new bound on frequency hopping sequence sets and its optimal constructions in this paper we derive a new bound on maximum nontrivial hamming correlation of frequency hopping fh sequences from the singleton bound in error correcting code literature and we discuss the relation between the new bound and the known ones on fh sequences further we construct two classes of fh sequences from punctured reed solomon codes and one class of fh sequences from polynomial functions which meet the new bound

a class of optimal frequency hopping sequences with new parameters in this paper we propose an interleaving construction of new sets of frequency hopping sequences from the known ones by choosing suitable known optimal frequency hopping sequences and sets of frequency hopping sequences and then recursively applying the proposed construction optimal frequency hopping sequences and sets of frequency hopping sequences with new parameters can be obtained

new families of optimal frequency hopping sequence sets frequency hopping sequences fhss are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems in this paper we present combinatorial constructions for fhs sets including direct constructions by using cyclotomic classes recursive constructions based on cyclic difference matrices merging blocks and discrete logarithm by these constructions a number of series of new fhs sets are then produced these fhs sets are optimal with respect to the peng fan bounds

weighted max norms splittings and overlapping additive schwarz iterations summary weighted max norm bounds are obtained for algebraic additive schwarz iterations with overlapping blocks for the solution of ax b when the coefficient matrix a is an m matrix the case of inexact local solvers is also covered these bounds are analogous to those that exist using a norms when the matrix a is symmetric positive definite a new theorem concerningp regular splittings is presented which provides a useful tool for the a norm bounds furthermore a theory of splittings is developed to represent algebraic additive schwarz iterations this representation makes a connection with multisplitting methods with this representation and using a comparison theorem it is shown that a coarse grid correction improves the convergence of additive schwarz iterations when measured in weighted max norm

frequency hopping code sequence designs having large linear span in frequency hopping spread spectrum multiple access communication systems it is desirable to use sets of hopping patterns that in addition to having good hamming correlation properties and large period are also derived from sequences having large linear span here two such frequency hopping code sequence designs that are based on generalized bent functions and generalized bent sequences are presented the hamming correlation properties of the designs are optimal in the first case and close to optimal in the second in terms of the alphabet size p required to be prime in both cases the period and family size of the two designs are given by p sup 2 p and p sup n p sup n 2 1 n an even integer respectively the finite field sequences underlying the patterns in the first design have linear span exceeding p whereas still larger linear spans when compared to the sequence period can be obtained using the second design method

rbf fd formulas and convergence properties the local rbf is becoming increasingly popular as an alternative to the global version that suffers from ill conditioning in this paper we study analytically the convergence behavior of the local rbf method as a function of the number of nodes employed in the scheme the nodal distance and the shape parameter we derive exact formulas for the first and second derivatives in one dimension and for the laplacian in two dimensions using these formulas we compute taylor expansions for the error from this analysis we find that there is an optimal value of the shape parameter for which the error is minimum this optimal parameter is independent of the nodal distance our theoretical results are corroborated by numerical experiments

the weight distribution of some irreducible cyclic codes irreducible cyclic codes have been an interesting subject of study for a long time their weight distribution is known in only a few cases in this paper the weight distribution of the irreducible cyclic codes in a number of other cases is determined the number of nonzero weights in the codes dealt with in this paper varies between one and four

minimal positive stencils in meshfree finite difference methods for the poisson equation meshfree finite difference methods for the poisson equation approximate the laplace operator on a point cloud desirable are positive stencils i e all neighbor entries are of the same sign classical least squares approaches yield large stencils that are in general not positive we present an approach that yields stencils of minimal size which are positive we provide conditions on the point cloud geometry so that positive stencils always exist the new discretization method is compared to least squares approaches in terms of accuracy and computational performance

a new construction of frequency hopping sequences with optimal partial hamming correlation frequency hopping sequences fhss with favorable partial hamming correlation properties have important applications in many synchronization and multiple access systems in this paper lower bounds on the partial hamming correlation of fhss and fhs sets are proposed they slightly improve the known bounds by eun et al and zhou et al a construction of fhss and fhs sets having optimal partial hamming correlation with respect to the improved bounds is also presented based on the theory of generalized cyclotomy our construction yields optimal fhss and fhs sets with new and flexible parameters not covered in this paper

