new homotopic factorization and symmetrization techniques for newton s and newton structured iteration we modify our earlier homotopic continuation process for iterative matrix inversion to improve the choice of the initial approximate inverse at every homotopic step this enables us to control the condition of the auxiliary matrices and to accelerate the convergence of the iteration the algorithm also extends our earlier approach where we factorized the input matrix into the product of better conditioned factors we accelerate our new algorithm in the case of a toeplitz like input comment on the extensions to the computations with other structured matrices such as cauchy pick and banded matrices and propose new techniques for the compression of the displacement of hermitian matrices

a family of space time block codes achieving full diversity with linear receivers in this paper we propose a design scheme for a family of space time block codes stbcs that achieve full diversity when linear receivers such as zero forcing zf or minimum mean square error mmse receivers are used new stbcs obtained based on this design scheme are characterized by their special structure that combines overlays orthogonal stbcs ostbcs and toeplitz codes together which are called group orthogonal toeplitz codes gotcs by choosing different parameters codes with different symbol rates and orthogonality can be obtained it is indicated that the existing stbcs achieving full diversity with linear receivers such as the toeplitz codes and overlapped alamouti codes oacs recently proposed in the literature and the ostbcs are three members of the gotcs with different parameters it is also shown that the time reversal space time block codes tr stbcs and delay diversity codes ddcs for frequency selective channels are equivalent to oacs and toeplitz codes respectively and thus they both can achieve full space frequency diversity with only linear receivers furthermore simulations show that with linear receivers gotcs outperforming the above mentioned three codes can be obtained from the proposed design scheme

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

the method of particular solutions for solving nonlinear poisson problems abstract based on the recent development in the method of particular solutions we re exam three approaches using different basis functions for solving nonlinear poisson problems we further propose to simplify the solution procedure by removing the insolvency condition when the radial basis functions are augmented with high order polynomial basis functions we also specify the deficiency of some of these methods and provide necessary remedy the traditional picard method is introduced to compare with the recent proposed methods using matlab optimization toolbox solver for solving nonlinear poisson equations ranking on these three approaches are given based on the results of numerical experiment

on optimal multilayer cyclotomic space time code designs high rate and large diversity product or coding advantage or coding gain or determinant distance or minimum product distance are two of the most important criteria often used for good space time code designs in recent linear lattice based space time code designs more attention is paid to the high rate criterion but less to the large diversity product criterion in this paper we consider these two criteria together for multilayer cyclotomic space time code designs in a previous paper we recently proposed a systematic cyclotomic diagonal space time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas where diagonal codes correspond to single layer codes in this paper in this paper we first propose a general multilayer cyclotomic space time codes we present a general optimality theorem for these infinitely many cyclotomic diagonal or single layer space time codes over general cyclotomic number rings for a general number of transmit antennas we then present optimal multilayer full rate cyclotomic space time code designs for two and three transmit antennas we also present an optimal two layer cyclotomic space time code design for three and four transmit antennas the optimality here is in the sense that for a fixed mean transmission signal power its diversity product is maximized or equivalently for a fixed diversity product its mean transmission signal power is minimized it should be emphasized that all the optimal multilayer cyclotomic space time codes presented in this paper have the nonvanishing determinant property

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

on space time code design with a conditional pic group decoding space time code designs based on a partial interference cancellation pic group decoding have been recently proposed the pic group decoding complexity depends on the group size and is between the lowest linear receiver complexity and the highest ml decoding complexity the symbol rate for a space time code achieving full diversity with the pic group decoding is also between those for the linear receivers and the ml decoding in this paper we propose a new decoding called conditional pic group decoding that is between the pic group decoding and the ml decoding with the proposed new decoding we obtain a new design criterion for space time codes to achieve full diversity which is also between the one with the pic group decoding and the one with the ml decoding we then present some designs that satisfy the new criterion and in the meantime have higher symbol rates than that for the pic group decoding

a note on computational algorithm for the inverse of a square matrix this short note gives some comments on computational algorithm for inverse of a square matrix considered in paper h saberi najafi m shams solary computational algorithms for computing the inverse of a square matrix quasi inverse of a non square matrix and block matrices appl math comput in press doi 10 1016 j amc 2006 05 108 and supplements the discussion on this topic

space time block codes achieving full diversity with linear receivers in most of the existing space time code designs achieving full diversity is based on maximum likelihood ml decoding at the receiver that is usually computationally expensive and may not have soft outputs recently zhang liu wong introduced toeplitz codes and showed that toeplitz codes achieve full diversity when a linear receiver zero forcing zf or minimum mean square error mmse receiver is used motivated from zhang liu wong s results on toeplitz codes in this paper we propose a design criterion for space time block codes stbc in which information symbols and their complex conjugates are linearly embedded to achieve full diversity when zf or mmse receiver is used the complex orthogonal stbc ostbc satisfy the criterion as one may expect we also show that the symbol rates of stbc under this criterion are upper bounded by 1 subsequently we propose a novel family of stbc that satisfy the criterion and thus achieve full diversity with zf or mmse receiver our newly proposed stbc are constructed by overlapping the 2times2 alamouti code and hence named overlapped alamouti codes in this paper the new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas simulation results show that overlapped alamouti codes significantly outperform toeplitz codes for all numbers of transmit antennas and also outperform ostbc when the number of transmit antennas is above 4

on the minimum decoding delay of balanced complex orthogonal designs a complex orthogonal design cod with parameter p n k is a combinatorial design used in space time block codes stbcs for stbcs n is the number of antennas k p is the rate and p is the decoding delay a class of rate 1 2 cods called balanced complex orthogonal designs bcods has been proposed by adams et al who constructed bcods with rate k p 1 2 and decoding delay p 2 m for n 2m furthermore they proved that the constructions have optimal decoding delay when m is congruent to 1 2 or 3 modulo 4 they conjectured that for the case m 0 mod 4 2 m is also a lower bound on p in this paper we prove this conjecture

