a complex variable boundary point interpolation method for the nonlinear signorini problem abstract a complex variable boundary point interpolation method cvbpim is presented for numerical analysis of the nonlinear signorini problem to reduce the computational cost and to improve the stability of the point interpolation method a complex variable point interpolation method cvpim is developed to construct meshless shape functions with interpolation properties by using a projection technique to deal with the nonlinear inequality boundary conditions and combining boundary integral equations with the cvpim to establish discrete linear algebraic systems the cvbpim is an easy to implement and boundary only meshless method for nonlinear signorini problems numerical results are presented to show the accuracy and efficiency of the method

asymptotically optimal optical orthogonal codes with new parameters optical orthogonal codes oocs are widely used as spreading codes in optical fiber networks an n w a c ooc with size l is a family of l 0 1 sequences with length n weight w maximum autocorrelation a and maximum cross correlation c in this paper we present two new constructions for oocs with a c 1 which are asymptotically optimal with respect to the johnson bound we first construct an asymptotically optimal mpn m 1 1 ooc with size pn 1 m by using the structure of zpn the ring of integers modulo pn where p is an odd prime with m p 1 and n is a positive integer we then present another asymptotically optimal mp1 pk m 1 1 ooc with size p1 pk 1 m from a product of k finite fields where pi is an odd prime and m is a positive integer such that m pi 1 for 1 i k in particular it is optimal in the case that k 1 and m 1 2 p1 1

the method of fundamental solutions for the numerical solution of the biharmonic equation abstract the method of fundamental solutions mfs is a relatively new technique for the numerical solution of certain elliptic boundary value problems it falls in the class of methods generally called boundary methods and like the well known boundary integral equation method is applicable when a fundamental solution of the differential equation is known in the mfs the approximate solution is a linear combination of fundamental solutions with singularities placed outside the domain of the problem the locations of the singularities are either preassigned or determined along with the coefficients of the fundamental solutions so that the approximate solution satisfies the boundary conditions as well as possible in many applications these quantities are determined by a least squares fit of the boundary conditions a nonlinear problem which is solved using standard software in this paper the mfs is formulated for biharmonic problems and is applied to a variety of standard test problems as well as to problems arising in elasticity and fluid flow

standard paths and standard monomials fixed by a diagram automorphism abstract we show that the standard paths and the standard monomials fixed by a diagram automorphism for a kac moody algebra g can be identified with the standard paths and the standard monomials for the orbit lie algebra of g respectively by using these results we give a combinatorial proof of twining character formulas for an integrable highest weight module and for a demazure module within the framework of path models

automorphisms of borcherds superalgebras and fixed point subalgebras abstract let g be a borcherds superalgebra and let be a finite order automorphism of g satisfying certain conditions we prove that the fixed point subalgebra g is equal to a borcherds superalgebra we also compute the trace of on g from the twisted denominator identity of g and derive closed form formula for root multiplicities of g

optical orthogonal codes new bounds and an optimal construction a technique for constructing optimal oocs optical orthogonal codes is presented it provides the only known family of optimal with respect to family size oocs having lambda 2 the parameters n omega lambda are respectively p sup 2m 1 p sup m 1 2 where p is any prime and the family size is p sup m 2 three distinct upper bounds on the size of an ooc are presented that for many values of the parameter set n omega lambda improve upon the tightest previously known bound

analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions abstract the localized method of fundamental solutions lmfs is an efficient meshless collocation method that combines the concept of localization and the method of fundamental solutions mfs the resultant system of linear algebraic equations in the lmfs is sparse and banded and thus drastically reduces the storage and computational burden of the mfs in the lmfs the moving least square mls approximation based on fundamental solutions is used to construct approximate solution at each node in this paper this fundamental solutions based mls approximation named as an augmented mls amls approximation is generalized to any point in the computational domain computational formulas theoretical properties and error estimates of the amls approximation are derived then taking laplace equation as an example this paper sets up a framework for the theoretical error analysis of the lmfs finally numerical results are presented to verify the efficiency and theoretical results of the amls approximation and the lmfs convergence and comparison researches are conducted to validate the accuracy convergence and efficiency

weyl s character formula for non connected lie groups and orbital theory for twisted affine lie algebras abstract we generalize i frenkel s orbital theory for non twisted affine lie algebras to the case of twisted affine lie algebras using a character formula for certain non connected compact lie groups