strictly optimal frequency hopping sequence sets with optimal family sizes frequency hopping sequences fhss with favorable partial hamming correlation properties are desirable in many synchronization and multiple access systems an fhs set is said to be strictly optimal if it has optimal partial hamming correlation for any correlation window in this paper we derive upper bounds on the family sizes of fhs sets with respect to partial hamming correlation from some classical bounds on error correcting codes we then present strictly optimal fhs sets having optimal family sizes with respect to one of the new bounds in particular our construction gives new parameters not covered in the literature

the approximation power of moving least squares a general method for near best approximations to functionals on r d using scattered data information is discussed the method is actually the moving least squares method presented by the backus gilbert approach it is shown that the method works very well for interpolation smoothing and derivatives approximations for the interpolation problem this approach gives mclain s method the method is near best in the sense that the local error is bounded in terms of the error of a local best polynomial approximation the interpolation approximation in r d is shown to be a c function and an approximation order result is proven for quasi uniform sets of data points

a meshfree generalized finite difference method for surface pdes abstract in this paper we propose a novel meshfree generalized finite difference method gfdm approach to discretize pdes defined on manifolds derivative approximations for the same are done directly on the tangent space in a manner that mimics the procedure followed in volume based meshfree gfdms as a result the proposed method not only does not require a mesh it also does not require an explicit reconstruction of the manifold in contrast to some existing methods it avoids the complexities of dealing with a manifold metric while also avoiding the need to solve a pde in the embedding space a major advantage of this method is that all developments in usual volume based numerical methods can be directly ported over to surfaces using this framework we propose discretizations of the surface gradient operator the surface laplacian and surface diffusion operators possibilities to deal with anisotropic and discontinuous surface properties with large jumps are also introduced and a few practical applications are presented

five families of three weight ternary cyclic codes and their duals as a subclass of linear codes cyclic codes have applications in consumer electronics data storage systems and communication systems as they have efficient encoding and decoding algorithms in this paper five families of three weight ternary cyclic codes whose duals have two zeros are presented the weight distributions of the five families of cyclic codes are settled the duals of two families of the cyclic codes are optimal

improved treatment of wall boundary conditions for a particle method with consistent spatial discretization abstract in recent years consistent spatial discretization schemes for meshfree particle methods to numerically simulate incompressible flow have been studied by many researchers this study is focused on the treatment of solid wall boundary conditions for one of those schemes namely the least squares mps lsmps scheme and proposes a new technique to deal with no slip and free slip wall boundary conditions with the proposed treatment wall geometries are expressed by surface meshes i e polygons in 3d and line segments in 2d thus complicated geometries can be handled easily based on a taylor series expansion wall boundary conditions are incorporated into the differential operators acting on fluid particles located in the vicinity of a wall through a least squares approach as a consequence neumann boundary conditions can be treated quite efficiently to verify consistency of the proposed discretization scheme a convergence study was carried out as numerical examples couette flow plane poiseuille flow gravity driven flow in a 3d square duct a rigid rotation problem taylor green vortices and lid driven cavity flow have been calculated using the proposed boundary treatment with both no slip and free slip conditions applied as a result the present method agreed well with the reference solutions which verified its computational accuracy

a family of five weight cyclic codes and their weight enumerators cyclic codes are a subclass of linear codes and have applications in consumer electronics data storage systems and communication systems as they have efficient encoding and decoding algorithms in this paper a family of p ary cyclic codes whose duals have three pairwise nonconjugate zeros is proposed the weight distribution of this family of cyclic codes is determined it turns out that the proposed cyclic codes have five nonzero weights

