unattainability of carnot efficiency in the brownian heat engine we discuss the reversibility of the brownian heat engine we perform an asymptotic analysis of the kramers equation on a buttiker landauer system and show quantitatively that carnot efficiency is unattainable even in the fully overdamped limit the unattainability is attributed to inevitable irreversible heat flow over the temperature boundary

simplified analytical model for sound level prediction at shielded urban locations involving multiple diffraction and reflections accurate and efficient prediction of the sound field in shadow zones behind obstacles is a challenging task but essential to produce urban noise maps a simplified method is presented to predict sound levels at shielded urban locations including multi edge diffraction over successive buildings and multiple reflections between parallel facades the model is essentially based on pierce s diffraction theory where the fresnel integral is approximated by trigonometric functions for efficient evaluation and parameterized for urban environments the model has been validated for idealized urban configurations by comparing to the results of pierce s theory and a full wave numerical method in case of multi edge diffraction over buildings in absence of a source or receiver canyon deviations from the full wave simulations are smaller than 2 db for the octave bands with central frequencies ranging from 125 to 1000 hz however larger errors are made when receivers are close to the extension line from the diffraction edge closest to the receiver in case of combining the simplified multi edge diffraction model with an efficient approach for including the series of mirror sources and mirror receivers based on the hurwitz lerch transcendent this same accuracy is obtained

fokker planck equations for time delayed systems via markovian embedding for stochastic systems with discrete time delay the fokker planck equation fpe of the one time probability density function pdf does not provide a complete self contained probabilistic description it explicitly involves the two time pdf and represents in fact only the first member of an infinite hierarchy we here introduce a new approach to obtain a fokker planck description by using a markovian embedding technique and a subsequent limiting procedure on this way we find a closed complete fpe in an infinite dimensional space from which one can derive a hierarchy of fpes while the first member is the well known fpe for the one time pdf we obtain as second member a new representation of the equation for the two time pdf from a conceptual point of view our approach is simpler than earlier derivations and it yields interesting insight into both the physical meaning and the mathematical structure of delayed processes we further propose an approximation for the two time pdf which is a central quantity in the description of these non markovian systems as it directly gives the correlation between the present and the delayed state application to a prototypical bistable system reveals that this approximation captures the non trivial effects induced by the delay remarkably well despite its surprisingly simple form moreover it outperforms earlier approaches for the one time pdf in the regime of large delays

nonequilibrium thermodynamics of stochastic systems with odd and even variables the total entropy production of stochastic systems can be divided into three quantities the first corresponds to the excess heat while the second two comprise the housekeeping heat we denote these two components the transient and generalized housekeeping heat and we obtain an integral fluctuation theorem for the latter valid for all markovian stochastic dynamics a previously reported formalism is obtained when the stationary probability distribution is symmetric for all variables that are odd under time reversal which restricts consideration of directional variables such as velocity

the residue theorem via an explicit construction of traces abstract let x be a locally noetherian scheme and y x be a morphism of finite type whose fibers have bounded dimensions given a residual complex m x on x with cousin data a residual complex m x on y with cousin data has been constructed in this article transitivity of residual complexes is clarified and a trace map tr y x m x m x is constructed in terms of cousin data with these concrete data the residue theorem is directly proved

higher adeles and non abelian riemann roch abstract we show a riemann roch theorem for group ring bundles over an arithmetic surface this is expressed using the higher adeles of beilinson parshin and the tame symbol via a theory of adelic equivariant chow groups and chern classes the theorem is obtained by combining a group ring coefficient version of the local riemann roch formula as in kapranov vasserot with results on k groups of group rings and an explicit description of group ring bundles over p 1 our set up provides an extension of several aspects of the classical frohlich theory of the galois module structure of rings of integers of number fields to arithmetic surfaces

the complete extension of the biot tolstoy solution to the density contrast wedge with sample calculations the biot tolstoy exact time domain solution for the three dimensional impulse response of an impenetrable wedge is extended to accommodate the isovelocity or density contrast wedge fourier transformation of the time and axial variables along with a kantorovich lebedev transform applied to the cylindrical radial coordinate leads to a solution in terms of residue series when the wedge angle is a rational fraction of the residue series can be reduced to a finite sum which is evaluated for some special cases the total pressure field consists of geometrical acoustics contributions as predicted by snell s laws plus a modified version of the biot tolstoy diffraction field

