the bunch kaufman factorization of symmetric matrices signature similar to sign regular matrices abstract the bunch kaufman pivoting strategy is a most commonly used method in practice to factor symmetric indefinite matrices however this method in general may destroy the band structure of banded matrices and its growth factor bound of 2 57 n 1 can almost be attained in this paper we investigate the behavior of the method for factorizing symmetric indefinite matrices that are signature similar to sign regular matrices with signature the growth factor bound depending on flips in the signature is derived for factorizing such banded matrices if the bunch kaufman pivoting strategy is modified as suggested by sorensen and van loan then not only do the same growth factor bounds hold but also the bandwidth is nicely preserved

a note on a conjecture on permanents abstract let kn denote the set of all n n nonnegative matrices whose entries have sum n and let be a real function on kn defined by x ni 1 nj 1xij nj 1 ni 1xij per x for x xij kn a matrix a kn is called a maximizing matrix on kn if a x for all x kn it is conjectured that jn 1 n n n is the unique maximizing matrix on kn in this note the following are proved i if a is a positive maximizing matrix then a jn ii if a is a row stochastic maximizing matrix then a jn iii every row sum and every column sum of a maximizing matrix lies between 1 2 n nn and 1 n 1 2 n nn iv for any p s d symmetric a kn a 2 n nn with equality iff a jn v attains a strict local maximum on kn at jn

on the symmetric doubly stochastic inverse eigenvalue problem abstract let 1 2 n be a list of real numbers the symmetric doubly stochastic inverse eigenvalue problem hereafter sdiep is to determine the list which can occur as the spectrum of an n n symmetric doubly stochastic matrix a if the matrix a is positive we can necessarily obtain a subproblem symmetric positive doubly stochastic inverse eigenvalue problem hereafter spdiep of the sdiep in this paper we give some sufficient conditions for the sdiep and spdiep and prove that the set formed by the spectra of all n n symmetric positive doubly stochastic matrices is non convex for n 4

quasi ldu factorization of nonsingular totally nonpositive matrices abstract let a a ij r n n be a nonsingular totally nonpositive matrix in this paper we describe some properties of these matrices when a11 0 and obtain a characterization in terms of the quasi ldu factorization of a where l is a block lower triangular matrix d is a diagonal matrix and u is a unit upper triangular matrix

almost strictly sign regular rectangular matrices abstract almost strictly sign regular matrices are sign regular matrices with a special zero pattern and whose nontrivial minors are nonzero in this paper we provide several properties of almost strictly sign regular rectangular matrices of maximal rank and analyze their q r factorization

low density parity check codes based on finite geometries a rediscovery and new results this paper presents a geometric approach to the construction of low density parity check ldpc codes four classes of ldpc codes are constructed based on the lines and points of euclidean and projective geometries over finite fields codes of these four classes have good minimum distances and their tanner 1981 graphs have girth 6 finite geometry ldpc codes can be decoded in various ways ranging from low to high decoding complexity and from reasonably good to very good performance they perform very well with iterative decoding furthermore they can be put in either cyclic or quasi cyclic form consequently their encoding can be achieved in linear time and implemented with simple feedback shift registers this advantage is not shared by other ldpc codes in general and is important in practice finite geometry ldpc codes can be extended and shortened in various ways to obtain other good ldpc codes several techniques of extension and shortening are presented long extended finite geometry ldpc codes have been constructed and they achieve a performance only a few tenths of a decibel away from the shannon theoretical limit with iterative decoding

total nonpositivity of nonsingular matrices in this paper nonsingular totally nonpositive matrices are studied and new characterizations are provided in terms of the signs of minors with consecutive initial rows or consecutive initial columns these characterizations extend an existing characterization that uses some restrictive hypotheses

doubly stochastic matrices whose powers eventually stop abstract in this note we characterize doubly stochastic matrices a whose powers a a 2 a 3 eventually stop i e a p a p 1 for some positive integer p the characterization enables us to determine the set of all such matrices

