performance of optimum and suboptimum combining diversity reception for binary and quadrature dpsk over independent nonidentical rayleigh fading channels this paper is concerned with the error performance analysis of binary and quadrature differential phase shift keying with differential detection over the nonselective rayleigh fading channel with combining diversity reception the diversity channels are independent but have nonidentical statistics the fading process in each channel is assumed to have an arbitrary doppler spectrum with arbitrary doppler bandwidth both optimum diversity reception and suboptimum diversity reception are considered results available previously apply only to the case of second order diversity and require numerical integration for their actual evaluation our results are more general in that the order of diversity is arbitrary moreover the bit error probability bep result is obtained in an exact closed form expression which shows the behavior of the bep as an explicit function of the one symbol interval fading correlation coefficient at the matched filter output the mean received signal to noise ratio per symbol per channel and the order of diversity

optimal detection of digital data over the nonselective rayleigh fading channel with diversity reception based on the criterion of minimum symbol error probability an analysis is made of symbol by symbol detection of a sequence of digital data transmitted using linear suppressed carrier modulation over l independent diversity channels with awgn additive white gaussian noise and slow nonselective rayleigh fading the optimal receiver is derived but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length suboptimal decision feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers the exact bit error probabilities of these suboptimal receivers are obtained tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal to noise ratio and order of diversity a main conclusion of this work is that optimal data detection on a fading channel should be performed using mmse minimum mean squared error estimates of the quadrature amplitudes of the channel fading processes as a coherent reference

lie bialgebroids and poisson groupoids lie bialgebras arise as infinitesimal invariants of poisson lie groups a lie bialgebra is a lie algebra g with a lie algebra structure on the dual g which is compatible with the lie algebra g in a certain sense for a poisson group g the multiplicative poisson structure induces a lie algebra structure on the lie algebra dual g which makes g g into a lie bialgebra in fact there is a one one correspondence between poisson lie groups and lie bialgebras if the lie groups are assumed to be simply connected 7 16 19 the importance of poisson lie groups themselves arises in part from their role as classical limits of quantum groups 8 and in part because they provide a class of poisson structures for which the realization problem is tractable 15 poisson groupoids were introduced by weinstein 24 as a generalization of both poisson lie groups and the symplectic groupoids which arise in the integration of arbitrary poisson manifolds 4 11 he noted that the lie algebroid dual a g of a poisson groupoid g itself has a lie algebroid structure but did not develop the infinitesimal structure further in this paper we introduce and study a natural infinitesimal invariant for poisson groupoids the lie bialgebroids of the title our ultimate purpose is to develop a lie theory for poisson groupoids parallel to that for poisson groups in this paper we are primarily concerned with the first half of this process that is with the construction of the lie bialgebroid of a poisson groupoid after the preliminary 2 in which we describe the generalization to arbitrary lie algebroids of the exterior calculus and schouten calculus in 3 we define a lie bialgebroid to be a lie algebroid a whose dual a is also equipped with a lie algebroid structure such that the coboundary operator d a a associated to a satisfies a cocycle equation with respect to a the lie algebra of sections of a this is clearly a straightforward extension of the concept of a lie bialgebra 16 but cannot be formalized in lie algebroid cohomological terms since there is no satisfactory adjoint representation for a general lie algebroid most of 3 is devoted to proving that this definition is self dual if a a is a lie bialgebroid then a a is also in 4 we briefly consider the special case of lie bialgebroids satisfying a triangularity condition which include some important examples such as the usual triangular lie bialgebras and lie bialgebroids associated to poisson manifolds the techniques used in 2 4 are similar to those known for lie bialgebras it would be possible by suitably generalizing the proof for poisson groups to prove

lie theory of multiplicative tensors we study tensors on lie groupoids suitably compatible with the groupoid structure called multiplicative our main result gives a complete description of these objects only in terms of infinitesimal data special cases include the infinitesimal counterparts of multiplicative forms multivector fields and holomorphic structures obtained through a unifying and conceptual method we also give a full treatment of multiplicative vector valued forms particularly nijenhuis operators and related structures