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

algebraic constructions of optimal frequency hopping sequences frequency hopping fh spread spectrum and direct sequence spread spectrum are two main spread coding technologies frequency hopping sequences are needed in fh code division multiple access cdma systems in this correspondence three classes of optimal frequency hopping sequences are constructed with algebraic methods the three classes are based on perfect nonlinear functions power functions and norm functions respectively both individual optimal frequency hopping sequences and optimal families of frequency hopping sequences are presented

positive versus compact support solutions to a singular elliptic problem abstract the semilinear elliptic problem u k x u q u p u 0 in u 0 on is considered in this paper where is a bounded domain of r n n 2 with c 2 boundary 0 q p 1 and k x as x we mainly study the effect of the blow up rate of k x near to the existence of positive and compact support solutions furthermore an optimal compact support principle is given for a class of elliptic differential inequalities

optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings we construct new sequences over finite rings having optimal hamming correlation properties these sequences are useful in frequency hopping multiple access fhma spread spectrum communication systems our constructions can be classified into linear and nonlinear categories both giving optimal hamming correlations according to lempel greenberger 1974 bound the nonlinear sequences have large linear complexity and can be seen as a generalized version of gmw sequences over fields

optimal variable shape parameter for multiquadric based rbf fd method in this follow up paper to our previous study in bayona et al 2011 2 we present a new technique to compute the solution of pdes with the multiquadric based rbf finite difference method rbf fd using an optimal node dependent variable value of the shape parameter this optimal value is chosen so that to leading order the local approximation error of the rbf fd formulas is zero in our previous paper bayona et al 2011 2 we considered the case of an optimal constant value of the shape parameter for all the nodes our new results show that if one allows the shape parameter to be different at each grid point of the domain one may obtain very significant accuracy improvements with a simple and inexpensive numerical technique we analyze the same examples studied in bayona et al 2011 2 both with structured and unstructured grids and compare our new results with those obtained previously we also find that if there are a significant number of nodes for which no optimal value of the shape parameter exists then the improvement in accuracy deteriorates significantly in those cases we use generalized multiquadrics as rbfs and choose the exponent of the multiquadric at each node to assure the existence of an optimal variable shape parameter

optimal frequency hopping sequences via cyclotomy using cyclotomic numbers a simple construction is presented for frequency hopping fh sequences having optimal autocorrelation with respect to the well known lempel greenberger bound some optimal families of fh sequences are constructed the simplicity of this technique makes it attractive for practical use

a note on comparison theorems for splittings and multisplittings of hermitian positive definite matrices abstract we discuss iterative methods for the solution of the linear system ax b which are based on a single splitting or a multisplitting of a in order to compare different methods it is common to compare the spectral radius of the iterative matrix for m matrices a and weak regular splittings there exist well known comparison theorems here we give a comparison theorem for splittings of hermitian positive definite matrices furthermore we establish a comparison theorem for multisplittings of a hermitian positive definite matrix

optimal sets of frequency hopping sequences from linear cyclic codes in communication systems frequency hopping spread spectrum and direct sequence spread spectrum are two main spread coding technologies frequency hopping sequences are used in fh cdma systems in this paper an earlier idea of constructing optimal sets of frequency hopping sequences is further investigated new optimal parameters of sets of frequency hopping sequences are obtained with subcodes of the reed solomon codes optimal sets of frequency hopping sequences are constructed with a class of irreducible cyclic codes as a byproduct the weight distribution of a subclass of irreducible cyclic codes is determined

analysis of non overlapping domain decomposition algorithms with inexact solves in this paper we construct and analyze new non overlapping domain decomposition preconditioners for the solution of second order elliptic and parabolic boundary value problems the preconditioners are developed using uniform preconditioners on the subdomains instead of exact solves they exhibit the same asymptotic condition number growth as the corresponding preconditioners with exact subdomain solves and are much more efficient computationally moreover this asymptotic condition number growth is bounded independently of jumps in the operator coefficients across subdomain boundaries we also show that our preconditioners fit into the additive schwarz framework with appropriately chosen subspace decompositions condition numbers associated with the new algorithms are computed numerically in several cases and compared with those of the corresponding algorithms in which exact subdomain solves are used

algebraic theory of multiplicative schwarz methods the convergence of multiplicative schwarz type methods for solving linear systems when the coefficient matrix is either a nonsingular m matrix or a symmetric positive definite matrix is studied using classical and new results from the theory of splittings the effect on convergence of algorithmic parameters such as the number of subdomains the amount of overlap the result of inexact local solves and of coarse grid corrections global coarse solves is analyzed in an algebraic setting results on algebraic additive schwarz are also included