growth factors of pivoting strategies associated with neville elimination neville elimination is a direct method for solving linear systems several pivoting strategies for neville elimination including pairwise pivoting are analyzed bounds for two different kinds of growth factors are provided finally an approximation of the average normalized growth factor associated with several pivoting strategies is computed and analyzed using random matrices

partitioning the edge set of a bipartite graph into chain packings complexity of some variations abstract an extension of the decomposition theorem of birkhoff von neumann theorem is given for the case where entries can be positive or negative the special case of an integral matrix is discussed and some balancing properties which are trivial for the classical case non negative entries only in the matrix are shown to be np complete some relaxations are presented for solving the balancing problem

the locally finite part of the dual coalgebra of quantized irreducible flag manifolds for quantized irreducible flag manifolds the locally finite part of the dual coalgebra is shown to coincide with a natural quotient coalgebra overline u of u q mathfrak g on the way the coradical filtration of overline u is determined a graded version of the duality between overline u and the quantized coordinate ring is established this leads to a natural construction of several examples of quantized vector spaces as an application covariant first order differential calculi on quantized irreducible flag manifolds are classified

the dirac operator on compact quantum groups for the q deformation gq 0 q 1 of any simply connected simple compact lie group g we construct an equivariant spectral triple which is an isospectral deformation of that defined by the dirac operator d on g our quantum dirac operator dq is a unitary twist of d considered as an element of ug cl g the commutator of dq with a regular function on gq consists of two parts one is a twist of a classical commutator and so is automatically bounded the second is expressed in terms of the commutator of the associator with an extension of d we show that in the case of the drinfeld associator the latter commutator is also bounded

a stable test for strict sign regularity a stable test to check if a given matrix is strictly sign regular is provided among other nice properties we prove that it has an optimal growth factor the test is compared with other alternative tests appearing in the literature and its advantages are shown

on the extension of some total positivity inequalities abstract some inequalities recently obtained for totally positive matrices are extended to more general classes of matrices among these larger classes of matrices sign consistent sign regular and matrices with signed bidiagonal decomposition are considered the class of matrices with a signed bidiagonal decomposition contains the nonsingular totally positive matrices and their inverses

conditioning and accurate computations with pascal matrices a result on the ill conditioning of pascal matrices is proved however it is shown that bidiagonal factorizations of pascal matrices can be applied to perform computations with high relative accuracy

general forms for maximal ratio diversity with weighting errors this paper introduces two general relationships concerning the output signal to noise ratio distribution and the bit error performance of the nonideal maximal ratio combiner the imperfections are modeled as gaussian distributed weighting errors in the channel gain estimates used for coherent combination the general form for the bit error rate is applicable to any modulation format

qr decomposition of almost strictly sign regular matrices in this paper l d u factorization of nonsingular sign regular and almost strictly sign regular matrices is analyzed besides nonsingular almost strictly sign regular matrices are characterized through the q r factorization illustrative numerical examples are included

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

characterizations of jacobi sign regular matrices abstract several characterizations of jacobi nonsingular sign regular matrices are presented moreover a stable test of o n elementary operations is obtained to check if an n n jacobi nonsingular matrix is sign regular

on minimum wer performance of a class of ldpc codes for the bsc e under extended bounded distance decoding we study the word error rate wer performance and the wer minimizing decision thresholds plusmnt for the class of row column diagonal rcd array codes and their generalizations on the binary symmetric channel with erasures bsc e where decoding is via an extended bounded distance decoder e bdd this model applies to very high data rate systems where soft decision iterative decoding is impractical we demonstrate that substantial wer performance gain can be obtained especially at higher channel signal to noise ratio csnr csnr delta 10 log10 1 2sigma2 values by employing two optimal thresholds plusmnt chosen to minimize wer we study the wer improvement and signal to noise ratio snr performance gain as a function of code length n for fixed minimum distance dmin and as a function of dmin for fixed n a distinct difference in the behavior of wer versus the threshold t and the optimal threshold t versus snr is observed between codes with odd and even dmin with the even dmin codes exhibiting larger performance improvements when employing a bsc e instead of a bsc