block ilu factorization preconditioners for a block tridiagonal h matrix abstract we propose new parallelizable block ilu incomplete lu factorization preconditioners for a nonsymmetric block tridiagonal h matrix theoretical properties of these block ilu preconditioners are compared with those of block ilu preconditioners for the corresponding comparison matrix numerical results of the bicgstab using these block preconditioners are compared with those of the bicgstab using a standard ilu factorization preconditioner to see the effectiveness of the block ilu preconditioners lastly parallel computations of the block ilu preconditioners are carried out and evaluated on the cray c90

high rate and full diversity space time block codes with low complexity partial interference cancellation group decoding in this letter we propose a systematic design of space time block codes stbc which can achieve high rate and full diversity when the partial interference cancellation pic group decoding is used at receivers the proposed codes can be applied to any number of transmit antennas and admit a low decoding complexity while achieving full diversity for m transmit antennas in each codeword real and imaginary parts of pm complex information symbols are parsed into p diagonal layers and then encoded respectively with pic group decoding it is shown that the decoding complexity can be reduced to a joint decoding of m 2 real symbols in particular for 4 transmit antennas the code has real symbol pairwise i e single complex symbol decoding that achieves full diversity and the code rate is 4 3 simulation results demonstrate that the full diversity is offered by the newly proposed stbc with the pic group decoding

square matrix embeddable space time block codes for complex signal constellations space time block codes for providing transmit diversity in wireless communication systems are considered based on the principles of linearity and unitarity a complete classification of linear codes is given in the case when the symbol constellations are complex and the code is based on a square matrix or restriction of such by deleting columns antennas maximal rate delay optimal codes are constructed within this category the maximal rates allowed by linearity and unitarity fall off exponentially with the number of transmit antennas

power fluctuations in stochastic models of dissipative systems we consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions actually the associated large deviation functions of the time averaged injected power required to sustain a nontrivial stationary state we discuss the results and in particular draw from our results some general features shared by these distributions in realistic dissipative systems

finding generalized inverses by a fast and efficient numerical method in this paper a method with very high order of convergence is constructed and analyzed the method is used to compute generalized inverses the efficiency index has been employed to show its superiority numerical experiments re verify that the proposed iterative expression is more effective than the existing methods of the same type

quasi orthogonal time reversal space time block coding for frequency selective fading channels quasi orthogonal space time block codes qo stbcs are a powerful code family designed for more than two transmit antennas in contrast to their orthogonal counterparts designed for the same number of transmit antennas qo stbcs are able to provide full rate transmission rate while original qo stbcs enjoy only a partial diversity the recently proposed rotated versions of qo stbcs achieve the maximum diversity order which is equal to the number of transmit antennas since qo stbcs have been originally proposed for frequency flat fading channels it is a challenging design problem to apply them over frequency selective channels the dispersive nature of such channels results in intersymbol interference which needs to be carefully handled at the receiver in this paper we investigate time domain equalization for qo stbc exploiting the embedded quasi orthogonal structure to design low complexity receivers we also present diversity gains for the proposed scheme through pairwise error probability pep derivation and analysis which are further confirmed by monte carlo simulations

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

full diversity space frequency codes for frequency asynchronous cooperative relay networks with linear receivers in this paper we propose a family of distributed space frequency codes sfcs for frequency asynchronous cooperative relay networks with multiple carrier frequency offsets cfos and flat fading channels the codes have the special structures that the columns of each code matrix can be divided into several orthogonal groups and each group is stacked by several sub blocks with toeplitz structure these codes possess two interesting properties a even under the frequency asynchronous scenario the codes can namely if r relay nodes participate the cooperation adopting the proposed sfcs then at the destination node the achievable diversity order is r b only such as zero forcing zf and minimum mean square error mmse receivers are required to collect the full cooperative diversity instead of the maximum likelihood ml detector as utilized in most existing stc sfc schemes the codes in this family have different symbol rates orthogonality and performances for different numbers of relay nodes which can be adjusted by choosing different design parameters it is shown that frequency reversal sfc fr sfc and frequency shift sfc fs sfc proposed in previous papers are only two special members of the code family and new sfcs outperforming both of them are proposed

complete characterization of the equivalent mimo channel for quasi orthogonal space time codes recently a quasi orthogonal space time block code qstbc capable of achieving a significant fraction of the outage mutual information of a multiple input multiple output mimo wireless communication system for the case of nt 4 transmit and nr 1 receive antennas was proposed we generalize these results to nt 2n transmit and an arbitrary number of receive antennas furthermore we completely characterize the structure of the equivalent channel for the general case and show that for all nt 2n and nr the eigenvectors of the equivalent channel are fixed and independent from the channel realization furthermore the eigenvalues of the equivalent channel are independent identically distributed random variables each following a noncentral chi square distribution with 4nr degrees of freedom based on these important insights into the structure of the qstbc we derive tight lower and upper bounds for the outage probability achieved with qstbc finally by utilizing the special structure of the qstbc we propose a new transmit strategy which decouples the signals transmitted from different antennas in order to detect the symbols separately with a linear ml detector rather than joint detection an up to now only known advantage of orthogonal space time block codes ostbc

energy profile fluctuations in dissipative nonequilibrium stationary states the exact large deviation function ldf for the fluctuations of the energy density field is computed for a chain of ising or more generally potts spins driven by a zero temperature dissipative glauber dynamics and sustained in a nontrivial stationary regime by an arbitrary energy injection mechanism at the boundary of the system it is found that this ldf is independent of the dynamical details of the energy injection and that the energy fluctuations unlike conservative systems in a nonequilibrium state are not spatially correlated in the stationary regime

computational algorithms for computing the inverse of a square matrix quasi inverse of a non square matrix and block matrices in this paper we have written out some methods to find the inverse of a non singular matrix and also the quasi inverse of a singular matrix the corresponding algorithms have been used to solve the linear system of equations ax b as x a 1b a comparison table of the numerical results has been designed in each case to compare the implementation of the algorithms with each other the important part of the paper is presenting a block matrix method for finding the inverse matrix the block method finds the inverse matrix with a simple and easy algorithm