poisson harmonic forms kostant harmonic forms and the s1 equivariant cohomology ofk t abstract we characterize the harmonic forms on a flag manifold k t defined by kostant in 1963 in terms of a poisson structure namely they are poisson harmonic with respect to the so called bruhat poisson structure on k t this enables us to give poisson geometrical proofs of many of the special properties of these harmonic forms in particular we construct explicit representatives for the schubert basis of the s 1 equivariant cohomology of k t where the s 1 action is defined by using a simple argument in equivariant cohomology we recover the connection between the kostant harmonic forms and the schubert calculus on k t that was found by kostant and kumar in 1986 by using a family of symplectic structures on k t we also show that the kostant harmonic forms are limits of the more familiar hodge harmonic forms with respect to a family of hermitian metrics on k t

poisson structures on complex flag manifolds associated with real forms for a complex semisimple lie group g and a real form go we define a poisson structure on the variety of borel subgroups of g with the property that all go orbits in x as well as all bruhat cells for a suitable choice of a borel subgroup of g are poisson submanifolds in particular we show that every non empty intersection of a go orbit and a bruhat cell is a regular poisson manifold and we compute the dimension of its symplectic leaves

group orbits and regular partitions of poisson manifolds we study a large class of poisson manifolds derived from manin triples for which we construct explicit partitions into regular poisson submanifolds by intersecting certain group orbits examples include all varieties mathcal l of lagrangian subalgebras of reductive quadratic lie algebras mathfrak d with poisson structures defined by lagrangian splittings of mathfrak d in the special case of mathfrak g oplus mathfrak g where mathfrak g is a complex semi simple lie algebra we explicitly compute the ranks of the poisson structures on mathcal l defined by arbitrary lagrangian splittings of mathfrak g oplus mathfrak g such lagrangian splittings have been classified by p delorme and they contain the belavin drinfeld splittings as special cases

computation of the bit error rate of coherent m ary psk with gray code bit mapping efficient computation of the bit error rate ber for the coherent m ary psk signals with gray code bit mapping is considered a closed form expression for the exact ber of 8 ary psk is presented tight upper and lower bounds on ber are also obtained for m ary psk with larger m

derivations the lawrence sullivan interval and the fiorenza manetti mapping cone we describe the rational homotopy type of any component of the based mapping space map x y as an explicit l algebra defined on the desuspended and positive derivations between quillen models of x and y when considering the lawrence sullivan model of the interval we obtain an l model of the contractible path space of y we then relate this in a geometrical and natural manner to the l structure on the fiorenza manetti mapping cone of any differential graded lie algebra morphism two in principal different algebraic objects in which bernoulli numbers appear

cohomology of nilpotent groups of class 2 abstract we compute the cohomology rings of a number of nilpotent groups of class 2 for appropriate coefficients and we do some more sample calculations of various cohomology groups the basic tool is a suitable small free resolution for an arbitrary nilpotent group of class 2 constructed in a previous paper

on the t leaves of some poisson structures related to products of flag varieties abstract for a connected abelian lie group t acting on a poisson manifold y by poisson isomorphisms the t leaves of in y are the orbits of the symplectic leaves of under t and the leaf stabilizer of a t leaf is the subspace of the lie algebra of t that is everywhere tangent to all the symplectic leaves in the t leaf in this paper we first develop a general theory on t leaves and leaf stabilizers for a class of poisson structures defined by lie bialgebra actions and quasitriangular r matrices we then apply the general theory to four series of holomorphic poisson structures on products of flag varieties and related spaces for a complex semi simple lie group g we describe their t leaf decompositions where t is a maximal torus of g in terms of open generalized richardson varieties and generalized double bruhat cells associated to conjugacy classes of g and we compute their leaf stabilizers and the dimension of the symplectic leaves in each t leaf

