2000 pp 301 324 of vector spaces with non categorical symmetry we remove the finiteness restriction from the objects by using the terms of hopf algebras and lie coalgebras

connected braided hopf algebras abstract we prove a braided version of kostant cartier milnor moore theorem the category of connected cocommutative 2 id braided hopf algebras over a field of zero characteristic is equivalent via the enveloping construction to the category of generalized lie algebras this statement includes an embedding of any generalized lie algebra into its universal enveloping algebra the isomorphism h u prim h and primitive generation results the embedding theorem may be derived from the poincare birkhoff witt theorem for quadratic algebras of koszul type remark c we also provide a direct proof that uses neither koszul cohomologies nor the algebraic deformation theory we consider the primitive generation problem for subalgebras biideals and homomorphic images of connected braided hopf algebras in much more general context when the braiding is not necessary involutive and even it is not necessary invertible

quantum symmetric algebras ii abstract m rosso has generalized g lusztig s construction of the drinfeld jimbo quantum group g lusztig in progr math vol 110 birkhauser boston 1993 by associating to any finite dimensional braided vector space v two twisted bialgebras namely the quantum shuffle algebra t v and a subalgebra s v of t v called the quantum symmetric algebra when is lusztig s braiding s v is isomorphic to the plus part u of a certain quantum group u q g rosso invent math 133 1998 399 416 generalizes this by using a braiding determined by a family of parameters t ij and our paper d flores j a green algebr represent theory 4 2001 55 76 was concerned with this case in the present work we study twisted bialgebras in more general context and get results on rosso s s v for arbitrary braidings it is useful to consider a pair t u t v of twisted bialgebras which are adjoint under a given non degenerate bilinear form we give explicit formulae for the comultiplication of t v and also for its antipode under suitable conditions s v is self adjoint this generalizes the part of lusztig s construction which allows the drinfeld double construction

a milnor moore type theorem for primitively generated braided bialgebras abstract a braided bialgebra is called primitively generated if it is generated as an algebra by its space of primitive elements we prove that any primitively generated braided bialgebra is isomorphic to the universal enveloping algebra of its infinitesimal braided lie algebra notions hereby introduced this result can be regarded as a milnor moore type theorem for primitively generated braided bialgebras and leads to the introduction of a concept of braided lie algebra for an arbitrary braided vector space

poincare birkhoff witt theorem for quadratic algebras of koszul type abstract in this paper we prove a general poincare birkhoff witt theorem for quadratic koszul algebras the result is similar to that obtained by polischuk and positselsky but the proof is entirely different and uses algebraic deformation theory in particular we obtain a new proof of the classical pbw theorem for lie algebras based on deformation theory

holder continuity of solutions to the complex monge ampere equation with the right hand side in l p the case of compact kahler manifolds we prove that on compact kahler manifolds solutions to the complex monge ampere equation with the right hand side in lp p 1 are holder continuous

braided bialgebras of hecke type abstract the paper is devoted to prove a version of milnor moore theorem for connected braided bialgebras that are infinitesimally cocommutative namely in characteristic different from 2 we prove that for a given connected braided bialgebra a c a which is infinitesimally cocommutative for some element 0 that is not a root of one in the base field then the infinitesimal braiding of a is of hecke type of mark and a is isomorphic as a braided bialgebra to the symmetric algebra of the braided subspace of its primitive elements

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

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

an existence condition for multilinear quantum operations abstract it is found to be a necessary and sufficient condition for a set of quantum variables x 1 x 2 x n to have a nonzero multilinear quantum operation it is proved that if no one proper subset of this set satisfies this condition then a space of all multilinear quantum operations is of dimension n 2

interpretation of distortion product otoacoustic emission measurements i two stimulus tones the interpretation of common but poorly understood observed characteristics of distortion product emissions is assisted by the development of a simple model this model essentially includes only saturation of the cochlear amplifier with emissions arising naturally from the same nonlinear processes which cause the saturation the model provides useful physical explanations of emission behavior particularly considered as a function of the stimulus intensities of the two primaries i e behavior with fixed stimulus frequencies it is assumed that emission generation consists of two main components which are always present in the total emission but which most often have approximately opposite i e canceling phases one component arises in a small region centered about the peak of the emission generation function while the other arises from the region basal to this peak at low stimulus levels with normal cochlear amplifier operation the peak of the emission generation function is sharp so the emission from the peak region dominates the total emission this peak emission has typically been characterized as the active emission at high stimulus levels where saturation is important or at all levels when the gain of the cochlear amplifier is reduced the summed basal component dominates the total emission the characteristics of this basal emission are similar to and continuous with the characteristics of the truly passive emission i e the emission observed when the cochlear amplifier gain is identically zero under circumstances when the emissions from the peak and basal components are approximately equal there is seen a sharp notch characteristic of phase cancellation the simple model produces emission distributions as a function of independent variation of the two stimulus amplitudes which are in good agreement with observation it is shown that the furosemide assay provides a good estimate of cochlear amplifier gain when a correction factor of about 10 db is added however when using two stimulus tones neither absolute emission amplitudes or emission input output functions or the furosemide assay can adequately distinguish between cases of moderate versus poor cochlear amplifier dysfunction when the cochlear amplifier gains are in the range from about half normal to zero