a further extended tanh function method and new soliton like solutions to the integrable broer kaup bk equations in 2 1 dimensional spaces based on an extended tanh function method a further extended tanh function method is suggested to obtain multiple exact solutions for nonlinear partial differential equations which including soliton like solutions solitary waves and trigonometric function solutions the validity and reliability of the method is tested by its application to the integrable broer kaup equations in 2 1 dimensional spaces more new explicit exact solutions are found

modified extended tanh function method and its applications to nonlinear equations new exact travelling wave solutions for the generalized shallow water wave equation the improved boussinesq equation and the coupled system for the approximate equations for water waves are found using a modified extended tanh function method the obtained results include rational periodic singular and solitary wave solutions

the discrete memoryless interference channel with one sided generalized feedback and secrecy we study the interference channel with one sided generalized feedback and secrecy requirement in our model message 1 that is known just to encoder 1 should be decoded by both receivers message 2 known only to encoder 2 should be decoded by decoder 2 and kept as secret as possible from decoder 1 the uncertainty of decoder 1 about message 2 is measured by means of the equivocation rate in addition a noisy feedback is provided to encoder 2 we derive an outer bound on the capacity equivocation region for this model that is valid for the noisy cribbing regime the gap between this upper bound and the inner bound reported before is just in the markov conditions satisfied by one of the auxiliary random variables furthermore we consider a simplified causal cognitive interference model the interference channel with a cribbing encoder we show that when conditioned on the input of encoder 1 the interference channel is degraded our outer bound is tight thereby establishing the capacity equivocation region for this case

exact solutions to the two dimensional korteweg de vries burgers equation two methods are described for obtaining exact travelling monotone shock wave solutions to the two dimensional korteweg de vries burgers equation they are compared with two methods that have been reported recently by other authors

a family of exact travelling wave solutions to nonlinear evolution and wave equations a family q of the multicomponent special functions is defined for obtaining the exact travelling wave solutions to nonlinear evolution and wave equations it is shown that the functions qn from q for some n 2 4 are closely related to the special unitary groups su n the necessary and sufficient conditions for existence of a family of the exact multicomponent travelling wave solutions to a quasilinear evolution equation are given an efficiency of the method based on q functions is demonstrated on several classes of the nonlinear partial differential equations

improved wavelet based watermarking through pixel wise masking a watermarking algorithm operating in the wavelet domain is presented performance improvement with respect to existing algorithms is obtained by means of a new approach to mask the watermark according to the characteristics of the human visual system hvs in contrast to conventional methods operating in the wavelet domain masking is accomplished pixel by pixel by taking into account the texture and the luminance content of all the image subbands the watermark consists of a pseudorandom sequence which is adaptively added to the largest detail bands as usual the watermark is detected by computing the correlation between the watermarked coefficients and the watermarking code and the detection threshold is chosen in such a way that the knowledge of the watermark energy used in the embedding phase is not needed thus permitting one to adapt it to the image at hand experimental results and comparisons with other techniques operating in the wavelet domain prove the effectiveness of the new algorithm

backlund transformations and abundant exact explicit solutions of the sharma tasso olver equation abstract by using an extension of the homogeneous balance method and maple the backlund transformations for the sharma tasso olver equation are derived the connections between the sharma tasso olver equation and some linear partial differential equations are found with the aid of the transformations given here and the computer program maple 12 abundant exact explicit special solutions to the sharma tasso olver equation are constructed in addition to all known solutions re deriving in a systematic way several entirely new and more general exact explicit solitary wave solutions can also be obtained these solutions include a the algebraic solitary wave solution of rational function b single soliton solutions c double soliton solutions d n soliton solutions e singular traveling solutions f the periodic wave solutions of trigonometric function type and g many non traveling solutions by using the airy s function and the backlund transformations obtained here the exact explicit solution of the initial value problem for the sto equation is presented the variety of the structure of the solutions for the sharma tasso olver equation is illustrated

solitary wave solutions of nonlinear evolution and wave equations using a direct method and macsyma the direct algebraic method for constructing travelling wave solutions on nonlinear evolution and wave equations has been generalized and systematized the class of solitary wave solutions is extended to analytic rather than rational functions of the real exponential solutions of the linearized equation expanding the solutions in an infinite series in these real exponentials an exact solution of the nonlinear pde is obtained whenever the series can be summed methods for solving the nonlinear recursion relation for the coefficients of the series and for summing the series in closed form are discussed the algorithm is now suited to solving nonlinear equations by any symbolic manipulation program this direct method is illustrated by constructing exact solutions of a generalized kdv equation the kuramoto sivashinski equation and a generalized fisher equation

the discrete memoryless interference channel with one sided generalized feedback we study the interference channel with one sided generalized feedback and secrecy requirements in our model message 1 that is known just to encoder 1 should be decoded by both receivers message 2 known only to encoder 2 should be decoded by decoder 2 and kept as secret as possible from decoder 1 the uncertainty of decoder 1 about message 2 is measured by means of the equivocation rate in addition a noisy feedback is provided to encoder 2 we derive an achievable rate equivocation region for this model and an outer bound for the noisy cribbing regime without secrecy the gap being the markov conditions satisfied by one of the auxiliary random variables furthermore we consider a simplified causal cognitive interference model the interference channel with a cribbing encoder we derive an inner bound on the rate region for this model and prove that when the interference channel is degraded conditionally on the input of encoder 1 our inner bound is tight

