a quintic b spline finite elements scheme for the kdvb equation abstract an algorithm for solving the korteweg de vries burgers kdvb equation based on the collocation method with quintic b spline finite elements is set up to simulate the solutions of the kdv burgers and the kdvb equations the migration of solitary waves and temporal evolution of a maxwellian initial pulse are studied for the kdv equation burgers equation is solved for different values of reynolds number the time evaluation of the solutions of the kdvb equation with different values for the diffusion and dispersion coefficients is studied invariants and error norms are studied wherever possible to determine the conservation properties of the algorithm a linear stability analysis shows the scheme to be unconditionally stable

projective techniques and functional integration for gauge theories a general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact hausdorff spaces the procedure is then applied to gauge theories to carry out integration over the non linear infinite dimensional spaces of connections modulo gauge transformations this method of evaluating functional integrals can be used either in the euclidean path integral approach or the lorentzian canonical approach a number of measures discussed are diffeomorphism invariant and therefore of interest to the connection dynamics version of quantum general relativity the account is pedagogical in particular prior knowledge of projective techniques is not assumed

sequence folding lattice tiling and multidimensional coding folding a sequence b into a multidimensional box is a well known method which is used as a multidimensional coding technique the operation of folding is generalized in a way that the sequence b can be folded into various shapes and not just a box the novel definition of folding is based on a lattice tiling for the given shape s and a direction in the d dimensional integer grid necessary and sufficient conditions that a lattice tiling for s combined with a direction define a folding of a sequence into s are derived the immediate and most impressive applications are some new lower bounds on the number of dots in two dimensional synchronization patterns asymptotically optimal such patterns were known only for rectangular shapes we show asymptotically optimal such patterns for a large family of hexagons this is also generalized for multidimensional synchronization patterns the best known patterns in terms of dots for circles and other polygons are also given the technique and its application for two dimensional synchronization patterns raises some interesting problems in discrete geometry we will also discuss these problems it is also shown how folding can be used to construct multidimensional error correcting codes finally by using the new definition of folding new types of multidimensional pseudo random arrays with various shapes are generated

mds array codes for correcting a single criss cross error we present a family of maximum distance separable mds array codes of size p 1 spl times p 1 p a prime number and minimum criss cross distance 3 i e the code is capable of correcting any row or column in error without a priori knowledge of what type of error occurred the complexity of the encoding and decoding algorithms is lower than that of known codes with the same error correcting power since our algorithms are based on exclusive or operations over lines of different slopes as opposed to algebraic operations over a finite field we also provide efficient encoding and decoding algorithms for errors and erasures

a small time solutions for the korteweg de vries equation using spline approximation in this paper the one dimensional nonlinear korteweg de vries kdv equation is numerically solved using second order spline approximation the test problems concerning the propagation of a solution and two solution interaction are used to validate the proposal scheme and it is found to be both accurate and efficient at small times also it is shown that the second order spline approximation may be used effectively at small times when the exact solution of the kdv equation is not known

maximum rank array codes and their application to crisscross error correction a mu n n k array code c over a field f is a k dimensional linear space of n n matrices over f such that every nonzero matrix in c has rank or mu it is first shown that the dimension of such array codes must satisfy the singleton like bound k

the galerkin method for the kdv equation using a new basis of smooth piecewise cubic polynomials abstract in this paper we introduce the galerkin method using a new basis of smooth piecewise cubic polynomials for the one dimensional nonlinear kdv equation the stability analysis shows that the present method is unconditionally stable in l 2 norm numerical experiments show that the proposed method preserves the conservation laws and is effective for simulating the motions and the interactions of solitary waves

the fourier pseudospectral method with a restrain operator for the korteweg de vries equation abstract in this paper we develop a fourier pseudospectral method with a restrain operator for the korteweg de vries equation we prove the generalized stability of the schemes and give convergence estimations depending on the smoothness of the solution of the p d e

bounds for the size of radar arrays etablissement de bornes ameliorees superieure et inferieure pour la taille des tableaux radars formes de matrices rectangulaires a elements 0 et 1

proof of a conjecture by lewandowski and thiemann it is proven that for compact connected and semisimple structure groups every degenerate labelled web is strongly degenerate this conjecture by lewandowski and thiemann implies that diffeomorphism invariant operators in the category of piecewise smooth immersive paths preserve the decomposition of the space of integrable functions w r t the degeneracy and symmetry of the underlying labelled webs this property is necessary for lifting these operators to well defined operators on the space of diffeomorphism invariant states