a modified chebyshev s iterative method with at least sixth order of convergence this paper is devoted to the construction and analysis of a high order variant of the classical chebyshev method the method has order of convergence at least six for simple roots the extension to system of equations and its semilocal convergence for nonlinear equations are presented finally an application to well known algebraic riccati equation is considered

exact large deviation functional of a stationary open driven diffusive system the asymmetric exclusion process we consider the asymmetric exclusion process asep in one dimension on sites i 1 n in contact at sites i 1 and i n with infinite particle reservoirs at densities a and b as a and b are varied the typical macroscopic steady state density profile x x a b obtained in the limit n l b a exhibits shocks and phase transitions here we derive an exact asymptotic expression for the probability of observing an arbitrary macroscopic profile rho x text p n rho x sim exp l mathcal f a b rho x rho a rho b so that mathcal f is the large deviation functional a quantity similar to the free energy of equilibrium systems we find as in the symmetric purely diffusive case q 1 treated in an earlier work that mathcal f is in general a non local functional of x unlike the symmetric case however the asymmetric case exhibits ranges of the parameters for which mathcal f rho x is not convex and others for which mathcal f rho x has discontinuities in its second derivatives at x x in the latter ranges the fluctuations of order 1 sqrt n in the density profile near x are then non gaussian and cannot be calculated from the large deviation function

the minimum decoding delay of maximum rate complex orthogonal space time block codes the growing demand for efficient wireless transmissions over fading channels motivated the development of space time block codes space time block codes built from generalized complex orthogonal designs are particularly attractive because the orthogonality permits a simple decoupled maximum likelihood decoding algorithm while achieving full transmit diversity the two main research problems for these complex orthogonal space time block codes costbcs have been to determine for any number of antennas the maximum rate and the minimum decoding delay for a maximum rate code the maximum rate for costbcs was determined by liang in 2003 this paper addresses the second fundamental problem by providing a tight lower bound on the decoding delay for maximum rate codes it is shown that for a maximum rate costbc for 2m 1 or 2m antennas a tight lower bound on decoding delay is r m 1 2m this lower bound on decoding delay is achievable when the number of antennas is congruent to 0 1 or 3 modulo 4 this paper also derives a tight lower bound on the number of variables required to construct a maximum rate costbc for any given number of antennas furthermore it is shown that if a maximum rate costbc has a decoding delay of r where r r les 2r then r 2r this is used to provide evidence that when the number of antennas is congruent to 2 modulo 4 the best achievable decoding delay is 2 m 1 2m

low delay high rate nonsquare complex orthogonal designs the maximal rate of a nonsquare complex orthogonal design for n transmit antennas is 1 2 1 n if n is even and 1 2 1 n 1 if n is odd and the codes have been constructed for all n by liang 2003 and lu 2005 to achieve this rate a lower bound on the decoding delay of maximal rate complex orthogonal designs has been obtained by adams 2007 and it is observed that liang s construction achieves the bound on delay for n equal to 1 and 3 modulo 4 while lu et al s construction achieves the bound for n 0 1 3 mod 4 for n 2 mod 4 adams 2010 have shown that the minimal decoding delay is twice the lower bound in which case both liang s and lu et al s construction achieve the minimum decoding delay for large value of n it is observed that the rate is close to half and the decoding delay is very large a class of rate 1 2 codes with low decoding delay for all n has been constructed by tarokh 1999 in this paper another class of rate 1 2 codes is constructed for all n in which case the decoding delay is half the decoding delay of the rate 1 2 codes given by tarokh this is achieved by giving first a general construction of square real orthogonal designs which includes as special cases the well known constructions of adams lax and phillips and the construction of geramita and pullman and then making use of it to obtain the desired rate 1 2 codes for the case of nine transmit antennas the proposed rate 1 2 code is shown to be of minimal delay the proposed construction results in designs with zero entries which may have high peak to average power ratio and it is shown that by appropriate postmultiplication a design with no zero entry can be obtained with no change in the code parameters

an optimal zero forcing pic group decoding for two user layered alamouti code the decoding complexity of the layered alamouti code with the maximum likelihood ml receiver is high partial interference cancellation pic group decoding is an attractive method to reduce the ml decoding complexity however different grouping schemes for the pic group decoding may have different performances in this letter by fully taking advantage of the alamouti code structure we analytically calculate the power gains of the information symbols after the pic for a grouping scheme where the zero forcing zf operator is used for the pic we then propose an optimal grouping scheme for the pic group decoding by proposing a criterion to choose the grouping schemes adaptively so that the power gains of the information symbols are maximized after the pic

full diversity codes for miso systems equipped with linear or ml detectors in this paper a general criterion for space time block codes stbc to achieve full diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas multiple input single output miso particularly the stbc with toeplitz structure satisfies this criterion and therefore enables full diversity further examination of this toeplitz stbc reveals the following important properties 1 the symbol transmission rate can be made to approach unity 2 applying the toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a nonvanishing determinant in addition if quadratic amplitude modulation qam is used as the signalling scheme then for independent miso flat fading channels the toeplitz codes is proved to approach the optimal diversity versus multiplexing tradeoff with a zero forcing zf receiver when the number of channel uses is large this is so far the first nonorthogonal stbc shown to achieve the optimal tradeoff for such a receiver on the other hand when maximum likelihood ml detection is employed in a miso system the toeplitz stbc achieves the maximum coding gain for independent channels when the channel fading coefficients are correlated the inherent transmission matrix in the toeplitz stbc can be designed to minimize the average worst case pairwise error probability

