adaptive minimum symbol error rate equalization for quadrature amplitude modulation we propose the adaptive minimum symbol error rate algorithm which is a low complexity technique for adapting the coefficients of a linear equalizer in systems using pulse amplitude or quadrature amplitude modulation the proposed algorithm very nearly minimizes error probability in white gaussian noise and can significantly outperform the minimum mean squared error equalizer by as much as 16 db when the number of equalizer coefficients is small relative to the severity of the intersymbol interference

spin structures and spectra of ℤ 2 k manifolds we give necessary and sufficient conditions for the existence of pin and spin structures on riemannian manifolds with holonomy group 2 k for any n 4 resp n 6 we give examples of pairs of compact manifolds resp compact orientable manifolds m 1 m 2 non homeomorphic to each other that are laplace isospectral on functions and on p forms for any p and such that m 1 admits a pin resp spin structure whereas m 2 does not

dynamical spectral rigidity among mathbb z _2 symmetric strictly convex domains close to a circle appendix b coauthored with h hezari

compact isospectral sets of surfaces on etudie des ensembles de surfaces qui sont isospectrales par rapport a l operateur de laplace beltrami

geodesics and commensurability classes of arithmetic hyperbolic 3 manifolds this sharpens 10 where it was shown that the complex length spectrum of m determines its commensurability class suppose m is an arithmetic hyperbolic 3 manifold which is not commensurable to m theorem 1 1 implies ql m 6 ql m though by example 2 1 below it is possible that one of ql m or ql m contains the other by the length formulas recalled in 2 1 and 2 2 each element of ql m ql m is a rational multiple of the logarithm of a real algebraic number as noted by prasad and rapinchuk in 9 the gelfond schneider theorem 1 implies that a ratio of such logarithms is transcendental if it is irrational thus if ql m ql m then is transcendental for all non zero ql m recently prasad and rapinchuk have shown in 9 that if m is an arithmetic hyperbolic manifold of even dimension then ql m and the commensurability class of m determine one another in addition they have shown that this is not always true for arithmetic hyperbolic 5 manifolds however they have announced a proof that for all locally symmetric spaces associated to a specified absolutely simple lie group there are only finitely many commensurability classes of arithmetic lattices giving rise to a given rational length spectrum it is known see 4 pp 415 417 that for closed hyperbolic manifolds the spectrum of the laplace beltrami operator action on l2 m counting multiplicities determines the set of lengths of closed geodesics on m without counting multiplicities hence theorem 1 1 implies

isospectral graphs with identical nodal counts according to a recent conjecture isospectral objects have different nodal count sequences gnutzmann et al 2005 j phys a math gen 38 8921 33 we study generalized laplacians on discrete graphs and use them to construct the first non trivial counterexamples to this conjecture in addition these examples demonstrate a surprising connection between isospectral discrete and quantum graphs

an analogue of the prime number theorem for closed orbits of axiom a flows for an axiom a flow restricted to a basic set we extend the zeta function to an open set containing w s h where h is the topological entropy this enables us to give an asymptotic formula for the number of closed orbits by adapting the wiener ikehara proof of the prime number theorem

twisted perron frobenius theorem and l functions abstract a theorem of perron frobenius type and its twisted version are established in a setting of topological graphs the applications include a partial extension of selberg s results on his zeta functions and a result by parry and pollicott on meromorphic continuations of dynamical zeta functions to certain l functions associated to a dynamical system of anosov type

adaptive minimum ber linear multiuser detection for ds cdma signals in multipath channels the problem of constructing adaptive minimum bit error rate mber linear multiuser detectors is considered for direct sequence code division multiple access ds cdma signals transmitted through multipath channels based on the approach of kernel density estimation for approximating the bit error rate ber from training data a least mean squares lms style stochastic gradient adaptive algorithm is developed for training linear multiuser detectors computer simulation is used to study the convergence speed and steady state ber misadjustment of this adaptive mber linear multiuser detector and the results show that it outperforms an existing lms style adaptive mber algorithm presented by yeh et al see proc globecom sydney australia p 3590 95 1998

calcul du spectre d une nilvariete de rang deux et applications on calcule en utilisant la theorie des orbites de kirillov le spectre d une nilvariete compacte de rang deux puis on utilise ce calcul pour etudier et caracteriser les deformations isospectrales de ces varietes