constructions for optimal spl upsi 4 1 optical orthogonal codes four direct constructions three of which are by way of skew starters are given in this correspondence for optimal spl upsi 4 1 optical orthogonal codes ooc s these improve the known existence results concerning optimal spl upsi 4 1 oocs in particular it is shown that an optimal spl upsi 4 1 ooc exists for all positive integers spl upsi spl equiv 6 mod 12 or spl upsi spl equiv 24 mod 48 it is also shown that an optimal 12 spl upsi 4 1 ooc exists for any positive integer spl upsi whose prime factors are all congruent to 1 modulo 4

a unified approach to whiteman s and ding helleseth s generalized cyclotomy over residue class rings the theory of cyclotomy dates back to gauss and has a number of applications in combinatorics coding theory and cryptography cyclotomy over a residue class ring bbzv can be divided into classical cyclotomy or generalized cyclotomy depending on v prime or composite in this paper we introduce a generalized cyclotomy of order d over bbzp1e1p2e2 pnen which includes whiteman s and ding helleseth s generalized cyclotomy as special cases here p1 p2 pn are pairwise distinct odd primes satisfying d pi 1 for all 1 i n and e1 e2 en are positive integers we derive some basic properties of the corresponding cyclotomic numbers and obtain a general formula to compute them via classical cyclotomic numbers as applications we completely solve an open problem and a conjecture on whiteman s generalized cyclotomy of order four over bbzp1p2 besides we also construct an infinite series of near optimal codebooks over bbzp1p2 as well as some infinite series of asymptotically optimal difference systems of sets over bbzp1e1p2e2 pnen

two dimensional optical orthogonal codes and semicyclic group divisible designs a nxm k two dimensional optical orthogonal code 2 d ooc c is a family of nxm 0 1 arrays of constant weight k such that i 1n j 0m 1a i j b i j m for any arrays a b in c and any integer except when a b and 0 mod m where m denotes addition modulo m such codes are of current practical interest as they enable optical communication at lower chip rate to simplify practical implementation the am oppw at most one pulse per wavelength restriction is often appended to a 2 d ooc an am oppw 2 d ooc is optimal if its size is the largest possible in this paper the notion of a perfect am oppw 2 d ooc is proposed which is an optimal nxm k am oppw 2 d ooc with cardinality m n n 1 n k k 1 k a link between optimal nxm k am oppw 2 d oocs and block designs is developed some new constructions for such optimal codes are described by means of semicyclic group divisible designs several new infinite families of perfect nxm k 1 am oppw 2 d oocs with k 2 3 4 are thus produced

optimal 2 d n times m 3 2 1 optical orthogonal codes optical orthogonal codes are commonly used as signature codes for optical code division multiple access systems so far research on 2 d optical orthogonal codes has mainly concentrated on the same autocorrelation and cross correlation constraints in this paper we are concerned about optimal 2 d optical orthogonal codes with the autocorrelation a and the cross correlation 1 some combinatorial constructions for 2 d n m k a 1 optical orthogonal codes are presented when k 3 and a 2 the exact number of codewords of an optimal 2 d n m 3 2 1 optical orthogonal code is determined for any positive integers n 0 1 3 6 9 10 mod 12 and m 2 mod 4

monstrous moonshine and monstrous lie superalgebras we prove conway and norton s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by frenkel lepowsky and meurman to do this we use the no ghost theorem from string theory to construct a family of generalized kac moody superalgebras of rank 2 which are closely related to the monster and several of the other sporadic simple groups the denominator formulas of these superalgebras imply relations between the thompson functions of elements of the monster i e the traces of elements of the monster on frenkel lepowsky and meurman s representation which are the replication formulas conjectured by conway and norton these replication formulas are strong enough to verify that the thompson functions have most of the moonshine properties conjectured by conway and norton and in particular they are modular functions of genus 0 we also construct a second family of kac moody superalgebras related to elements of conway s sporadic simple group col these superalgebras have even rank between 2 and 26 for example two of the lie algebras we get have ranks 26 and 18 and one of the superalgebras has rank 10 the denominator formulas of these algebras give some new infinite product identities in the same way that the denominator formulas of the a n n e kac moody algebras give the macdonald identities