formality and kontsevich duflo type theorems for lie pairs newcommand poly operatorname poly bullet newcommand td operatorname td l a nabla frac 1 2 newcommand cx 1 operatorname tot big gamma lambda bullet a vee otimes r mathcal 1 poly big newcommand cy 1 mathbb h bullet operatorname ce a mathcal 1 poly kontsevich s formality theorem states that there exists an l infty quasi isomorphism from the dgla t poly m of polyvector fields on a smooth manifold m to the dgla d poly m of polydifferential operators on m which extends the classical hochschild kostant rosenberg map in this paper we extend kontsevich s formality theorem to lie pairs a framework which includes a range of diverse geometric contexts such as complex manifolds foliations and mathfrak g manifolds the spaces cx t and cx d associated with a lie pair l a each carry an l infty algebra structure canonical up to l infty isomorphism these two spaces serve as replacements for the spaces of polyvector fields and polydifferential operators respectively their corresponding cohomology groups cy t and cy d admit canonical gerstenhaber algebra structures we establish the following formality theorem for lie pairs there exists an l infty quasi isomorphism from cx t to cx d whose first taylor coefficient is equal to operatorname hkr circ td here td acts on cx t by contraction furthermore we prove a kontsevich duflo type theorem for lie pairs the hochschild kostant rosenberg map twisted by the square root of the todd class of the lie pair l a is an isomorphism of gerstenhaber algebras from cy t to cy d as applications we establish formality theorems and kontsevich duflo type theorems for complex manifolds foliations and mathfrak g manifolds in the case of complex manifolds we recover the kontsevich duflo theorem of complex geometry

gibbs phenomenon for fourier partial sums on zp abstract it is of interest to know whether the gibbs phenomenon occurs on a local field a p adic heaviside function on the group of p adic integers is defined as an analogy of real variable heaviside function and it is also shown that there exists the gibbs phenomenon with an undershoot of at least 1 p 1 as an approximate level as a consequence of the theorem we see that the fourier partial sum for a heaviside function does not converge at the point of discontinuity

lie algebroid cohomology as a derived functor abstract we show that the hypercohomology of the chevalley eilenberg de rham complex of a lie algebroid l over a scheme with coefficients in an l module can be expressed as a derived functor we use this fact to study a hochschild serre type spectral sequence attached to an extension of lie algebroids

generalized quadratic receivers for orthogonal signals over the gaussian channel with unknown phase fading the orthogonal signal structure has been shown to be the superposition of an antipodal signal set and an unmodulated pilot tone component which can be used for channel measurement starting from this point of view the quadratic receiver for orthogonal signals over the gaussian channel with unknown phase fading has been shown to be equivalent to a detector estimator receiver the estimator makes an optimum estimate of the unknown complex channel gain based on the channel measurement provided by the unmodulated component of the received signal this channel estimate then forms a partially coherent reference for the detector in detecting the data carried by the antipodal signaling component of the received signal this paper exploits this detector estimator structure of the quadratic receiver and generalizes it to a receiver in which the estimator makes an estimate of the channel gain in each signaling interval based on the totality of signals received over all the signaling intervals or a subset of these intervals the generalized quadratic receiver is just as simple to implement as the conventional quadratic receiver and theoretical and simulation results show that it can achieve substantial performance gains over the conventional receiver a theory is presented to show that the generalized quadratic receiver is an implementable approximation to the optimum symbol by symbol receiver for uncoded orthogonal signals over the gaussian channel with unknown phase fading the theory shows that the structure provides a unified and systematic approach to the design of coherent symbol by symbol receivers and shows that the conventional carrier loop type receivers are ad hoc

weyl manifolds and deformation quantization this paper deals with non commutative objects based on the weyl algebra from the differential geometric point of view we propose to extend familiar notions from manifolds to non commutative objects in this algebraic approach the basic object is not a point of a space but certain sections of bundles