the covering spectrum of a compact length space we define a new spectrum for compact length spaces and riemannian manifolds called the covering spectrum which roughly measures the size of the one dimensional holes in the space more specifically the covering spectrum is a set of real numbers 0 which identify the distinct covers of the space we investigate the relationship between this covering spectrum the length spectrum the marked length spectrum and the laplace spectrum we analyze the behavior of the covering spectrum under gromov hausdorff convergence and study its gap phenomenon

on minimum ber linear multiuser detection for ds cdma channels the minimum bit error rate mber linear multiuser detection of direct sequence code division multiple access ds cdma communications is considered it is shown that the problem of mber linear multiuser detection is equivalent to a constrained optimization problem where the constrained space is the surface and interior of a hyperellipsoid it is further shown that any solution of the constrained optimization problem must be a solution of a set of nonlinear equations based on these the mber linear multiuser detector of the two user case is obtained for general cases we propose a convex subspace of the constrained space and show that the ber cost function is convex on the subspace and therefore has a unique solution some sufficient conditions that guarantee the convex subspace always contains the global minimizer are provided which show that if the signal to noise ratio snr is sufficiently large the convex subspace always contains the global minimizer a newton method is developed for the set of nonlinear equations and computer simulation gives some illustrative examples

jointly minimum ber transmitter and receiver fir mimo filters for binary signal vectors a theory is developed for jointly minimizing the bit error rate ber between the desired and decoded signals with respect to the coefficients of transmitter and receiver finite impulse response fir multiple input multiple output mimo filters the original signal is assumed to be a vector time series with equally likely memoryless bernoulli vector components the channel model constitutes of a known fir mimo transfer function and gaussian additive noise independent of the original signal the channel input signal is assumed to be power constrained based on the formulas obtained an iterative numerical optimization algorithm is proposed when compared with other design methods available in the literature the proposed method yields better results due to the generality of the model considered and the joint optimization of the transmitter receiver pair

gradient estimation for sensitivity analysis and adaptive multiuser interference rejection in code division multiple access systems in this paper we consider a direct sequence code division multiple access ds cdma system in the framework of a discrete event dynamic system deds in order to optimize the system performance based on this formulation we develop infinitesimal perturbation analysis ipa for estimating the sensitivity of the average probability of bit error to factors ranging from near far effects to imperfections in power control the above estimates are shown to be unbiased and this technique is then further incorporated into a stochastic gradient algorithm for achieving adaptive multiuser interference rejection for such systems which is also subject to frequency nonselective slow fading we use an ipa based stochastic training algorithm for developing an adaptive linear detector with the average probability of error being the minimization criterion we also develop a practical implementation of such an adaptive detector where we use a joint estimation detection algorithm for minimizing the average probability of bit error a sequential implementation that does not require a stochastic training sequence or a preamble is also developed

robust linear mimo receivers a minimum error rate approach this paper looks at the linear reception of spatially multiplexed signals across mimo channels we address the problem of robustness in the presence of detrimental effects such as correlation and ricean components we consider the error rate performance of mimo linear filters as these can be used in purely linear receivers or as part of each stage in successive interference canceling sic receivers we know from multiuser detection theory that minimum error rate mer linear receivers significantly outperform minimum mean square error mmse receivers when correlation is high however no direct method exist to design the mer receiver simply we derive a scheme allowing a closed form approximate solution to this problem the solution is a good approximation to the true mer receiver upon fulfillment of a certain easily checkable channel related condition the algorithms are derived first for the two input many output case a generalized scheme is provided for the case of arbitrary number of inputs and outputs the performance gain compared with that mmse is significant and evaluated for various correlated and ricean channels and transmit power allocation strategies

a soft switching blind equalization scheme via convex combination of adaptive filters blind equalizers avoid the transmission of pilot sequences allowing a more efficient use of the channel bandwidth normally after a first rough equalization is achieved it is necessary to switch these equalizers to a decision directed dd mode to reduce the steady state mean square error mse to acceptable levels the selection of an appropriate mse threshold for switching between the blind and the dd modes is critical to obtain a good overall performance however this is not an easy task since it depends on several factors such as the signal constellation the communication channel or the signal to noise ratio in this paper we propose an equalization scheme that adaptively combines a blind and a dd equalizers running in parallel the combination is itself adapted in a blind manner and as a result the overall scheme can automatically switch between the component filters avoiding the need to set the transition mse level a priori the performance of our proposal is illustrated both analytically and through an extensive set of simulations where we show its advantages with respect to existing hard and soft switching equalization schemes