quantum group gauge theory on quantum spaces we construct quantum group valued canonical connections on quantum homogeneous spaces including aq deformed dirac monopole on the quantum sphere of podles with quantum differential structure coming from the 3d calculus of woronowicz onsu q 2 the construction is presented within the setting of a general theory of quantum principal bundles with quantum group hopf algebra fibre associated quantum vector bundles and connection one forms both the base space spacetime and the total space are non commutative algebras quantum spaces

dirac operators on quantum projective spaces we construct a family of self adjoint operators d n n is an element of z which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space cpql for any l 2 and 0 q 1 they provide 0 dimensional equivariant even spectral triples if l is odd and n 1 2 l 1 the spectral triple is real with ko dimension 2l mod 8

almost strictly totally negative matrices a real matrix a a i j 1 i j n is said to be almost strictly totally negative if it is almost strictly sign regular with signature e 1 1 1 which is equivalent to the property that all its nontrivial minors are negative in this paper an algorithmic characterization of nonsingular almost strictly totally negative matrices is presented

uncoded and coded performance of mfsk and dpsk in nakagami fading channels the author presents uncoded and coded performance results for noncoherent m ary frequency shift keying mfsk and differentially coherent binary phase shift keying dpsk in a slow nonselective nakagami m 1960 fading channel he gives simple expressions for the asymptotic slopes of probability of bit error for large signal to noise ratio and shows that the effective order of diversity compared to an uncoded rayleigh channel is the product of two parameters one for the channel and one for the code he also compares the uncoded nakagami m results to those of the rician channel in order to show performance differences between these two generalized fading channel models

new analytical probability of error expressions for classes of orthogonal signals in rayleigh fading new exact expressions for the symbol error rate and bit error rate of coherent 3 ary and 4 ary orthogonal and transorthogonal signaling in slowly fading rayleigh channels are derived new exact error probability expressions for coherent 6 ary and 8 ary biorthogonal signaling in slow rayleigh fading are also presented the use of these exact expressions as accurate approximations for the error rates of m ary orthogonal biorthogonal and transorthogonal signaling with arbitrary m is illustrated

an optimum time slot assignment algorithm for an ss tdma system with variable number of transponders in this paper we consider an ss tdma system with m uplink beams n downlink beams and k 1 leq k leq min m n transponders an optimal time slot assignment algorithm for any m n k and any traffic matrix is presented where optimality means achieving the minimal possible total duration for the given traffic matrix the number of switching matrices generated by the algorithm is bounded above by n 2 n 1 for k m n and mn k 1 otherwise extensive simulation results on randomly generated matrices are carried out showing that the average number of switching matrices generated is substantially lower than the bounds

on the symbol error probability of maximum selection diversity reception schemes over a rayleigh fading channel the symbol error probability of two selection schemes namely maximum signal to noise ratio m gamma selection and maximum output mo selection for m ary multidiversity reception over a rayleigh fading channel are discussed the symbol error probability of the mo scheme is lower than that of the m gamma scheme the more diversity receptions that are used the larger is the difference a simple expression of crossover average signal to noise ratio per bit is presented as a guideline for increasing the number of diversity receptions

quantum bundle description of quantum projective spaces we realise heckenberger and kolb s canonical calculus on quantum projective n 1 space c q c p n 1 as the restriction of a distinguished quotient of the standard bicovariant calculus for the quantum special unitary group c q su n we introduce a calculus on the quantum sphere c q s 2n 1 in the same way with respect to these choices of calculi we present c q c p n 1 as the base space of two different quantum principal bundles one with total space c q su n and the other with total space c q s 2n 1 we go on to give c q c p n 1 the structure of a quantum framed manifold more specifically we describe the module of one forms of heckenberger and kolb s calculus as an associated vector bundle to the principal bundle with total space c q su n finally we construct strong connections for both bundles

required nonzero patterns for nonsingular sign regular matrices abstract an n n real matrix is called sign regular if for each k 1 k n all its minors of order k have the same nonstrict sign the zero entries which can appear in a nonsingular sign regular matrix depend on its signature because the signature can imply that certain entries are necessarily nonzero the patterns for the required nonzero entries of nonsingular sign regular matrices are analyzed