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

two designs of space time block codes achieving full diversity with partial interference cancellation group decoding a partial interference cancellation pic group decoding based space time block code stbc design criterion was recently proposed by guo and xia where the decoding complexity and the code rate traeoff is dealt when the full diversity is achieved in this paper two designs of stbc are proposed for any number of transmit antennas that can obtain full diversity when a pic group decoding with a particular grouping scheme is applied at receiver with the pic group decoding and an appropriate grouping scheme for the decoding the proposed stbc are shown to obtain the same diversity gain as the ml decoding but have a low decoding complexity the first proposed stbc is designed with multiple diagonal layers and it can obtain the full diversity for two layer design with the pic group decoding and the rate is up to 2 symbols per channel use with pic sic group decoding the first proposed stbc can obtain full diversity for any number of layers and the rate can be full the second proposed stbc can obtain full diversity and a rate up to 9 4 with the pic group decoding some code design examples are given and simulation results show that the newly proposed stbc can well address the rate performance complexity tradeoff of the mimo systems

single symbol ml decodable distributed stbcs for cooperative networks in this correspondence the distributed orthogonal space time block codes dostbcs which achieve the single symbol maximum likelihood ml decodability and full diversity order are first considered however systematic construction of the dostbcs is very hard since the noise covariance matrix is not diagonal in general thus some special dostbcs which have diagonal noise covariance matrices at the destination terminal are investigated these codes are referred to as the row monomial dostbcs an upper bound of the data rate of the row monomial dostbc is derived and it is approximately twice higher than that of the repetition based cooperative strategy furthermore systematic construction methods of the row monomial dostbcs achieving the upper bound of the data rate are developed when the number of relays and or the number of information bearing symbols are even

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

the final case of the decoding delay problem for maximum rate complex orthogonal designs complex orthogonal space time block codes costbcs based on generalized complex orthogonal designs cods have been successfully implemented in wireless systems with multiple transmit antennas and single or multiple receive antennas it has been shown that for a maximum rate cod with 2m 1 or 2m columns a lower bound on decoding delay is m 1 2m and this delay is achievable when the number of columns is congruent to 0 1 or 3 modulo 4 in this paper the final case is addressed and it is shown that when the number of columns is congruent to 2 modulo 4 the lower bound on decoding delay cannot be achieved in this case the shortest decoding delay a maximum rate cod can achieve is twice the lower bound new techniques for analyzing cods are introduced with connections to binary vector spaces

spatially modulated orthogonal space time block codes with non vanishing determinants this paper proposes a multiple input multiple output mimo transmission scheme for m ary modulations called spatially modulated orthogonal space time block coding sm ostbc based on the concept of spatial constellation sc codewords introduced by le at el in the proposed scheme transmit codeword matrices are generated by multiplying sc matrices with codewords constructed from orthogonal space time block codes o stbc the maximum spectral efficiency of the proposed scheme is equal to n t 2 log 2 m bpcu where n t is the number of transmit antennas and m is the modulation order the sc matrices provide a means of carrying information bits together with the o stbc codewords and allow the sm ostbc scheme to achieve second order transmit diversity by satisfying the non vanishing determinant property a systematic method to design the sc codewords for an even number of transmit antennas greater than 3 is presented a single stream maximum likelihood ml decoder which requires a low computational complexity thanks to the structure of the sm ostbc codewords and to the orthogonality of the o stbcs and a sphere decoder with further reduced signal processing complexity are developed the bit error rate ber performance of the proposed scheme is studied by using both theoretical union bound analysis and computer simulations finally simulation results are presented in order to compare ber performance energy efficiency and decoding complexity of the proposed scheme with those of several existing mimo transmission schemes

two generalized complex orthogonal space time block codes of rates 7 11 and 3 5 for 5 and 6 transmit antennas space time block codes from orthogonal designs have two advantages namely fast maximum likelihood ml decoding and full diversity rate 1 real pulse amplitude modulation pam space time codes real orthogonal designs for multiple transmit antennas have been constructed from the real hurwitz radon families which also provides the rate 1 2 complex quadrature amplitude modulation qam space time codes complex orthogonal designs for any number of transmit antennas rate 3 4 complex orthogonal designs space time codes for three and four transmit antennas have existed in the literature but no high rate 1 2 complex orthogonal designs for other numbers of transmit antennas exist we present rate 7 11 and rate 3 5 generalized complex orthogonal designs for five and six transmit antennas respectively

complex orthogonal designs with forbidden 2 times 2 submatrices complex orthogonal designs cods are used to construct space time block codes cod oz with parameter p n k is a p n matrix where nonzero entries are filled zi by zi i 1 2 k or such that ozhoz z1 2 z2 2 zk 2 in n define oz a first type cod if and only if oz does not contain submatrix zj 0 0 zj or zj 0 0 zj it is already known that all cods with maximal rate i e maximal k p are of the first type in this paper we will determine all achievable parameters p n k of first type cod as well as all their possible structures the existence of parameters is proved by explicit form constructions new cods with parameters p n k n w 1 n w 1 n n w for 0 w n are constructed which demonstrate the possibility of sacrificing code rate to reduce decoding delay it is worth mentioning that all maximal rate minimal delay cods are contained in our constructions and their uniqueness under equivalence operation is proved

closed form designs of complex orthogonal space time block codes of rates k 1 2k for 2k 1 or 2k transmit antennas in this correspondence we present systematic and closed form constructions of complex orthogonal space time block codes from complex orthogonal designs of rates k 1 2k for 2k 1 or 2k transmit antennas for any positive integer k

space time block codes a maximum snr approach in tarokh et al 1999 space time block codes were introduced to obtain coded diversity for a multiple antenna communication system in this work we cast space time codes in an optimal signal to noise ratio snr framework and show that they achieve the maximum snr and in fact they correspond to a generalized maximal ratio combiner the maximum snr framework also helps in calculating the distribution of the snr and in deriving explicit expressions for bit error rates we bring out the connection between the theory of amicable orthogonal designs and space time codes based on this we give a much simpler proof to one of the main theorems on space time codes for complex symbols we present a rate 1 2 code for complex symbols which has a smaller delay than the code already known we also present another rate 3 4 code which is simpler than the one already known in the sense it does not involve additions or multiplications we also point out the connection between generalized real designs and generalized orthogonal designs