subgroups of finite soluble groups inducing the same permutation character in this paper there are found necessary and sufficient conditions that a pair of solvable finite groups say g and k must satisfy for the existence of a solvable finite group l containing two isomorphic copies of g and h inducing the same permutation character also a construction of l is given as an iterated wreath product with respect to their actions on their natural modules of finite one dimensional affine groups

discrete exact solutions of modified volterra and volterra lattice equations via the new discrete sine gordon expansion algorithm abstract recently we have presented a sine gordon expansion method to construct new exact solutions of a wide of continuous nonlinear evolution equations in this paper we further develop the method to be the discrete sine gordon expansion method in nonlinear differential difference equations in particular discrete soliton equations we choose the modified volterra lattice and volterra lattice equation to illustrate the new method such as many types of new exact solutions are obtained moreover some figures display the profiles of the obtained solutions our method can be also applied to other discrete soliton equations

coarse non amenability and covers with small eigenvalues given a closed riemannian manifold m and a virtual epimorphism pi 1 m twoheadrightarrow mathbb f 2 of the fundamental group onto a free group of rank 2 we construct a tower of finite sheeted regular covers left m n right n 0 infty of m such that 1 mn 0 as n this is the first example of such a tower which is not obtainable up to uniform quasi isometry or even up to uniform coarse equivalence by the previously known methods where 1 m is supposed to surject onto an amenable group

counting isospectral manifolds abstract given a simple lie group h of real rank at least 2 we show that the maximum cardinality of a set of isospectral non isometric h locally symmetric spaces of volume at most x grows at least as fast as x c log x log log x 2 where c c h is a positive constant in contrast with the real rank 1 case this bound comes surprisingly close to the total number of such spaces as estimated in a previous work of belolipetsky and lubotzky 2 our proof uses sunada s method results of 2 and some deep results from number theory we also discuss an open number theoretical problem which would imply an even faster growth estimate

infinitely many conservation laws and integrable discretizations for some lattice soliton equations in this paper by means of the lax representations we demonstrate the existence of infinitely many conservation laws for the general toda type lattice equation the relativistic volterra lattice equation the suris lattice equation and some other lattice equations the conserved density and the associated flux are given formulaically we also give an integrable discretization for a lattice equation with n dependent coefficients

cospectral graphs gm switching and regular rational orthogonal matrices of level p abstract the gm switching invented by godsil and mckay is a powerful method to construct cospectral graphs in its simplest version the method can be roughly described as follows let a g be the adjacency matrix of a graph g on n vertices let q diag r i n 2 m be a block diagonal matrix where r 1 m j i 2 m is an orthogonal matrix of order 2m j is the all one matrix and i k denotes the identity matrix of order k if g satisfies certain conditions then q t a g q is an adjacency matrix of a graph g which is cospectral with g with cospectral complements in this paper we consider the problem of replacing the above r with another rational orthogonal matrix u of order 2p p an odd prime we characterize all graphs g admitting a gm switching corresponding to q diag u i n 2 p i e such that q t a g q is an adjacency matrix of a graph g and hence giving a counterpart of the gm switching method for generating cospectral graphs with cospectral complements which can be used to construct pairs of non isomorphic cospectral graphs that are not obtainable by the original gm switching method next we consider the problem of how to determine whether a given graph has a non trivial gm switching associated with some u a simple algebraic condition is presented which partially answers this question

integral gassman equivalence of algebraic and hyperbolic manifolds in this paper we construct arbitrarily large families of smooth projective varieties and closed riemannian manifolds that share many algebraic and analytic invariants for instance every non arithmetic closed hyperbolic 3 manifold admits arbitrarily large collections of non isometric finite covers which are strongly isospectral length isospectral and have isomorphic integral cohomology where the isomorphisms commute with restriction and co restriction we can also construct arbitrarily large collections of pairwise non isomorphic smooth projective surfaces where these isomorphisms in cohomology are natural with respect to hodge structure or as galois modules in particular the projective varieties have isomorphic picard and albanese varieties and they also have isomorphic effective chow motives our construction employs an integral refinement of the gassman sunada construction that has recently been utilized by d prasad one application of our work shows the non injectivity of the map from the grothendieck group of varieties over overline mathbf q to the grothendieck group of the category of effective chow motives we also answer a question of d prasad