an mgf based performance analysis of generalized selection combining over rayleigh fading channels using the notion of the spacing between ordered exponential random variables a performance analysis of the generalized selection combining gsc diversity scheme over rayleigh fading channels is presented and compared with that of the conventional maximal ratio combining and selection combining schemes starting with the moment generating function mgf of the gsc output signal to noise ratio snr we derive closed form expressions for the average combined snr outage probability and average error probability of a wide variety of modulation schemes operating over independently identically distributed i i d diversity paths because of their simple form these expressions readily allow numerical evaluation for cases of practical interest the results are also extended to the case of non i i d diversity paths

total positivity and neville elimination abstract neville elimination is described in terms of schur complements of matrices and used to improve some well known characterizations of totally positive and strictly totally positive matrices

sign structure preserves for m banded factorizations of sign regular matrices abstract a square matrix a a ij is called m banded if a ij 0 for all i j m motivated by the results of rainey and habetler j w rainey g j habetler tridiagonalization of completely nonnegative matrices math comp 26 1972 121 128 we provide m banded factorizations of sign regular matrices that preserve their sign structures as applications some eigenvalue interlacing properties and majorization relations are obtained for certain sign regular matrices

inner totally positive matrices abstract suppose a m n is a staircase matrix with row and column staircase sequences 1 2 n 1 2 n a minor a det a with 1 k 1 k is said to be an inner minor of a if i i i i for i 1 2 k a is said to be inner totally positiv e itp if every inner minor of a is positive we prove that a is itp if a 0 for all inner minors with q k n 0 k 1 2 n also a m n is itp iff it is totally non negative and its extreme inner minors are positive we show that an itp matrix may be reduced by similarity transformations to an itp band matrix and may alternatively be filled in by similarity transformations to become a tp matrix in both the reduction and the filling in the matrix is itp at each stage the analysis is applied to some inverse eigenvalue problems for band matrices

on a spectral property of doubly stochastic matrices and its application to their inverse eigenvalue problem abstract in this note we present a useful theorem concerning the spectral properties of doubly stochastic matrices as applications we use this result together with some known results that we recall as a tool for extracting new sufficient conditions for the inverse eigenvalue problem for doubly stochastic matrices

on nonsingular sign regular matrices abstract an m n matrix a is sign regular if for each k 1 k min m n all k k submatrices of a have determinant with the same nonstrict sign the zero pattern of nonsingular sign regular matrices is analyzed it is proved that the number of zero entries which can appear in a nonsingular sign regular matrix depends on its signature a matrix is totally nonpositive if all its minors are nonpositive a test for recognizing nonsingular totally nonpositive matrices is also provided

combined matrices of almost strictly sign regular matrices abstract the combined matrix is a very useful concept for many applications almost strictly sign regular assr matrices form an important structured class of matrices with two possible zero patterns which are either type i staircase or type ii staircase we prove that under an irreducibility condition the pattern of zero and nonzero entries of an assr matrix is preserved by the corresponding combined matrix without the irreducibility condition it is proved that type i and type ii staircases are still preserved illustrative numerical examples are included

sign regular matrices and neville elimination abstract a pivoting strategy of o n operations for the neville elimination of n n nonsingular sign regular matrices is introduced among other nice properties it is proved that it preserves sign regularity it is also shown its relationship with scaled partial pivoting strategies for neville elimination

combined matrices in special classes of matrices abstract the combined matrix of a nonsingular matrix a is the matrix a a 1 t where means the hadamard entrywise product it has simple properties its row as well as column sums are always one and it is not changed if a is multiplied from either side by a nonsingular diagonal matrix although it is usually difficult to compute its further properties deserve attention in the paper we concentrate on the sequence of the diagonal entries of combined matrices in various classes of matrices

