a new method for adding a parameter to a family of distributions with application to the exponential and weibull families summary a new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two parameter extension of the exponential distribution which may serve as a competitor to such commonly used two parameter families of life distributions as the weibull gamma and lognormal distributions in addition the general method is applied to yield a new three parameter weibull distribution families expanded using the method introduced here have the property that the minimum of a geometric number of independent random variables with common distribution in the family has a distribution again in the family bivariate versions are also considered

length constrained map decoding of variable length encoded markov sequences in this paper we consider the problem of length constrained maximum a posteriori decoding of a markov sequence that is variable length encoded and transmitted over a binary symmetric channel we convert this problem into one of a maximum weight k link path in a weighted directed acyclic graph the induced graph optimization problem can be solved by a fast parameterized search algorithm that finds either the optimal solution with high probability or a good approximate solution otherwise the proposed algorithm has lower complexity and superior performance than the previous approximation algorithms

on multiple solutions of a semilinear schrodinger equation with periodic potential abstract this paper is concerned with the semilinear schrodinger equation s u v x u f x u u h 1 r n where v and f are periodic in the x variables f is a superlinear and subcritical nonlinearity and 0 lies in a spectral gap of u v it is shown that if f is odd in u then s has infinitely many large energy solutions the proof relies on a generalized variant fountain theorem for strongly indefinite functionals established in this paper

existence of solution for a class of quasilinear schrodinger equation in rn with zero mass abstract in this paper we use variational methods to establish a berestycki lions type result for two classes of quasilinear schrodinger equations in r n in the zero mass situation

index assignment optimization for joint source channel map decoding channel optimized quantizer index assignment and maximum a posteriori map decoding have been extensively studied for error resilient communications an interesting and largely untreated problem is how to optimize the index assignment with respect to joint source channel map decoding in this paper we formulate the above problem as one of quadratic assignment and discuss its solutions from very general to some special cases for highly correlated gaussian markov sources and hamming distortion we can construct the optimal index assignment analytically for general cases simulated annealing algorithm is adopted to search for the optimal index assignment experimental results are presented to demonstrate the performance improvement of the index assignments optimized for map decoding over those designed for hard decision decoding e g gray code the reduction of symbol error rate and mean squared error can be as large as 40 and 50 respectively for highly correlated gaussian markov sources

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

quantization of memoryless and gauss markov sources over binary markov channels joint source channel coding for stationary memoryless and gauss markov sources and binary markov channels is considered the channel is an additive noise channel where the noise process is an mth order markov chain two joint source channel coding schemes are considered the first is a channel optimized vector quantizer optimized for both source and channel the second scheme consists of a scalar quantizer and a maximum a posteriori detector in this scheme it is assumed that the scalar quantizer output has residual redundancy that can be exploited by the maximum a posteriori detector to combat the correlated channel noise these two schemes are then compared against two schemes which use channel interleaving numerical results show that the proposed schemes outperform the interleaving schemes for very noisy channels with high noise correlation gains of 4 5 db in signal to noise ratio are possible

on ground states of superlinear p laplacian equations in rn abstract we consider superlinear p laplacian equations in r n with a potential which is periodic or has a bounded potential well without assuming the ambrosetti rabinowitz type condition and the monotonicity of the function t f x t t p 1 we prove the existence of ground states even for the case p 2 our results extend the recent results of li wang and zeng ann inst h poincare anal non lineaire 23 2006 829 837

monotonicity based fast algorithms for map estimation of markov sequences over noisy channels in this correspondence we study algorithmic approach to solving the problem of maximum a posteriori map estimation of markov sequences transmitted over noisy channels which is also known as the map decoding problem for the class of memoryless binary channels that produce independent substitution and erasure errors the map sequence estimation problem can be formulated and solved as one of the longest path in a weighted directed acyclic graph but for algorithm efficiency we transform the graph problem to one of matrix search if the underlying matrix is totally monotone then the complexity of map sequence estimation can be greatly reduced we give a sufficient condition for the matrix induced by map sequence estimation to be totally monotone which is indeed the case if the input sequence is gaussian markov under this condition the complexity of map decoding can be reduced from o n sup 2 m to o nm where n is the size of source alphabet and m is the length of input sequence furthermore for markov sequences of fixed length code we propose a block parsing strategy to reduce the complexity of map sequence estimation to o m n sup 2 m logm or to o m nm logm depending on if the total monotonicity holds another significance of this correspondence lies in the applicability of the presented algorithmic approach which has been thoroughly studied in computer science literature to many other discrete optimization problems encountered in both source and channel coding ranging from optimal multiresolution and multiple description quantizer design to context quantization for minimum conditional entropy and to optimal packetization with uneven error protection

on ground states for the kirchhoff type problem with a general critical nonlinearity abstract in this paper we consider the following kirchhoff type problem a b r 3 u 2 u f u in r 3 u h 1 r 3 u 0 in r 3 where a b 0 are constants and f has a critical growth the aim of this paper is to study the existence of ground state solutions for kirchhoff type equations with a general nonlinearity in the critical growth without the assumption of the monotonicity of the function t f t t 3 moreover we will show that the mountain pass value gives the least energy level and also obtain a mountain pass solution

