subblock constrained codes for real time simultaneous energy and information transfer consider an energy harvesting receiver that uses the same received signal both for decoding information and for harvesting energy which is employed to power its circuitry in the scenario where the receiver has limited battery size a signal with bursty energy content may cause power outage at the receiver since the battery will drain during intervals with low signal energy in this paper we analyze subblock energy constrained codes seccs which ensure that sufficient energy is carried within every subblock duration we consider discrete memoryless channels and characterize the secc capacity and the secc error exponent and provide useful bounds for these values we also study constant subblock composition codes csccs which are a subclass of seccs where all the subblocks in every codeword have the same fixed composition and this subblock composition is chosen to maximize the rate of information transfer while meeting the energy requirement compared with constant composition codes cccs we show that csccs incur a rate loss and that the error exponent for csccs is also related to the error exponent for cccs by the same rate loss term we exploit the symmetry in csccs to obtain a necessary and sufficient condition on the subblock length for avoiding power outage at the receiver furthermore for cscc sequences we present a tight lower bound on the average energy per symbol within a sliding time window we provide numerical examples highlighting the tradeoff between the delivery of sufficient energy to the receiver and achieving high information transfer rates it is observed that the ability to use energy in real time imposes less of penalty compared with the ability to use information in real time

variable structure control of dynamical systems with mismatched norm bounded uncertainties an lmi approach in this paper we propose a new sliding surface design method for a class of uncertain systems with mismatched unstructured uncertainties we relax the matching assumption of traditional vsc design methods and the uncertain system under consideration may have mismatched parameter uncertainties in the state matrix as well as the input matrix in terms of linear matrix inequalities lmis we give a sufficient condition for the existence of linear sliding surfaces guaranteeing asymptotic stability of the reduced order equivalent sliding mode dynamics we give an lmi parameterization of such sliding surfaces together with a switched feedback control strategy we also give an lmi existence condition of linear sliding surfaces guaranteeing the prescribed decay rate finally we give simulation results to show the effectiveness of our method

estimates on the size of symbol weight codes the study of codes for powerline communications has garnered much interest over the past decade various types of codes such as permutation codes frequency permutation arrays and constant composition codes have been proposed over the years in this paper we study a type of code called bounded symbol weight codes which was first introduced by versfeld in 2005 and a related family of codes that we term constant symbol weight codes we provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes we also give direct and recursive constructions of codes for certain parameters

vacuum energy for 3 1 dimensional space time with compact hyperbolic spatial part the vacuum energy for a massless scalar field defined on a hyperbolic manifold h3 is evaluated using zeta function and heat kernel regularization techniques and selberg trace formula for cocompact group a negative contribution to the vacuum energy associated with trivial line bundle related to character 1 is found

optimal ternary constant composition codes of weight four and distance five constant composition codes cccs are a generalization of constant weight codes and permutation codes the concept of group divisible codes an analog of group divisible designs in combinatorial design theory was first introduced by chee et al this new class of codes has been shown to be useful in recursive constructions of constant weight codes and constant composition codes in this paper we consider the problem of determining the maximal sizes of ternary constant composition codes of weight four and distance five using group divisible codes as the main tools we determine the exact values for these parameters the previously known results are those with code length no greater than 10

stable relative bessel distributions on gl n over a quadratic extension we study regularized periods of eisenstein series over unitary groups they play an important role in the study of unitary periods of cusp forms a stabilization is used to express the periods in terms of l functions thanks to recent developments of jacquet and lapid we obtain certain bessel identities that generalize identities obtained by lapid rogawski these identities are applied in compact unitary periods by lapid and offen

zonal spherical functions on the complex reflection groups and n 1 m 1 hypergeometric functions abstract the pair of groups complex reflection group g r 1 n and symmetric group s n is a gelfand pair its zonal spherical functions are expressed in terms of multivariate hypergeometric functions called n 1 m 1 hypergeometric functions since the zonal spherical functions have orthogonality they form discrete orthogonal polynomials also shown is a relation between monomial symmetric functions and the n 1 m 1 hypergeometric functions