noncommutative riemannian and spin geometry of the standard q sphere we study the quantum sphere open image in new window as a quantum riemannian manifold in the quantum frame bundle approach we exhibit its 2 dimensional cotangent bundle as a direct sum 0 1 1 0 in a double complex we find the natural metric volume form hodge operator laplace and maxwell operators and projective module structure we show that the q monopole as spin connection induces a natural levi civita type connection and find its ricci curvature and q dirac operator open image in new window we find the possibility of an antisymmetric volume form quantum correction to the ricci curvature and lichnerowicz type formulae for open image in new window we also remark on the geometric q borel weil bott construction

constructing coset codes with optimal same symbol weight for detecting narrowband interference in m fsk systems narrowband interference can cause undetected errors when m fsk data is encoded with an algebraic code containing the all e codewords this is due to the fact that the narrowband interferer will cause the output of the m fsk demodulator to correspond to one of the all e codewords one possible solution is to use a coset code of a code containing the repetition code the choice of the coset leader should be such that the resulting coset code has minimum same symbol weight we give a general construction for generating coset codes with minimum same symbol weight and present results where an optimal coset code for an n k reed solomon code is applied in an m fsk environment with narrowband interference from the results it is evident that the optimal coset codes outperform linear codes when narrowband interference is present

a note on the boundary of the set where the decreasingly ordered spectra of symmetric doubly stochastic matrices lie abstract in this paper we study the region n s of r n where the decreasingly ordered spectra of all the n n symmetric doubly stochastic matrices lie with emphasis on the boundary set of n s as applications we study the case n 4 and in particular we solve the inverse eigenvalue problem for 4 4 symmetric doubly stochastic matrices of trace zero by using different techniques than that used in h perfect l mirsky spectral properties of doubly stochastic matrices monatsh math 69 1965 35 57 also we solve the same problem for 4 4 symmetric doubly stochastic matrices of trace two which serves only to illustrate this paper s method in addition we describe a nonconvex region ef of 4 s which corresponds to new sufficient conditions for the 4 4 symmetric doubly stochastic matrices at the end we conjecture that e f 4 s

asymptotic performance of m ary orthogonal signals in worst case partial band interference and rayleigh fading it is shown that for worst case partial band jamming the error probability performance for fixed e sub b n sub i becomes worse with increasing m for m 16 the asymptotic probability of error is not zero for any e sub b n sub i ln 2 but decreases inverse linearly with respect to it in the fading case the error probability performance for fixed e sub b n sub 0 improves with m for noncoherent detection but worsens with m for coherent detection for large e sub b n sub 0 the performance of the rayleigh fading channel asymptotically approaches the same limit as the worst case partial band jammed channel however for values of m at least up to 4096 the partial band jammed channel does better while it is unlikely that an m ary orthogonal signal set with m 1024 will be used in a practical situation these results suggest an important theoretical problem namely what signal set achieves reliable communication

an algorithm for constructing doubly stochastic matrices for the inverse eigenvalue problem abstract in this note we present an algorithm that yields a new method for constructing doubly stochastic and symmetric doubly stochastic matrices for the inverse eigenvalue problem in addition we introduce new open problems in this area that lay the ground for future work

a test for strict sign regularity a characterization of strict sign regular matrices is obtained it is given in an algorithmic form which allows the easy construction of a test to check if a matrix is strictly sign regular the test is based on the neville elimination of several submatrices of a and requires less computational work than those which can be derived from other previously known characterizations of these matrices

some applications of doubly stochastic matrices abstract we discuss primarily two applications of doubly stochastic matrices and related matrices the first concerns a topic in communication theory called satellite switched time division multiple access systems and we attempt to illuminate some results which have occured in the engineering literature the second concerns a recent notion of a doubly stochastic automorphism of a graph we prove several new theorems about doubly stochastic automorphisms of certain classes of graphs and in particular obtain a theorem of which birkhoff s theorem for doubly stochastic matrices is a special case