higher chern classes in iwasawa theory we begin a study of mth chern classes and mth characteristic symbols for iwasawa modules which are supported in codimension at least m this extends the classical theory of characteristic ideals and their generators for iwasawa modules which are torsion i e supported in codimension at least 1 we apply this to an iwasawa module constructed from an inverse limit of p parts of ideal class groups of abelian extensions of an imaginary quadratic field when this module is pseudo null which is conjecturally always the case we determine its second chern class and show that it has a characteristic symbol given by the steinberg symbol of two katz p adic l functions

role of sufficient statistics in stochastic thermodynamics and its implication to sensory adaptation a sufficient statistic is a significant concept in statistics which means a probability variable that has sufficient information required for an inference task we investigate the roles of sufficient statistics and related quantities in stochastic thermodynamics specifically we prove that for general continuous time bipartite networks the existence of a sufficient statistic implies that an informational quantity called the sensory capacity takes the maximum since the maximal sensory capacity imposes a constraint that the energetic efficiency cannot exceed one half our result implies that the existence of a sufficient statistic is inevitably accompanied by energetic dissipation we also show that in a particular parameter region of linear langevin systems there exists the optimal noise intensity at which the sensory capacity the information thermodynamic efficiency and the total entropy production are optimized at the same time we apply our general result to a model of sensory adaptation of e coli and find that the sensory capacity is nearly maximal with experimentally realistic parameters

acoustic diffraction by deformed edges of finite length theory and experiment the acoustic diffraction by deformed edges of finite length is described analytically and in the frequency domain through use of an approximate line integral formulation originally applied to deformed finite length cylinders t k stanton j acoust soc am 86 691 705 1989 in this case of edges the factor to the integral specific to the scattering per unit length by the cylinder is replaced by one specific to edge diffraction the formulation is applied to laboratory data involving elastic disks of finite thickness by incorporating an approximate double edge diffraction formula for three sided semi infinite barriers based on modified solutions of pierce a d pierce j acoust soc am 55 941 955 1974 the diffraction in the backscatter direction by individual elastic disks was measured using a variety of disks spanning a range of diameters thicknesses and two material properties a broadband acoustic source was used and the disks rotated over 360 in 1 increments given the overlap betw

abelian differentials on singular varieties and variations on a theorem of lie griffiths we compare various notions of meromorphic and holomorphic differential forms on singular analytic varieties in particular we find that every meromorphic form gives rise to a canonical principal value current with support in the variety demanding that this current be closed we obtain a useful analytic description of the dualizing sheaf we then go on to generalize the lie griffiths theorem on one hand it is shown that a rational trace is enough to ensure algebraicity of the data on the other hand we prove that zero trace implies that the form is holomorphic in the sense of currents in fact we prove a more general local version of the theorem

katoʼs residue homomorphisms and reciprocity laws on arithmetic surfaces abstract we explicitly study kato s residue homomorphisms in milnor k theory which are closely related to contou carrere symbols as applications we establish several reciprocity laws for certain locally defined maps on k groups that are associated to arithmetic surfaces

localization in equivariant intersection theory and the bott residue formula we prove the localization theorem for torus actions in equivariant intersection theory using the theorem we give another proof of the bott residue formula for chern numbers of bundles on smooth complete varieties in addition our techniques allow us to obtain residue formulas for bundles on a certain class of singular schemes which admit torus actions this class is rather special but it includes some interesting examples such as complete intersections and schubert varieties 1 introduction the purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory using the theorem we give another proof of the bott residue formula for chern numbers of bundles on smooth complete varieties in addition our techniques allow us to obtain residue formulas for bundles on a certain class of singular schemes which admit torus actions this class is rather special but it includes some interesting examples such as complete intersections cf bfq and schubert varieties let t be a split torus acting on a scheme x the 7 equivariant chow groups of x are a module over rt sym t where f is the character group of t the localization theorem states that up to torsion the equivariant chow groups of the fixed locus xt are isomorphic to those of x such a theorem is a hallmark of any equivariant theory the earliest version for equivariant cohomology is due to borel bo subsequently it theory versions were proved by segal se in topological a theory quart qu for actions of a cyclic group and thomason th2 for algebraic theory th2 for equivariant chow groups the localization isomorphism is given by the equivariant push forward induced by the inclusion of xt to x an interesting aspect of this theory is that the push forward is naturally defined on the level of cycles even in the singular case the closest topological analogue of this is equivariant borel moore homology see e g3 for a definition and a similar proof establishes localization in that theory for smooth spaces the inverse to the equivariant push forward can be written explicitly it was realized independently by several authors i n a b b v

