aggregating local image descriptors into compact codes this paper addresses the problem of large scale image search three constraints have to be taken into account search accuracy efficiency and memory usage we first present and evaluate different ways of aggregating local image descriptors into a vector and show that the fisher kernel achieves better performance than the reference bag of visual words approach for any given vector dimension we then jointly optimize dimensionality reduction and indexing in order to obtain a precise vector comparison as well as a compact representation the evaluation shows that the image representation can be reduced to a few dozen bytes while preserving high accuracy searching a 100 million image data set takes about 250 ms on one processor core

asymptotic properties of solutions of difference equations with several delays and volterra summation equations we study a scalar linear difference equation with several delays by transforming it to a system of volterra equations without delays the results obtained for this system are then used to establish oscillation criteria and asymptotic properties of solutions of the considered equation

on families of bounded continuous solutions of some systems of functional difference equations on half intervals some sufficient conditions for the existence of families of bounded continuous solutions of some classes of systems of functional difference equations on the intervals 0 and 0 are given

oscillation for difference equations with continuous variable consider the delay difference equation y t y t p t h y t t t 0 where 0 0 and p c r r f c r r h c r r some oscillation criteria for this equation are obtained

stability and asymptoticity of volterra difference equations a progress report we survey some of the fundamental results on the stability and asymptoticity of linear volterra difference equations the method of z transform is heavily utilized in equations of convolution type an example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty it is shown that the two notions are equivalent if the kernel decays exponentially for equations of nonconvolution type liapunov functions are used to find explicit criteria for stability moreover the resolvent matrix is defined to produce a variation of constants formula the study of asymptotic equivalence for difference equations with infinite delay is carried out in section 6 finally we state some problems

stability and synchronization analysis of neural networks via halanay type inequality in this paper not only some novel sufficient criteria for stability of discrete delay neural networks but also a new discriminant method for self synchronization of hopfield neural networks are considered some novel stability criteria for discrete delay neural networks are obtained if the time average of the difference for two coefficients on some fixed lengths is lower bounded by some positive numbers moreover a new discrete halanay inequality is given which extends the existing results based on the halanay inequality a novel sufficient criterion on self synchronization of hopfield neural networks with time delay is obtained two numerical examples are given to demonstrate the effectiveness of proposed methods

weighted convergent and bounded solutions of difference systems abstract using a summable dichotomy and fixed point theorems we prove the existence of convergent and bounded solutions of nonlinear difference systems

oscillation and nonoscillation theorems for second order difference equations in this paper we are concerned with the oscillatory and nonoscillatory behavior of the solutions of some second order difference equations let r be the set of real numbers n n n l where n is given nonnegative integer for the function x n t r the difference operator d l1 a is fixed real constant will be defined as follows d x x ax n e n instead of a we shall write a we define inductively a x a atix for k 1 we shall study difference equations of the form

trajectory based place recognition for efficient large scale localization place recognition is a core competency for any visual simultaneous localization and mapping system identifying previously visited places enables the creation of globally accurate maps robust relocalization and multi user mapping to match one place to another most state of the art approaches must decide a priori what constitutes a place often in terms of how many consecutive views should overlap or how many consecutive images should be considered together unfortunately such threshold dependencies limit their generality to different types of scenes in this paper we present a placeless place recognition algorithm using a novel match density estimation technique that avoids heuristically discretizing the space instead our approach considers place recognition as a problem of continuous matching between image streams automatically discovering regions of high match density that represent overlapping trajectory segments the algorithm uses well studied statistical tests to identify the relevant matching regions which are subsequently passed to an absolute pose algorithm to recover the geometric alignment we demonstrate the efficiency and accuracy of our methodology on three outdoor sequences including a comprehensive evaluation against ground truth from publicly available datasets that shows our approach outperforms several state of the art algorithms for place recognition furthermore we compare our overall algorithm to the currently best performing system for global localization and show how we outperform the approach on challenging indoor and outdoor datasets

the extended tanh method for new solitons solutions for many forms of the fifth order kdv equations abstract the extended tanh method is used to derive new solitons solutions for several forms of the fifth order nonlinear kdv equation the forms include the lax sawada kotera sk sawada kotera parker dye skpd kaup kupershmidt kk kaup kupershmidt parker dye kkpd and the ito equations the criteria established in a m wazwaz abundant solitons solutions for several forms of the fifth order kdv equation by using the tanh method appl math comput in press doi 10 1016 j amc 2006 02 047 to build up reliable relations between the parameters of the equation are confirmed by using this new approach entirely new bell shaped solitons are determined