functional integration on spaces of connections suppose thatgis a compact connected lie group andp mis a smooth principalg bundle we define a cylinder function on the space a of smooth connections onpto be a continuous complex function of the holonomies along finitely many piecewise smoothly immersed curves inm completing the algebra of cylinder functions in the sup norm we obtain a commutative c algebra fun a let a generalized measure on a be a bounded linear functional on fun a we construct a generalized measure 0on a that is invariant under all automorphisms of the bundlep not necessarily fixing the basem this result extends previous work which assumedmwas real analytic and used only piecewise analytic curves in the definition of cylinder functions as before any graph withnedges embedded inmdetermines a c subalgebra of fun a isomorphic toc gn and the generalized measure 0 fun a c restricts to the linear functional onc gn given by integration against normalized haar measure ongn our result implies that the group g of gauge transformations acts as unitary operators onl2 a the hilbert space completion of fun a in the norm f 2 0 f 2 1 2 using spin networks we construct explicit functions spanning the subspacel2 a g l2 a consisting of vectors invariant under the action of g

optimal error estimates of the legendre petrov galerkin method for the korteweg de vries equation in this paper the legendre petrov galerkin method for the korteweg de vries equation with nonperiodic boundary conditions is analyzed the nonlinear term is computed with the legendre spectral method and some pseudospectral methods respectively optimal error estimates in l2 norm are obtained for both semidiscrete and fully discrete schemes the method is also applicable to some 2m 1 th order differential equations

two dimensional synchronization patterns for minimum ambiguity a number of closely related combinatorial problems corresponding to specific assumptions about the type of time frequency sequence which may be appropriate in a particular application are formulated in terms of square or rectangular arrays of dots with appropriate constraints on the two dimensional correlation function the current state of knowledge concerning each of these problems is summarized it is hoped that more general constructions may be found leading to larger families of solutions as well as better computational algorithms for finding individual solutions which may lie outside of the general families

a small time solutions for the korteweg de vries equation in this paper a heat balance integral hbi method is applied to the one dimensional non linear korteweg de vries kdv equation prescribed by appropriate homogenous boundary conditions and a set of initial conditions to obtain its approximate analytical solutions at small times it is shown that the hbi solutions obtained by the method may be used effectively at small times when the exact solution of the kdv equation is not known

uniqueness of diffeomorphism invariant states on holonomy flux algebras loop quantum gravity is an approach to quantum gravity that starts from the hamiltonian formulation in terms of a connection and its canonical conjugate quantization proceeds in the spirit of dirac first one defines an algebra of basic kinematical observables and represents it through operators on a suitable hilbert space in a second step one implements the constraints the main result of the paper concerns the representation theory of the kinematical algebra we show that there is only one cyclic representation invariant under spatial diffeomorphisms while this result is particularly important for loop quantum gravity we are rather general the precise definition of the abstract algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group the variables are constructed from the holonomy map and from the fluxes of the momentum conjugate to the connection the uniqueness result is relevant for any such theory invariant under spatial diffeomorphisms or being a part of a diffeomorphism invariant theory

a hybrid numerical method for the kdv equation by finite difference and sinc collocation method abstract in this paper we propose a hybrid numerical method for the kdv equation more precisely we discretize the temporal derivative of kdv equation by a weighted scheme and treat the implicitly nonlinear term with the combination of finite difference and sinc collocation method the stability analysis is presented and numerical experiments illustrate the efficiency and stability of the proposed hybrid method the motions and the interactions of solitary waves relying on particular initial boundary conditions are also simulated

a local discontinuous galerkin method for the korteweg de vries equation with boundary effect a local discontinuous galerkin method for solving korteweg de vries kdv type equations with non homogeneous boundary effect is developed we provide a criterion for imposing appropriate boundary conditions for general kdv type equations the discussion is then focused on the kdv equation posed on the negative half plane which arises in the modeling of transition dynamics in the plasma sheath formation h liu m slemrod kdv dynamics in the plasma sheath transition appl math lett 17 4 2004 401 410 the guiding principle for selecting inter cell fluxes and boundary fluxes is to ensure the l 2 stability and to incorporate given boundary conditions the local discontinuous galerkin method thus constructed is shown to be stable and efficient numerical examples are given to confirm the theoretical result and the capability of this method for capturing soliton wave phenomena and various boundary wave patterns

conservative numerical methods for solitary wave interactions the purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation it is shown that the so called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision

stratification of the generalized gauge orbit space different versions for defining ashtekar s generalized connections are investigated depending on the chosen smoothness category for the paths and graphs the label set for the projective limit our definition covers the analytic case as well as the case of webs