performance analysis of orthogonal space time block codes over time selective channels and applications to code design of gi systems many existing works on space time block codes stbc assume the channels are block wise constant but this assumption does not always hold in the more general case of time selective channels the channel matrix is no longer orthogonal so inter symbol interference esi is generated and the performance is greatly reduced several decoders have been proposed to eliminate the esi but it remains unclear how and to what extent the performance is affected by the isi in this paper we introduce an approach to analyze the performance of stbc over time selective channels with arbitrary numbers of antennas for which orthogonal stbc s are defined exact error performances are obtained in closed form furthermore the analysis reveals the relationship between the isi and the structure of stbc matrices considering g i systems we then propose one proposition and two design criteria following which it is easy to design or search for better stbc s that have less isi compared with the original code matrix

bit error probabilities mdpsk over the nonselective rayleigh fading channel with diversity reception data transmission using m ary differential phase shift keying mdpsk over the nonselective rayleigh fading channel with diversity reception is considered while previous studies on error probability mostly assume no fading fluctuation the author considers exclusively the case in which the fading process fluctuates from one symbol interval to the next exact bit error probability results for 2 4 and 8 dpsk as well as tight upper bounds are derived some applications of the results are discussed

a poisson structure on compact symmetric spaces we present some basic results on a natural poisson structure on any compact symmetric space the symplectic leaves of this structure are related to the orbits of the corresponding real semisimple group on the complex flag manifold

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

fedosov dg manifolds associated with lie pairs given any pair l a of lie algebroids we construct a differential graded manifold l 1 oplus l a q which we call fedosov dg manifold we prove that the homological vector field q constructed on l 1 oplus l a by the fedosov iteration method arises as a byproduct of the poincare birkhoff witt map established in 18 finally using the homological perturbation lemma we establish a quasi isomorphism of dolgushev fedosov type the differential graded algebras of functions on the dg manifolds a 1 d a and l 1 oplus l a q are homotopy equivalent

algebraic constructions in the category of lie algebroids the aim of this paper is to give the first general and abstract treatment of the algebraic properties of lie algebroids the concept of lie algebroid was introduced in 1967 by pradines ls as the basic infinitesimal invariant of a differentiable groupoid the construction of the lie algebroid of a differentiable groupoid is a direct generalization of the construction of the lie algebra of a lie group and 183 described a full lie theory for differentiable groupoids and lie algebroids encompassing many phenomena in the foundations of differential geometry a more detailed account and further references are given in 13 however at this stage the algebraic properties of lie algebroids were not pursued in 13 iii section 2 iv section 11 one of us gave a fairly detailed account of the abstract algebra of lie algebroids over a fixed base lie algebroids are vector bundles with several additional structures and a category of lie algebroids on a given base and morphisms which preserve that base has properties similar to those of the category of lie algebras using this algebra it was demonstrated in 13 that the lie theory of a category of locally trivial differentiable lie groupoids over a fixed base and the corresponding category of transitive lie algebroids over that base is coextensive with the standard theory of connections in principal bundles we now propose to show that the lie functor from the category of all differentiable groupoids over arbitrary bases and arbitrary smooth morphisms to the category of all lie algebroids preserves the basic algebraic constructions known to be possible in the category of differentiable groupoids the main work is to give abstract formulations of the corresponding lie algebroid concepts the groupoid results with which we

on the perturbation algebra we introduce a certain differential graded bialgebra neither commutative nor cocommutative that governs perturbations of a differential on complexes supplied with an abstract hodge decomposition this leads to a conceptual treatment of the homological perturbation lemma and its multiplicative version as an application we give an explicit form of the decomposition theorem for a algebras and a modules and more generally for twisted objects in differential graded categories