line graphs and the transplantation method abstract we study isospectrality for mixed dirichlet neumann boundary conditions and extend the previously derived graph theoretic formulation of the transplantation method led by the theory of brownian motion we introduce vertex colored and edge colored line graphs that give rise to block diagonal transplantation matrices in particular we rephrase the transplantation method in terms of representations of free semigroups and provide a method for generating adjacency cospectral weighted directed graphs

can one hear the shape of a drum revisited a famous inverse problem posed by m kac can one hear the shape of a drum is concerned with isospectrality of drums or planer billiards and the first counter example was constructed by gordon webb and wolpert 1992 invent math 110 1 here we present pieces of numerical evidence showing that one can distinguish isospectral drums by measuring the scattering poles of exterior neumann problems this is based on the observation that the fredholm determinant appearing in the boundary element method admits a factorization into interior and exterior parts

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

isospectral cayley graphs of some finite simple groups we apply spectral analysis of quotients of the bruhat tits buildings of type ad 1 to construct isospectral non isomorphic cayley graphs of the finite simple groups psld fq for every d 5 d 6 6 and prime power q 2

dirac and laplace operators on some non orientable conformally flat orbifolds abstract in this paper we present an explicit construction of the fundamental solution to the dirac and laplace operator on some non orientable conformally flat manifolds and special orbifolds we first treat a class of projective cylinders and tori where we can study monogenic sections with values in different pin bundles then we discuss the mobius strip the klein bottle and higher dimensional generalizations of them we present integral representation formulas together with some elementary tools of harmonic analysis on these manifolds resp orbifolds

discrete homotopies and the fundamental group abstract we generalize and strengthen the theorem of gromov that the fundamental group of any compact riemannian manifold of diameter at most d has a set of generators g 1 g k of length at most 2 d and relators of the form g i g m g j in particular we obtain an explicit bound for the number k of generators in terms of the number of short loops at every point and the number of balls required to cover a given semi locally simply connected geodesic space as a corollary we obtain a fundamental group finiteness theorem new even for riemannian manifolds that replaces the curvature and volume conditions of anderson and the 1 systole bound of shen wei by more general geometric hypothesis implied by these conditions this theorem in turn is a special case of a theorem for arbitrary compact geodesic spaces proved using the method of discrete homotopies introduced by the first author and v n berestovskii central to the proof is the notion of homotopy critical spectrum introduced in this paper as a natural consequence of discrete homotopy methods this spectrum is closely related to the sormani wei covering spectrum which is a subset of the classical length spectrum studied by de verdiere and duistermaat guillemin it is completely determined including multiplicity by special closed geodesics called essential circles

some conformally flat spin manifolds dirac operators and automorphic forms abstract in this paper we study clifford and harmonic analysis on some examples of conformal flat manifolds that have a spinor structure or more generally at least a pin structure the examples treated here are manifolds that can be parametrized by u where u is a subdomain of either s n or r n and is a kleinian group acting discontinuously on u the examples studied here include rp n and the hopf manifolds s 1 s n 1 also some hyperbolic manifolds will be treated special kinds of clifford analytic automorphic forms associated to the different choices of are used to construct explicit cauchy kernels cauchy integral formulas green s kernels and formulas together with hardy spaces and plemelj projection operators for l p spaces of hypersurfaces lying in these manifolds

integrable discretizations of the 2 1 dimensional sinh gordon equation in this paper we propose two semi discrete equations and one fully discrete equation and study them by hirota s bilinear method these equations have continuum limits into a system which admits the 2 1 dimensional generalization of the sinh gordon equation as a result two integrable semi discrete versions and one fully discrete version for the sinh gordon equation are found backlund transformations nonlinear superposition formulae determinant solution and lax pairs for these discrete versions are presented

