multiplicity results for asymptotically linear elliptic problems at resonance in this paper several new multiplicity results for asymptotically linear elliptic problem at resonance are obtained via morse theory and minimax methods some new observations on the critical groups of a local linking type critical point are used to deal with the resonance case at 0

multiple periodic solutions of ordinary differential equations with double resonance abstract in this paper we study by morse theory the existence of multiple periodic solutions of a class of ordinary differential equation with double resonance at infinity between two consecutive eigenvalues and with resonance at origin

upper bounds on generalized distances we derive new asymptotic bounds for generalized distances our approach extends the classical hamming plotkin and elias bounds the latter bound involves extending the definition of generalized distances to nonlinear codes

on the dimension of subfield subcodes a new lower bound for the dimension of a subfield subcode is given this bound improves the well known lower bound of p delsarte 1975 and coincides in many cases with the true dimension of the code alternant codes and geometric goppa codes are discussed as special cases

the trace operator and redundancy of goppa codes the dimension of subfield subcodes and in particular generalized goppa codes is studied using the kernel of an associated trace map bounds on the dimension for a particular general class of binary goppa codes are obtained deeper study of some special cases and other related polynomials yields still tighter bounds for any s 1

nontrivial solutions for impulsive fractional differential equations via morse theory abstract in this paper we study the existence of nontrivial solutions for an impulsive fractional differential equation with dirichlet boundary conditions by using morse theory coupled with local linking arguments we obtain some new criteria to guarantee that the impulsive fractional differential equations have at least one nontrivial solution

dirichlet problems with double resonance and an indefinite potential abstract we consider semilinear dirichlet problems with an unbounded and indefinite potential and with a caratheodory reaction we assume that asymptotically at infinity the problem exhibits double resonance using variational methods together with morse theory and flow invariance arguments we prove multiplicity theorems producing three five six or seven nontrivial smooth solutions in most multiplicity theorems we provide precise sign information for all the solutions established

solutions of asymptotically linear operator equations via morse theory abstract in this paper we use the classical morse theory of critical points to study the existence and multiplicity of solutions of a class of asymptotically linear operator equations as special cases we include multiplicity results for semilinear elliptic bvp s as well as existence and multiplicity of periodic solutions of semilinear wave equation and of hamiltonian systems these results simplify and complement recent work of amann zehnder and castro lazer author

critical groups at zero and multiple solutions for a quasilinear elliptic equation abstract in this paper by morse theory we will compute the critical groups at zero for a functional i w 0 1 p r defined by setting i u 1 p u p d x 1 2 u 2 d x f x u d x where p 2 is a bounded domain in r n f x u 0 u f x t d t and we assume that f is resonant at zero for the spectrum of in w 0 1 2 as an application of these critical groups estimates some multiplicity results are also given

an elliptic resonance problem with multiple solutions in this paper we study the existence of multiple nontrivial solutions for a semilinear elliptic equation at resonance by the minimax methods and morse theory

generalized hamming weights of linear codes the generalized hamming weight d sub r c of a binary linear code c is the size of the smallest support of any r dimensional subcode of c the parameter d sub r c determines the code s performance on the wire tap channel of type ii bounds on d sub r c and in some cases exact expressions are derived in particular a generalized griesmer bound for d sub r c is presented and examples are given of codes meeting this bound with equality

asymptotically linear elliptic equations without nonresonance conditions abstract in this paper we are concerned with the existence of nontrivial solutions of a semilinear elliptic equation when the nonresonance condition at infinity is not satisfied we consider a strongly resonant case in the first part and a sort of resonance under density assumptions in the second part