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

on superlinear p x laplacian equations in rn abstract we consider the p x laplacian equations in r n the nonlinearity is superlinear but does not satisfy the ambrosetti rabinowitz type condition we obtain ground states of the equations improving a recent result of fan x l fan p x laplacian equations in r n with periodic data and nonperiodic perturbations j math anal appl 341 2008 103 119 we also establish a bartsch wang type compact embedding theorem for variable exponent spaces then a multiplicity result for the equations is proved for odd nonlinearity

resource scalable joint source channel map and mmse estimation of multiple descriptions a joint source channel multiple description jsc md framework for signal estimation and communication in resource constrained lossy networks is presented to keep the encoder complexity at a minimum a signal is coded by a multiple description quantizer mdq with neither entropy nor channel coding the code diversity of mdq and the path diversity of the network are exploited by decoders to combat transmission errors a key design objective is resource scalability powerful nodes in the network can perform jsc md estimation under the criteria of maximum a posteriori probability map or minimum mean square error mmse while primitive nodes resort to simpler md decoding all working with the same mdq code the application of jsc md to distributed estimation of hidden markov models in a sensor network is demonstrated the proposed jsc md map estimator is an algorithm of the longest path in a weighted directed acyclic graph while the jsc md mmse decoder is an extension of the well known forward backward algorithm to multiple descriptions both algorithms simultaneously exploit the source memory the redundancy of the fixed rate mdq and the inter description correlations they outperform the existing hard decision mdq decoders by large margins up to 8 db for gaussian markov sources the complexity of jsc md distributed map sequence estimation can be made as low as that of typical single description viterbi type algorithms

superlinear schrodinger operators abstract we find nontrivial and ground state solutions for the nonlinear schrodinger equation under conditions weaker than those previously assumed

multiple solutions for a nonhomogeneous schrodinger maxwell system in r 3 abstract the paper considers the following nonhomogeneous schrodinger maxwell system sm u u x u u p 1 u g x x r 3 u 2 x r 3 where 0 p 1 5 and 0 g x g x l 2 r 3 there seem to be no results on the existence of multiple solutions to problem sm for p 1 3 in this paper we find that there is a constant c p 0 such that problem sm has at least two solutions for all p 1 5 provided that g l 2 c p however for p 1 2 we need 0 is small moreover c p p 1 2 p p 1 s p 1 2 p 1 p 1 where s is the sobolev constant

solutions of superlinear elliptic equations and their morse indices we consider here solutions of semilinear second order elliptic equations with superlinear nonlinearities and we present some relationships between their morse indices and some qualitative properties in particular we show that for uo subcritical nonlinearities bounds on solutions are equivalent to bounds on their morse indices

fast joint source channel decoding of convolutional coded markov sequences with monge property this work addresses the problem of joint source channel decoding of a markov sequence which is first encoded by a source code then encoded by a convolutional code and sent through a noisy memoryless channel it is shown that for markov sources satisfying the so called monge property both the maximum a posteriori probability map sequence decoding as well as the soft output max log map decoding can be accelerated by a factor of k without compromising the optimality where k is the size of the markov source alphabet the key to achieve a higher decoding speed is a convenient organization of computations at the decoder combined with a fast matrix search technique enabled by the monge property the same decrease in complexity follows as a by product of the development for the soft output max log map joint source channel decoding in the case when the convolutional coder is absent result which was not known previously

nonlinear degenerate elliptic equation with hardy potential and critical parameter abstract some embedding inequalities in hardy sobolev spaces with general weight functions were proved and a positive answer to an open problem raised by brezis vazquez was given in the weighted hardy sobolev spaces the existence of nontrivial many solutions to the corresponding nonlinear degenerated elliptic equations with hardy potential and critical parameter under conditions weaker than ambrosetti rabinowitz condition was obtained

on the complexity of joint source channel decoding of markov sequences over memoryless channels we investigate the complexity of joint source channel maximum a posteriori map decoding of a markov sequence which is first encoded by a source code then encoded by a convolutional code and sent through a noisy memoryless channel as established previously the map decoding can be performed by a viterbi like algorithm on a trellis whose states are triples of the states of the markov source source coder and convolutional coder the large size of the product space in the order of k2n where k is the number of source symbols and n is the number of states of the convolutional coder appears to prohibit such a scheme we show that for finite impulse response convolutional codes the state space size of joint source channel decoding can be reduced to o k2 n log n hence the decoding time becomes o tk2 tn log n where t is the length in bits of the decoded bitstream we further prove that an additional complexity reduction can be achieved when k n if the logarithm of the source transition probabilities satisfy the so called monge property this decrease becomes more significant as the tree structure of the source code is more unbalanced the reduction factor ranges between o k n for a fixed length source code and o k log n for golomb rice code

