on oscillation of nonlinear second order differential equation with damping term we present new oscillation criteria for the second order nonlinear differential equation with damping our theorems are stated in general form they complement and extend related results known in the literature the relevance of our results is illustrated with a number of examples to facilitate computations in these examples we use mathematica r a symbolic computer language

new kamenev type oscillation criteria for second order neutral nonlinear differential equations abstract in this paper some new oscillation criteria for second order neutral nonlinear differential equation r t y t p t y t i 1 n q i t f i y i t 0 t t 0 are established new oscillation criteria are different from most known ones in the sense that they are based on a class of new functions t s l defined in the sequel our results are sharper than some previous results which can be seen by the example at the end of this paper

embedded image compression based on wavelet pixel classification and sorting the method of modeling and ordering in wavelet domain is very important to design a successful algorithm of embedded image compression in this paper the modeling is limited to pixel classification the relationship between wavelet pixels in significance coding similarly the ordering is limited to pixel sorting the coding order of wavelet pixels we use pixel classification and sorting to provide a better understanding of previous works the image pixels in wavelet domain are classified and sorted either explicitly or implicitly for embedded image compression a new embedded image code is proposed based on a novel pixel classification and sorting pcas scheme in wavelet domain in pcas pixels to be coded are classified into several quantized contexts based on a large context template and sorted based on their estimated significance probabilities the purpose of pixel classification is to exploit the intraband correlation in wavelet domain pixel sorting employs several fractional bit plane coding passes to improve the rate distortion performance the proposed pixel classification and sorting technique is simple yet effective producing an embedded image code with excellent compression performance in addition our algorithm is able to provide either spatial or quality scalability with flexible complexity

oscillation results for a second order damped differential equation with nonmonotonous nonlinearity abstract we present new oscillation criteria for a nonlinear second order differential equation with a damping term an essential feature of our results is that we do not require the nonlinearity to be nondecreasing furthermore as opposed to the recent results by s r grace 1989 math nachr 141 117 127 1992 j math anal appl 171 220 241 and s r grace and b s lalli 1990 j math anal appl 149 277 311 we do not impose any additional condition on the damping term p t consequently our theorems apply to new classes of equations which are not covered by the known criteria the relevance of the results obtained is illustrated with a number of carefully selected examples

periodic and chaotic behaviour in a reduction of the perturbed korteweg de vries equation the dynamical behaviour of a reduction of the forced and damped korteweg de vries equation is studied numerically chaos arising from subharmonic instability and homoclinic crossings are observed both period doubling bifurcations and the melnikov sequence of subharmonic bifurcations are found and lead to chaotic behaviour here characterised by a positive lyapunov exponent supporting theoretical analysis includes the construction of periodic solutions and homoclinic orbits and their behaviour under perturbation using melnikov functions

oscillation criteria for second order nonlinear damped differential equations abstract this paper discusses a class of second order nonlinear damped differential equations by using the generalized riccati technique and the integral averaging technique new oscillation criteria are obtained

embedded image coding using zerotrees of wavelet coefficients the embedded zerotree wavelet algorithm ezw is a simple yet remarkably effective image compression algorithm having the property that the bits in the bit stream are generated in order of importance yielding a fully embedded code the embedded code represents a sequence of binary decisions that distinguish an image from the null image using an embedded coding algorithm an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly also given a bit stream the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream in addition to producing a fully embedded bit stream the ezw consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images yet this performance is achieved with a technique that requires absolutely no training no pre stored tables or codebooks and requires no prior knowledge of the image source the ezw algorithm is based on four key concepts 1 a discrete wavelet transform or hierarchical subband decomposition 2 prediction of the absence of significant information across scales by exploiting the self similarity inherent in images 3 entropy coded successive approximation quantization and 4 universal lossless data compression which is achieved via adaptive arithmetic coding

oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities abstract we present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities p t x q t x i 1 n q i t x i sgn x e t where p t q t q i t e t c 0 p t is positive and differentiable 1 m 1 m 1 n no restriction is imposed on the forcing term e t to be the second derivative of an oscillatory function when n 1 our results reduce to those of el sayed m a el sayed an oscillation criterion for a forced second order linear differential equation proc amer math soc 118 1993 813 817 wong j s w wong oscillation criteria for a forced second linear differential equations j math anal appl 231 1999 235 240 sun ou and wong y g sun c h ou j s w wong interval oscillation theorems for a linear second order differential equation comput math appl 48 2004 1693 1699 for the linear equation nazr a h nazr sufficient conditions for the oscillation of forced super linear second order differential equations with oscillatory potential proc amer math soc 126 1998 123 125 for the superlinear equation and sun and wong y g sun j s w wong note on forced oscillation of nth order sublinear differential equations j math anal appl 298 2004 114 119 for the sublinear equation