impulse response of density contrast wedge using normal coordinates the exact impulse response of a point source to a rigid wedge was first derived by biot and tolstoy in normal coordinates i tolstoy and c s clay ocean acoustics theory and experiment in underwater sound american institute of physics new york 1987 appendix 5 the solution is compact and includes both reflected and diffracted waves explicitly kinney et al j acoust soc am 73 183 194 1983 introduced the solution of free wedge pressure release which is similar to the rigid case except sign changes for certain terms the solutions have been verified in laboratory experiments however neither model can be applied directly to many actual cases such as ocean floor where the ratio of density of the base sediment to that of the water is neither infinite ridge nor zero pressure release the normal coordinate solution presented here is the impulse response to an isovelocity c c and density contrast wedge it is an extension to the solution given by biot and tolstoy the eigenva

an explicit construction of residual complexes let y x be a morphism of finite type between locally noetherian schemes whose fibers have bounded dimensions given concretely a residual complex on x we construct canonically a concrete residual complex on cy

adelic chern forms and applications let x be a variety over a field of characteristic 0 given a vector bundle e on x we construct chern forms c v t x ax here a x is the sheaf of beilinson adeles and v is an adelic connection when x is smooth wt x a x h r x the algebraic de rham cohomology and c q v are the usual chern classes we include three applications of the construction 1 existence of adelic secondary chern simons characteristic classes on any smooth x and any vector bundle e 2 proof of the bott residue formula for a vector field action and 3 proof of a gauss bonnet formula on the level of differential forms namely in the de rham residue complex 0 introduction let x be a scheme of finite type over a field k according to beilinson be given any quasi coherent x module m and an integer q9 there is a flasque ox module a dcm called the sheaf of adeles this is a gen eralization of the classical adeles of number theory cf example 2 3 moreover there are homomorphisms d aj ed m a m which make ared m into a complex and m ared m is quasi isomorphism now let qx be the algebra of kahler differential forms on x in hy we proved that the sheaf

bott s formula and enumerative geometry we outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of bott as an example gromov witten numbers of twisted cubic and elliptic quartic curves on some general complete intersection in projective space are computed the results are consistent with predictions made from mirror symmetry compu tations we also compute degrees of some loci in the linear system of plane curves of degrees less than 10 like those corresponding to sums of powers of linear forms and curves carrying inscribed polygons mathematical institute university of oslo p 0 box 1053 n 0316 oslo norway e mail address ellingsr0math uio no mathematical institute university of bergen alleg 55 n 5007 bergen norway e mail address strommeti i uib no this content downloaded from 157 55 39 29 on tue 12 apr 2016 10 23 14 utc all use subject to http about jstor org terms

the impulse response of an aperture numerical calculations within the framework of the wedge assemblage method a numerical calculation technique applicable to arbitrary aperture shapes on which dirichlet soft or neumann hard boundary conditions exist is described the method is based on a generalization of the wedge assemblage wa method to fully two dimensional surfaces and yields the impulse response directly benchmark tests of the technique are conducted for the case of a circular aperture the results are in near perfect agreement with the reference solution provided by a t matrix code in addition to a solid validation of the extended wa method it is shown in this paper that multiple scattering effects can be accurately included finally the physical insight that the wa method offers is demonstrated through its ability to completely and accurately dissect the scattered field into reflected diffracted and multiple diffracted components

kontsevich s graph complex grt and the deformation complex of the sheaf of polyvector fields we generalize kontsevich s construction of l1 derivations of polyvector elds from the ane space to an arbitrary smooth algebraic variety more precisely we construct a map in the homotopy category from kontsevich s graph complex to the deformation complex of the sheaf of polyvector elds on a smooth algebraic variety we show that the action of deligne drinfeld

integral fluctuation theorem for the housekeeping heat the housekeeping heat qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states by analysing the evolution of its probability distribution we prove an integral fluctuation theorem exp qhk 1 valid for arbitrary driven transitions between steady states we discuss gaussian limiting cases and the difference between the new theorem and both the hatano sasa and the jarzynski relation