state amplification we consider the problem of transmitting data at rate over a state dependent channel with state information available at the sender and at the same time conveying the information about the channel state itself to the receiver the amount of state information that can be learned at the receiver is captured by the mutual information between the state sequence and the channel output the optimal tradeoff is characterized between the information transmission rate and the state uncertainty reduction rate when the state information is either causally or noncausally available at the sender in particular when state transmission is the only goal the maximum uncertainty reduction rate is given by this result is closely related and in a sense dual to a recent study by merhav and shamai which solves the problem of masking the state information from the receiver rather than conveying it

new exact solutions of burgers s equation an extension to the direct method of clarkson and kruskal new exact solutions of burgers s equation which is the simplest evolution equation to embody nonlinearity and dissipation are obtained these solutions are obtained by extending the method for finding symmetry reductions due to clarkson and kruskal new similarity solutions of the boussinesq equation j math phys 30 2201 2213 1989 the novel feature of this extended method is that one can seek reductions to a system of ordinary differential equations rather than the usual single equation and this leads to a wider class of solutions one is able to complete the calculations necessary for burgers s equation in all but a single case where it is necessary to integrate an abel equation of the second kind this indicates that the method is practicable in contrast it is often the case that new methods are of limited use in practice in particular solutions in terms of a class of confluent hypergeometric functions are computed by comparison solutions found by the original method due to clarkson and kruskal and other reduction methods are in terms of parabolic cylinder functions or airy functions which are special cases of this class

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

an image adaptive wavelet based watermarking of digital images in digital management multimedia content and data can easily be used in an illegal way being copied modified and distributed again copyright protection intellectual and material rights protection for authors owners buyers distributors and the authenticity of content are crucial factors in solving an urgent and real problem in such scenario digital watermark techniques are emerging as a valid solution in this paper we describe an algorithm called wm2 0 for an invisible watermark private strong wavelet based and developed for digital images protection and authenticity using discrete wavelet transform dwt is motivated by good time frequency features and well matching with human visual system directives these two combined elements are important in building an invisible and robust watermark wm2 0 works on a dual scheme watermark embedding and watermark detection the watermark is embedded into high frequency dwt components of a specific sub image and it is calculated in correlation with the image features and statistic properties watermark detection applies a re synchronization between the original and watermarked image the correlation between the watermarked dwt coefficients and the watermark signal is calculated according to the neyman pearson statistic criterion experimentation on a large set of different images has shown to be resistant against geometric filtering and stirmark attacks with a low rate of false alarm

a liouville integrable hamiltonian system associated with a generalized kaup newell spectral problem abstract starting from a generalized kaup newell spectral problem involving an arbitrary function we derive a hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as kaup newell equation chen lee liu equation gerdjikov ivanov equation burgers equation modified korteweg de vries equation and sharma tasso olever equation it is also shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure

non classical symmetries and the singular manifold method the burgers and the burgers huxley equations in this paper a generalization of the direct method of clarkson and kruskal 1989 for finding similarity reductions of partial differential equations is found and discussed for the burgers and burgers huxley equations the generalization incorporates the singular manifold method largely based upon the painleve property this singular manifold can be used as a reduced variable furthermore a sort of inverse procedure is hereby developed through which we find the equations that yield the vector field components associated to the symmetries of the pde this procedure also displays the profound relationship among the symmetries and the singular manifold as a reduced variable the symmetries found in this way are shown to be those corresponding to the so called non classical symmetries by bluman and cole 1974 and olver and rosenau 1986

matrix solutions of wave equations and clifford algebras we are extending the formation of matrix solutions un for linear and nonlinear wave equations by construction of unitary anti hermitian anti commuting matrices up to the eighth order we use clifford algebras c 0 n with periodicity in modulo 8 to construct coupled matrix solutions we also propose to use the matrix solutions for describing the intrinsic rotations of particles

a new approach to pre processing digital image for wavelet based watermark the growth of the internet has increased the phenomenon of digital piracy in multimedia objects like software image video audio and text therefore it is strategic to individualize and to develop methods and numerical algorithms which are stable and have low computational cost that will allow us to find a solution to these problems we describe a digital watermarking algorithm for color image protection and authenticity robust not blind and wavelet based the use of discrete wavelet transform is motivated by good time frequency features and a good match with human visual system directives these two combined elements are important for building an invisible and robust watermark moreover our algorithm can work with any image thanks to the step of pre processing of the image that includes resize techniques that adapt to the size of the original image for wavelet transform the watermark signal is calculated in correlation with the image features and statistic properties in the detection step we apply a re synchronization between the original and watermarked image according to the neyman pearson statistic criterion experimentation on a large set of different images has been shown to be resistant against geometric filtering and stirmark attacks with a low rate of false alarm