minimum bit error rate design for space time equalization based multiuser detection a novel minimum bit error rate mber space time equalization ste based multiuser detector mud is proposed for multiple receive antenna assisted space division multiple access systems it is shown that the mber ste aided mud significantly outperforms the standard minimum mean square error design in terms of the achievable bit error rate ber adaptive implementations of the mber ste are considered and both the block data based and sample by sample adaptive mber algorithms are proposed the latter referred to as the least ber lber algorithm is compared with the most popular adaptive algorithm known as the least mean square lms algorithm it is shown that in case of binary phase shift keying the computational complexity of the lber ste is about half of that required by the classic lms ste simulation results demonstrate that the lber algorithm performs consistently better than the classic lm salgorithm both in terms of its convergence speed and steady state ber performance

stochastic unbiased minimum mean error rate algorithm for decision feedback equalizers capitalizing on a well known minimum mean square error mmse property for decision feedback equalization dfe along with the use of stochastic gradient approach we formulate an adaptive minimum error rate mer algorithm for dfe over m ary pam channels to be named as stochastic unbiased minimum mean error rate summer comparisons are made between our algorithm and existing mer algorithms in the literature also by invoking the central limit theorem we present an analytical proof that an unbiased mmse equalizer will approach an mer equalizer when the equalizer length approaches infinity thereby we obtain a lower bound expression for mer

an overview of periodic elliptic operators the article surveys the main techniques and results of the spectral theory of periodic operators arising in mathematical physics and other areas close attention is paid to studying analytic properties of bloch and fermi varieties which influence significantly most properties of such operators the approaches described are applicable not only to the standard model example of schrodinger operator with periodic electric potential v x but to a wide variety of elliptic periodic equations and systems equations on graphs operator and other operators on abelian coverings of compact bases many important applications are mentioned however due to the size restrictions they are not dealt with in details

on adaptive minimum probability of error linear filter receivers for ds cdma channels receiver architectures in the form of a linear filter front end followed by a hard limiting decision maker are considered for ds cdma communication systems based on stochastic approximation concepts a recursive algorithm is developed for the adaptive optimization of the linear filter front end in the minimum ber sense the recursive form is decision driven and distribution free for additive white gaussian noise awgn channels theoretical analysis of the ber surface of linear filter receivers identifies the subset of the linear filter space where the optimal receiver lies and offers a formal proof of guaranteed global optimization with probability one for the two user case to the extent that the output of a linear ds cdma filter can be approximated by a gaussian random variable a minimum mean square error optimized linear filter approximates the minimum ber solution numerical and simulation results indicate that for realistic awgn ds cdma systems with reasonably low signature cross correlations the linear minimum ber filter and the mmse filter exhibit approximately the same performance the linear minimum ber receiver is superior however when either the signature cross correlation is high or the background noise is non gaussian

adaptive reduced rank receive processing based on minimum symbol error rate criterion for large scale multiple antenna systems in this work we propose a novel adaptive reduced rank receive processing strategy based on joint preprocessing decimation and filtering jpdf for large scale multiple antenna systems in this scheme a reduced rank framework is employed for linear receive processing and multiuser interference suppression based on the minimization of the symbol error rate ser cost function we present a structure with multiple processing branches that performs a dimensionality reduction where each branch contains a group of jointly optimized preprocessing and decimation units followed by a linear receive filter we then develop stochastic gradient sg algorithms to compute the parameters of the preprocessing and receive filters along with a low complexity decimation technique for both binary phase shift keying bpsk and m ary quadrature amplitude modulation qam symbols in addition an automatic parameter selection scheme is proposed to further improve the convergence performance of the proposed reduced rank algorithms simulation results are presented for time varying wireless environments and show that the proposed jpdf minimum ser receive processing strategy and algorithms achieve a superior performance than existing methods with a reduced computational complexity

integrable discretizations of derivative nonlinear schrodinger equations we propose integrable discretizations of derivative nonlinear schrodinger dnls equations such as the kaup newell equation the chen lee liu equation and the gerdjikov ivanov equation by constructing lax pairs the discrete dnls systems admit the reduction of complex conjugation between two dependent variables and possess bi hamiltonian structure through transformations of variables and reductions we obtain novel integrable discretizations of the nonlinear schrodinger nls modified kdv mkdv mixed nls matrix nls matrix kdv matrix mkdv coupled nls coupled hirota coupled sasa satsuma and burgers equations we also discuss integrable discretizations of the sine gordon equation the massive thirring model and their generalizations