the asymptotic estimates of solutions of difference equations abstract the asymptotic estimate of the solution y t of linear difference equations with almost constant coefficients and the condition of asymptotic equivalence between y t and y 0 t are given where y 0 t is the corresponding solution of linear equations with constant coefficients a brief and elementary proof of the results is presented the method of proof carries over to differential equations in which some similar results are stated

asymmetric distances for binary embeddings in large scale query by example retrieval embedding image signatures in a binary space offers two benefits data compression and search efficiency while most embedding algorithms binarize both query and database signatures it has been noted that this is not strictly a requirement indeed asymmetric schemes that binarize the database signatures but not the query still enjoy the same two benefits but may provide superior accuracy in this work we propose two general asymmetric distances that are applicable to a wide variety of embedding techniques including locality sensitive hashing lsh locality sensitive binary codes lsbc spectral hashing sh pca embedding pcae pcae with random rotations pcae rr and pcae with iterative quantization pcae itq we experiment on four public benchmarks containing up to 1m images and show that the proposed asymmetric distances consistently lead to large improvements over the symmetric hamming distance for all binary embedding techniques

exp function method exactly solving a kdv equation with forcing term in this paper the exp function method is used to construct generalized solitonary solutions and periodic solutions of a kdv equation with forcing term it is shown that the exp function method with the help of symbolic computation provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations with forcing term in mathematical physics

asymptotic behavior of volterra difference equations abstract in this paper we investigate boundedness and stability properties of some classes of discrete volterra equations the main tool in this work is the use of a representation formula which allows us to express the solution of discrete volterra equations in terms of the resolvent matrix of the corresponding system of volterra difference equations

optimized product quantization product quantization pq is an effective vector quantization method a product quantizer can generate an exponentially large codebook at very low memory time cost the essence of pq is to decompose the high dimensional vector space into the cartesian product of subspaces and then quantize these subspaces separately the optimal space decomposition is important for the pq performance but still remains an unaddressed issue in this paper we optimize pq by minimizing quantization distortions w r t the space decomposition and the quantization codebooks we present two novel solutions to this challenging optimization problem the first solution iteratively solves two simpler sub problems the second solution is based on a gaussian assumption and provides theoretical analysis of the optimality we evaluate our optimized product quantizers in three applications i compact encoding for exhaustive ranking 1 ii building inverted multi indexing for non exhaustive search 2 and iii compacting image representations for image retrieval 3 in all applications our optimized product quantizers outperform existing solutions

oscillation of certain second order nonlinear difference equations abstract in this paper we consider the second order nonlinear difference equation formula where y n y n 1 y n is the forward difference operator f c r r f is nondecreasing and uf u 0 as u 0 q n is a real sequence some new sufficient conditions for the oscillation of all solutions of 1 are obtained

structured stability radii and exponential stability tests for volterra difference systems uniform exponential ue stability of linear difference equations with infinite delay is studied using the notions of a stability radius and a phase space the state space x is an abstract banach space we work with non fading phase spaces c 0 z x and z x and with exponentially fading phase spaces of the p and c 0 types for equations of the convolution type several criteria of ue stability are obtained in terms of the z transform email protected z of the convolution kernel k in terms of the input state operator and of the resolvent fundamental matrix these criteria do not impose additional positivity or compactness assumptions on coefficients k j time varying non convolution difference equations are studied via structured ue stability radii r t of convolution equations these radii correspond to a feedback scheme with delayed output and time varying disturbances we also consider stability radii r c associated with a time invariant disturbance operator unstructured stability radii and stability radii corresponding to delayed feedback for all these types of stability radii two sided estimates are obtained the estimates from above are given in terms of the z transform email protected z the estimate from below via the norm of the input output operator these estimates turn into explicit formulas if the state space x is hilbert or if disturbances are time invariant the results on stability radii are applied to obtain various exponential stability tests for non convolution equations several examples are provided

stability analysis of discrete recurrence equations of volterra type with degenerate kernels abstract stability criteria are derived for difference equations of volterra type with degenerate kernels the main tool in this analysis is the use of the new representation formula which allows us to express the solution of discrete volterra equation with degenerate kernel in terms of the fundamental matrix of the corresponding first order system of the difference equations