optimal cyclic codes with generalized niho type zeros and the weight distribution in this paper we extend two earlier works further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions it is interesting to note that many cyclic codes in the family are optimal and have only a few non zero weights besides using similar ideas we carry out some subtle manipulation of certain exponential sums

on a singular nonlinear semilinear elliptic problem where k x c2 b v9 a p 0 1 and l is a real parameter such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts nonnewtonian fluids and also the theory of heat conduction in electrically conducting materials see 3 5 8 9 for a detailed discussion obviously 1 1 cannot have a solution u c2 v9 if k x is not vanishing near v however under various appropriate assumptions on k x we will obtain classical solutions of 1 1 for l belonging to a certain range and we will also obtain some uniqueness criteria here a classical solution is a solution u of 1 1 which belongs to c2 v mc v9 with u 0 in v we also study the boundary behaviour of solutions of 1 1 and we will show that the solution u of 1 1 lies in a certain holder class the special case when k x is negative and l 0 has been studied by several authors the existence and uniqueness of the solution were established by crandall rabinowitz and tartar 6 del pino 7 gomes 10 and lazer and mckenna

a compact support principle for singular elliptic differential inequalities with a gradient term abstract in this paper a compact support principle is established for the elliptic differential inequality u u p k x f u u 0 for x large where p 1 k x 0 and f satisfies conditions f1 f3 below the main feature of this note is the presence of the gradient term u p and the singular coefficient function k x the result is optimal in some sense related to the power p and the decaying rate of k x at and the proof is based on finding appropriate comparison functions we also give a similar result in a bounded domain of r n n 2

meshfree finite difference approximations for functions of the eigenvalues of the hessian we introduce meshfree finite difference methods for approximating nonlinear elliptic operators that depend on second directional derivatives or the eigenvalues of the hessian approximations are defined on unstructured point clouds which allows for very complicated domains and a non uniform distribution of discretisation points the schemes are monotone which ensures that they converge to the viscosity solution of the underlying pde as long as the equation has a comparison principle numerical experiments demonstrate convergence for a variety of equations including problems posed on random point clouds complex domains degenerate equations and singular solutions

an algebraic convergence theory for restricted additive schwarz methods using weighted max norms convergence results for the restrictive additive schwarz ras method of cai and sarkis siam j sci comput 21 1999 pp 792 797 for the solution of linear systems of the form ax b are provided using an algebraic view of additive schwarz methods and the theory of multisplittings the linear systems studied are usually discretizations of partial differential equations in two or three dimensions it is shown that in the case of a symmetric positive definite the projections defined by the methods are not orthogonal with respect to the inner product defined by a and therefore the standard analysis cannot be used here the convergence results presented are for the class of m matrices and more generally for h matrices using weighted max norms comparison between different versions of the ras method are given in terms of these norms a comparison theorem with respect to the classical additive schwarz method makes it possible to indirectly get quantitative results on rates of convergence which otherwise cannot be obtained by the theory several ras variants are considered including new ones and two level schemes

overlapping blocks by growing a partition with applications to preconditioning starting from a partitioning of an edge weighted graph into subgraphs we develop a method which enlarges the respective sets of vertices to produce a decomposition with overlapping subgraphs the vertices to be added when growing a subset are chosen according to a criterion which measures the strength of connectivity with this subset by using our method on the directed graph associated with a matrix we obtain an overlapping decomposition of the set of variables which can be used for algebraic additive and multiplicative schwarz preconditioners we present a complexity analysis of this block growing method thus proving its computational efficiency numerical results for problems stemming from various application areas show that with these overlapping schwarz preconditioners we usually substantially improve gmres convergence as compared to preconditioners based on a nonoverlapping decomposition or an overlapping decomposition based on level sets without other criteria as well as incomplete lu

branches of positive and free boundary solutions for some singular quasilinear elliptic problems we study the existence and multiplicity of solutions strictly positive or nonnegative having a free boundary the boundary of the set where the solution vanishes of some one dimensional quasilinear problems of eigenvalue type with possibly singular nonlinear terms

complex codebooks from combinatorial designs codebooks also called signal sets meeting the welch bounds are desirable in code division multiple access cdma systems in 2003 binary codebooks meeting welch s bounds were constructed using difference sets by ding golin and kloslashve recently a generic construction of codebooks with cyclic difference sets meeting welch s bound on the maximum cross correlation amplitude was developed by xia in this correspondence the idea of xia is extended and related constructions of optimal codebooks with both cyclic and noncyclic difference sets are presented these codebooks are optimal in the sense that they also meet this welch bound in addition complex codebooks that almost meet welch s bound on the maximum cross correlation amplitude are also constructed with almost difference sets