entropy production and fluctuation theorems for langevin processes under continuous non markovian feedback control continuous feedback control of langevin processes may be non markovian due to a time lag between the measurement and the control action we show that this requires one to modify the basic relation between dissipation and time reversal and to include a contribution arising from the noncausal character of the reverse process we then propose a new definition of the quantity measuring the irreversibility of a path in a nonequilibrium stationary state which can also be regarded as the trajectory dependent total entropy production this leads to an extension of the second law which takes a simple form in the long time limit as an illustration we apply the general approach to linear systems that are both analytically tractable and experimentally relevant

differential operators on rational projective curves fix a singular projective rational curve 3 over an algebraically closed field k of characteristic zero with normalisation map a p 3 and write s 5 r 9 for its ring of global differential operators we prove theorem 1 the ring g a is a noerherian domain finirely generated as a k algebra with a unique minimal non zero ideal j z moreover f y 9 j f is finite dimensional over k in the case when n is injective we give complete description of the structure of 2 x

on a generalization of solomon terao formula for subspace arrangements abstract we investigate in this paper a generalization of solomon terao formula for central equidimensional subspace arrangements we introduce generalized solomon terao functions based on the hilbert poincare series of the modules of multi logarithmic forms and logarithmic multi residues we show that as in the case of hyperplane arrangements these solomon terao functions are polynomial we then prove that if the solomon terao polynomial of the modules of multi residues satisfies a certain property then this polynomial is related to the characteristic polynomial of the subspace arrangement in particular we prove that this generalized solomon terao formula holds for any line arrangement of any codimension

newton okounkov bodies semigroups of integral points graded algebras and intersection theory generalizing the notion of newton polytope we dene the newtonokounkov body respectively for semigroups of integral points graded algebras and linear series on varieties we prove that any semigroup in the lattice z n is asymptotically approximated by the semigroup of all the points in a sublattice and lying in a convex cone applying this we obtain several results we show that for a large class of graded algebras the hilbert functions have polynomial growth and their growth coecients satisfy a brunn minkowski type inequality we prove analogues of the fujita approximation theorem for semigroups of integral points and graded algebras which imply a generalization of this theorem for arbitrary linear series applications to intersection theory include a far reaching generalization of the kushnirenko theorem from newton polytope theory and a new version of the hodge inequality we also give elementary proofs of the alexandrov fenchel inequality in convex geometry and its analogue in algebraic geometry

limits of compactified jacobians and d modules on smooth projective curves abstract letsbe a smooth projective curve and d sits sheaf of differential operators this paper classifies the rank one torsion free d s modules up to isomorphism such a module e has a degree which depends on the homological properties of e furthermore the set of isomorphism classes with fixed degreed say bijects to lim j d x x the set of points of the limit of compactified jacobians of curves with injective normalization s x here if f is a rank one torsion free o x module of degreed x representing the point of the limit corresponding to a torsion free d s module e then e d o s f the sheaf of differential operators from o sto f as an application we classify the domains morita equivalent to d p 1 we also study d f the ring of globally defined differential operators on a rank one torsion free sheaf over a curve with injective normalization p 1 x it is shown that the finite dimensional simple d f modules are preciselyhi x f when they are non zero and that the non vanishing ofhi x f determines the morita equivalence class of d f

diffusion effusion and chaotic scattering an exactly solvable liouvillian dynamics we study diffusion and chaotic scattering in a chain of baker maps coupled together which forms an area preserving mapping of an infinitely extended strip onto itself this exactly solvable mapping sustains chaotic behaviors and diffusion processes the relationship between the diffusion coefficient the lyapunov exponent and the entropy per unit time is derived the long lived classical resonances of the liouville evolution operator are proved to converge toward the eigenvalues of the phenomenological diffusion equation in this sense there is a quasi isomorphism between the resonance spectrum of the liouville evolution and the eigenvalue spectrum of the phenomenological diffusion equation furthermore we show that a fractal repeller is associated to each non equilibrium state in the isolated and finite multibaker chain the nonequilibrium states are all unstable with respect to the equilibrium validating a weak form of the second principle of thermodynamics for the present dynamical system consequences of nonequilibrium fractals on classical measurements are discussed we then describe the open multibaker chain as a scattering system fractal properties of chaotic scattering are here shown to be related to diffusion in the chain