variation diminishing transformations a direct approach to total positivity and its statistical applications abstract karlin has shown that the variation diminishing property possessed by totally positive distributions allows a unified and straightforward presentation of many basic properties of hypothesis tests his work in fact reveals that total positivity is equivalent to a suitably formulated variation diminishing property this largely expository article begins with the latter concept and consequently gives a more direct account of the theory this approach avoids the extensive mathematical preliminaries previously required and isolates the more important statistical property

a note on ss tdma satellite communication abstract in a recent paper of lewandowski and liu a scheduling problem for a satellite switched time division multiple access scheme is discussed it consists in covering a traffic matrix t by a defined set of 0 1 matrices we show that the existence of optimal schedules is a consequence of known results on polyhedral decomposition furthermore a simple decomposition procedure is outlined for constructing schedules having special types of switching matrices

coding for frequency hopped spread spectrum communication with partial band interference part i capacity and cutoff rate the performance of optimal codes on frequency hopped channels with partial band interference is investigated the performance measures considered are channel capacity and cutoff rate worst case partial band gaussian noise interference is assumed with the interference independent of the transmitted signal the capacity and cutoff rate are calculated as a function of the signal to noise ratio we consider soft decision receivers and hard decision receivers with and without side information optimal code rates are found for each of the above cases the required signal to noise ratio for reliable communication when codes are used is determined as a function of the code rate

almost strictly sign regular matrices and neville elimination with two determinant pivoting in 2007 cortes and pena introduced a pivoting strategy for the neville elimination of nonsingular sign regular matrices and called it two determinant pivoting neville elimination has been very useful for obtaining theoretical and practical properties for totally positive negative matrices and other related types of matrices a real matrix is said to be almost strictly sign regular if all its nontrivial minors of the same order have the same strict sign in this paper some nice properties related with the application of neville elimination with two determinant pivoting strategy to almost strictly sign regular matrices are presented

comparison of diversity combining techniques for rayleigh fading channels several methods of diversity combining for a rayleigh faded channel are evaluated and compared the methods considered are for coherent reception maximal ratio combining mrc selection combining sc and a generalization of sc whereby the two three signals with the two three largest amplitudes are coherently combined we will call this method second third order sc and denote it sc2 sc3 similar techniques are also investigated for noncoherent reception with equal gain combining egc replacing mrc and noncoherent versions of sc2 and sc3 numerical results indicate that sc2 and sc3 significantly enhances the bit error rate ber performance relative to that achievable with sc and under certain conditions approaches the performance achieved by mrc or egg the performance enhancement of sc2 and sc3 is especially noticable for noncoherent reception where egc is seen to provide the best performance only for low ber values in fact when the ber is 10 sup 3 or greater sc2 and sc3 performed comparably to egg and in some cases performed better than egc

consecutive column and row properties of matrices and the loewner neville factorization abstract we say that a square matrix over a ring with identity has the consecutive column property if for all k all its relevant submatrices having k consecutive rows and the first k columns are invertible similarly the consecutive row cr is defined we show that analogously to the commutative case for totally positive matrices a matrix has both cc and cr properties if and only if it admits a certain loewner neville type factorization with invertible entries this factorization is unique since the result is proved for matrices in such generality it holds also for block matrices over a field with all blocks square explicit both ways formulae are found between two sets of parameters the loewner neville coefficients in the factorization and the schur complements of relevant submatrices in relevant submatrices larger by one we also show that for lower triangular matrices the cc property is preserved by inversion

comparing pivoting strategies for almost strictly sign regular matrices abstract in this paper some properties of two determinant pivoting for neville elimination are presented in particular we consider a zero increasing property and we show an optimal normwise growth factor comparisons with other pivoting strategies for neville elimination and with gaussian elimination with partial pivoting of almost strictly sign regular matrices are performed numerical examples are included

backward stability with almost strictly sign regular matrices a sign regular matrix is almost strictly sign regular if all its nontrivial minors of the same order have the same strict sign these matrices form a subclass of sign regular matrices matrices whose minors of the same order have the same sign in this paper the backward stability for almost strictly sign regular matrices is studied when neville elimination with two determinant pivoting strategy is applied in addition several numerical experiments are also presented