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

error bounds for kernel based numerical differentiation the literature on meshless methods shows that kernel based numerical differentiation formulae are robust and provide high accuracy at low cost this paper analyzes the error of such formulas using the new technique of growth functions it allows to bypass certain technical assumptions that were needed to prove the standard error bounds on interpolants and their derivatives since differentiation formulas based on polynomials also have error bounds in terms of growth functions we have a convenient way to compare kernel based and polynomial based formulas it follows that kernel based formulas are comparable in accuracy to the best possible polynomial based formulas a variety of examples is provided

hopf boundary maximum principle violation for semilinear elliptic equations abstract we consider elliptic equations with non lipschitz nonlinearity u u 1 u u 1 u in a smooth bounded domain r n with dirichlet boundary conditions here 0 1 we prove the existence of a weak nonnegative solution which does not satisfy the hopf boundary maximum principle provided that is large enough and n max 2 2 1 1 1 1

convergence theory of restricted multiplicative schwarz methods convergence results for the restricted multiplicative schwarz rms method the multiplicative version of the restricted additive schwarz ras method for the solution of linear systems of the form ax b are provided an algebraic approach is used to prove convergence results for nonsymmetric m matrices several comparison theorems are also established these theorems compare the asymptotic rate of convergence with respect to the amount of overlap the exactness of the subdomain solver and the number of domains moreover comparison theorems are given between the rms and ras methods as well as between the rms and the classical multiplicative schwarz method

uniform convergence of the schwarz alternating method for solving singularly perturbed advection diffusion equations our purpose in this paper is to study the convergence rate of some variants of the schwarz alternating method for solving two types of singularly perturbed advection diffusion equations one in which the advection term first order term dominates and the other in which the lowest order term zeroth order term dominates for such problems boundary or other layer regions may be present for singular perturbation problems in which the advection dominates we choose two overlapping subregions one corresponding to an outer or elliptic region and the other corresponding to an inner or hyperbolic region our main result for this problem shows that if the subdomains can be chosen to follow the flow i e if the boundary interface of one of the subdomains corresponds to an outflow boundary for the streamlines of the flow then the schwarz iterates converge in the maximum norm with an error reduction factor per iteration that exponentially decays with increasing overlap or decreasing diffusion for the singular perturbation problem in which the lowest order term dominates we consider many overlapping subregions with no special requirement on outflow or inflow boundaries our main result here which is valid for two variants of the classical schwarz algorithm shows that the error reduction factor per iteration decays exponentially in the maximum norm with increasing overlap and increasing dominance of the zeroth order term for both problems our proofs rely on the maximum principle and the construction of barrier functions

regularity of an elliptic problem with a singular nonlinearity we study a semilinear boundary value problem with the feature that the vanishing boundary value makes the equation singular we prove that the positive solution is in general holder continuous up to the boundary and has even better regularity in some special cases

on some convergence results for fdm with irregular mesh abstract the proof of convergence of the finite difference method with arbitrary irregular meshes for some class of elliptic problems is presented by the use of the truncation error technique and stability analysis it was showed that max i u i u h i ch i e the solution u h converges linearly with the size of the star correctness of this theorem was also confirmed by numerical tests

compact moving least squares an optimization framework for generating high order compact meshless discretizations abstract a generalization of the optimization framework typically used in moving least squares is presented that provides high order approximation while maintaining compact stencils and a consistent treatment of boundaries the approach which we refer to as compact moving least squares resembles the capabilities of compact finite differences but requires no structure in the underlying set of nodes an efficient collocation scheme is used to demonstrate the capabilities of the method to solve elliptic boundary value problems in strong form stably without the need for an expensive weak form the flexibility of the approach is demonstrated by using the same framework to both solve a variety of elliptic problems and to generate implicit approximations to derivatives finally an efficient preconditioner is presented for the steady stokes equations and the approach s efficiency and high order of accuracy is demonstrated for domains with curvi linear boundaries