on the asymptotic behavior of solutions of certain second order nonlinear differential equations on considere l equation differentielle py qy g t y y ou p p t est une fonction positive continument differentiable sur i a a telle que p a 1 q q t est une fonction continue sur i a et g g t u v est une fonction continue sur i a r 2 qui verifie certaines conditions

boundedness of discrete volterra equations abstract investigation of the boundedness of the solutions of volterra equations with discrete time by means of the direct liapunov method and comparison theorems is performed boundedness conditions of solutions of some particular classes of equations are derived using such conditions stability of direct quadrature methods for second kind volterra equations is analyzed

asymptotically periodic solutions of volterra system of difference equations a volterra system of difference equations of the form x s n 1 a s n b s n x s n email protected email protected i 0nk s p n i x p i where email protected n a s b s x s n r and k s p nxn r s 1 2 r is studied sufficient conditions for the existence of asymptotically periodic solutions of this system are derived

oscillation criteria for second order functional difference equations with summation small coefficient we consider the second order functional difference equation a n n p n x g n 0 where n p n are sequences of integers with a n 0 0 g n n limn g n p n 0 and p n 0 we obtain some necessary conditions for equation 1 exists nonoscillatory solutions and some sufficient conditions for equation 1 is oscillatory

a nonlinear fractional sharma tasso olver equation due to its importance in scientific applications the fractional nonlinear sharma tasso olver equation has been studied by several authors from point of view of exact solutions in this paper new explicit and exact solutions are obtained by using the fractional complex transform and the improved extended tanh coth method the results can be compared with other methods used to solve the same model

the ordinal relation preserving binary codes hashing algorithm has been widely used for efficient approximate nearest neighbor ann search learning optimal hashing functions has been given focus and it is still a challenge this paper aims to effectively and efficiently generate relative similarity preserving binary codes most existing hashing methods try to preserve the locality similarity by preserving direct distance similarity while ignoring the relative similarity which advantages in ann search in this paper this issue is solved by proposing the relative error which emphasizes that the ordinal relations in hamming space and euclidean space should be consistent with each other we learn hashing projection functions via two steps the first step adopts the lookup based mechanism to find the optimal binary codes of training data which can preserve the relative similarity and simultaneously adapt to data distribution the binary codes in the first step are considered as supervision information in the second step the objective of the second step is to learn hashing projection functions which can efficiently regenerate the binary codes in the first step aim to be in accordance with the property of data distribution the hyper internal tangent planes of two specified spheres are chosen as hashing projection functions assisted by these projection functions the time complexity of encoding process is greatly reduced experimental results on four public data sets demonstrate that our method outperforms many other state of the art methods author highlightsan effective and efficient binary coding framework which enjoys the merits of lookup based and hamming based methods is proposed relative error is proposed to preserve the relative sensitivity the effective tangent planes are adopted as hashing functions to avoid computing the complex classification problem the encoding error guarantees that the selected hashing functions have good performance

bilinear optimized product quantization for scalable visual content analysis product quantization pq has been recognized as a useful technique to encode visual feature vectors into compact codes to reduce both the storage and computation cost recent advances in retrieval and vision tasks indicate that high dimensional descriptors are critical to ensuring high accuracy on large scale data sets however optimizing pq codes with high dimensional data is extremely time consuming and memory consuming to solve this problem in this paper we present a novel pq method based on bilinear projection which can well exploit the natural data structure and reduce the computational complexity specifically we learn a global bilinear projection for pq where we provide both non parametric and parametric solutions the non parametric solution does not need any data distribution assumption the parametric solution can avoid the problem of local optima caused by random initialization and enjoys a theoretical error bound besides we further extend this approach by learning locally bilinear projections to fit underlying data distributions we show by extensive experiments that our proposed method dubbed bilinear optimization product quantization achieves competitive retrieval and classification accuracies while having significant lower time and space complexities

on unbounded positive solutions of second order difference equations with a singular nonlinear term abstract in this paper several necessary and or sufficient conditions are given for the existence of unbounded positive solutions of nonlinear difference equations of the form r n x n f n x n 0 n n n 0 where n n0 n0 n0 1 n0 is a fixed nonnegative integer rn 0 for n n0 such that n n0 1 rn and f n n0 r r is a real valued continuous function such that f n x 0 for all n x n n0 0

on asymptotic stability of delay difference systems in this paper we obtain some criteria for determining the asymptotic stability of the zero solution for some classes of delay difference systems by using a discrete version of the second lyapunov method our results can be well suited for computational purposes