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

optical orthogonal codes their bounds and new optimal constructions a v k spl lambda sub a spl lambda sub c optical orthogonal code ooc c is a family of 0 1 sequences of length v and weight k satisfying the following two correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda sub a for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c and any integer i not equivalent 0 mod v and 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda sub b for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c y y sub 0 y sub 1 spl middot spl middot spl middot y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v the study of optical orthogonal codes is motivated by an application in optical code division multiple access communication systems in this paper upper bounds on the size of an optical orthogonal code are discussed several new constructions for optimal optical orthogonal codes with weight k spl ges 4 and correlation constraints spl lambda sub a spl lambda sub c 1 are described by means of optimal cyclic packings many new infinite series of such optimal optical orthogonal codes are thus produced

large families of asymptotically optimal two dimensional optical orthogonal codes nine new two dimensional optical orthogonal codes 2 d oocs are presented here all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature each of these constructions is either optimal or asymptotically optimal with respect to either the original johnson bound or else a nonbinary version of the johnson bound introduced in this paper the first five codes are constructed using polynomials over finite fields the first construction is optimal while the remaining four are asymptotically optimal the next two codes are constructed using rational functions in place of polynomials and these are asymptotically optimal the last two codes also asymptotically optimal are constructed by composing two of the above codes with a constant weight binary code also presented is a three dimensional optical orthogonal code 3 d ooc that exploits the polarization dimension finally phase encoded optical cdma is considered and construction of two efficient codes are provided

method of fundamental solutions with optimal regularization techniques for the cauchy problem of the laplace equation with singular points the purpose of this study is to propose a high accuracy and fast numerical method for the cauchy problem of the laplace equation our problem is directly discretized by the method of fundamental solutions mfs the tikhonov regularization method stabilizes a numerical solution of the problem for given cauchy data with high noises the accuracy of the numerical solution depends on a regularization parameter of the tikhonov regularization technique and some parameters of the mfs the l curve determines a suitable regularization parameter for obtaining an accurate solution numerical experiments show that such a suitable regularization parameter coincides with the optimal one moreover a better choice of the parameters of the mfs is numerically observed it is noteworthy that a problem whose solution has singular points can successfully be solved it is concluded that the numerical method proposed in this paper is effective for a problem with an irregular domain singular points and the cauchy data with high noises

localized mfs for the inverse cauchy problems of two dimensional laplace and biharmonic equations abstract this paper makes a first attempt to use a new localized method of fundamental solutions lmfs to accurately and stably solve the inverse cauchy problems of two dimensional laplace and biharmonic equations in complex geometries the lmfs firstly divides the whole physical domain into several small overlapping subdomains and then employs the traditional method of fundamental solutions mfs formulation in every local subdomain for calculating the unknown coefficients on the local fictitious boundary after that a sparse linear system is formed by using the governing equation for interior nodes and the nodes on under specified boundary and by using the given boundary conditions for the nodes on over specified boundary finally the numerical solutions of the inverse problems can be obtained by solving the resultant sparse system compared with the traditional mfs with the global boundary discretization the lmfs requires less computational cost which may make the lmfs suitable for solving large scale problems numerical experiments demonstrate the validity and accuracy of the proposed lmfs for the inverse cauchy problems of two dimensional laplace and biharmonic equations with noisy boundary data

generalized cyclotomic codes of length p sub 1 sup e 1 p sub t sup e t we first introduce a generalized cyclotomy of order 2 with respect to p sub 1 sup e 1 p sub t sup e t we then present two classes of new error correcting binary cyclic codes of length p sub 1 sup e 1 p sub t sup e t based on this generalized cyclotomy we prove either a square root bound or a similar bound on the minimum odd weight of those codes with length n p sub 1 sup e 1 p sub 2 sup e 2

on the application of the method of fundamental solutions to boundary value problems with jump discontinuities abstract two meshfree methods are proposed for the numerical solution of boundary value problems bvps for the laplace equation coupled with boundary conditions with jump discontinuities in the first case the bvp is solved in two steps using a subtraction of singularity approach here the singular subproblem is solved analytically while the classical method of fundamental solutions mfs is applied for the solution of the regular subproblem in the second case the total bvp is solved using a variant of the mfs where its approximation basis is enriched with a set of harmonic functions with singular traces on the boundary of the domain the same singularity capturing functions motivated by the boundary element method bem are used for the singular part of the solution in the first method and for augmenting the mfs basis in the second method comparative numerical results are presented for 2d problems with discontinuous dirichlet boundary conditions in particular the inappropriate oscillatory behavior of the classical mfs solution due to the gibbs phenomenon is shown to vanish