on the diagonal approximation of full matrices in this paper the construction of diagonal matrices in some sense approximating the inverse of a given square matrix is described the matrices are constructed using the well known computer algebra system maple the techniques we show are applicable to square matrices in general results are given for use in parallel diagonal implicit runge kutta pdirk methods for an s stage radau iia corrector we conjecture s possibilities for the diagonal matrices

additive preconditioning and aggregation in matrix computations we combine our novel svd free additive preconditioning with aggregation and other relevant techniques to facilitate the solution of a linear system of equations and other fundamental matrix computations our analysis and experiments show the power of our algorithms guide us in selecting most effective policies of preconditioning and aggregation and provide some new insights into these and related subjects compared to the popular svd based multiplicative preconditioners our additive preconditioners are generated more readily and for a much larger class of matrices furthermore they better preserve matrix structure and sparseness and have a wider range of applications e g they facilitate the solution of a consistent singular linear system of equations and of the eigenproblem

on the relation of ostbc and code rate one qstbc average rate ber and coding gain recently the statistical properties of the equivalent channel representation of a multiple input multiple output mimo system employing code rate one quasi orthogonal space time block codes qstbc which are constructed by using orthogonal space time block codes ostbc as building elements was characterized based on these characterizations we analyze the average rate or mean mutual information the bit error rate performance and the coding gain achieved with qstbc for any number of receive and nt 2n n ges 2 transmit antennas first we study constellation rotation using a systematic approach in order to maximize the coding gain and to achieve full diversity qstbc moreover we present an upper bound on the coding gain we derive a lower and upper bound on the ber performance for qstbc furthermore we analyze the average rate achievable with qstbc in case of an uninformed transmitter and also the case in which the transmitter knows the mean channel matrix whereas the receiver has perfect csi along with the analysis we compare all the results of these performance measures with the results achieved with ostbc revealing important connections between ostbc and qstbc for example the coding gain of a qstbc is upper bounded by the coding gain of the underlying ostbc also the ber of a qstbc for nt transmit and nr receive antennas is tightly lower bounded by the ber of a full diversity providing intersymbol interference free system in addition to that we show that gains in terms of average rate by using a qstbc and thus with higher nt instead of the underlying ostbc are only attainable if the available channel state information at the transmitter csit is utilized finally we illustrate our theoretical results using numerical simulations

exact exponent for the number of persistent spins in the zero temperature dynamics of the one dimensional potts model for the zero temperature glauber dynamics of theq state potts model the fractionr q t of spins which never flip up to timet decays like a power lawr q t t q when the initial condition is random by mapping the problem onto an exactly soluble one species coagulation model a a a or alternatively by transforming the problem into a free fermion model we obtain the exact expression of q for all values ofq the exponent q is in general irrational 3 0 53795082 4 0 63151575 with the exception ofq 2 andq for which 2 3 8 and 1

an exactly solvable dissipative transport model we introduce a class of one dimensional lattice models in which a quantity which may be thought of as an energy is either transported from one site to a neighbouring one or locally dissipated transport is controlled by a continuous bias parameter q which allows us to study symmetric as well as asymmetric cases we derive sufficient conditions for the factorization of the n body stationary distribution and give an explicit solution for the latter before briefly discussing physically relevant situations

exact diffusion constant for one dimensional asymmetric exclusion models the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions is considered on a ring of size n the steady state of this system is known all configurations have equal weight which allows for easy computation of the average velocity of a particle in the steady state here an exact expression for the diffusion constant of a particle is obtained for arbitrary number of particles and system size by using a matrix formulation two limits of infinite system size n are discussed firstly when the number of particles remains finite as n to infinity the diffusion constant remains dependent on the exact number of particles due to correlations between successive collisions secondly when the density p of particles is non zero i e when the number of particles is equal to n rho as n to infinity the diffusion constant scales as n 12 the exponent 1 2 is related to the dynamic exponent z 3 2 of the kpz equation in 1 1 dimensions

orthogonal like space time coded cpm systems with fast decoding for three and four transmit antennas the alamouti orthogonal space time block code for two transmit antennas was designed primarily for qam and psk modulations and we have previously generalized it for the continuous phase modulation cpm denoted as ost cpm by maintaining the orthogonality for the fast ml decoding demodulation and the phase continuity of two signals from two transmit antennas in this paper we design orthogonal like space time coded cpm systems for three and four transmit antennas based on orthogonal and quasi orthogonal space time codes although the signals from transmit antennas in the proposed orthogonal like space time coded cpm systems are not orthogonal the fast decoding demodulation is maintained like the two transmit antenna case simulation results show that the performance of the proposed orthogonal like space time coded cpm systems for four transmit antennas is much better than that of the ost cpm systems for two transmit antennas

an iterative method for computing the approximate inverse of a square matrix and the moore penrose inverse of a non square matrix in this paper an iterative scheme is proposed to find the roots of a nonlinear equation it is shown that this iterative method has fourth order convergence in the neighborhood of the root based on this iterative scheme we propose the main contribution of this paper as a new high order computational algorithm for finding an approximate inverse of a square matrix the analytical discussions show that this algorithm has fourth order convergence as well next the iterative method will be extended by theoretical analysis to find the pseudo inverse also known as the moore penrose inverse of a singular or rectangular matrix numerical examples are also made on some practical problems to reveal the efficiency of the new algorithm for computing a robust approximate inverse of a real or complex matrix

approximate iterations for structured matrices important matrix valued functions f a are e g the inverse a 1 the square root sqrt a and the sign function their evaluation for large matrices arising from pdes is not an easy task and needs techniques exploiting appropriate structures of the matrices a and f a often f a possesses this structure only approximately however intermediate matrices arising during the evaluation may lose the structure of the initial matrix this would make the computations inefficient and even infeasible however the main result of this paper is that an iterative fixed point like process for the evaluation of f a can be transformed under certain general assumptions into another process which preserves the convergence rate and benefits from the underlying structure it is shown how this result applies to matrices in a tensor format with a bounded tensor rank and to the structure of the hierarchical matrix technique we demonstrate our results by verifying all requirements in the case of the iterative computation of a 1 and sqrt a