an improvement on the gilbert varshamov bound for permutation codes permutation codes have been shown to be useful in power line communications block ciphers and multilevel flash memory models construction of such codes is extremely difficult in fact the only general lower bound known is the gilbert varshamov type bound in this paper we establish a connection between permutation codes and independent sets in certain graphs using the connection we improve the gilbert varshamov bound asymptotically by a factor log n when the code length n goes to infinity

on the eigenvalues of certain cayley graphs and arrangement graphs abstract in this paper we show that the eigenvalues of certain classes of cayley graphs are integers the n k r arrangement graph a n k r is a graph with all the k permutations of an n element set as vertices where two k permutations are adjacent if they differ in exactly r positions we establish a relation between the eigenvalues of the arrangement graphs and the eigenvalues of certain cayley graphs as a result the conjecture on integrality of eigenvalues of a n k 1 follows

on the labeling problem of permutation group codes under the infinity metric we consider codes over permutations under the infinity norm given such a code we show that a simple relabeling operation which produces an isomorphic code may drastically change the minimal distance of the code thus we may choose a code structure for efficient encoding procedures and then optimize the code s minimal distance via relabeling to establish that the relabeling problem is hard and is of interest we formally define it and show that all codes may be relabeled to get a minimal distance at most 2 on the other hand the decision problem of whether a code may be relabeled to distance 2 or more is shown to be np complete and calculating the best achievable minimal distance after relabeling is proved to be hard to approximate up to a factor of 2 we then consider general bounds on the relabeling problem we specifically construct the optimal relabeling for transitive cyclic groups we conclude with the main result a general probabilistic bound which we then use to show both the agl p group and the dihedral group on p elements may be relabeled to a minimal distance of p o p in p

unitary periods hermitian forms and points on flag varieties let e be an imaginary quadratic extension of mathbb q of class number one we examine certain representation numbers associated to hermitian forms over e which involve counting integral points on flag varieties

generalized characters of the symmetric group normalized irreducible characters of the symmetric group s n can be understood as zonal spherical functions of the gelfand pair s n s n diags n they form an orthogonal basis in the space of the functions on the group s n invariant with respect to conjugations by s n in this paper we consider a different gelfand pair connected with the symmetric group that is an unbalanced gelfand pair s n s n 1 diags n 1 zonal spherical functions of this gelfand pair form an orthogonal basis in a larger space of functions on s n namely in the space of functions invariant with respect to conjugations by s n 1 we refer to these zonal spherical functions as normalized generalized characters of s n the main discovery of the present paper is that these generalized characters can be computed on the same level as the irreducible characters of the symmetric group the paper gives a murnaghan nakayama type rule a frobenius type formula and an analogue of the determinantal formula for the generalized characters of s n

group divisible codes and their application in the construction of optimal constant composition codes of weight three the concept of group divisible codes a generalization of group divisible designs with constant block size is introduced in this paper this new class of codes is shown to be useful in recursive constructions for constant weight and constant composition codes large classes of group divisible codes are constructed which enabled the determination of the sizes of optimal constant composition codes of weight three and specified distance leaving only four cases undetermined previously the sizes of constant composition codes of weight three were known only for those of sufficiently large length

zeta functions of binary hermitian forms and special values of eisenstein series on three dimensional hyperbolic space the present work contains a systematic investigation of zeta functions of binary hermitian forms over the ring o of integers of an imaginary quadratic number field k tl with discriminant d 0 the resulting relations between these zetafunctions have numerous applications to the computation of special values of the eisenstein series for the group psl 2 o acting on the three dimensional hyperbolic space i i in particular we reprove many known formulae for representation numbers for quaternary quadratic forms over z and we obtain many explicit new results for such representation numbers in sect 2 we develop a theory of representations of numbers by binary hermitian forms over o which parallels the classical theory of representations of integers by binary quadratic forms over a key result is a certain bijection described in theorem 2 3 this bijection means that the sum of the numbers of representations modulo sl 2 o units of an integer k 0 by a set of representatives of the sl 2 o classes of binary hermitian forms over o with discriminant a is equal to the number of cosets 2 ko with 2 o 22 a 0 m o d k the number of these cosets is explicitly computed in sect 2 in all cases hence a certain mean value of the representation numbers is known whereas simple formulae for the individual representation numbers do not exist we apply the formulae of sect 2 to the study of zeta functions of definite or indefinite hermitian forms for simplicity we restrict in this introduction to the case of positive definite forms over o although the results of chap i are valid in the indefinite case as well let f be a positive definite binary hermitian form over o with sl 2 o unit group gl f then we define