optimal frequency hopping sequences of odd length in this paper a new generalized cyclotomy with respect to a positive odd integer is introduced and a construction of frequency hopping sequence sets and two constructions of frequency hopping sequences are proposed as its applications the frequency hopping sequence sets and frequency hopping sequences obtained in this paper can be optimal with respect to the peng fan bound and lempel greenberger bound respectively further the length of sequences in the optimal frequency hopping sequence sets can be any odd integer larger than 3 some of them have new parameters

combinatorial constructions for optimal two dimensional optical orthogonal codes optical orthogonal codes oocs have been designed for ocdma a one dimensional 1 d optical orthogonal code 1 d ooc is a set of one dimensional binary sequences having good auto and cross correlations one limitation of 1 d ooc is that the length of the sequence increases rapidly when the number of users or the weight of the code is increased which means large bandwidth expansion is required if a big number of codewords is needed to lessen this problem two dimensional 2 d coding also called multiwavelength oocs was invested a two dimensional 2 d optical orthogonal code 2 d ooc is a set of utimesv matrices with 0 1 elements having good auto and cross correlations recently many researchers are working on constructions and designs of 2 d oocs in this paper we shall reveal the combinatorial properties of 2 d oocs and give an equivalent combinatorial description of a 2 d ooc based on this we are able to use combinatorial methods to obtain many optimal 2 d oocs

from dynkin diagram symmetries to fixed point structures any automorphism of the dynkin diagram of a symmetrizable kac moody algebra g induces an automorphism of g and a mapping between highest weight modules of g for a large class of such dynkin diagram automorphisms we can describe various aspects of these maps in terms of another kac moody algebra the orbit lie algebra g in particular the generating function for the trace of over weight spaces which we call the twining character of g with respect to the automorphism is equal to a character of g the orbit lie algebras of untwisted affine lie algebras turn out to be closely related to the fixed point theories that have been introduced in conformal field theory orbit lie algebras and twining characters constitute a crucial step towards solving the fixed point resolution problem in conformal field theory

constructions of optimal 2 d optical orthogonal codes via generalized cyclotomic classes optical orthogonal codes oocs are widely used as spreading codes in optical fiber networks in this paper a bound on the code size of 2 d oocs with both at most one pulse per wavelength am oppw and at most one pulse per time slot am oppts is derived accordingly two constructions of optimal 2 d oocs with both am oppw and am oppts are proposed via the generalized cyclotomic classes furthermore optimal 2 d ooc with am oppw can be also constructed by adding more codewords into the 2 d oocs with both am oppw and am oppts

the method of fundamental solutions and quasi monte carlo method for diffusion equations the laplace transform is applied to remove the time dependent variable in the diffusion equation for non harmonic initial conditions this gives rise to a non homogeneous modified helmholtz equation which we solve by the method of fundamental solutions to do this a particular solution must be obtained which we find through a method suggested by atkinson to avoid costly gaussian quadratures we approximate the particular solution using quasi monte carlo integration which has the advantage of ignoring the singularity in the integrand the approximate transformed solution is then inverted numerically using stehfest s algorithm two numerical examples are given to illustrate the simplicity and effectiveness of our approach to solving diffusion equations in 2 d and 3 d 1998 john wiley sons ltd

generalized kac moody algebras on etudie une classe d algebres de lie qui ont une forme bilineaire contravariante qui est presque definie positive ces algebres generalisent celles de kac moody et peuvent etre considerees comme des algebres de kac moody avec des racines simples imaginaires

the action of outer automorphisms on bundles of chiral blocks on the bundles of wzw chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine lie algebra these bundle isomorphisms respect the knizhnik zamolodchikov connection and have finite order when all primary fields are fixed points the isomorphisms are endomorphisms in this case the bundle of chiral blocks is typically a reducible vector bundle a conjecture for the trace of such endomorphisms is presented the proposed relation generalizes the verlinde formula our results have applications to conformal field theories based on non simply connected groups and to the classification of boundary conditions in such theories

new construction of multiwavelength optical orthogonal codes we investigate multiwavelength optical orthogonal codes mwoocs for optical code division multiple access particularly we present a new construction method for mn spl lambda 2 spl lambda mwoocs with the number of available wavelengths m codeword length n and constant hamming weight spl lambda 2 that have autocorrelation and cross correlation values not exceeding spl lambda in the proposed scheme there is no constraint on the relationship between the number of available wavelengths and the codeword length and it is also possible to use an arbitrary spl lambda we show that the constructed code is optimal especially for spl lambda 1 finally we analyze the bit error rate of the new code and compare it with that of other optical codes