entropy constrained vector quantization an iterative descent algorithm based on a lagrangian formulation for designing vector quantizers having minimum distortion subject to an entropy constraint is discussed these entropy constrained vector quantizers ecvqs can be used in tandem with variable rate noiseless coding systems to provide locally optimal variable rate block source coding with respect to a fidelity criterion experiments on sampled speech and on synthetic sources with memory indicate that for waveform coding at low rates about 1 bit sample under the squared error distortion measure about 1 6 db improvement in the signal to noise ratio can be expected over the best scalar and lattice quantizers when block entropy coded with block length 4 even greater gains are made over other forms of entropy coded vector quantizers for pattern recognition it is shown that the ecvq algorithm is a generalization of the k means and related algorithms for estimating cluster means in that the ecvq algorithm estimates the prior cluster probabilities as well experiments on multivariate gaussian distributions show that for clustering problems involving classes with widely different priors the ecvq outperforms the k means algorithm in both likelihood and probability of error

adaptive entropy coded subband coding of images the authors describe a design approach called 2 d entropy constrained subband coding ecsbc based upon recently developed 2 d entropy constrained vector quantization ecvq schemes the output indexes of the embedded quantizers are further compressed by use of noiseless entropy coding schemes such as huffman or arithmetic codes resulting in variable rate outputs depending upon the specific configurations of the ecvq and the ecpvq over the subbands many different types of sbc schemes can be derived within the generic 2 d ecsbc framework among these the authors concentrate on three representative types of 2 d ecsbc schemes and provide relative performance evaluations they also describe an adaptive buffer instrumented version of 2 d ecsbc called 2 d ecsbc aec for use with fixed rate channels which completely eliminates buffer overflow underflow problems this adaptive scheme achieves performance quite close to the corresponding ideal 2 d ecsbc system

oscillation criteria for second order quasi linear neutral delay differential equations abstract in this paper some new oscillation criteria for second order neutral nonlinear differential equation r t x t p t x t m 1 x t p t x t q t f x t 0 are established new oscillation criteria are different from most known ones in the sense that they are based on a class of new functions t s l defined in the sequel

oscillation theorems for certain nonlinear differential equations of second order abstract we present new oscillation criteria for the second order nonlinear differential equations these criteria involve the use of averaging functions our theorems are stated in general form they complement and extend related results known in the literature also the relevance of our results is to show that some of manojlovic s results contain the superfluous condition

oscillation criteria for second order nonlinear differential equations involving general means consider the second order nonlinear differential equation e y a t f y 0 where a t c 0 f y c1 f y 0 and yf y 0 for y 0 furthermore f y also satisfies either a superlinear or a sublinear condition which covers the nonlinear function f y y y 1 with 1 and 0 1 respectively commonly known as the emden fowler case here the coefficient function a t is allowed to be negative for arbitrarily large values of t kamenev type oscillation criteria involving integral averages for the linear equations l y a t y 0 are extended to the nonlinear equation e by using more general means the results extend similar results on general means by philos for the linear equation l and also results based upon kamenev s integral averaging method concerning the nonlinear equation e

image coding based on a morphological representation of wavelet data an experimental study of the statistical properties of wavelet coefficients of image data is presented as well as the design of two different morphology based image coding algorithms that make use of these statistics a salient feature of the proposed methods is that by a simple change of quantizers the same basic algorithm yields high performance embedded or fixed rate coders another important feature is that the shape information of morphological sets used in this coder is encoded implicitly by the values of wavelet coefficients thus avoiding the use of explicit and rate expensive shape descriptors these proposed algorithms while achieving nearly the same objective performance of state of the art zerotree based methods are able to produce reconstructions of a somewhat superior perceptual quality due to a property of joint compression and noise reduction they exhibit