higher order acoustic diffraction by edges of finite thickness generalized temporal and spectral solutions of acoustic diffraction by edges of finite thickness involving higher orders diffraction are presented the solution in the time domain is an extension of medwins double edge second order diffraction solution h medwin et al j acoust soc am 72 1005 1013 1982 which is based on the huygens principle while the solution in the frequency domain is an extension of the asymptotic formulas for the double edge second order diffraction via amplitude and phase matching given by pierce a d pierce j acoust soc am 55 943 955 1974 since both solutions are approximate they have different advantages and disadvantages the contribution from higher order diffraction depends strongly on the thickness and geometry of the edges comparison between the theory and experimental diffraction data demonstrates that for edges of finite thickness the first order diffraction alone under estimates the total diffraction field significantly especially when the flat en

on the intersection of algebraic curves and hypersurfaces many classical theorems about the intersection of plane algebraic curves can be derived from and generalized by the algebraic theory of residues in higher dimensional spaces one obtains results about the intersection of curves and hypersurfaces in various degrees of generality this was pointed out f i in s gh k2 and hu in the present note we wish to prove higher dimensional analogues of theorems of waring g humbert and reiss for arbitrary curves in affine n space and their intersection with hypersurfaces see theorems 4 1 5 1 and 6 2 below by a curve hypersurface we mean a closed subscheme in projective or affine n space of pure dimension 1 pure codimension 1 having no embedded components our considerations are based on the residue theorem for complete integral algebraic curves

fluctuation theorem for hidden entropy production elimination of seemingly unnecessary variables in markovian models may cause a difference in the value of irreversible entropy production between the original and reduced dynamics we show that such difference which we call the hidden entropy production obeys an integral fluctuation theorem if all variables are time reversal invariant or if the density function is symmetric with respect to the change of sign of the time reversal antisymmetric variables the theorem has wide applicability since the proposed condition is mostly satisfied in the case where the hidden fast variables are equilibrated the main consequence of this theorem is that the entropy production decreases by the coarse graining procedure by contrast in the case where a stochastic process is obtained by coarse graining a deterministic and reversible dynamics the entropy production may increase implying that the integral fluctuation theorem should not hold for such reductions we reveal with an explicit example that the nonequilibrated time reversal antisymmetric variables play a crucial role in distinguishing these two cases thus guaranteeing the consistency of the presented theorem

time reversibility and nonequilibrium thermodynamics of second order stochastic processes nonequilibrium thermodynamics of a general second order stochastic system is investigated we prove that at steady state under inversion of velocities the condition of time reversibility over the phase space is equivalent to the antisymmetry of spatial flux and the symmetry of velocity flux then we show that the condition of time reversibility alone cannot always guarantee the maxwell boltzmann distribution comparing the two conditions together we find that the frictional force naturally emerges as the unique odd term of the total force at thermodynamic equilibrium and is followed by the einstein relation the two conditions respectively correspond to two previously reported different entropy production rates in the case where the external force is only position dependent the two entropy production rates become one we prove that such an entropy production rate can be decomposed into two non negative terms expressed respectively by the conditional mean and variance of the thermodynamic force associated with the irreversible velocity flux at any given spatial coordinate in the small inertia limit the former term becomes the entropy production rate of the corresponding overdamped dynamics while the anomalous entropy production rate originates from the latter term furthermore regarding the connection between the first law and second law we find that in the steady state of such a limit the anomalous entropy production rate is also the leading order of the boltzmann factor weighted difference between the spatial heat dissipation densities of the underdamped and overdamped dynamics while their unweighted difference always tends to vanish

the intersection homology d module in finite characteristic for y a closed normal subvariety of codimension c of a smooth variety x brylinski and kashiwara showed that the local cohomology module c y x x contains a unique simple x submodule denoted by y x in this paper the analogous result is shown for x and y defined over a perfect field of finite characteristic moreover a local construction of y x is given relating it to the theory of tight closure from the construction one obtains a criterion for the x simplicity of c y x x