error correction of multidimensional bursts we present several methods and constructions to generate binary codes for correction of a multidimensional cluster error whose shape can be a box error a lee sphere error or an error with an arbitrary shape our codes have very low redundancy close to optimal and a large range of parameters of arrays and clusters our main results are summarized as follows 1 a construction of two dimensional codes capable to correct a rectangular error with considerably more flexible parameters from previously known constructions this construction is easily generalized for d dimensions 2 a novel method based on d colorings of the d dimensional space for constructing d dimensional codes correcting a d dimensional cluster error of various shapes 3 a transformation of the d dimensional space into another d dimensional space in a way that a d dimensional lee sphere is transformed into a shape located in a d dimensional box of a relatively small size 4 applying the coloring method to correct more efficiently a two dimensional error whose shape is a lee sphere 5 a construction of d dimensional codes capable to correct a d dimensional cluster error of size b in which the number of erroneous positions is relatively small compared to b 6 we present a code which corrects a d dimensional arbitrary cluster error with relatively small redundancy

new bounds for the sizes of radar arrays improved upper bounds for the size of radar arrays are found by using the window method new general constructions and computer searched examples are presented the radar array problem is generalized to include arrays with sidelobes greater than 1

when do measures on the space of connections support the triad operators of loop quantum gravity in this work we investigate the question under what conditions hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non abelian analogues of the electric flux we give the problem a precise mathematical formulation and start its investigation for the technically simple case of u 1 as gauge group we establish a number of no go theorems asserting that for certain classes of measures the flux operators can not be represented on the corresponding hilbert spaces the flux observables we consider play an important role in loop quantum gravity since they can be defined without recurse to a background geometry and they might also be of interest in the general context of quantization of non abelian gauge theories

integer sets with distinct sums and differences and carrier frequency assignments for nonlinear repeaters the problem of assigning n carrier frequencies so as to avoid certain types third and fifth order of intermodulation interference is discussed for the third order case close upper and lower bounds on the optimal solution are established and close to optimal solutions are given for n previously suboptimal solutions were known only for n leq 23 for the fifth order case it is shown that some existing results can be applied to this problem and suboptimal solutions obtained by this construction are given for n leq 17 no solutions were known previously

an analytical numerical method for solving the korteweg de vries equation in this paper an analytical numerical method is applied to the one dimensional korteweg de vries equation with a variant of boundary and initial conditions to obtain its numerical solutions at small times two test problem with known exact solutions are studied to demonstrate the accuracy of the present method the obtained results are compared with the exact solution of each problem and are found to be in good agreement with each other the numerical scheme is also compared with earlier work and shown to be accurate and efficient

a systematic construction for radar arrays the radar array problem arises from the need to design frequency hopping sequences with small out of phase autocorrelations it assumes the reflected signals have negligible doppler shifts so the correlations are calculated along the time axis only in this correspondence a systematic construction for radar arrays is provided by means of homogeneous uniform difference matrices a systematic construction for properly centered permutation matrices a special kind of homogeneous uniform difference matrices is also provided which partially solves the open problems posed by zhang and tu

diffeomorphism invariant spin network states abstract we extend the theory of diffeomorphism invariant spin network states from the real analytic category to the smooth category suppose that g is a compact connected semisimple lie group and p m is a smooth principal g bundle a cylinder function on the space of smooth connections on p is a continuous complex function of the holonomies along finitely many piecewise smoothly immersed curves in m we construct diffeomorphism invariant functionals on the space of cylinder functions from spin networks graphs in m with edges labeled by representations of g and vertices labeled by intertwining operators using the group averaging technique of ashtekar marolf mourao and thiemann we equip the space spanned by these diffeomorphism invariant spin network states with a natural inner product

symmetric golomb squares inspection of optimum golomb squares found by exhaustive computer search shows some are symmetric with respect to diagonal reflection this suggests searching for such symmetric golomb squares might be an efficient way to find good squares in this correspondence we find the best symmetric n spl times n golomb squares for n spl les 22 some appear to be the best known

structured light using pseudorandom codes we solve the correspondence problem in active stereo vision using a novel pseudorandom coded structured light sl this coding scheme performs well in the presence of occlusion in settings where color coding is feasible 3d information can be obtained using a single image

projective loop quantum gravity i state space instead of formulating the state space of a quantum field theory over one big hilbert space it has been proposed by kijowski to describe quantum states as projective families of density matrices over a collection of smaller simpler hilbert spaces beside the physical motivations for this approach it could help designing a quantum state space holding the states we need in a latter work by okolow the description of a theory of abelian connections within this framework was developed an important insight being to use building blocks labeled by combinations of edges and surfaces the present work generalizes this construction to an arbitrary gauge group g in particular g is neither assumed to be abelian nor compact this involves refining the definition of the label set as well as deriving explicit formulas to relate the hilbert spaces attached to different labels if the gauge group happens to be compact we also have at our disposal the well established ashtekar lewandowski hilbert space which is