complexity regularized image denoising we study a new approach to image denoising based on complexity regularization this technique presents a flexible alternative to the more conventional l sup 2 l sup 1 and besov regularization methods different complexity measures are considered in particular those induced by state of the art image coders we focus on a gaussian denoising problem and derive a connection between complexity regularized denoising and operational rate distortion optimization this connection suggests the use of efficient algorithms for computing complexity regularized estimates bounds on denoising performance are derived in terms of an index of resolvability that characterizes the compressibility of the true image comparisons with state of the art denoising algorithms are given

an oscillation criterion for second order sublinear differential equations abstract an oscillation criterion is given for the second order sublinear differential equation y a t f y 0 where a t is not assumed to be non negative and f y is non decreasing in y and yf y 0 for y 0 f y also satisfies a sublinear condition which includes the special case f y y y sgn y 0 this result extends earlier oscillation theorems of philos and the first author

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

on oscillation of nonlinear second order differential equations with damping term the paper is concerned with oscillation of a novel class of nonlinear differential equations with a damping term first it is demonstrated how known oscillation results for another intensively studied class of equations can be translated to the one in question and vice versa advantages and drawbacks of such translation are carefully examined then an oscillation criterion for the new class of equations is established the principal result of the paper is compared to those reported in the literature and an illustrative example to which known oscillation criteria fail to apply is provided

new kamenev type oscillation criteria for second order nonlinear differential equations with damping abstract some new oscillation criteria are established for the nonlinear damped differential equation r t y p t y q t f y 0 that are different from most known ones in the sense that they are based on a class of new functions t s r defined in the sequel our results are sharper than some previous results which can be seen by the examples at the end of this paper

interval oscillation criteria for second order neutral nonlinear differential equations some oscillation criteria for the second order neutral nonlinear differential equation y t p t y s t email protected i 1 nq i t f i y t i t 0 t t 0are established new oscillation criteria are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are more natural according to the sturm separation theorem

oscillation of sublinear differential equations of second order on etudie les solutions d equations differentielles qui existent sur des intervalles de la forme t

space frequency quantization for wavelet image coding a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree structured quantization related to spatial structures has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation this paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder we consider zerotree quantization zeroing out tree structured sets of wavelet coefficients and the simplest form of scalar quantization a single common uniform scalar quantizer applied to all nonzeroed coefficients and we formalize the problem of optimizing their joint application we develop an image coding algorithm for solving the resulting optimization problem despite the basic form of the two quantizers considered the resulting algorithm demonstrates coding performance that is competitive often outperforming the very best coding algorithms in the literature

curved wavelet transform for image coding the conventional two dimensional wavelet transform used in existing image coders is usually performed through one dimensional 1 d filtering in the vertical and horizontal directions which cannot efficiently represent edges and lines in images the curved wavelet transform presented in this paper is carried out by applying 1 d filters along curves rather than being restricted to vertical and horizontal straight lines the curves are determined based on image content and are usually parallel to edges and lines in the image to be coded the pixels along these curves can be well represented by a small number of wavelet coefficients the curved wavelet transform is used to construct a new image coder the code stream syntax of the new coder is the same as that of jpeg2000 except that a new marker segment is added to the tile headers results of image coding and subjective quality assessment show that the new image coder performs better than or as well as jpeg2000 it is particularly efficient for images that contain sharp edges and can provide a psnr gain of up to 1 67 db for natural images compared with jpeg2000

information theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients this paper presents an information theoretic analysis of statistical dependencies between image wavelet coefficients the dependencies are measured using mutual information which has a fundamental relationship to data compression estimation and classification performance mutual information is computed analytically for several statistical image models and depends strongly on the choice of wavelet filters in the absence of an explicit statistical model a method is studied for reliably estimating mutual information from image data the validity of the model based and data driven approaches is assessed on representative real world photographic images our results are consistent with empirical observations that coding schemes exploiting inter and intrascale dependencies alone perform very well whereas taking both into account does not significantly improve coding performance a similar observation applies to other image processing applications

new oscillation criteria for second order nonlinear neutral delay differential equations in this paper several new oscillation criteria for the second order nonlinear neutral delay differential equation r t x t p t x s t m 1 x t p t x s t q t f x t t 0 t t 0 are established these oscillation criteria extend and improve some known results an interesting example illustrating the importance of our results is also provided