on the weight distribution of cyclic codes with niho exponents recently there has been intensive research on the weight distributions of cyclic codes in this paper we compute the weight distributions of three classes of cyclic codes with niho exponents more specifically we obtain two classes of binary three weight and four weight cyclic codes and a class of nonbinary four weight cyclic codes the weight distributions follow from the determination of value distributions of certain exponential sums several examples are presented to show that some of our codes are optimal and some have the best known parameters

a domain decomposition method with lagrange multipliers and inexact solvers for linear elasticity a new domain decomposition method with lagrange multipliers for elliptic problems is introduced it is based on a reformulation of the well known finite element tearing and interconnecting feti method as a saddle point problem with both primal and dual variables as unknowns the resulting linear system is solved with block structured preconditioners combined with a suitable krylov subspace method this approach allows the use of inexact subdomain solvers for the positive definite subproblems it is shown that the condition number of the preconditioned saddle point problem is bounded independently of the number of subregions and depends only polylogarithmically on the number of degrees of freedom of individual local subproblems numerical results are presented for a plane stress cantilever membrane problem

lower bounds on the hamming auto and cross correlations of frequency hopping sequences frequency hopping fh sequences have found wide applications in various modern fh spread spectrum communications and radar systems in fh spread spectrum communications the interference occurs when two distinct transmitters use the same frequency simultaneously in order to evaluate the goodness of fh sequence design the hamming correlation function is used as an important measure in this correspondence by considering separately the maximum hamming autocorrelation sidelobe h sub a and the maximum hamming cross correlation h sub c several new lower bounds on the size p of the frequency slot set f the sequence length l the family size m and correlation properties are established the new periodic bounds include the known lempel greenberger bounds as special case when m 2 and are tighter than the seay bounds under certain conditions when m 2 furthermore the new bounds disclose more information on the relationship between the maximum autocorrelation sidelobe and the maximum cross correlation compared with the lempel greenberger bounds and seay bounds besides the aperiodic fh bounds which have not yet been previously reported are also presented and discussed in this correspondence

a compact support principle for a class of elliptic differential inequalities abstract in this paper we establish a compact support principle for a class of elliptic differential inequalities such as u c x u q for x large where q 0 1 and 1 q n 2q is optimal in the sense that it cannot be replaced by any larger number applying this principle we also consider the existence and nonexistence of compact support solutions for a semilinear elliptic equation

schwarz methods of neumann neumann type for three dimensional elliptic finite element problems several domain decomposition methods of neumann neumann type are considered for solving the large linear systems of algebraic equations that arise from discretizations of elliptic problems by finite elements we will only consider problems in three dimensions several new variants of the basic algorithm are introduced in a schwarz method framework that provides tools which have already proven very useful in the design and analysis of other domain decomposition and multi level methods the neumann neumann algorithms have several advantages over other domain decomposition methods the subregions which define the subproblems only share the boundary degrees of freedom with their neighbors the subregions can also be of quite arbitrary shape and many of the major components of the preconditioner can be constructed from subprograms available in standard finite element program libraries in its original form however the algorithm lacks a mechanism for global transportation of information and its performance therefore suffers when the number of subregions increases in the new variants of the algorithms considered in this paper the preconditioners include global components of low rank to overcome this difficulty bounds are established for the condition number of the iteration operator which are independent of the number of subregions and depend only polylogarithmically on the number of degrees of freedom of individual local subproblems results are also given for problems with arbitrarily large jumps in the coefficients across the interfaces separating the subregions 1995 john wiley sons inc

optimal frequency hopping sequences a combinatorial approach frequency hopping multiple access fhma spread spectrum communication systems employing multiple frequency shift keying mfsk as data modulation technique are investigated from a combinatorial approach a correspondence between optimal frequency hopping fh sequences and partition type difference packings is first established by virtue of this correspondence fhma systems with a single optimal fh sequence each are constructed from various combinatorial structures such as affine geometries cyclic designs and difference families combinatorial recursive constructions are also presented many new infinite series of optimal fh sequences are thus obtained these new fh sequences are also useful in ultra wideband uwb communication systems