error estimates of the semi discrete local discontinuous galerkin method for nonlinear convection diffusion and kdv equations in this paper we provide l 2 error estimates for the semi discrete local discontinuous galerkin methods for nonlinear convection diffusion equations and kdv equations with smooth solutions the main technical difficulty is the control of the inter element jump terms which arise because of the nonlinearity of the pdes and the discontinuous nature of the numerical method

golomb rectangles as folded rulers a correspondence between two dimensional golomb rectangles and one dimensional golomb rulers is given results are translated from rulers to rectangles the extension of these results to an arbitrary number of dimensions is given a new bound is developed on the number of ones in a golomb array of any dimension some new optimum golomb squares rectangles and higher dimensional arrays are given

a legendre petrov galerkin and chebyshev collocation method for third order differential equations a legendre petrov galerkin lpg method for the third order differential equation is developed by choosing appropriate base functions the method can be implemented efficiently also this new approach enables us to derive an optimal rate of convergence in l2 norm the method is applied to some nonlinear problems such as the korteweg de vries kdv equation with the chebyshev collocation treatment for the nonlinear term it is a legendre petrov galerkin and chebyshev collocation lpg cc method numerical experiments are given to confirm the theoretical result

a class of burst error correcting array codes corresp the usual k 2 1 times k 1 1 array code in which the last row and the last column contain redundant bits can correct any single error however if the bits are read diagonally instead of horizontally the code can correct bursts of errors it is shown that the k 2 1 times k 1 1 array code with diagonal readout can correct any burst of length up to k 1 if and only if k 2 geq 2 k 1 1

representations of the weyl algebra in quantum geometry the weyl algebra mathfrak a of continuous functions and exponentiated fluxes introduced by ashtekar lewandowski and others in quantum geometry is studied it is shown that in the piecewise analytic category every regular representation of mathfrak a having a cyclic and diffeomorphism invariant vector is already unitarily equivalent to the fundamental representation additional assumptions concern the dimension of the underlying analytic manifold at least three the finite wide triangulizability of surfaces in it to be used for the fluxes and the naturality of the action of diffeomorphisms but neither any domain properties of the represented weyl operators nor the requirement that the diffeomorphisms act by pull backs for this the general behaviour of c algebras generated by continuous functions and pull backs of homeomorphisms as well as the properties of stratified analytic diffeomorphisms are studied additionally the paper includes also a short and direct proof of the irreducibility of mathfrak a

genetic search for golomb arrays genetic search with a decision level chromosome is used to search efficiently for golomb 1982 arrays a golomb array a is a binary array with three values for its discrete autocorrelation function m the number of ones in a for no offset 1 when there is partial overlap and 0 otherwise in one dimension a is known as a golomb ruler the method yields improvement because the genetic search considers only feasible solutions in the most likely portion of the search space each chromosome bit represents a decision to place a one in an iterative construction the representation includes all possible arrays since the chromosome bits represent binary decisions in the search space genetic operations such as crossover and mutation always result in feasible descendent chromosomes experimental results include comparison to previously known search methods and several new arrays these results indicate that the proposed search is significantly more efficient than prior methods

two dimensional patterns with distinct differences constructions bounds and maximal anticodes a two dimensional 2 d grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope these configurations are known to have many applications such as radar sonar physical alignment and time position synchronization rather than restricting dots to lie in a square or rectangle as previously studied we restrict the maximum distance between dots of the configuration the motivation for this is a new application of such configurations to key distribution in wireless sensor networks we consider configurations in the hexagonal grid as well as in the traditional square grid with distances measured both in the euclidean metric and in the manhattan or hexagonal metrics we note that these configurations are confined inside maximal anticodes in the corresponding grid we classify maximal anticodes for each diameter in each grid we present upper bounds on the number of dots in a pattern with distinct differences contained in these maximal anticodes our bounds settle in the negative a question of golomb and taylor on the existence of honeycomb arrays of arbitrarily large size we present constructions and lower bounds on the number of dots in configurations with distinct differences contained in various 2 d shapes such as anticodes by considering periodic configurations with distinct differences in the square grid

numerical solution of korteweg de vries equation by galerkin b spline finite element method a finite element solution of the kdv equation is presented to demonstrate the efficiency of the method two test problems are considered the numerical solutions of the kdv equation are compared with both the exact solutions and other numerical solutions in the literature the numerical solutions are found to be in good agreement with the exact solutions

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

golomb rectangles there are a number of communications problems involving two dimensional arrays with constrained correlation functions golomb s two classes of radar arrays and sonar arrays are examined improved bounds optimal cases and computational procedures are reported