asymptotically linear schrodinger equation with potential vanishing at infinity we are concerned with the existence of bound states and ground states of the following nonlinear schrodinger equation

existence and nonexistence of positive solutions for a class of generalized quasilinear schrodinger equations involving a kirchhoff type perturbation with critical sobolev exponent in this paper by variational methods we study the existence and nonexistence of positive solutions for a class of generalized quasilinear schrodinger equations involving a kirchhoff type perturbation with critical sobolev exponent in particular the first result is based on the ambrosetti rabinowitz condition moreover the second results are established via the poho aev identity finally the last results are not based on the ambrosetti rabinowitz condition and we use generalized conditions to prove the results

new classes of power series bivariate copulas abstract zhang et al 2016 introduced a copula based on the geometric distribution here we introduce general classes of copulas containing zhang et al 2016 s copula as a particular case physical motivations are given for the general classes one of the general classes is shown to be more flexible by reanalyzing the two real data sets in zhang et al 2016

berestycki lions conditions on ground state solutions for kirchhoff type problems with variable potentials based on the strategy introduced by chen and tang adv nonlinear anal 9 496 515 2020 and some new tricks we prove that the nonlinear problem of kirchhoff type a b r3 u 2dx u v x u f u x r3 in h1 r3 admits two classes of ground state solutions under the general berestycki lions assumptions on the nonlinearity f which are almost necessary conditions as well as some weak assumptions on the potential v moreover we also give a simple minimax characterization of the ground state energy our results improve and extend recent theorems in several directions

steep potential well may help kirchhoff type equations to generate multiple solutions abstract in this paper we consider a nonlinear kirchhoff type problem with steep potential well a r 3 u 2 d x b u v x u f x u p 2 u in r 3 u h 1 r 3 where a b 0 2 p 4 v c r 3 r and f l r 3 r such problem cannot be studied by applying variational methods in a standard way even by restricting its corresponding energy functional on the nehari manifold because palais smale sequences may not be bounded in this paper we introduce a novel constraint method to prove the existence of one and two positive solutions under the different assumptions on v respectively we conclude that steep potential well v may help kirchhoff type equations to generate multiple solutions which has never been involved before

quantizer monotonicities and globally optimal scalar quantizer design new monotonicity properties of optimal scalar quantizers are discussed these monotonicities reveal a globally optimal scalar quantizer structure depending on the probability mass functions and on the number of quantizer levels by incorporating the monotone quantizer structure into a dynamic programming process the time complexities of previous algorithms for designing globally optimal scalar quantizers can be significantly reduced for very general classes of distortion measures

the existence of a nontrivial solution to a nonlinear elliptic boundary value problem of p laplacian type without the ambrosetti rabinowitz condition abstract in this paper we study the existence of a nontrivial solution to the following nonlinear elliptic boundary value problem of p laplacian type p p u f x u x u 0 x where p 1 r 1 r n is a bounded domain and p u d i v u p 2 u is the p laplacian of u f c 0 r 1 r 1 is p superlinear at t 0 and subcritical at t we prove that under suitable conditions for all 0 the problem p has at least one nontrivial solution without assuming the ambrosetti rabinowitz condition our main result extends a result for p for when p 2 given by miyagaki and souto 2008 in 8 to the general problem p where p 1 meanwhile our result is stronger than a similar result of li and zhou 2003 given in 15

solutions in spectral gaps for a nonlinear equation of schrodinger type abstract in this paper we study the existence of a nontrivial h2 r n solution for an equation of the form u x p x u x f x u x u x x r n r where p l r n is a periodic function we assume that the operator p h2 r n l2 r n l2 r n is strongly indefinite and invertible and that x r r is odd and satisfies some superlinear but subcritical growth conditions we extend the class of nonlinearities which has been studied up to now in particular under standard technical restrictions the existence of a solution is derived when lim x f x s f s 0 exists for all s r if we assume that f x s f s for all s r and a e on r n

some results on connecting orbits for a class of hamiltonian systems abstract the existence of various kinds of connecting orbits is established for a certain hamiltonian system as well as its time dependent analogue for the autonomous case our main assumption is that v has a global maximum e g at x o and we find a various kinds of orbits terminating at o for the time dependent case v has a local but not global maximum at x o and we find a homoclinic orbit emanating from and terminating at o keywords periodic solution