oscillation of second order functional differential equations with mixed nonlinearities and oscillatory potentials in this paper we study oscillation of second order functional differential equations with mixed nonlinearities p t x t q t x t t i 1nq i t x t t a isgnx t t e t where t 0 p t c 1 0 q t q i t e t c 0 p t 0 a 1 a m 1 a m 1 a n 0 n m 1 without assuming that q t q i t and e t are nonnegative the results given in y g sun f w meng interval criteria for oscillation of second order differential equations with mixed nonlinearities appl math comput 198 2008 375 381 have been extended to the aforementioned functional differential equation

multiple description wavelet based image coding we consider the problem of coding images for transmission over error prone channels the impairments we target are transient channel shutdowns as would occur in a packet network when a packet is lost or in a wireless system during a deep fade when data is delivered it is assumed to be error free but some of the data may never reach the receiver the proposed algorithms are based on a combination of multiple description scalar quantizers with techniques successfully applied to the construction of some of the most efficient subband coders a given image is encoded into multiple independent packets of roughly equal length when packets are lost the quality of the approximation computed at the receiver depends only on the number of packets received but does not depend on exactly which packets are actually received when compared with previously reported results on the performance of robust image coders based on multiple descriptions on standard test images our coders attain similar psnr values using typically about 50 60 of the bit rate required by these other state of the art coders while at the same time providing significantly more freedom in the mechanism for allocation of redundancy among descriptions

oscillation theorems for nonlinear differential equations of second order abstract in this paper we present some new criteria for the oscillation of the differential equation a t x t x t p t x t q t f x t 0 the obtained results extend improve and correlate a number of existing criteria

oscillation theorems for nonlinear second order differential equations in this paper some new oscillation criteria are given for the second order nonlinear differential equation r t x t x t c t x t 0 t t0 where r c t0 0 c c t0 r c r r and r r is defined by s s p 2s with p 1 a fixed real number these criteria involve the use of averaging functions

oscillation criteria for second order sublinear differential equation abstract the basic purpose of this paper is to present a new oscillation criteria for second order sublinear differential equation a t x t x t q t t 0 t t 0 0 where a a c 1 t 0 is positive function q c t 0 has no restriction on its sign c 1 r are such that x 0 x x 0 for x 0

successive refinement of information the successive refinement of information consists of first approximating data using a few bits of information then iteratively improving the approximation as more and more information is supplied the goal is to achieve an optimal description at each stage in general an ongoing description which is rate distortion optimal whenever it is interrupted is sought it is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a markov chain in particular all finite alphabet signals with hamming distortion satisfy these requirements it is also shown that the same is true for gaussian signals with squared error distortion and for laplacian signals with absolute error distortion a simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented

an investigation of wavelet based image coding using an entropy constrained quantization framework wavelet image decompositions generate a tree structured set of coefficients providing an hierarchical data structure for representing images a new class of previously proposed image compression algorithms has focused on new ways for exploiting dependencies between this hierarchy of wavelet coefficients using zero tree data structures this paper presents a new framework for understanding the efficiency of one specific algorithm in this class we introduced previously and dubbed the space frequency quantization sfq based coder it describes at a higher level how the sfq based image coder of our earlier work can be construed as a simplified attempt to design a global entropy constrained vector quantizer ecvq with two noteworthy features i it uses an image sized codebook dimension departing from conventional small dimensional codebooks that are applied to small image blocks and ii it uses an on line image adaptive application of constrained ecvq which typically uses off line training data in its codebook design phase the principal insight offered by the new framework is that improved performance is achieved by more accurately characterizing the joint probabilities of arbitrary sets of wavelet coefficients we also present an empirical statistical study of the distribution of the wavelet coefficients of high frequency bands which are responsible for most of the performance gain of the new class of algorithms this study verifies that the improved performance achieved by the new class of algorithms like the sfq based coder can be attributed to its being designed around one conveniently structured and efficient collection of such sets namely the zero tree data structure the results of this study further inspire the design of alternative novel data structures based on nonlinear morphological operators

interval oscillation criteria for second order nonlinear differential equations with damping new oscillation criteria are established for the nonlinear damped differential equation ry py qf y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results and extend and improve the recent interval criteria of kong and huang and can be applied to extreme cases such as t0 q s ds in particular several examples that dwell upon the sharp conditions of our results are also included