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

hamming weights of the duals of cyclic codes with two zeros cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms in this paper let bbb f r be a finite field with r q m suppose that g 1 g 2 in bbb f r are not conjugates over bbb f q operatorname ord g 1 n 1 operatorname ord g 2 n 2 d gcd n 1 n 2 and n n 1n 2 d let bbb f q g 1 bbb f q m 1 bbb f q g 2 bbb f q m 2 and text t i denote the trace function from bbb f q m i to bbb f q for i 1 2 we define a cyclic code mathcal c q m n 1 n 2 c a b a in bbb f q m 1 b in bbb f q m 2 where c a b text t 1 ag 1 0 text t 2 bg 2 0 text t 1 ag 1 1 text t 2 bg 2 1 ldots text t 1 ag 1 n 1 text t 2 bg 2 n 1 we mainly use gauss periods to present the weight distribution of the cyclic code mathcal c q m n 1 n 2 as applications we determine the weight distribution of cyclic code mathcal c q m q m 1 1 q m 2 1 with gcd m 1 m 2 1 in particular it is a three weight cyclic code if gcd q 1 m 1 m 2 1 we also explicitly determine the weight distributions of some classes of cyclic codes including several classes of four weight cyclic codes

a combinatorial construction for strictly optimal frequency hopping sequences frequency hopping sequences fhss with favorable partial hamming correlation properties have important applications in many synchronization and multiple access systems strictly optimal fhss are those fhss with optimal partial hamming autocorrelation irrespective of the correlation window length in this paper strictly optimal fhss are investigated from a combinatorial approach a generic connection between strictly optimal fhss and disjoint cyclic perfect mendelsohn difference families is established by virtue of this connection new strictly optimal fhss are generated from some disjoint cpmdfs these strictly optimal fhss have new parameters not covered in the literature

a cell centred finite volume method for the poisson problem on non graded quadtrees with second order accurate gradients this paper introduces a two dimensional cell centred finite volume discretization of the poisson problem on adaptive cartesian quadtree grids which exhibits second order accuracy in both the solution and its gradients and requires no grading condition between adjacent cells at t junction configurations which occur wherever resolution differs between neighboring cells use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation to properly recover second order accuracy in the resulting numerical gradients prior work addressing block structured grids and graded trees has shown that quadratic rather than linear interpolation is required the gradients otherwise exhibit only first order convergence which limits potential applications such as fluid flow however previous schemes fail or lose accuracy in the presence of the more complex t junction geometries arising in the case of general non graded quadtrees which place no restrictions on the resolution of neighboring cells we therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed the method handles complex tree topologies and large resolution jumps between neighboring cells even along the domain boundary and both dirichlet and neumann boundary conditions are supported numerical experiments confirm the overall second order accuracy of the method in the l norm

optimal constant shape parameter for multiquadric based rbf fd method radial basis functions rbfs have become a popular method for interpolation and solution of partial differential equations pdes many types of rbfs used in these problems contain a shape parameter and there is much experimental evidence showing that accuracy strongly depends on the value of this shape parameter in this paper we focus on pde problems solved with a multiquadric based rbf finite difference rbf fd method we propose an efficient algorithm to compute the optimal value of the shape parameter that minimizes the approximation error the algorithm is based on analytical approximations to the local rbf fd error derived in 1 we show through several examples in 1d and 2d both with structured and unstructured nodes that very accurate solutions compared to finite differences can be achieved using the optimal value of the constant shape parameter

extensions of certain graph based algorithms for preconditioning the original tpablo algorithms are a collection of algorithms which compute a symmetric permutation of a linear system such that the permuted system has a relatively full block diagonal with relatively large nonzero entries this block diagonal can then be used as a preconditioner we propose and analyze three extensions of this approach we incorporate a nonsymmetric permutation to obtain a large diagonal we use a more general parametrization for tpablo and we use a block gauss seidel preconditioner which can be implemented to have the same execution time as the corresponding block jacobi preconditioner experiments are presented showing that for certain classes of matrices the block gauss seidel preconditioner used with the system permuted with the new algorithm can outperform the best ilut preconditioners in a large set of experiments