an efficient computation of generalized inverse of a matrix abstract we propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves 18th order of convergence by using only seven matrix multiplications per iteration loop this yields a high efficiency index for that computational task the algorithm has a relatively mild numerical instability and we stabilize it at the price of adding two extra matrix multiplications per iteration loop this implies an efficiency index that exceeds the known record for numerically stable iterations for this task which means substantial acceleration of the long standing algorithms for an important problem of numerical linear algebra our numerical tests cover a variety of examples in the category of generalized inverses such as drazin case rectangular case and preconditioning of linear systems the test results are in good accordance with our formal study

a counterexample for the open problem on the minimal delays of orthogonal designs with maximal rates x liang systematically investigated orthogonal designs with maximal rates gave the maximal rates of complex orthogonal designs and a concrete construction procedure for complex orthogonal designs with the maximal rates he also posed an open problem on the minimal decoding delays of complex orthogonal designs with maximal rates and proved that the problem is correct for less than or equal to six transmit antennas in this correspondence we give a counterexample for the open problem for n 8 and prove that the minimal delay for complex orthogonal designs with eight columns is 56 hence we give a negative answer for the open problem

geometric constructions of iterative functions to solve nonlinear equations in this paper we present the geometrical interpretation of several iterative methods to solve a nonlinear scalar equation in addition we also review the extension to general banach spaces and some computational aspects of these methods

an improvement on a new upper bound for moduli of eigenvalues of iterative matrices in this paper some improvements on int j comput math 80 june 2003 799 803 are presented for a bound for moduli of eigenvalues of iterative matrices and subsequently we investigate the relationships among them and show that the new bounds are better than the earlier ones int j comput math 53 1994 203 217 j comput math 7 2 1986 41 46 int j comput math 80 june 2003 799 803 under some conditions

an efficient maps for solving fourth order partial differential equations using trigonometric functions abstract in this paper we apply the method of approximate particular solutions maps based on the trigonometric functions to solve the fourth order partial differential equations pdes through the use of particular solutions of two second order differential equations the derivation of the closed form particular solutions for higher order pdes is a challenge and could be tedious such task can be achieved by a simple algebraic procedure to alleviate the difficulty of the derivation of particular solutions for fourth order pdes since the closed form particular solutions for the second order pdes with constant coefficients are known the proposed solution procedure is simple and direct five numerical examples are illustrated to demonstrate the feasibility and effectiveness of the proposed method

on the nonexistence of rate one generalized complex orthogonal designs orthogonal space time block coding proposed recently by alamouti 1998 and tarokh et al 1999 is a promising scheme for information transmission over rayleigh fading channels using multiple transmit antennas due to its favorable characteristics of having full transmit diversity and a decoupled maximum likelihood ml decoding algorithm tarokh et al extended the theory of classical orthogonal designs to the theory of generalized real or complex linear processing orthogonal designs and then applied the theory of generalized orthogonal designs to construct space time block codes stbc with the maximum possible diversity order while having a simple decoding algorithm for any given number of transmit and receive antennas it has been known that the stbc constructed in this way can achieve the maximum possible rate of one for every number of transmit antennas using any arbitrary real constellation and for two transmit antennas using any arbitrary complex constellation contrary to this in this correspondence we prove that there does not exist rate one stbc from generalized complex linear processing orthogonal designs for more than two transmit antennas using any arbitrary complex constellation

homotopic residual correction processes we present and analyze homotopic continuation residual correction algorithms for the computation of matrix inverses for complex indefinite hermitian input matrices our homotopic methods substantially accelerate the known nonhomotopic algorithms unlike the nonhomotopic case our algorithms require no pre estimation of the smallest singular value of an input matrix furthermore we guarantee rapid convergence to the inverses of well conditioned structured matrices even where no good initial approximation is available in particular we yield the inverse of a well conditioned n x n matrix with a structure of toeplitz hankel type in o n log 3 n flops for a large class of input matrices our methods can be extended to computing numerically the generalized inverses our numerical experiments confirm the validity of our analysis and the efficiency of the presented algorithms for well conditioned input matrices and furnished us with the proper values of the parameters that define our algorithms

a two step inexact newton chebyshev like method for inverse eigenvalue problems abstract a two step inexact newton chebyshev like method is proposed to solve inverse eigenvalue problems unlike general newton type methods which need to invert the jacobian matrix that may lead to an unexpected instability the proposed method can guarantee the numerical stability by exploiting the chebyshev method to approximate the inverse of the jacobian matrix theoretically we prove that the proposed method converges cubically numerical examples are given to demonstrate the effectiveness of our method

finite dimensional representations of the quadratic algebra applications to the exclusion process we study the one dimensional partially asymmetric simple exclusion process asep with open boundaries that describes a system of hard core particles hopping stochastically on a chain coupled to reservoirs at both ends derrida and coworkers showed in 1993 that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra closely related to the deformed oscillator algebra we construct all finite dimensional irreducible representations of this algebra this enables us to compute the stationary bulk density as well as all correlation lengths for the asep on a set of special curves of the phase diagram

comparisons of weak regular splittings and multisplitting methods comparison results for weak regular splittings of monotone matrices are derived as an application we get upper and lower bounds for the convergence rate of iterative procedures based on multisplittings this yields a very simple proof of results of neumann plemmons on upper bounds and establishes lower bounds which has in special cases been conjectured by these authors