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

parameters of goppa codes revisited we discuss parameters of goppa 1970 codes such as minimum distance covering radius distance distribution and generalized hamming weights by a variation on the exponential sums method and combinatorial arguments we sharpen known bounds on these parameters

pairs of nontrivial solutions for resonant neumann problems abstract we study a semilinear neumann problem which is resonant at with respect to any eigenvalue different from the first and the second eigenvalue of n the negative neumann laplacian using a combination of variational methods with morse theoretic techniques we show that the problem has at least two nontrivial smooth solutions

on estimating distribution functions and quantiles from survey data using auxiliary information summary ratio and difference estimators of a population distribution function under a general sampling design are obtained using auxiliary population information the relative mean errors and relative mean square errors of these estimators and a model based estimator of chambers dunstan 1986 are compared through a simulation study the advantages of the design based estimators over the model based estimator under model misspecifications especially for large samples are demonstrated ratio and difference estimators of a population quantile are also studied

multiple solutions for semilinear resonance elliptic problems with nonconstant coefficients at infinity in this paper we study a class of semilinear elliptic equations which are completely resonant with nonconstant coefficients at origin and at infinity by applying morse theory and minimax method we obtain the existence of multiple nontrivial solutions for the equations

geometric approach to higher weights the notion of higher or generalized weights of codes is just as natural as that of the classical hamming weight the authors adopt the geometric point of view and always treat the q ary case some results and proofs being new the main goal is to present a clear picture of what is known on the subject

solutions to a gradient system with resonance at both zero and infinity in this paper we study the existence and multiplicity of nontrivial solutions for a gradient system with resonance at both zero and infinity via morse theory

multiple solutions for semilinear elliptic boundary value problems with double resonance abstract in this paper we study the multiplicity of nontrivial solutions of semilinear elliptic boundary value problems which may be double resonance near infinity between two consecutive eigenvalues of with zero dirichlet boundary data the methods we use here are morse theory minimax methods and bifurcation theory

on spectra of bch codes derives an estimate for the error term in the binomial approximation of spectra of bch codes this estimate asymptotically improves on the bounds by sidelnikov 1971 kasami et al 1985 and sole 1990

subclass of binary goppa codes with minimal distance equal to the design distance a subclass of binary goppa codes specified by a separable polynomial g x x sup t a and a subset l of elements of gf 2 sup m no element of l may be a root of g x and t 2 sup m 1 a is a tth power in gf 2 sup m 0 is studied for such codes it is shown that their minimal distance is equal to the design distance d 2t 1

applications of local linking to critical point theory we prove the existence of nontrivial critical points of functionals with a local linking at 0 applications to elliptic boundary value problems and to hamiltonian systems are given c 1995 academic press inc

a class of estimators of the population mean in survey sampling using auxiliary information summary for estimating the mean of a finite population using information on an auxiliary variable a class of estimators is defined as a function of the ratio of sample mean to population mean and the ratio of sample variance to population variance of the auxiliary variable asymptotic expressions for bias and mean squared error are obtained a condition is given for the minimum mean squared error of estimators of this class to be smaller than those which use only the ratio of sample mean to population mean of the auxiliary variable

an asymmetric superlinear elliptic problem at resonance abstract in this article we study the existence and multiplicity of solutions to the problem u g x u in u 0 on where is a bounded domain in r n n 2 with smooth boundary and g r r is a differentiable function we will assume that g x s has a resonant behavior for large negative values of s and that a landesman lazer type condition is satisfied we also assume that g x s is superlinear but subcritical for large positive values of s we prove the existence and multiplicity of solutions for problem 1 1 by using minimax methods and infinite dimensional morse theory

on a robin problem with indefinite weight and asymmetric reaction superlinear at abstract the existence of at least three nontrivial smooth solutions to a semilinear robin problem with indefinite potential and asymmetric nonlinearity super linear at is established both crossing and resonance are allowed proofs exploit variational methods truncation techniques and morse theory

on solvability for a class of quasilinear resonance elliptic equations abstract in this paper we obtain an existence result for a class of high order quasilinear elliptic equations with higher eigenvalues the proofs rely on galerkin type techniques brouwer s fixed points theorem in this case the nonlinearity is unbounded and satisfies sublinear growth the equation is one of the most useful sets of navier stokes equations which describe the motion of viscous fluid substances such as liquids gases and so on