consistency conditions for the influence graphs generalized finite difference method the modeling of physical phenomena is most often conveyed through partial differential equations governing continuous fields computational approaches are used afterwards in order to approximate the solutions to these equations in doing so a discretized version of the initial model must be set up using one of the numerous available methods this paper illustrates how influence graphs weighted digraphs with geometrical attributes may behave in the same way as differential operators in so far as a set of appropriate conditions of consistency are satisfied these conditions are written explicitly for the most often used cases including differential boundary operators on the one hand a consistent neighborhood may be regarded as a generalization of a classical finite difference scheme on the other hand a consistent influence graph is a discrete object modeling a physical behavior as well as its continuous counterpart numerical experimentations address firstly the second order diffusion model and lastly the fourth order kirchhoff theory of plate deflection

optimal frequency hopping sequences auto and cross correlation properties frequency hopping fh sequences play a key role in frequency hopping spread spectrum communication systems in order to evaluate the performance of fh sequences lempel and greenberger 1974 and peng and fan 2004 derived lower bounds on their hamming auto and cross correlations in this paper we construct families of fh sequences with hamming correlations meeting those bounds by combinatorial and algebraic techniques we first construct optimal families consisting of a single fh sequence with maximum hamming correlation equal to 2 from a combinatorial approach then we investigate families consisting of multiple fh sequences we provide a combinatorial characterization for such families and present a recursive method to construct them by means of this characterization we also describe two algebraic constructions for such families of fh sequences generalizing those of ding moisio and yuan 2007 as a consequence many new optimal families of fh sequences are obtained

minimal numerical differentiation formulas we investigate numerical differentiation formulas on irregular centers in two or more variables that are exact for polynomials of a given order and minimize an absolute seminorm of the weight vector error bounds are given in terms of a growth function that carries the information about the geometry of the centers specific forms of weighted ell 1 and weighted least squares minimization are proposed that produce numerical differentiation formulas with particularly good performance in numerical experiments the results are of interest in particular for meshless generalized finite difference methods as they provide a consistency error analysis for such methods

a new method to construct strictly optimal frequency hopping sequences with new parameters in order to evaluate the goodness of frequency hopping fh sequence design the periodic hamming correlation function is used as an important measure usually the length of correlation window is shorter than the period of the chosen fh sequence so the study of the partial hamming correlation of fh sequence is particularly important if an fh sequence or an fh sequence set has an optimal partial hamming correlation with respect to the partial hamming correlation bound for all length of correlation window then the fh sequence or the fh sequence set is said to be strictly optimal in this paper we first prove that there is no strictly optimal fh sequence set of family size m and sequence length n over a frequency slot set of size q with respect to the partial hamming correlation bound derived by niu et al when n q 2 m and q geq 2 and that by cai et al when n q 2 m and q geq 2n n 2 furthermore we define a special partition type difference packing dp called n nabla h a l pdp and give several classes of n nabla h a l pdps then we present a new construction of strictly optimal fh sequences by choosing different pdps the fh sequences constructed can give new and flexible parameters by utilizing this construction method recursively we can obtain new n nabla h a l pdps which lead to infinitely many classes of strictly optimal fh sequences with new parameters moreover based upon an n nabla h a l pdp we present a construction of strictly optimal fh sequence sets by preceding construction method and recursive construction we can also obtain infinite classes of strictly optimal fh sequence sets which can give new and flexible parameters

adaptive meshless centres and rbf stencils for poisson equation we consider adaptive meshless discretisation of the dirichlet problem for poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions new meshless stencil selection and adaptive refinement algorithms are proposed in 2d numerical experiments show that the accuracy of the solution is comparable with and often better than that achieved by the mesh based adaptive finite element method

are 2 weight projective cyclic codes irreducible we prove the following result on a 2 weight projective cyclic code c over fq if q 2 then c is irreducible if qne2 then either c is irreducible or c is the direct sum of two 1 weight irreducible cyclic codes