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

single symbol ml decoding for orthogonal and quasi orthogonal stbc in clipped mimo ofdm systems using a clipping noise model with gaussian approximation an efficient way to reduce the peak to average power ratio papr in ofdm systems is clipping after the clipping in an mimo ofdm system the additive noise may not be white in this paper we develop fast single symbol ml decoding algorithms for orthogonal space time block codes ostbc and linearly transformed quasi orthogonal space time block codes qostbc in clipped mimo ofdm systems by using a clipping noise model with gaussian approximation by using the statistics of the clipping distortions our newly developed fast ml decoding algorithms improve the performance for clipped mimo ofdm systems with ostbc and qostbc while the decoding complexities are not increased simulation results are presented to illustrate the improvement

lower bounds on the minimal delay of complex orthogonal designs with maximal rates the maximal rates and the minimal delays are basic problems of space time block codes from complex orthogonal designs liang systematically solved the problem on the maximal rates of complex orthogonal designs and posed an open problem on the minimal delays recently the authors gave the negative answer for the open problem in this letter we give lower bounds on the minimal delays

upper bounds of rates of complex orthogonal space time block codes we derive some upper bounds of the rates of generalized complex orthogonal space time block codes we first present some new properties of complex orthogonal designs and then show that the rates of complex orthogonal space time block codes for more than two transmit antennas are upper bounded by 3 4 we show that the rates of generalized complex orthogonal space time block codes for more than two transmit antennas are upper bounded by 4 5 where the norms of column vectors may not be necessarily the same we also present another upper bound under a certain condition for a generalized complex orthogonal design its variables are not restricted to any alphabet sets but are on the whole complex plane a generalized complex orthogonal design with variables over some alphabet sets on the complex plane is also considered we obtain a condition on the alphabet sets such that a generalized complex orthogonal design with variables over these alphabet sets is also a conventional generalized complex orthogonal design and therefore the above upper bounds on its rate also hold we show that commonly used quadrature amplitude modulation qam constellations of sizes above 4 satisfy this condition

systematic and optimal cyclotomic lattices and diagonal space time block code designs in this correspondence a new and systematic design of cyclotomic lattices with full diversity is proposed by using some algebraic number theory this design provides infinitely many full diversity cyclotomic lattices for a given lattice size based on the packing theory and the concrete form of the design optimal cyclotomic lattices are presented by minimizing the mean transmission signal power for a given minimum diversity product or equivalently maximizing the minimum product for a given mean transmission signal power the newly proposed cyclotomic lattices can be applied to both space time code designs for multi antenna systems and linear precode design for signal space diversity in single antenna systems over fast rayleigh fading channels although there are some cyclotomic lattices space time codes existing in the literature most of them are not optimal

signal constellations for quasi orthogonal space time block codes with full diversity space time block codes stbcs from orthogonal designs proposed by alamouti and tarokh jafarkhani calderbank have attracted considerable attention lately due to their fast maximum likelihood ml decoding and full diversity however the maximum symbol transmission rate of an stbc from complex orthogonal designs for complex signals is only 3 4 for three and four transmit antennas and it is difficult to construct complex orthogonal designs with rate higher than 1 2 for more than four transmit antennas recently jafarkhani tirkkonen boariu hottinen and papadias foschini proposed stbcs from quasi orthogonal designs where the orthogonality is relaxed to provide higher symbol transmission rates with the quasi orthogonal structure the quasi orthogonal stbcs still have a fast ml decoding but do not have the full diversity the performance of these codes is better than that of the codes from orthogonal designs at low signal to noise ratio snr but worse at high snr this is due to the fact that the slope of the performance curve depends on the diversity it is desired to have the quasi orthogonal stbcs with full diversity to ensure good performance at high snr in this paper we achieve this goal by properly choosing the signal constellations specifically we propose that half of the symbols in a quasi orthogonal design are chosen from a signal constellation set a and the other half of them are chosen from a rotated constellation e sup j spl phi a the resulting stbcs can guarantee both full diversity and fast ml decoding moreover we obtain the optimum selections of the rotation angles spl phi for some commonly used signal constellations simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high snrs

low ml decoding complexity stbcs via codes over the klein group in this paper we give a new framework for constructing low ml decoding complexity space time block codes stbcs using codes over the klein group k almost all known low ml decoding complexity stbcs can be obtained via this approach new full diversity stbcs with low ml decoding complexity and cubic shaping property are constructed via codes over k for number of transmit antennas n 2m m 1 and rates r 1 complex symbols per channel use when r n the new stbcs are information lossless as well the new class of stbcs have the least known ml decoding complexity among all the codes available in the literature for a large set of n r pairs

on full diversity space time block codes with partial interference cancellation group decoding in this paper we propose a partial interference cancellation pic group decoding strategy scheme for linear dispersive space time block codes stbc and a design criterion for the codes to achieve full diversity when the pic group decoding is used at the receiver a pic group decoding decodes the symbols embedded in an stbc by dividing them into several groups and decoding each group separately after a linear pic operation is implemented it can be viewed as an intermediate decoding between the maximum likelihood ml receiver that decodes all the embedded symbols together i e all the embedded symbols are in a single group and the zero forcing zf receiver that decodes all the embedded symbols separately and independently i e each group has and only has one embedded symbol after the zf operation is implemented the pic group decoding provides a framework to adjust the complexity performance tradeoff by choosing the sizes of the information symbol groups our proposed design criterion group independence for the pic group decoding to achieve full diversity is an intermediate condition between the loosest ml full rank criterion of codewords and the strongest zf linear independence condition of the column vectors in the equivalent channel matrix we also propose asymptotic optimal ao group decoding algorithm which is an intermediate decoding between the mmse decoding algorithm and the ml decoding algorithm the design criterion for the pic group decoding can be applied to the ao group decoding algorithm because of its asymptotic optimality it is well known that the symbol rate for a full rank linear stbc can be full i e nt for nt transmit antennas it has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver the intermediate criterion proposed in this paper provides the possibility for codes of rates between nt and 1 that achieve full diversity with the pic group decoding this therefore provides a complexity performance rate tradeoff some design examples are given

chebyshev type methods and preconditioning techniques recently a newton s iterative method is attracting more and more attention from various fields of science and engineering this method is generally quadratically convergent in this paper some chebyshev type methods with the third order convergence are analyzed in detail and used to compute approximate inverse preconditioners for solving the linear system ax b theoretic analysis and numerical experiments show that chebyshev s method is more effective than newton s one in the case of constructing approximate inverse preconditioners