performance limits of m fsk with reed solomon coding and diversity combining this paper examines the asymptotic m spl rarr spl infin performance of m ary frequency shift keying m fsk in multi channels or multiple frequency nonselective slowly fading channels with coding side information and diversity reception in particular reed solomon rs coding is considered in conjunction with the ratio threshold test rtt which generates side information regarding the reliability of received symbols the asymptotic performance of orthogonal signaling in multichannels with maximal ratio combining mrc postdetection equal gain combining egc hybrid selection combining h sc and selection combining sc is derived for an arbitrary statistical fading model and diversity order the derivations reveal that coherent and noncoherent implementations of diversity combining schemes yield the same performance asymptotically in addition the asymptotic results are evaluated assuming a nakagami m fading model and the effect of fading severity diversity order code rate and side information upon the performance of the various diversity combiners is investigated the minimum signal to noise ratio snr required to achieve arbitrarily reliable or error free communication as well as the associated optimal rs code rate are determined for various cases

adaptive orthogonal signaling with diversity in a frequency nonselective rayleigh fading channel power and rate adaptations with diversity are considered for m ary orthogonal signals in a frequency nonselective rayleigh fading channel we derived the minimum required e sub b n sub 0 for a given probability of error the maximum average data rate and the outage probability when maximal ratio combining is performed with an imperfect channel estimation we analyzed the effects of channel estimation errors on the required e sub b n sub 0 and outage probability as a function of diversity order and adaptation methods the relative benefits of rate and power control techniques are further presented in terms of channel estimation error diversity order and outage probability the minimum required e sub b n sub 0 with reed solomon codes is also presented for comparison purposes

computing the nearest doubly stochastic matrix with a prescribed entry in this paper a nearest doubly stochastic matrix problem is studied this problem is to find the closest doubly stochastic matrix with the prescribed 1 1 entry to a given matrix according to the well established dual theory in optimization the dual of the underlying problem is an unconstrained differentiable but not twice differentiable convex optimization problem a newton type method is used for solving the associated dual problem and then the desired nearest doubly stochastic matrix is obtained under some mild assumptions the quadratic convergence of the proposed newton method is proved the numerical performance of the method is also demonstrated by numerical examples

performance limits of reed solomon coded cdma with orthogonal signaling in a rayleigh fading channel the asymptotic performance of reed solomon rs coded m ary orthogonal signaling with ratio threshold test rtt type demodulation in a rayleigh fading channel is considered we show that the minimum e sub b n sub 0 needed for error free communication is eln2 2 75 db with rtt and 4 79 6 8 db with hard decisions the optimum code rate that minimizes the required e sub b n sub 0 is e sup 1 with rtt and 0 46 with hard decision and the optimum ratio threshold approaches 1 for large m next we investigate the fundamental limit in a direct sequence spread spectrum multiple access ds ssma system employing an m ary orthogonal code of length n mm which is obtained by spreading every row of an m spl times m hadamard matrix with a user specific random sequence of length n we derive the minimum e sub b n sub 0 for error free communication as a function of the number of users the optimum code rate that minimizes e sub b n sub 0 and the maximum limit on the total information transmission rate then we consider a multirate ds ssma system where a population of users simultaneously transmit at different power levels a variety of traffic types of different information rates we derive the minimum required e sub b n sub 0 and the optimum code rate for each traffic type

combined matrices of sign regular matrices abstract the combined matrix of a nonsingular matrix a is the hadamard entry wise product c a a a 1 t since each row and column sum of c a is equal to one the combined matrix is doubly stochastic when it is nonnegative in this work we study the nonnegativity of the combined matrix of sign regular matrices based upon their signature in particular a few coordinates of the signature e of a play a crucial role in determining whether or not c a is nonnegative