hadamard based soft decoding for vector quantization over noisy channels we present an estimator based or soft vector quantizer decoder for communication over a noisy channel the decoder is optimal according to the mean square error criterion and hadamard based in the sense that a hadamard transform representation of the vector quantizer is utilized in the implementation of the decoder an efficient algorithm for optimal decoding is derived we furthermore investigate suboptimal versions of the decoder providing good performance at lower complexity the issue of joint encoder decoder design is considered both for optimal and suboptimal decoding results regarding the channel distortion and the structure of a channel robust code are also provided through numerical simulations soft decoding is demonstrated to outperform hard decoding in several aspects

two positive solutions for the kirchhoff type elliptic problem with critical nonlinearity in high dimension abstract we investigate the kirchhoff type elliptic problem with critical nonlinearity 1 u 2 d x u u q u 2 1 u 0 in u 0 on where n 5 r n is a bounded domain with smooth boundary 0 r 2 2 n n 2 and q 1 2 1 we prove the existence of two solutions of it via the variational method since n 5 and 0 the uniqueness assertion for the associated limiting problem may fail this causes serious difficulties in controlling concentrating palais smale sequences we overcome these by introducing new techniques for a mountain pass type solution we utilize the limit function of the fibering maps of the concentrating palais smale sequence this tool is based on our careful setting of nehari type sets on the other hand a suitable modification to a concentrating minimizing sequence enables us to obtain a global minimum solution this is the first work which proves the multiplicity of positive solutions of the kirchhoff type critical problem in high dimension

bifurcation in lp rn for a semilinear elliptic equation keywords lsp p bifurcation constrained minimization sobolev spaces nonlinear eigenvalue problem semilinear spectrum linearisation variational structure reference ana article 1988 001doi 10 1112 plms s3 57 3 511 record created on 2008 12 10 modified on 2016 08 08

existence of multiple positive solutions to nonhomogeneous schrodinger poisson system in this paper we consider the existence of multiple solutions to the following nonhomogeneous generalized schrodinger poisson system u ku q f u g u h x in r 3 2 qf u in r 3 where q 0 is a parameter 0 h x h x l 2 r 3 and g is asymptotically linear or superliner at infinity we show that there exists q 0 0 such that the system has at least two positive radial solutions for q 0 q 0

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

nonstationary homoclinic orbits for an infinite dimensional hamiltonian system we study the following system of diffusion equations on r rn tu xu v x u g t x v tv xv v x v f t x u where z u v r rn r2 v c rn r g t x v f t x u are periodic in t x and superlinear at infinity by a variant linking theorem and concentration compactness arguments we establish the existence of nonstationary homoclinic type solutions of least energy for this systems

new conditions on nonlinearity for a periodic schrodinger equation having zero as spectrum abstract we consider the semilinear schrodinger equation u v x u f x u for x r n u x 0 as x where f is a superlinear and subcritical nonlinearity we mainly study the case when both v and f are periodic in x and 0 is a boundary point of a spectral gap of v we extend a linking theorem of kryszewski and szulkin 15 and establish a new variational setting which is more suitable to the above case we obtain two theorems on the existence of ground state solutions with mild assumptions on f

map decoding of variable length codes with self synchronization strings maximum a posteriori probability map decoding of huffman equivalent variable length codes vlcs has two undesired features one is the high decoding complexity and the other is the discrepancy between the objective of map decoding and the levenshtein distance which is commonly used as the performance metric in this correspondence improvement over these two issues is targeted through extracting self synchronization information in vlc coded sequence and incorporating it into map decoding it shown that self synchronization strings ssss are concatenation of huffman codewords and can be readily found occurrence probabilities of ssss are then analyzed by using this self synchronization information map decoding is split into multiple decoding of short data segments so that both decoding performance improvement and complexity reduction are obtained simulation results demonstrate the effectiveness of the proposed method

an asymptotically periodic and asymptotically linear schrodinger equation with indefinite linear part abstract we consider the semilinear schrodinger equation u v x u f x u x r n u h 1 r n where v x is asymptotically periodic and sign changing f x u is asymptotically periodic in x and asymptotically linear as u under some weak assumptions on v and f we prove that the above problem has a nontrivial solution

compactness results for schrodinger equations with asymptotically linear terms abstract we study the nonlinear problem u v x f x u x r n lim x u x 0 where the schrodinger operator v is semibounded and the nonlinearity f is linearly bounded we establish compactness of palais smale sequences and cerami sequences for the associated energy functional under general spectral theoretic assumptions applying these results we obtain existence of three nontrivial solutions if the energy functional has a mountain pass geometry

semiclassical solutions for the nonlinear schrodinger maxwell equations abstract in this paper by using variational methods and critical point theory we study the existence of semiclassical solutions for the following nonlinear schrodinger maxwell equations e 2 u v x u u f x u in r 3 4 u 2 in r 3 where e 0 and v x 0 for all x r 3 under some weaker assumptions on v and f we prove that the system has at least one nontrivial solution for sufficient small e 0