distributed adaptive binary quantization for fast nearest neighbor search hashing has been proved an attractive technique for fast nearest neighbor search over big data compared with the projection based hashing methods prototype based ones own stronger power to generate discriminative binary codes for the data with complex intrinsic structure however existing prototype based methods such as spherical hashing and k means hashing still suffer from the ineffective coding that utilizes the complete binary codes in a hypercube to address this problem we propose an adaptive binary quantization abq method that learns a discriminative hash function with prototypes associated with small unique binary codes our alternating optimization adaptively discovers the prototype set and the code set of a varying size in an efficient way which together robustly approximate the data relations our method can be naturally generalized to the product space for long hash codes and enjoys the fast training linear to the number of the training data we further devise a distributed framework for the large scale learning which can significantly speed up the training of abq in the distributed environment that has been widely deployed in many areas nowadays the extensive experiments on four large scale up to 80 million data sets demonstrate that our method significantly outperforms state of the art hashing methods with up to 58 84 performance gains relatively

linearized stability analysis of discrete volterra equations abstract various different types of stability are defined in a unified framework for discrete volterra equations of the type x n f n n j 0 k n j x n n 0 under appropriate assumptions stability results are obtainable from those valid in the linear case k n j x n b n j x j and a linearized stability theory is studied here by using the fundamental and resolvent matrices several necessary and sufficient conditions for stability are obtained for solutions of the linear equation by considering the equations in various choices of banach space b the elements of which are sequences of vectors x n f n e d b n j e d e d n j 0 etc we show that the theory including a number of new results as well as results already known can be presented in a systematic framework in which results parallel corresponding results for classical volterra integral equations of the second kind

asymptotic behavior of solutions of second order nonlinear difference equations 0 2 j 1 b n u n g n y y h 1 1 or equivalently e y a0 by g n y ey where e is the operator defined by ey n y n 1 2 let z z2 be a fundamental system of solutions of the linear difference equation lz e2z f aez bz 0 3 satisfying z o 1 z l 0 zz o 0 22 l 1 4 we will prove that there exists a ball b 0 p c r2 such that if y o y 1 e b 0 p then the solution y of equation 1 is defined on all n and for n co it satisfies

linear oscillation of second order nonlinear difference equations with damped term abstract in this paper we shall establish relations between the oscillation of second order nonlinear difference equations with damped term and the oscillation of their linear limiting equations

stability regions for linear fractional differential systems and their discretizations this paper concerns with basic stability properties of linear autonomous fractional differential and difference systems involving derivative operators of the riemann liouville type we derive stability regions for special discretizations of the studied fractional differential systems including a precise description of their asymptotics our analysis particularly shows that discretizations based on backward differences can retain the key qualitative properties of underlying fractional differential systems in addition we introduce the backward discrete laplace transform and employ some of its properties as the main proof tool

robust quantization for general similarity search the recent years have witnessed the emerging of vector quantization vq techniques for efficient similarity search vq partitions the feature space into a set of codewords and encodes data points as integer indices using the codewords then the distance between data points can be efficiently approximated by simple memory lookup operations by the compact quantization the storage cost and searching complexity are significantly reduced thereby facilitating efficient large scale similarity search however the performance of several celebrated vq approaches degrades significantly when dealing with noisy data in addition it can barely facilitate a wide range of applications as the distortion measurement only limits to ell 2 norm to address the shortcomings of the squared euclidean ell 2 2 norm loss function employed by the vq approaches in this paper we propose a novel robust and general vq framework named rgvq to enhance both robustness and generalization of vq approaches specifically a ell p q norm loss function is proposed to conduct the ell p norm similarity search rather than the ell 2 norm search and the q th order loss is used to enhance the robustness despite the fact that changing the loss function to ell p q norm makes vq approaches more robust and generic it brings us a challenge that a non smooth and non convex orthogonality constrained ell p q norm function has to be minimized to solve this problem we propose a novel and efficient optimization scheme and specify it to vq approaches and theoretically prove its convergence extensive experiments on benchmark data sets demonstrate that the proposed rgvq is better than the original vq for several approaches especially when searching similarity in noisy data

asymptotic properties of solutions of some volterra difference equations and second order difference equations abstract we give sufficient conditions for the existence of a bounded resp convergent solution of a class of difference equations and volterra difference equation