minimum bayes risk adaptive linear equalizers this paper introduces bayes risk expected loss as a criterion for linear equalization since the probability of error is equal to the bayes risk br for a particular binary loss function this work is a natural generalization of previous works on minimum probability of error pe equalizers adaptive equalization algorithms are developed that minimize the br like the minimum pe equalizers the br algorithms have low computational complexity which is comparable to that of the lms algorithm the advantage of the br criterion is that the loss function can be specified in a manner that accelerates adaptive equalizer convergence relative to the minimum pe adaptive algorithm as illustrated in simulation examples besides introducing a new criterion this paper provides another independent contribution to the field of pe minimizing equalization while most prior works focus on m ary qam type modulations with rectangular decision regions this paper uses upper bounds on the probabilities of certain events to yield tractable mathematics that apply to two dimensional constellations with arbitrarily shaped decision regions the resulting adaptive algorithm use the full information available in the phase of the error signal whereas previous algorithms use a quantized version of this error phase

asymptotic analysis of stochastic gradient based adaptive filtering algorithms with general cost functions this paper presents an analysis of stochastic gradient based adaptive algorithms with general cost functions the analysis holds under mild assumptions on the inputs and the cost function the method of analysis is based on an asymptotic analysis of fixed stepsize adaptive algorithms and gives almost sure results regarding the behavior of the parameter estimates whereas previous stochastic analyses typically considered mean and mean square behavior the parameter estimates are shown to enter a small neighborhood about the optimum value and remain there for a finite length of time furthermore almost sure exponential bounds are given for the rate of convergence of the parameter estimates the asymptotic distribution of the parameter estimates is shown to be gaussian with mean equal to the optimum value and covariance matrix that depends on the input statistics specific adaptive algorithms that fall under the framework of this paper are signed error least mean square lms dual sign lms quantized state lms least mean fourth dead zone algorithms momentum algorithms and leaky lms

length spectra and degeneration of flat metrics in this paper we consider flat metrics semi translation structures on surfaces of finite type there are two main results the first is a complete description of when a set of simple closed curves is spectrally rigid that is when the length vector determines a metric among the class of flat metrics secondly we give an embedding into the space of geodesic currents and use this to obtain a compactification for the space of flat metrics the geometric interpretation is that flat metrics degenerate to mixed structures on the surface part flat metric and part measured foliation

the spectrum of twisted dirac operators on compact flat manifolds let m be an orientable compact flat riemannian manifold endowed with a spin structure in this paper we determine the spectrum of dirac operators acting on smooth sections of twisted spinor bundles of m and we derive a formula for the corresponding eta series in the case of manifolds with holonomy group z k 2 we give a very simple expression for the multiplicities of eigenvalues that allows us to compute explicitly the series in terms of values of hurwitz zeta functions and the invariant we give the dimension of the space of harmonic spinors and characterize all z k 2 manifolds having asymmetric dirac spectrum furthermore we exhibit many examples of dirac isospectral pairs of z k 2 manifolds which do not satisfy other types of isospectrality in one of the main examples we construct a large family of dirac isospectral compact flat n manifolds pairwise nonhomeomorphic to each other of the order of a n

transplantation and jacobians of sunada isospectral riemann surfaces abstract we consider relations among the jacobians of isospectral compact riemann surfaces constructed using sunada s theorem we use a simple algebraic formulation of transplantation of holomorphic 1 forms and singular 1 cycles to obtain two main results first we obtain a geometric proof of a result of prasad and rajan that sunada isospectral riemann surfaces have isogenous jacobians second we determine a relationship weaker than isogeny that holds among the jacobians of sunada isospectral riemann surfaces when the jacobians extra structure as principally polarized abelian varieties is taken into account we also show all sunada isospectral manifolds have isomorphic real cohomology algebras finally we exhibit transplantation of cycles explicitly in a concrete example of a pair of isospectral riemann surfaces constructed by brooks and tse

diffractive orbits in isospectral billiards isospectral domains are non isometric regions of space for which the spectra of the laplace beltrami operator coincide in the two dimensional euclidean space instances of such domains have been given it has been proved for these examples that the length spectrum that is the set of the lengths of all periodic trajectories coincides as well however there is no one to one correspondence between the diffractive trajectories it will be shown here how the diffractive contributions to the green functions match nevertheless in a one to three correspondence