cohomology of metacyclic groups group n by a finite cyclic group k using homological perturbation theory we introduce the beginning of a free resolution of the integers z over the group ring zg of g in such a way that the resolution reflects the structure of g as an extension of n by k and we use this resolution to compute the additive structure of the integral cohomology of g in many cases we proceed by first establishing a number of special cases thereafter constructing suitable cohomology classes thereby obtaining a lower bound then computing characteristic classes introduced in an earlier paper and finally exploiting these classes obtaining upper bounds for the cohomology via the integral cohomology spectral sequence of the extension e the calculation is then completed by comparing the two bounds

on the cohomology of the holomorph of a finite cyclic group abstract we determine the mod 2 cohomology algebra of the holomorph of any finite cyclic group whose order is a power of 2

p adic models of ultrametric diffusion constrained by hierarchical energy landscapes we demonstrate that the p adic analysis is a natural basis for the construction of a wide variety of models of ultrametric diffusion constrained by hierarchical energy landscapes a general analytical description in terms of the p adic analysis is given for a class of models two exactly solvable examples i e the ultrametric diffusion constrained by the linear energy landscape and the ultrametric diffusion with a reaction sink are considered we show that such models can be applied to both the relaxation in complex systems and the rate processes coupled to rearrangement of the complex surrounding

from atiyah classes to homotopy leibniz algebras a celebrated theorem of kapranov states that the atiyah class of the tangent bundle of a complex manifold x makes t x 1 into a lie algebra object in d x the bounded below derived category of coherent sheaves on x furthermore kapranov proved that for a kahler manifold x the dolbeault resolution omega bullet 1 t x 1 0 of t x 1 is an l algebra in this paper we prove that kapranov s theorem holds in much wider generality for vector bundles over lie pairs given a lie pair l a i e a lie algebroid l together with a lie subalgebroid a we define the atiyah class e of an a module e as the obstruction to the existence of an a compatible l connection on e we prove that the atiyah classes l a and e respectively make l a 1 and e 1 into a lie algebra and a lie algebra module in the bounded below derived category d mathcal a where mathcal a is the abelian category of left mathcal u a modules and mathcal u a is the universal enveloping algebra of a moreover we produce a homotopy leibniz algebra and a homotopy leibniz module stemming from the atiyah classes of l a and e and inducing the aforesaid lie structures in d mathcal a

open closed homotopy algebra in mathematical physics in this paper we discuss various aspects of open closed homotopy algebras ochas presented in our previous paper inspired by zwiebach s open closed string field theory but that first paper concentrated on the mathematical aspects here we show how an ocha is obtained by extracting the tree part of zwiebach s quantum open closed string field theory we clarify the explicit relation of an ocha with kontsevich s deformation quantization and with the b models of homological mirror symmetry an explicit form of the minimal model for an ocha is given as well as its relation to the perturbative expansion of open closed string field theory we show that our open closed homotopy algebra gives us a general scheme for deformation of open string structures a algebras by closed strings l algebras

bit error probability for noncoherent orthogonal signals in fading with optimum combining for correlated branch diversity due to the interest in wireless personal communications there has been a lot of research on the performance of receivers with diversity most analyses assume the diversity branches are independent this paper presents an analysis of the bit error probability for receivers in which the diversity branches are correlated noncoherent orthogonal digital modulation ncodm with rician and rayleigh slow nonselective fading models are assumed through the use of the diagonalization of quadratic forms most of the calculations of the bit error probability can be reduced to a two dimensional numerical integration for some cases for dual diversity a closed form expression for the error probability is given a number of diversity combining laws including square law and maximum likelihood are considered we find that rician fading can be worse than rayleigh fading in correlated diversity environments a situation quite different from the independent diversity case also for the rayleigh fading model with correlated branch diversity we find that an equal weight square law combiner usually has the same error performance as the more complex maximum likelihood combiner however this is not the case for a rician fading model with the same correlation environment simple diagonalization methods that compensate for the lossy effect of correlation are specified and found to be effective when the dominant noise and interference have almost the same correlation distribution as the fading signals