two dimensional acoustical diffraction by a penetrable wedge a problem that has consistently defied rigorous analysis is the construction of the time periodic green s function for an acoustic line source in the presence of a penetrable wedge with distinct wave speed this paper begins by noting that in the soft limit density ratio becoming zero the interior field must become null and hence it is sensible to express the required green s function as a series in powers of the density ratio applications of green s theorem then reduce the problem to a sequence of integral equations for the determination of the coefficients in a similar expansion of the normal velocity at the wedge boundary the exterior hard green s function now appears as the kernel while the interior hard green s function appears in the forcing terms to take account of penetration into the wedge after observing that the velocity coefficients can be calculated recursively in terms of the solution of a single integral equation of the first kind the latter is itself transformed to an equatio

sound diffraction by a many sided barrier or pillar abstract the sound field produced when a spherical sound wave is incident on a rigid many sided barrier or pillar is calculated on the basis of keller s geometrical theory of diffraction kouyoumjian and pathak s asymptotic solution for a single wedge and pierce s method for a doubly diffracted wave from a comparison between calculated results and experimental results it is shown that the method described is applicable to the prediction of the propagation of noise around a thick barrier a building a number of these obstacles or a number of thin barriers with an extremely high accuracy

sound propagation over a large wedge a comparison between the geometrical theory of diffraction and the parabolic equation low frequency propagation over wedges hills and barriers is an important problem with many applications two different propagation models are used to compare the sound field generated by a steady single frequency source in front of over and behind a large rigid v shaped wedge predictions along the boundary made with both models at several frequencies are compared and found to be in excellent agreement the results provide additional evidence that the parabolic approximation is able to account accurately for propagation effects caused by terrain irregularities

bivariance grothendieck duality and hochschild homology ii the fundamental class of a flat scheme map fix a noetherian scheme s for any flat map f x y of separated essentially finite type perfect s schemes we define a canonical derived category map cf hx f hy the fundamental class of f where hz is the pre hochschild complex of an s scheme z and f is the twisted inverse image coming from grothendieck duality theory when y s and f is essentially smooth of relative dimension n this gives an isomorphism fn n h n hx n f os we focus mainly on transitivity of c vis a vis compositions x y z and on the compatibility of c with flat base change these properties imply that c orients the flat maps in the bivariant theory of part i 1 compatibly with essentially etale base change furthermore c leads to a dual oriented bivariant theory whose homology is the classical hochschild homology of flat s schemes when y s c is used to define a duality map dx hx rhom hx f os an isomorphism if f is essentially smooth these results apply in particular to flat essentially finite type maps of noetherian rings

model simplification and loss of irreversibility in this paper we reveal a general relationship between model simplification and irreversibility based on the model of continuous time markov chains with time scale separation according to the topological structure of the fast process we divide the states of the chain into the transient states and the recurrent states we show that a two time scale chain can be simplified to a reduced chain in two different ways removal of the transient states and aggregation of the recurrent states both the two operations will lead to a decrease in the entropy production rate and its adiabatic part and will keep its nonadiabatic part the same this suggests that although model simplification can retain almost all the dynamic information of the chain it will lose some thermodynamic information as a trade off

deformation quantization in algebraic geometry abstract we study deformation quantizations of the structure sheaf o x of a smooth algebraic variety x in characteristic 0 our main result is that when x is d affine any formal poisson structure on x determines a deformation quantization of o x canonically up to gauge equivalence this is an algebro geometric analogue of kontsevich s celebrated result

hamiltonian derivation of a detailed fluctuation theorem we analyze the microscopic evolution of a system undergoing a far from equilibrium thermodynamic process explicitly accounting for the degrees of freedom of participating heat reservoirs we derive a hybrid result similar in form to both the fluctuation theorem and a statement of detailed balance we relate this result to the steady state fluctuation theorem and to a free energy relation valid far from equilibrium

twisted deformation quantization of algebraic varieties abstract let x be a smooth algebraic variety over a field k containing the real numbers we introduce the notion of twisted associative resp poisson deformation of the structure sheaf o x these are stack like versions of usual deformations we prove that there is a twisted quantization operation from twisted poisson deformations to twisted associative deformations which is canonical and bijective on gauge equivalence classes this result extends work of kontsevich and our own earlier work on deformation quantization of algebraic varieties