mber space time decision feedback equalization assisted multiuser detection for multiple antenna aided sdma systems this paper proposes a space time decision feedback equalization st dfe assisted multiuser detection mud scheme for multiple receiver antenna aided space division multiple access systems a minimum bit error rate mber design is invoked for the mud which is shown to be capable of improving the achievable bit error rate performance and enhancing the attainable system capacity over that of the standard minimum mean square error mmse design an adaptive implementation of the mber st dfe assisted mud is proposed using a stochastic gradient based least bit error rate algorithm which is demonstrated to consistently outperform the classical least mean square lms algorithm while achieving a lower computational complexity than the lms algorithm for the binary signalling scheme our simulation results demonstrate that the mber st dfe assisted mud is more robust to channel estimation errors as well as to potential error propagation imposed by decision feedback errors compared to the mmse st dfe assisted mud

adaptive minimum symbol error rate decision feedback equalization for multilevel pulse amplitude modulation the design of decision feedback equalizers dfes is typically based on the minimum mean square error mmse principle as this leads to effective adaptive implementation in the form of the least mean square algorithm it is well known however that in certain situations the mmse solution can be distinctly inferior to the optimal minimum symbol error rate mser solution we consider the mser design for multilevel pulse amplitude modulation block data adaptive implementation of the theoretical mser dfe solution is developed based on the parzen window estimate of a probability density function furthermore a sample by sample adaptive mser algorithm called the least symbol error rate lser is derived for adaptive equalization applications the proposed lser algorithm has a complexity that increases linearly with the equalizer length computer simulation is employed to evaluate the proposed alternative mser design for equalization application with multilevel signaling schemes

free energy as a geometric invariant the free energy plays a fundamental role in statistical and condensed matter physics a related notion of free energy plays an important role in the study of hyperbolic dynamical systems in this paper we introduce and study a natural notion of free energy for surfaces with variable negative curvature this geometric free energy encodes a new type of marked length spectrum of closed geodesics which lies between the well known marked length spectrum marked by the corresponding element of the fundamental group and the unmarked length spectrum we prove that the free energy parametrizes the boundary of the domain of convergence of a poincare series which also encodes this spectrum we also show that this new length spectrum or equivalently the geometric free energy is not an isometry invariant in the final section we use tools from multifractal analysis to effect a fine asymptotic comparison of word length and geodesic length of closed geodesics we hope that our geometric understanding of free energy will provide new insight into this fundamental physical and dynamical quantity

mathbb z _2 k manifolds are isospectral on forms we obtain a simple formula for the multiplicity of eigenvalues of the hodge laplace operator f acting on sections of the full exterior bundle lambda tm bigoplus p 0 n lambda p tm over an arbitrary compact flat riemannian n manifold m with holonomy group mathbb z 2 k 1 k n 1 this formula implies that any two such manifolds having isospectral lattices of translations are isospectral with respect to f as a consequence we construct a large family of pairwise f isospectral and nonhomeomorphic n manifolds of cardinality greater than 2 frac n 1 n 2 2

comment on resolving isospectral drums by counting nodal domains in gnutzmann et al 2005 j phys a math gen 38 8921 33 the authors studied the 4 parameter family of isospectral flat 4 tori t a b c d discovered by conway and sloane with a particular method of counting nodal domains they were able to distinguish these tori numerically by computing the corresponding nodal sequences relative to a few explicit tuples a b c d in this note we confirm the expectation expressed in gnutzmann et al 2005 j phys a math gen 38 8921 33 by proving analytically that their nodal count distinguishes any 4 tuple of distinct positive real numbers

an integrable coupled hybrid lattice and its exact solutions a coupled hybrid lattice system is proposed the model can be considered as one of the discrete forms of the coupled integrable korteweg de vries system which is a special case of some physically significant models the lax integrability of the coupled hybrid lattice system is proved by using a simple function expansion approach various novel types of exact solutions such as the kink soliton lattice the bell staggered soliton lattice the kink kink breather lattice and the soliton soliton breather lattice are found

integrable discretizations and soliton solution of kdv and mkdv equations abstract a method of integrable discretizations for soliton equations is presented which is based on the bilinear formalism taking the kdv equation and mkdv equation for example we discretize the corresponding bilinear equations through properly replacing hirota operator by the hyperbolic operator we also get the soliton solutions of these discrete equations by hirota s bilinear method