algebraic models of non connected spaces and homotopy theory of l algebras we develop a homotopy theory of l algebras based on the lawrence sullivan construction a complete differential graded lie algebra which as we show satisfies the necessary properties to become the right cylinder in this category as a result we obtain a general procedure to algebraically model the rational homotopy type of non connected spaces 2012 elsevier ltd

asymptotical behavior of one class of p adic singular fourier integrals abstract we study the asymptotical behavior of the p adic singular fourier integrals j m t f m x p x t x f f m t t p t q p where f m d q p is a quasi associated homogeneous distribution generalized function of degree x x p 1 1 x and order m x 1 x and p x are a multiplicative a normed multiplicative and an additive characters of the field q p of p adic numbers respectively d q p is a test function m 0 1 2 c if re 0 the constructed asymptotics constitute a p adic version of the well known erdelyi lemma theorems which give asymptotic expansions of singular fourier integrals are the abelian type theorems in contrast to the real case all constructed asymptotics have the stabilization property

a systematic approach to the design and analysis of optimum dpsk receivers for generalized diversity communications over rayleigh fading channels a generalized diversity channel is introduced that models a variety of wireless communication systems that use time frequency multipath and or antenna diversity with various interbranch correlations between signaling waveforms and the fading and additive noise processes in the context of this general model a systematic approach to the design and analysis of optimum noncoherent differential phase shift keying dpsk receivers is introduced in particular it is shown how the minimum error probability mep and the generalized likelihood ratio tests glrt can be applied to obtain optimal noncoherent combining rules a comparative error rate analysis of the glrt and mep detectors and an ad hoc equal gain combiner is provided for binary signaling and the suitability of the three schemes is determined as a function of fading characteristics the asymptotic bit error rate analysis is undertaken for the mep detector for slow and fast fading channels an estimator detector decomposition of the noncoherent mep rule is obtained which allows an insightful comparative study of the fundamental limits of binary phase shift keying and dpsk modulation detection methods for both slow and fast fading the results of this paper are also applicable to postdecorrelative receivers in multiuser channels

a simple bit error probability analysis for square qam in rayleigh fading with channel estimation a new approach is presented for analyzing the bit error probability bep of square multilevel quadrature amplitude modulation over a nonselective rayleigh fading channel with imperfect channel estimation employing pilot symbol assisted modulation it is much simpler and more powerful than those in the literature and the average bep is obtained by calculating the bep for each individual bit the results are given in simple exact closed form expressions that do not require any numerical integration these expressions show explicitly the behavior of the bep as a function of various system parameters three channel estimation schemes are investigated it is shown that existing channel estimation schemes using sinc interpolation and gaussian interpolation can be improved

achieving near optimum asymptotic efficiency and fading resistance over the time varying rayleigh faded cdma channel we study multiuser receiver design and analysis for synchronous code division multiple access cdma channels with time varying rayleigh fading starting from an error probability criterion we first derive a near optimum receiver for this channel that admits a detector estimator decomposition has certain asymptotic optimality properties and a complexity which is independent of the length of the observation interval the performance of this detector is analytically characterized and contrasted with that of the optimal multiuser detector for the time invariant or static cdma rayleigh fading channel when it is implemented over the time varying channel notable among our conclusions is the fact that unlike the static channel multiuser detector the time varying channel detector is able to withstand not only the estimated interference from the other system users but also the residual interference that cannot be estimated arising out of imperfect estimation of the interferer fading parameters using estimation error covariance information this detector shows flexibility in accommodating a wide range of interferer fading conditions

canonical functions differential graded symplectic pairs in supergeometry and alexandrov kontsevich schwartz zaboronsky sigma models with boundaries consistent boundary conditions for alexandrov kontsevich schwartz zaboronsky aksz sigma models and the corresponding boundary theories are analyzed as their mathematical structures we introduce a generalization of differential graded symplectic manifolds called twisted qp manifolds in terms of graded symplectic geometry canonical functions and qp pairs we generalize the aksz construction of topological sigma models to sigma models with wess zumino terms and show that all the twisted poisson like structures known in the literature can actually be naturally realized as boundary conditions for aksz sigma models