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

interval criteria for oscillation of second order differential equations with mixed nonlinearities abstract in this paper we establish interval criteria for oscillation of the second order forced ordinary differential equations with mixed nonlinearities p t x q t x i 1 n q i t x i sgn x e t where p t q t qi t e t are continuous functions defined on 0 p t is positive and differentiable 1 m 1 m 1 n 0 n m 1 no restriction is imposed on the potentials q t qi t and e t to be nonnegative

mutual information based analysis of jpeg2000 contexts context based arithmetic coding has been widely adopted in image and video compression and is a key component of the new jpeg2000 image compression standard in this paper the contexts used in jpeg2000 are analyzed using the mutual information which is closely related to the compression performance we first show that when combining the contexts the mutual information between the contexts and the encoded data will decrease unless the conditional probability distributions of the combined contexts are the same given i the initial number of contexts and f the final desired number of contexts there are s i f possible context classification schemes where s i f is called the stirling number of the second kind the optimal classification scheme is the one that gives the maximum mutual information instead of using an exhaustive search the optimal classification scheme can be obtained through a modified generalized lloyd algorithm with the relative entropy as the distortion metric for binary arithmetic coding the search complexity can be reduced by using dynamic programming our experimental results show that the jpeg2000 contexts capture the correlations among the wavelet coefficients very well at the same time the number of contexts used as part of the standard can be reduced without loss in the coding performance

oscillation criteria for second order nonlinear perturbed differential equations abstract we present new oscillation criteria for the second order nonlinear perturbed differential equations these criteria are of a high degree of generality and they extend and unify a number of existing results

oscillations in superlinear differential equations of second order abstract a new oscillation criterion is given for general superlinear ordinary differential equations of second order of the form x t a t f x t 0 where a c t 0 f c r with yf y 0 for y 0 and 1 1 f y dy and f is continuously differentiable on r 0 with f y 0 for all y 0 the coefficient a is not assumed to be eventually nonnegative and the oscillation cirterion obtained involves the average behavior of the integral of a in the special case of the differential equation x t a t x t sgn x t 0 1 this criterion improves a recent oscillation result due to wong oscillation theorems for second order nonlinear differential equations proc amer math soc 106 1989 1069 1077

spatial chaos in weakly dispersive and viscous media a nonperturbative theory of the driven kdv burgers equation abstract the asymptotic travelling wave solution of the kdv burgers equation driven by the long scale periodic driver is constructed the solution represents a shock train in which the quasi periodic sequence of dispersive shocks or soliton chains is interspersed by smoothly varying regions it is shown that the periodic solution which has the spatial driver period undergoes period doublings as the governing parameter changes two types of chaotic behavior are considered the first type is a weak chaos where only a small chaotic deviation from the periodic solution occurs the second type corresponds to the developed chaos where the solution ignores the driver period and represents a random sequence of uncorrelated shocks in the case of weak chaos the shock coordinate being repeatedly mapped over the driver period moves on a chaotic attractor while in the case of developed chaos it moves on a repeller both solutions depend on a parameter indicating the reference shock position in the shock train the structure of a one dimensional set to which this parameter belongs is investigated this set contains measure one intervals around the fixed points in the case of periodic or weakly chaotic solutions and it becomes a fractal in the case of strong chaos the capacity dimension of this set is calculated

integral averages and oscillation criteria of second order nonlinear differential equations the purpose of this paper is to present some new sufficient criteria for the oscillation of all solutions of the second order nonlinear differential equation a t j x x q t f x 0 t t 0 0 where a c 1 t 0 is a positive function qc t 0 has no restriction on its sign j c r c 1 r are such that 0 and j 0 email protected 0 for 0 these criteria are obtained by using a general class of the parameter functions in the averaging techniques and represent extension as well as improvement of known oscillation criteria of several authors for the generalized emden fowler equation

significance linked connected component analysis for wavelet image coding the success in wavelet image coding is mainly attributed to a recognition of the importance of data organization and representation there have been several very competitive wavelet coders developed namely shapiro s 1993 embedded zerotree wavelets ezw servetto et al s 1995 morphological representation of wavelet data mrwd and said and pearlman s see ieee trans circuits syst video technol vol 6 p 245 50 1996 set partitioning in hierarchical trees spiht we develop a novel wavelet image coder called significance linked connected component analysis slcca of wavelet coefficients that extends mrwd by exploiting both within subband clustering of significant coefficients and cross subband dependency in significant fields extensive computer experiments on both natural and texture images show convincingly that the proposed slcca outperforms ezw mrwd and spiht for example for the barbara image at 0 25 b pixel slcca outperforms ezw mrwd and spiht by 1 41 db 0 32 db and 0 60 db in psnr respectively it is also observed that slcca works extremely well for images with a large portion of texture for eight typical 256 spl times 256 grayscale texture images compressed at 0 40 b pixel slcca outperforms spiht by 0 16 db 0 63 db in psnr this performance is achieved without using any optimal bit allocation procedure thus both the encoding and decoding procedures are fast