existence of a nontrivial solution for a class of hemivariational inequality problems at double resonance abstract in this paper we discuss a class of semilinear elliptic hemivariational inequality problems by using the nonsmooth minimax principle for locally lipschitz functions we establish the existence of a nontrivial solution for the semilinear elliptic hemivariational inequality problem where incomplete double resonance occurs at infinity between two distinct consecutive eigenvalues

computations of critical groups and applications to some differential equations at resonance abstract in this paper we first consider the computations of the critical groups of a functional with generalized ahmad lazer paul type conditions both at zero and infinity then the abstract results are applied to investigate some new cases of the existence of nontrivial solutions of the second order hamiltonian systems and elliptic boundary value problems which may be resonant both at zero and infinity

ratio methods to the mean estimation with known quantiles we address the problem of estimating the finite population mean in survey sampling by exploiting any available auxiliary information in order to increase the precision of classical estimators the idea is to use any population quantiles of the available auxiliary variables which are known in many real situation from census administrative files etc this is achieved using these known quantities in the construction of the estimators by modifying the usual ratio estimation methods and afterwards defining a general class of exponentiation ratio estimators the advantages of the proposed estimators are demonstrated using theoretical asymptotic tools and through a simulation study

multiple nontrivial solutions for asymptotically linear discrete problem via computations of the critical groups in this paper we study the multiplicity of nontrivial solutions for asymptotically linear discrete problem by using critical point theory morse theory and minimax methods we obtained that the problem has at least two nontrivial solutions under various conditions

multiple solutions to a robin problem with indefinite weight and asymmetric reaction abstract the existence of two nontrivial smooth solutions to a semilinear robin problem with indefinite unbounded potential and asymmetric nonlinearity f is established both crossing and resonance are allowed a third nonzero solution exists provided f is c 1 proofs exploit variational methods truncation techniques and morse theory

robin problems with a general potential and a superlinear reaction abstract we consider semilinear robin problems driven by the negative laplacian plus an indefinite potential and with a superlinear reaction term which need not satisfy the ambrosetti rabinowitz condition we prove existence and multiplicity theorems producing also an infinity of smooth solutions using variational tools truncation and perturbation techniques and morse theory critical groups

on generalized hamming weights of bch codes introduces methods from algebraic geometry to determine generalized hamming weights of bch codes as an application of these methods the authors determine for primitive 2 resp 3 error correcting bch codes the third resp the second generalized hamming weight

applications of morse theory to some nonlinear elliptic equations with resonance at zero abstract in this paper we study the existence and multiplicity of solutions for some nonlinear elliptic boundary value problems with resonance at zero by applying morse theory we do not impose additional global condition on the nonlinearities except for a subcritical growth condition

nontrivial solutions of semilinear equations at resonance in this paper we prove new existence results concerning nontrivial solutions to semilinear elliptic problem at resonance the methods used here are based on combining the minimax methods and the morse theory

nontrivial critical points for asymptotically quadratic function abstract in this paper we study the existence of nontrivial critical points as applications we study the existence of nontrivial solutions of the dirichelet problem for nonlinear elliptic pde and periodic boundary value problem for nonlinear ope

finite population sampling with multivariate auxiliary information abstract this article examines strategies that are approximately design unbiased and nearly optimal assuming a large sample survey and a regression superpopulation model a new class of predictors is proposed to link certain features of optimal design unbiased and model unbiased predictors generalized regression predictors are shown to pervade the subclass of asymptotically design unbiased adu predictors generalized regression predictors are combined with model based stratification to construct highly efficient adu strategies

cyclotomic goppa codes the general goppa code construction is applied to certain so called cyclotomic fields of algebraic functions the resulting codes are metabelian group codes with binary subfield subcodes of minimum distance d or approximately 1 r n log sub 2 log sub 2 n for a given rate r and length n approaching infinity

on resonant neumann problems we consider semilinear neumann problems at resonance and prove existence and multiplicity theorems the existence theorems allow resonance with respect to any eigenvalue of the negative neumann laplacian the multiplicity theorems concern problems resonant at 0 the principal eigenvalue or at the first nonzero eigenvalue our approach uses tools from critical point theory and from morse theory