the flux theory of gravitation v the mathematics of the new physics the mathematics of the new physics developed in the series 11 14 that we summarize here is quite extensive however the reconstruction of the reals without the axiom of choice is the principle focus of this paper combined with the enrichment of the reals by completion in the standard metric algebraic extension and admission of a topological axiom the new reals is established and well defined it is further extended to the new nonstandard analysis which together has the following achievements developed in the series 1 countably infinite counterexamples to fermat s last theorem disproving the conjecture 2 solution of the problem of natural ordering of the new reals proof of goldbach s conjecture 13 resolution of the banach tarski and brouwers paradoxes 13 dynamic modeling of dark matter and the superstring and 3 characterization of undecidable propositions 14 which paved the way for the dynamic methodology the paper also introduces the calculus of set valued functions including the generalized integral and its application to quantum gravity with the dynamic methodology and its main component qualitative mathematics as alternative to the descriptive pragmatic methodology of physics major discoveries are achieved 1 the solution of the turbulence modeling and gravitational n body problems 11 20 23 2 discovery of ambiguous set e g chaos and proof that the real line is chaos 20 23 3 development of generalized fractal 15 23 24 algorithm for macro and quantum interactions 15 18 22 and development of the flux theory of gravitation the solution of modeling problem when the cosmos is the given physical system its adaptation to earth is the theory of turbulence a major achievement of qualitative mathematics the flux theory of gravitation unites all natural forces and interactions solves all the problems of physics and resolves its paradoxes and unanswered questions

exact solutions of equations for the burgers hierarchy some classes of the rational periodic and solitary wave solutions for the burgers hierarchy are presented the solutions for this hierarchy are obtained by using the generalized cole hopf transformation

travelling wave solutions to nonlinear evolution and wave equations we have studied a series of ansatze ordinary differential equations of the first order which correspond to the travelling and or solitary wave solutions of some nonlinear partial differential equations we have investigated the conditions under which the nonlinear partial differential equations have certain kinds of travelling and or solitary wave solutions as a consequence of applications we can take the trial procedures to obtain the travelling wave solutions which is a very efficient method for solving several classes of nonlinear partial differential equations

single and multi solitary wave solutions to a class of nonlinear evolution equations abstract in this paper an effective discrimination algorithm is presented to deal with equations arising from physical problems the aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations many examples are given to illustrate the algorithm at the same time some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations such as camassa holm equation kolmogorov petrovskii piskunov equation and so on then a direct constructive method called multi auxiliary equations expansion method is described to derive the multi solitary wave solutions of nonlinear evolution equations finally a class of novel multi solitary wave solutions of the 2 1 dimensional asymmetric version of the nizhnik novikov veselov equation are given by three direct methods the algorithm proposed in this paper can be steadily applied to some other nonlinear problems

a family of completely integrable multi hamiltonian systems explicitly related to some celebrated equations by introducing a spectral problem with an arbitrary parameter we derive a kaup newell type hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as the kundu equation the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the burgers equation the modified korteweg devries mkdv equation and the sharma tasso olver equation it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure under the bargann constraint between the potentials and the eigenfunctions the spectral problem is nonlinearized as a finite dimensional completely integrable hamiltonian system the involutive representation of the solutions for the kaup newell type hierarchy is also presented in addition an n fold darboux transformation of the kundu equation is constructed with the help of its lax pairs and a reduction technique according to the darboux transformation the solutions of the ku

the flux theory of gravitation xvii the new mathematics and physics the main contribution of the paper is the critique of j m henle s non nonstandard analysis the mathematical intelligencer 21 1 1999 67 the principal criticism of henle s work is the failure to do away with the axiom of choice as he claims he would therefore it suffers from the same flaw that robinson s nonstandard analysis has nonstandard analysis north holland amsterdam 1966 however the paper also summarizes the new mathematics and physics generated by the resolution of fermat s last theorem nonlinear studies 5 2 1998 227 and the solution of the gravitational n body problem nonlinear analysis 30 8 1997 5021 respectively including the resolution of the problems paradoxes contradictions and unanswered questions of mathematics and physics except the bieberbach s conjecture and the riemann hypothesis highlighted in the paper are astonishing results coming from the new real line i e the reconstructed real line as well as the proof of goldbach s conjecture and the natural ordering of the new real line which does not exist in the real line

integrable systems of derivative nonlinear schrodinger type and their multi hamiltonian structure a spectral problem and the associated hierarchy of schrodinger type equations are proposed it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure it is found that several kinds of important equation such as the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the modified korteweg de vries equation and the sharma tasso olever equation are members in the hierarchy as its special reductions moreover kn cll and gi equations are described by using a unified generalized derivative schrodinger equation involving a parameter and their hamiltonian structure and lax pairs are also given by unified and explicit formulae

geometrical properties of matrix solutions of the nonlinear klein gordon equation we have constructed some matrix solutions of a nonlinear klein gordon equation and proposed a relation between these solutions and su n matrix groups we have also established the correspondence between the solutions and the rotations around fixed vectors whose endpoints form an octahedron