a robust receiver structure for time varying frequency flat rayleigh fading channels a receiver structure for unknown time varying frequency flat rayleigh fading channels is proposed unlike the maximum likelihood receiver structure this receiver does not need any knowledge of the channel autocovariance or the received signal to noise ratio and yet analytic and simulation results show that its bit error rate performance is close to the optimal structure the receiver is applicable to signals with constant or approximately constant envelopes or to linearly modulated signals using nyquist pulses

classical dynamical r matrices and homogeneous poisson structures on g h and k t let g be a finite dimensional simple complex group equipped with the standard poisson lie group structure we show that all g homogeneous holomorphic poisson structures on g h where h g is a cartan subgroup come from solutions to the classical dynamical yang baxter equations which are classified by etingof and varchenko a similar result holds for a maximal compact subgroup k and we get a family of k homogeneous poisson structures on k t where t k h is a maximal torus of k this family exhausts all k homogeneous poisson structures on k t up to isomorphisms we study some poisson geometrical properties of members of this family such as their symplectic leaves their modular classes and the moment maps for the t action

covariant and equivariant formality theorems abstract we give a proof of kontsevich s formality theorem for a general manifold using fedosov resolutions of algebras of polydifferential operators and polyvector fields the main advantage of our construction of the formality quasi isomorphism is that it is based on the use of covariant tensors unlike kontsevich s original proof which is based on jets of polydifferential operators and polyvector fields using our construction we prove that if a group g acts smoothly on a manifold m and m admits a g invariant affine connection then there exists a g equivariant quasi isomorphism of formality this result implies that if a manifold m is equipped with a smooth action of a finite or compact group g or equipped with a free action of a lie group g then m admits a g equivariant formality quasi isomorphism in particular this gives a solution of the deformation quantization problem for an arbitrary poisson orbifold

multi derivation maurer cartan algebras and sh lie rinehart algebras abstract we extend the classical characterization of a finite dimensional lie algebra g in terms of its maurer cartan algebra the familiar differential graded algebra of alternating forms on g with values in the ground field endowed with the standard lie algebra cohomology operator to sh lie rinehart algebras to this end we first develop a characterization of sh lie rinehart algebras in terms of differential graded cocommutative coalgebras and lie algebra twisting cochains that extends the nowadays standard characterization of an ordinary sh lie algebra equivalently l algebra in terms of its associated generalized cartan chevalley eilenberg coalgebra our approach avoids any higher brackets but reproduces these brackets in a conceptual manner the new technical tool we develop is a notion of filtered multi derivation chain algebra somewhat more general than the standard concept of a multicomplex endowed with a compatible algebra structure the crucial observation just as for ordinary lie rinehart algebras is this for a general sh lie rinehart algebra the generalized cartan chevalley eilenberg operator on the corresponding graded algebra involves two operators one coming from the sh lie algebra structure and the other one from the generalized action on the corresponding algebra the sum of the two operators is defined on the algebra while the operators are individually defined only on a larger ambient algebra we illustrate the structure with quasi lie rinehart algebras

homotopy algebras inspired by classical open closed string field theory we define a homotopy algebra associated to classical open closed strings we call it an open closed homotopy algebra ocha it is inspired by zwiebach s open closed string field theory and also is related to the situation of kontsevich s deformation quantization we show that it is actually a homotopy invariant notion for instance the minimal model theorem holds also we show that our open closed homotopy algebra gives us a general scheme for deformation of open string structures a algebras by closed strings l algebras

perturbation theory and free resolutions for nilpotent groups of class 2 abstract using homological perturbation theory we construct a small free resolution for any nilpotent group g of class 2 which reflects the structure of g as a central extension of an abelian group by an abelian group