interval oscillation of a general class of second order nonlinear differential equations with nonlinear damping abstract the paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions examples are also given to illustrate the results in particular it is shown that under some very mild conditions on k 1 k 2 and f the equation k 1 x x cos tk 2 x x x sin tf x 0 is oscillatory which extends the result obtained by kwong and wong j math anal appl 288 2003 15

integral averaging techniques for the oscillation of second order nonlinear differential equations abstract in this paper we enlist some known and establish some new oscillation criteria for the second order nonlinear differential equations of the form if a t x t t su p t t q t f x t 0 where the coefficients p t and q t are not assumed to be nonnegative for all large values of t these criteria are obtained by using integral averaging techniques and can be applied to some special cases where other classical oscillation results are not applicable a systematic study is attempted to extend improve and correlate a number of existing results

integral averages and oscillation of second order nonlinear differential equations new oscillation criteria are given for the second order sublinear differential equation left a left t right psi left x left t right right x left t right right q left t right f left x left t right right 0 t geqslant t 0 0 where a c 1 t 0 is a nonnegative function f c with x 0 xf x x 0 for x 0 f have continuous derivative on 0 with f x x03c8 x 0 for x 0 and q c t 0 has no restriction on its sign this oscillation criteria involve integral averages of the coefficients q and a and extend known oscillation criteria for the equation x t q t x t 0

averaging technique and nonlinear second order elliptic oscillation abstract by using the refinement of the standard integral averaging technique we obtain new oscillation criteria for certain nonlinear second order damped elliptic differential equations we do not impose any additional conditions on the damping terms except for the continuity in particular when n 1 our results extend those of rogovchenko and tuncay yu v rogovchenko f tuncay oscillation criteria for second order nonlinear differential equations with damping nonlinear analysis 69 2008 208 221 for second order nonlinear differential equations with damping to damped elliptic differential equations when n 2 our results improve the oscillation criteria of xu jia ma z xu b jia d ma oscillation theorems for elliptic equations with damping appl math comput 156 2004 93 106 for second order elliptic equations with damping four examples are provided to illustrate the relevance of the main results

on chaotic wave patterns in periodically forced steady state kdvb and extended kdvb equations the periodically forced kdvb and extended kdvb equations are considered we investigate the structure of the totality of steady profiles the existence of profiles that are close to any shuffling o

periodic and chaotic behaviour in a reduced form of the perturbed generalized korteweg de vries and kadomtsev petviashvili equations abstract the dynamical behaviour of a reduced form of the perturbed generalized korteweg de vries and kadomtsev petviashvili equations extension of the korteweg de vries equation to two space variables are studied in this paper harmonic solutions of non resonance and primary resonance are obtained using the perturbation method chaotic motion under harmonic excitations is studied using the melnikov method a wide range of solutions for the reduced perturbed generalized korteweg de vries equations in which non linear phenomena appearing within transition from regular harmonic response periodic solutions to chaotic motion are obtained using the time integration runge kutta method when chaos is found it is detected by examining the phase plane the poincare map the sensitivity solution of the solution to initial conditions and by calculating the largest lyapunov exponent

an hvs based adaptive coder for perceptually lossy image compression abstract in this paper a locally adaptive wavelet image coder is presented it is based on an embedded human visual system model that exploits the space and frequency localization properties of wavelet decompositions for tuning the quantization step for each discrete wavelet transforms coefficient according to the local properties of the image a coarser quantization is performed in the areas of the image where the visibility of errors is reduced thus decreasing the total bit rate without affecting the resulting visual quality the size of the quantization step for each dwt coefficient is computed by taking into account the multiresolution structure of wavelet decompositions so that there is no need for any side information to be sent to the decoder or for prediction mechanisms perceptually lossless as well as perceptually lossy compression is supported the desired visual quality of the compressed image is set by means of a quality factor moreover the technique for tuning the target visual quality allows the user to define arbitrarily shaped regions of interest and to set for each one a different quality factor