quantum magic squares dilations and their limitations quantum permutation matrices and quantum magic squares are generalizations of permutation matrices and magic squares where the entries are no longer numbers but elements from arbitrary non commutative algebras the famous birkhoff von neumann theorem characterizes magic squares as convex combinations of permutation matrices in the non commutative case the corresponding question is as follows does every quantum magic square belong to the matrix convex hull of quantum permutation matrices that is does every quantum magic square dilate to a quantum permutation matrix here we show that this is false even in the simplest non commutative case we also classify the quantum magic squares that dilate to a quantum permutation matrix with commuting entries and prove a quantitative lower bound on the diameter of this set finally we conclude that not all arveson extreme points of the free spectrahedron of quantum magic squares are quantum permutation matrices

asymptotic performance of m ary orthogonal modulation in generalized fading channels the asymptotic m to infinity probability of symbol error p sub e sub m for m ary orthogonal modulation in a nakagami m fading channel is given by the incomplete gamma function p m mx where x in 2 e sub b n sub 0 and e sub b is the average energy per bit for large signal to noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of e sub b n sub 0 these channels exist for all m or 1 2 the special case of m 1 corresponds to rayleigh fading an inverse linear channel

generalized totally positive matrices abstract we say that a rectangular matrix over a in general noncommutative ring with identity having a positive part is generalized totally positive gtp if in all nested sequences of so called relevant submatrices the schur complements are positive here a relevant submatrix is such either having k consecutive rows and the first k columns or k consecutive columns and the first k rows this notion generalizes the usual totally positive matrices we prove e g that a square matrix is gtp if and only if it admits a certain factorization with bidiagonal type factors and certain invertible entries also the product of square gtp matrices of the same order is again a gtp matrix and its inverse has the checkerboard sign property

nonsingular almost strictly sign regular matrices abstract the class of nonsingular almost strictly totally positive matrices has been characterized m gasca j m pena characterizations and decompositions of almost strictly positive matrices siam j matrix anal appl 28 2006 1 8 in this paper we discuss the class of almost strictly sign regular matrices that includes almost strictly totally positive matrices a characterization is provided for these matrices in terms of their nontrivial minors using consecutive rows and consecutive columns in particular we present a characterization of certain almost strictly sign regular matrices in terms of a very reduced number of boundary almost trivial minors

projective module description of the q monopole the dirac q monopole connection is used to compute projector matrices of quantum hopf line bundles for arbitrary winding number the chern connes pairing of cyclic cohomology and k theory is computed for the winding number 1 the non triviality of this pairing is used to conclude that the quantum principal hopf fibration is non cleft among general results we provide a left right symmetric characterization of the canonical strong connections on quantum principal homogeneous spaces with an injective antipode we also provide for arbitrary strong connections on algebraic quantum principal bundles hopf galois extensions their associated covariant derivatives on projective modules

noncommutative kahler structures on quantum homogeneous spaces abstract building on the theory of noncommutative complex structures the notion of a noncommutative kahler structure is introduced in the quantum homogeneous space case many of the fundamental results of classical kahler geometry are shown to follow from the existence of such a structure allowing for the definition of noncommutative lefschetz hodge kahler dirac and laplace operators quantum projective space endowed with its heckenberger kolb calculus is taken as the motivating example the general theory is then used to show that the calculus has cohomology groups of at least classical dimension

a matricial description of neville elimination with applications to total positivity abstract the neville elimination process used by the authors in some previous papers in connection with totally positive matrices is studied in detail in the case of nonsingular matrices a wide class of matrices is found where neville elimination has a lower computational cost than gauss elimination finally some new characterizations are obtained for strictly totally positive and nonsingular totally positive matrices in terms of their neville elimination and that of their inverses

compact graphs and equitable partitions abstract let g be a graph with adjacency matrix a and let be the set of all permutation matrices which commute with a we call g compact if every doubly stochastic matrix which commutes with a is a convex combination of matrices from we characterize the graphs for which s a i and show that the automorphism group of a compact regular graph is generously transitive i e given any two vertices there is an automorphism which interchanges them we also describe a polynomial time algorithm for determining whether a regular graph on a prime number of vertices is compact

notes on hilbert and cauchy matrices inspired by examples of small hilbert matrices the author proves a property of symmetric totally positive cauchy matrices called at property and consequences for the hilbert matrix