noise attenuation by a hard wedge shaped barrier this paper is concerned with the problem of sound screening by a wedge like barrier the sound source is assumed to be point like and the receiver is located in the shadow of the source sound field so that according to geometrical optics only the field diffracted by the edge of the barrier is considered first for the hard wedge in space three models are used for calculating the amplitude of the edge diffracted field these are the uniform theory of diffraction utd the hadden pierce model both in the frequency domain and the biot tolstoy theory of diffraction which is a time domain formulation it is first shown that even at relatively low frequencies the frequency domain models perform quite satisfactorily as compared to the exact time domain theory hence and due to its relative simplicity the utd is proposed as an accurate calculation scheme for solving problems with edge diffraction by hard wedges it is also proved from theoretical calculations that the amplitude of the edge diffracted field increases for an increasing angle of the wedge and consequently the hard half plane gives the lowest field amplitude in the shadow zone some applications are then considered for evaluating the performance of a barrier on a flat ground either completely hard or with mixed homogeneous boundary conditions an improvement of the scheme for calculating the sound field in the all hard case is achieved through considering the multiple diffraction in this case only to the second order between the top of the wedge barrier and its base the results show that for usually occurring situations increasing the angle of the hard wedge barrier affects negatively its efficiency through diminishing its insertion loss these conclusions are also supported by the results of some experimental measurements conducted at a scale model level

an analytic secondary source model of edge diffraction impulse responses a new impulse response model for the edge diffraction from finite rigid or soft wedges is presented which is based on the exact biot tolstoy solution the new model is an extension of the work by medwin et al h medwin et al j acoust soc am 72 1005 1013 1982 in that the concept of secondary edge sources is used it is shown that analytical directivity functions for such edge sources can be derived and that they give the correct solution for the infinite wedge these functions support the assumption for the first order diffraction model suggested by medwin et al that the contributions to the impulse response from the two sides around the apex point are exactly identical the analytical functions also indicate that medwin s second order diffraction model contains approximations which however might be of minor importance for most geometries access to analytical directivity functions makes it possible to derive explicit expressions for the first and even second order diffraction for certain geometries an example of this is axisymmetric scattering from a thin circular rigid or soft disc for which the new model gives first order diffraction results within 0 20 db of published reference frequency domain results and the second order diffraction results also agree well with the reference results scattering from a rectangular plate is studied as well and comparisons with published numerical results show that the new model gives accurate results it is shown that the directivity functions can lead to efficient and accurate numerical implementations for first and second order diffraction

entropy production in stochastic systems with fast and slow time scales the behavior of stochastic systems with interacting fast and slow degrees of freedom is investigated both for discrete and continuous processes effective equations that govern the process on the slow timescale are derived by asymptotic methods both for the propagator and the entropy production of the systems it is found that in general the result of the limiting procedure for entropy does not coincide with the one defined for the effective slow process and features an additional contribution the specific conditions under which such a correction does or does not arise are stated and the general explicit form of this remnant entropy production is offered finally the fluctuation theorems that are satisfied by this additional term are given

algebraic chern simons theory a theory of secondary characteristic classes analogous to the classical chern simons theory is developed for algebraic vector bundles applications are made to questions involving finer charcterisitic classes for bundles with connection and to the griffiths group of algebraic cycles

exact explicit solutions for diffraction by hard sound barriers and seamounts a new method of obtaining exact explicit solutions for the diffraction of sound waves by truncated wedges is given which in conjunction with a previous study i tolstoy ieee j ocean eng in press 1989 can be applied to problems involving two parallel vertices and arbitrary wedge angles w w at these vertices the method combines exact explicit representations of the field diffracted by a single vertex with the classic multiple scatter algorithm to formulate the interaction between the line vertices the previous study had demonstrated the method only for cases in which w w were irrational fractions of as well as for the rather special case w w 2 i e for the hard strip in the latter case the calculations were carried out for wavenumbers k such that 1 kl 16 where l was the strip width and were shown to agree with experimental measurements h medwin et al j acoust soc am 72 1005 1013 1982 the present article extends the theory to cover the important remaining cases

residue complexes over noncommutative rings abstract residue complexes were introduced by grothendieck in algebraic geometry these are canonical complexes of injective modules that enjoy remarkable functorial properties traces in this paper we study residue complexes over noncommutative rings these objects have a more intricate structure than in the commutative case since they are complexes of bimodules we develop methods to prove uniqueness existence and functoriality of residue complexes for a polynomial identity algebra over a field admitting a noetherian connected filtration we prove existence of the residue complex and describe its structure in detail