nonoscillation oscillation and growth of solutions of nonlinear difference equations of second order abstract sufficient conditions are obtained which guarantee that all solutions or all bounded solutions of a class of second order nonlinear difference equations are nonoscillatory oscillation criteria and theorems concerning the growth of solutions are also given

almost periodic solutions of discrete volterra equations for discrete volterra equations with or without delay we obtain several results concerning almost periodic solutions and asymptotically almost periodic solutions under certain conditions we also investigate the relations among solutions of equations discussed and give an example to illustrate our results

necessary and sufficient condition for oscillation of higher order nonlinear delay difference equations this paper is concerned with the oscillation of solutions of higher order nonlinear delay difference equations with forcing terms of the form nx t f t x t x t h t t i 0 1 where is the forward difference operator defined by x t x t 1 x t and mx t m 1x t m 1 a necessary and sufficient condition is established under which every solution x t is oscillatory when n is even and is either oscillatory or strongly monotone when n is odd a sufficient condition for the oscillation of solutions of neutral type delay difference equations is also obtained

modified riemann liouville derivative and fractional taylor series of nondifferentiable functions further results the paper gives some results and improves the derivation of the fractional taylor s series of nondifferentiable functions obtained recently in the form f g h e a h ad g a f g 0 a 1 where e a is the mittag leffier function here one defines fractional derivative as the limit of fractional difference and by this way one can circumvent the problem which arises with the definition of the fractional derivative of constant using riemann liouville definition as a result a modified riemann liouville definition is proposed which is fully consistent with the fractional difference definition and avoids any reference to the derivative of order greater than the considered one s in order to support this f taylor series one shows how its first term can be obtained directly in the form of a mean value formula the fractional derivative of the dirac delta function is obtained together with the fractional taylor s series of multivariate functions the relation with irreversibility of time and symmetry breaking is exhibited and to some extent this f taylor s series generalizes the fractional mean value formula obtained a few years ago by kolwantar

oscillation results for second order scalar and matrix difference equations we consider the self adjoint second order scalar difference equation rn xn pnxn 1 0 1 and the matrix system rn xn pnxn 1 0 2 where rn 0 pn 0 rn 0 pn 0 are sequences of real numbers d d hermitian matrices with rn 0 rn 0 we obtain some new oscillation criteria through change of variable techniques combined with consideration of 1 and 2 as perturbations of the cases pn 0 pn 0

oscillation theorems for second order advanced functional difference equations abstract we consider the second order advanced functional difference equation a n n p n g n 0 where a n 0 s n 0 1 a s p n 0 p n 0 g n n 1 g n is a monotone increasing integer sequence we obtain some new oscillation criteria through an appropriate riccati equation

stability of difference volterra equations direct liapunov method and numerical procedure abstract a procedure to construct liapunov functionals for discrete volterra equations is proposed using this procedure stability conditions are derived for general volterra difference equations some applications of the proposed procedure for obtaining stability conditions for linear multistep methods for volterra integro differential equations are presented

comparison theorems for second order nonlinear difference equations abstract new oscillation results are obtained for the second order nonlinear difference equation r n f x n 1 g n x n 0 and its functional form r n f x n 1 g n x n 0 the role played by the argument n on the oscillation of the functional equation is explored in particular we characterize a class of sequences n which have a harmless effect on the oscillation of this type of equations some of our results generalize improve or unify known fundamental oscillation results for several particular cases of the above equations

asymptotic representation of solutions of linear second order difference equations abstract using dichotomy conditions we obtain asymptotic formulae for the solutions of perturbed linear second order difference equations

the asymptotic behavior of the solutions of a volterra difference equation the aim of the present paper is to study the asymptotic behavior of the sum difference equation of volterra type an xn bn xn cn n l 0n 1gl h n xn xn as n

riccati type transformations for second order linear difference equations abstract oscillation and comparison theorems for a linear homogeneous second order difference equation are proved by employing various equivalent non linear equations obtained by means of transformations analogous to the riccati transformation for ordinary differential equations