associated and quasi associated homogeneous distributions generalized functions in this paper analysis of the concept of associated homogeneous distributions generalized functions is given and some problems related to these distributions are solved it is proved that in the one dimensional case there exist only associated homogeneous distributions of order k 1 we introduce a definition of quasi associated homogeneous distributions which is a natural generalization of the notion of associated homogeneous distributions and provide a mathematical description of all quasi associated homogeneous distributions and their fourier transforms it is proved that the class of quasi associated homogeneous distributions coincides with the class of distributions introduced in i m gel fand g e shilov generalized functions vol 1 properties and operations academic press new york 1964 chapter i 4 as the class of associated homogeneous distributions for the multidimensional case it is proved that f is a quasi associated homogeneous distribution if and only if it satisfies an euler type system of differential equations a new type of functions generated by quasi associated homogeneous distributions is defined

generalized kahler geometry generalized kahler geometry is the natural analogue of kahler geometry in the context of generalized complex geometry just as we may require a complex structure to be compatible with a riemannian metric in a way which gives rise to a symplectic form we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure we prove that generalized kahler geometry is equivalent to the bi hermitian geometry on the target of a 2 dimensional sigma model with 2 2 supersymmetry we also prove the existence of natural holomorphic courant algebroids for each of the underlying complex structures and that these split into a sum of transverse holomorphic dirac structures finally we explore the analogy between pre quantum line bundles and gerbes in the context of generalized kahler geometry

a symbol by symbol channel estimation receiver for space time block coded systems and its performance analysis on the nonselective rayleigh fading channel we present a symbol by symbol channel estimation receiver for an orthogonal space time block coded system and derive its analytical performance on a slow nonselective rayleigh fading channel exact closed form expressions for its bit error probability bep performance for m ary phase shift keying modulations are obtained which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error our bep expressions show explicitly the dependence of bep on the mean square error of the channel estimates which in turn depend on the channel fading model and the channel estimator used tight upper bounds are presented that show more clearly the dependence of the bep on various system parameters simulation results using various fading models are obtained to demonstrate the validity of the analysis

higher order whitehead products and l structures on the homology of a dgl abstract we detect higher order whitehead products on the homology h of a differential graded lie algebra l in terms of higher brackets in the transferred l structure on h via a given homotopy retraction of l onto h

dg resolutions of nc smooth thickenings and nc fourier mukai transforms we give a construction of nc smooth thickenings a notion defined by kapranov j reine angew math 505 73 118 1998 of a smooth variety equipped with a torsion free connection we show that a twisted version of this construction realizes all nc smooth thickenings as 0 th cohomology of a differential graded sheaf of algebras similarly to fedosov s construction in j differ geom 40 213 238 1994 we use this dg resolution to construct and study sheaves on nc smooth thickenings in particular we construct an nc version of the fourier mukai transform from coherent sheaves on a commutative curve to perfect complexes on the canonical nc smooth thickening of its jacobian we also define and study analytic nc manifolds we prove nc versions of some of gaga theorems and give a c infty construction of analytic nc thickenings that can be used in particular for kahler manifolds with constant holomorphic sectional curvature finally we describe an analytic nc thickening of the poincare line bundle for the jacobian of a curve and the corresponding fourier mukai functor in terms of a infty structures

cotangent bundle quantization entangling of metric and magnetic field for manifolds of noncompact type endowed with an affine connection for example the levi civita connection and a closed 2 form magnetic field we define a hilbert algebra structure in the space and construct an irreducible representation of this algebra in this algebra is automatically extended to polynomial in momenta functions and distributions under some natural conditions this algebra is unique the non commutative product over is given by an explicit integral formula this product is exact not formal and is expressed in invariant geometrical terms our analysis reveals that this product has a front which is described in terms of geodesic triangles in the quantization of functions induces a family of symplectic reflections in and generates a magneto geodesic connection on this symplectic connection entangles on the phase space level the original affine structure on and the magnetic field in the classical approximation the 2 part of the quantum product contains the ricci curvature of and a magneto geodesic coupling tensor