constructions of permutation arrays a permutation array pa of length n and minimum distance d is a set of permutations of n elements such that any two permutations coincide in at most n d positions some constructions of pas are given

an lmi based switching surface design method for a class of mismatched uncertain systems in this note we consider the problem of designing linear sliding surfaces for multivariable uncertain systems with mismatched uncertainties in the state matrix in terms of linear matrix inequalities we give a new invariance condition guaranteeing the existence of a linear switching surface such that the reduced order equivalent sliding mode dynamics restricted to the switching surface is not only stable but completely invariant to mismatched uncertainties we also give an explicit formula of such linear switching surfaces together with a design example

a generalized hermite constant for imaginary quadratic fields we introduce the projective hermite constant for positive definite binary hermitian forms associated with an imaginary quadratic number field k it is a lower bound for the classical hermite constant and these two constants coincide when k has class number one using the geometric tools developed by mendoza 6 and vogtmann 15 for their study of the homology of the bianchi groups we compute the projective hermite constants for those k whose absolute discriminants are less than 70 and determine the hermitian forms that attain the projective hermite constants in these cases a comparison of the projective hermitian constant with some other generalizations of the classical hermite constant is also given

on the algebraic combinatorics of injections and its applications to injection codes we consider the algebraic combinatorics of the set of injections from a k element set to an n element set in particular we give a new combinatorial formula for the spherical functions of the gelfand pair s k times s n diag s k times s n k we use this combinatorial formula to give new delsarte linear programming bounds on the size of codes over injections

brief paper a singular system approach to robust sliding mode control for uncertain markov jump systems the robust sliding mode control for markov jump systems with parameter uncertainties and an unknown nonlinear function is discussed based on a singular system approach and linear matrix inequality lmi a sufficient condition which guarantees the existence of linear switching surface and the stochastic stability of sliding mode dynamics is given a sliding mode controller is designed such that the closed loop system is convergent to the switching surface in finite time a numerical example is given to show the effectiveness of the proposed method

determinant of the laplacian on a non compact three dimensional hyperbolic manifold with finite volume the functional determinant of laplace type operators on a three dimensional non compact hyperbolic manifold with invariant fundamental domain of finite volume is expressed via the selberg zeta function related to the picard group

permutation arrays for powerline communication and mutually orthogonal latin squares we develop a connection between permutation arrays that are used in powerline communication and well studied combinatorial objects mutually orthogonal latin squares mols from this connection many new results on permutation arrays can be obtained

algebraic constructions of constant composition codes constant composition codes are a special class of constant weight codes they include permutation codes as a subclass in this correspondence two classes of optimal constant composition codes are constructed both constructions employ perfect nonlinear functions but they are different

the pbd closure of constant composition codes we show an interesting pairwise balanced design pbd closure result for the set of lengths of constant composition codes whose distance and size meet certain conditions a consequence of this pbd closure result is that the size of optimal constant composition codes can be determined for infinite families of parameter sets from just a single example of an optimal code as an application the sizes of several infinite families of optimal constant composition codes are derived in particular the problem of determining the size of optimal constant composition codes having distance four and weight three is solved for all lengths sufficiently large this problem was previously unresolved for odd lengths except for lengths seven and eleven

murnaghan nakayama rules for characters of iwahori hecke algebras of classical type in this paper we give murnaghan nakayama type formulas for computing the irreducible characters of the iwahori hecke algebras of types an 1 bn and dn our method is a generalization of a derivation of the murnaghan nakayama formula for the irreducible characters of the symmetric group given by curtis greene greene s approach is to sum up the diagonal entries of the matrices of certain cycle permutations in young s seminormal representations the analogues of the young seminormal representations for the iwahori hecke algebras of types an 1 bn and dn were given by hoefsmit

the trace of the heat kernel on a compact hyperbolic 3 orbifold the heat coefficients related to the laplace beltrami operator defined on the hyperbolic compact manifold h3 are evaluated in the case in which the discrete group contains elliptic and hyperbolic elements it is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel elliptic elements modify all coefficients of the asymptotic expansion but the weyl term which remains unchanged some physical consequences are briefly discussed in the examples