a feasible method for optimization with orthogonality constraints minimization with orthogonality constraints e g x top x i and or spherical constraints e g vert x vert 2 1 has wide applications in polynomial optimization combinatorial optimization eigenvalue problems sparse pca p harmonic flows 1 bit compressive sensing matrix rank minimization etc these problems are difficult because the constraints are not only non convex but numerically expensive to preserve during iterations to deal with these difficulties we apply the cayley transform a crank nicolson like update scheme to preserve the constraints and based on it develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics the efficiency of the proposed algorithms is demonstrated on a variety of test problems in particular for the maxcut problem it exactly solves a decomposition formulation for the sdp relaxation for polynomial optimization nearest correlation matrix estimation and extreme eigenvalue problems the proposed algorithms run very fast and return solutions no worse than those from their state of the art algorithms for the quadratic assignment problem a gap 0 842 to the best known solution on the largest problem tai256c in qaplib can be reached in 5 min on a typical laptop

oscillation of second order perturbed nonlinear difference equations using the riccati transformation techniques we will establish some new oscillation criteria for the second order perturbed nonlinear difference equation d a n 1 dx n 1 c f n x n g n x n dx n n 1where c 0 is a quotient of odd positive integers some comparison between our theorems and those previously known results are indicated examples are interested in the text to illustrate the relevance of our results

asymptotic behavior of the solutions of second order difference equations abstract the asymptotic behavior of the solutions of the second order difference equation 2 x n n x n is considered

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

product quantization for nearest neighbor search this paper introduces a product quantization based approach for approximate nearest neighbor search the idea is to decompose the space into a cartesian product of low dimensional subspaces and to quantize each subspace separately a vector is represented by a short code composed of its subspace quantization indices the euclidean distance between two vectors can be efficiently estimated from their codes an asymmetric version increases precision as it computes the approximate distance between a vector and a code experimental results show that our approach searches for nearest neighbors efficiently in particular in combination with an inverted file system results for sift and gist image descriptors show excellent search accuracy outperforming three state of the art approaches the scalability of our approach is validated on a data set of two billion vectors

the cole hopf transformation and improved tanh coth method applied to new integrable system kdv6 abstract in this paper we study a new coupled system kdv6 from the point of view of constructing exact solutions for it by using the cole hopf transformation and one improved tanh coth method traveling wave solution which includes periodic and soliton solutions are formally derived

oscillation theorems for second order neutral difference equations abstract oscillation criteria for the second order difference equations of the form 2xn qnf xn r 0 and the neutral difference equation 2 xn pxn k qnf xn r 0 are established here xn xn 1 xn is the forward difference operator 1 p is a real number and k are nonnegative integers qn is a sequence of nonnegtive real numbers and f r r is continuous

classification and existence of positive solutions of systems of volterra nonlinear difference equations a classification scheme for the eventually positive solutions of a class of two dimensional volterra nonlinear difference equations is given in terms of their asymptotic magnitudes and necessary as well as sufficient conditions for the existence of such solutions are provided

uniform asymptotic stability in nonlinear volterra discrete systems abstract we employ the notion of total stability to obtain new criteria for uniform asymptotic stability of the zero solution of a nonlinear volterra discrete system resolvent equation methods are employed and a summability criterion on the resolvent kernel is obtained also we obtain a new difference equation that the resolvent r n s satisfies

on the asymptotic behavior of solutions of higher order nonlinear differential equations on considere l equation differentielle py n 1 i 1 n 1 b i t y i 1 g t y y y n 1 ou p p t est une fonction positive et continument derivable sur i a a telle que p a 1 h i h i t sont continues sur i a et g est continu sur i a r n verifiant quelques autres conditions en considerant un systeme fondamental de solutions on caracterise certaines solutions definies sur l intervalle i a entier

the asymptotic behavior of the solutions of a discrete reaction diffusion equation abstract by means of bihari type inequalities we derive sufficient conditions for solutions of a discrete reaction diffusion equation to be bounded or to converge to zero asymptotic representation of solutions are also derived our results yield estimates and explicit attractive regions for the solutions

on the existence of solutions of linear volterra difference equations asymptotically equivalent to a given sequence abstract schauder s fixed point technique is applied to asymptotical analysis of solutions of a linear volterra difference equation x n 1 a n b n x n i 0 n k n i x i where n n 0 x n 0 r a n 0 r k n 0 n 0 r and b n 0 r 0 is periodic in the paper sufficient conditions are derived for the validity of a property of solutions that for every admissible constant c r there exists a solution x x n such that x n c i 0 n 1 a i i 1 n where n j 0 n 1 b j for n and inequalities for solutions are derived relevant comparisons and illustrative examples are given as well