a transform approach to goppa codes based on a finite fourier transform of codewords over the finite field gf q m some basic properties of the class of goppa codes are presented a new lower bound on the minimum distance for these codes is derived and applied to a subclass of goppa codes which is in fact equivalent to a subset of punctured reversible cyclic codes furthermore it is shown how the class of goppa codes can be easily decoded in the context of this transformation by using the berlekamp massey decoding algorithm through a slight extension of the procedure it is also shown how this algorithm may be used m decode alternant codes up to their guaranteed error correction capability

non uniformly asymptotically linear p laplacian problems abstract we relax conditions on uniform convergences of f x s s p 2 s which are essential in many results on multiplicity for asymptotically linear p laplacian problems

nontrivial solutions for discrete boundary value problems with multiple resonance via computations of the critical groups abstract in this paper we study the existence of nontrivial solutions for a class of second order difference equations with multiple resonance at both infinity and the origin by applying the critical point theory and morse theory

nontrivial solutions of operator equations and morse indices of critical points of min max type on montre que si les hypotheses du theoreme de point selle sont satisfaites si dim y 2 et si f 1 c contient seulement des points critiques non degeneres alors f 1 c contient au moins un point critique u 0 tel que 2 indice de morse u 0 dim y

intersecting goppa codes bounds on the rates of intersecting goppa codes are derived and compared with previous bounds on intersecting codes intersecting self intersecting and highly intersecting goppa codes are discussed in detail it is shown that asymptotically good intersecting goppa codes exist and lower bounds are given on their rates six theorems for goppa codes are also presented

estimating distribution functions from survey data summary a simple method for estimating population distribution functions and associated quantiles from sample survey data is described and some asymptotic theory for it presented the method assumes a model based approach to survey estimation and allows auxiliary population information to be directly incorporated into the estimation process monte carlo results comparing the proposed method with conventional design based methods are given these suggest that the model based approach offers significant gains when the auxiliary population information is linearly related to the survey variables of interest

multiple solutions with precise sign for nonlinear parametric robin problems we consider a parametric nonlinear robin problem driven by the p laplacian we show that if the parameter 2 the second eigenvalue of the robin p laplacian then the problem has at least three nontrivial solutions two of constant sign and the third nodal in the semilinear case p 2 we show that we can generate a second nodal solution our approach uses variational methods truncation and perturbation techniques and morse theory in the process we produce two useful remarks about the first two eigenvalues of the robin p laplacian

on the parameters of goppa codes a proof of v d goppa s 1983 lower bound to the dimension of subfield subcodes of his geometric codes is given a result on the minimum distance of these subfield subcodes is also given that generalizes the well known bound minimum distance of gamma l g or 2 deg g x 1 for classical goppa codes gamma l g over the field f sub 2 with a square free goppa polynomial g g x

cryptanalysis of mceliece cryptosystem based on algebraic geometry codes and their subcodes we give polynomial time attacks on the mceliece public key cryptosystem based either on algebraic geometry ag codes or on small co dimensional subcodes of ag codes these attacks consist in the blind reconstruction either of an error correcting pair ecp or an error correcting array eca from the single data of an arbitrary generator matrix of a code an ecp provides a decoding algorithm that corrects up to d 1 g 2 errors where d denotes the designed distance and g denotes the genus of the corresponding curve while with an eca the decoding algorithm corrects up to d 1 2 errors roughly speaking for a public code of length n over mathbb f q these attacks run in o n 4 log n operations in mathbb f q for the reconstruction of an ecp and o n 5 operations for the reconstruction of an eca a probabilistic shortcut allows to reduce the complexities respectively to o n 3 varepsilon log n and o n 4 varepsilon compared with the previous known attack due to faure and minder our attack is efficient on codes from curves of arbitrary genus furthermore we investigate how far these methods apply to subcodes of ag codes