high rate full diversity space time frequency codes for broadband mimo block fading channels a systematic design of high rate full diversity space time frequency stf codes is proposed for multiple input multiple output frequency selective block fading channels it is shown that the proposed stf codes can achieve rate mt and full diversity mtmrmbl i e the product of the number of transmit antennas mt receive antennas mr fading blocks mb and channel taps l the proposed stf codes are constructed from a layered algebraic design where each layer of algebraic coded symbols are parsed into different transmit antennas orthogonal frequency division multiplexing tones and fading blocks without rate loss simulation results show that the proposed stf codes achieve higher diversity gain in block fading channels than some typical space frequency codes

on optimal quasi orthogonal space time block codes with minimum decoding complexity orthogonal space time block codes ostbc from orthogonal designs have both advantages of complex symbol wise maximum likelihood ml decoding and full diversity however their symbol rates are upper bounded by 3 4 for more than two antennas for complex symbols to increase the symbol rates they have been generalized to quasi orthogonal space time block codes qostbc in the literature but the diversity order is reduced by half and the complex symbol wise ml decoding is significantly increased to complex symbol pair wise pair of complex symbols ml decoding the qostbc has been modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pair wise ml decoding the optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equal literal triangular lattices have been found by su xia where the optimality means the optimal diversity product or product distance qostbc has also been modified by yuen guan tjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pair wise ml decoding the same complexity as complex symbol wise decoding and the optimal rotation angle for square and rectangular qam constellations has been found in this paper we systematically study general linear transformations of information symbols for qostbc to have both full diversity and real symbol pair wise ml decoding we present the optimal transformation matrices among all possible linear transformations not necessarily symbol rotations of information symbols for qostbc with real symbol pair wise ml decoding such that the optimal diversity product is achieved for both general square qam and general rectangular qam signal constellations furthermore our newly proposed optimal linear transformations for qostbc also work for general qam constellations in the sense that qostbc have full diversity with good diversity product property and real symbol pair wise ml decoding interestingly the optimal diversity products for square qam constellations from the optimal linear transformations of information symbols found in this paper coincide with the ones presented by yuen guan tjhung by using their optimal rotations however the optimal diversity products for nonsquare rectangular qam constellations from the optimal linear transformations of information symbols found in this paper are better than the ones presented by yuen guan tjhung by using their optimal rotations in this paper we also present the optimal transformations for the co ordinate interleaved orthogonal designs ciod proposed by khan rajan for rectangular qam constellations

third order iterative methods under kantorovich conditions we study a class of third order iterative methods for nonlinear equations on banach spaces a characterization of the convergence under kantorovich type conditions and optimal estimates of the error are found though in general these methods are not very extended due to their computational costs we will show some examples in which they are competitive and even cheaper than other simpler methods we center our analysis in both analytic and computational aspects

a geometric construction of iterative functions of order three to solve nonlinear equations in this paper we consider a geometric construction of iteration functions of order three to develop cubically convergent iterative methods for solving nonlinear equations this construction can be applied to any iteration function of order two to develop an iteration function of order three some examples are given of deriving several third order iteration methods and several numerical results follow to illustrate the performance of the derived methods

stair matrices and their generalizations with applications to iterative methods i a generalization of the successive overrelaxation method stair matrices and their generalizations are introduced some properties of the matrices are presented like triangular matrices this class of matrices provides bases of matrix splittings for iterative methods a remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation in particular a generalization of the successive overrelaxation sor method is introduced the sor theory on determination of the optimal parameter is extended to the generalized method to include a wide class of matrices the asymptotic rate of convergence of the new method is derived for hermitian positive definite matrices using bounds of the eigenvalues of jacobi matrices and numerical radius finally numerical tests are presented to corroborate the obtained results

injected power fluctuations in langevin equation in this paper we consider the langevin equation from an unusual point of view that is as an archetype for a dissipative system driven out of equilibrium by an external excitation using path integral method we compute exactly the probability density function of the power averaged over a time interval of length injected and dissipated by the random force into a brownian particle driven by a langevin equation the resulting distribution as well as the associated large deviation function display strong asymmetry whose origin is explained connections with the so called fluctuation theorem are thereafter discussed finally considering langevin equations with a pinning potential we show that the large deviation function associated with the injected power is completely insensitive to the presence of a potential

current fluctuations in the one dimensional symmetric exclusion process with open boundaries we calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of n sites with open boundary conditions for large system size n the generating function of the integrated current depends on the densities a and b of the two reservoirs and on the fugacity z the parameter conjugated to the integrated current through a single parameter based on our expressions for these first four cumulants we make a conjecture which leads to a prediction for all the higher cumulants in the case a 1 and b 0 our conjecture gives the same universal distribution as the one obtained by lee levitov and yakovets for one dimensional quantum conductors in the metallic regime

exact results for an asymmetric annihilation process with open boundaries we consider a nonequilibrium reaction diffusion model on a finite one dimensional lattice with bulk and boundary dynamics inspired by the glauber dynamics of the ising model we show that the model has a rich algebraic structure that we use to calculate its properties in particular we show that the markov dynamics for a system of a given size can be embedded into the dynamics of systems of higher sizes this remark leads us to devise a technique which we call the transfer matrix ansatz that allows us to determine the steady state distribution and correlation functions furthermore we show that the disorder variables satisfy very simple properties and we give a conjecture for the characteristic polynomial of markov matrices finally we compare the transfer matrix ansatz used here with the matrix product representation of the steady state of one dimensional stochastic models

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally

singularity wielandt s lemma and singular values in this study some upper and lower bounds for singular values of a general complex matrix are investigated according to singularity and wielandt s lemma of matrices especially some relationships between the singular values of the matrix a and its block norm matrix are established based on these relationships one may obtain the effective estimates for the singular values of large matrices by using the lower dimension norm matrices in addition a small error in piazza 2002 g piazza t politi an upper bound for the condition number of a matrix in spectral norm j comput appl math 143 1 2002 141 144 is also corrected some numerical experiments on saddle point problems show that these results are simple and sharp under suitable conditions