oscillation theorems for perturbed nonlinear second order difference equations abstract sufficient conditions for the oscillation of all solutions of perturbed difference equations of the form a n 1 y n 1 q n y n p n y n y n n n are obtained examples are inserted to illustrate the results

oscillation criteria for second order nonlinear difference equations with damped term abstract several oscillation criteria are established for the second order damped nonlinear difference equation a n 1 y n 1 p n 1 y n 1 q n y n 0 n n 0 0 where 0 is any quotient of odd integers p n and q n are real sequences and f c r r such that x f x 0 for x 0 several examples which dwell upon the importance of our results are also included

special symmetries to standard riccati equations and applications by using symmetries associated to riccati equation in standard form sre we obtain a family which can be integrated by quadratures as a consequence we get a new integrability condition for the generalized riccati equation gre we illustrate the result with some examples and we give some applications in the solitons theory

codewords distribution based optimal combination of equal average equal variance equal norm nearest neighbor fast search algorithm for vector quantization encoding vector quantization encoding requires expensive time to find the closest codeword through the codebook for each input vector a fast search algorithm for encoding is proposed in this paper the multilevel elimination criterion is still derived from the three features mean variance and norm inequalities constraints but the order of the three inequalities constraints instead of the predefined order like other conventional multilevel elimination criterion is optimized to speed up the encoding procedure in the proposed algorithm the elimination criterion at the first level is set to mean inequality constraint because of its narrower search width and the priority order at the second and or third level of variance and norm inequalities constraints is optimized based on the codewords distribution and the location of input vector in terms of the considered features the experimental results demonstrate the effectiveness of the proposed algorithm

the first integral method for some time fractional differential equations abstract in this paper the fractional derivatives in the sense of modified riemann liouville derivative and the first integral method are employed for constructing the exact solutions of nonlinear time fractional partial differential equations the power of this manageable method is presented by applying it to several examples this approach can also be applied to other nonlinear fractional differential equations

bounded and monotone properties of solutions of second order quasilinear forced difference equations abstract the authors consider the quasilinear difference equation p n 1 y n 1 q n y n r n and obtain results on the asymptotic behavior of solutions of including sufficient conditions for all solutions to be bounded or unbounded some results on the existence and behavior of nonincreasing solutions of are also obtained examples are inserted to illustrate the results

periodicity and stability of linear volterra difference systems abstract we give sufficient conditions for a system of volterra difference equations to have a unique periodic solution then a criterion for uniform asymptotic stability is established

an application of discrete inequality to second order nonlinear oscillation abstract by using some simple discrete inequalities oscillation criteria are provided for the second order difference equations 2 y n a n 1 y n 1 0 n n where the operator is defined by yn yn 1 yn an is a real sequence the function is such that u u 0 for u 0 and u v g u v u v for u v 0 for some nonnegative function g

asymptotic property of linear volterra difference systems by using the resolvent matrix and the comparison principle we investigate the asymptotic behavior of linear volterra difference systems

general theorems for stability and boundedness for nonlinear functional discrete systems abstract we consider the nonlinear functional discrete system x n 1 g n x s 0 s n def g n x and obtain sufficient conditions for stability properties of the zero solution and for the boundedness of solutions

stability results for difference equations of volterra type the stability of difference equations of volterra type is discussed for this purpose a method of finding a linear equation equivalent to a given difference equation of volterra type is considered employing this technique some stability properties of linear and nonlinear equations are investigated

an application of darbo s fixed point theorem in the investigation of periodicity of solutions of difference equations using the technique of darbo s fixed point theorem we investigate a nonlinear second order difference equation of the form d r n dx n a nf x n 1 where x n 0 r a r n 0 r and f r r is a continuous function additionally the sturm liouville difference equation is considered as a special case of the above equation sufficient conditions for the existence of an asymptotically periodic solution of this equation are obtained an example illustrates the result next the conditions under which this equation has no asymptotically periodic solutions are presented

asymptotically ordinary linear volterra difference equations with infinite delay abstract a class of linear volterra difference equations with infinite delay is considered it is shown that if the coefficient matrices are sufficiently small then the volterra difference equation is asymptotically equivalent to a linear ordinary difference equation at infinity the coefficient matrix of the ordinary difference equation is a solution of an associated matrix equation which can be obtained by successive approximations the eigenvalues of the approximating matrices converge exponentially to the characteristic roots of the volterra difference equation as a corollary an efficient new method is obtained for the computation of the characteristic roots with an explicit error estimate