second order and moderate deviations asymptotics for successive refinement we derive the optimal second order coding region and moderate deviations constant for successive refinement source coding with a joint excess distortion probability constraint we consider two scenarios 1 a discrete memoryless source dms and arbitrary distortion measures at the decoders and 2 a gaussian memoryless source gms and quadratic distortion measures at the decoders for a dms with arbitrary distortion measures we prove an achievable second order coding region using type covering lemmas by kanlis and narayan and by no ingber and weissman we prove the converse using the perturbation approach by gu and effros when the dms is successively refinable the expressions for the second order coding region and the moderate deviations constant are simplified and easily computable for this case we also obtain new insights on the second order behavior compared with the scenario where separate excess distortion proabilities are considered for example we describe a dms for which the optimal second order region transitions from being characterizable by a bivariate gaussian to a univariate gaussian as the distortion levels are varied we then consider a gms with quadratic distortion measures to prove the direct part we make use of the sphere covering theorem by verger gaugry together with appropriately defined gaussian type classes to prove the converse we generalize kostina and verdu s one shot converse bound for point to point lossy source coding we remark that this proof is applicable to general successively refinable sources in the proofs of the moderate deviations results for both scenarios we follow a strategy similar to that for the second order asymptotics and use the moderate deviations principle

a second wronskian formulation of the boussinesq equation a wronskian formulation leading to rational solutions is presented for the boussinesq equation it involves third order linear partial differential equations whose representative systems are systematically solved the resulting solutions formulas provide a direct but powerful approach for constructing rational solutions positon solutions and complexiton solutions to the boussinesq equation various examples of exact solutions of those three kinds are computed the newly presented wronskian formulation is different from the one previously presented by li et al which does not yield rational solutions

new interaction solutions for the 3 1 dimensional jimbo miwa equation abstract in this paper based on the hirota bilinear form and a rational cosh cos type test function we will study new interaction solutions among the lump waves kinky waves and periodic waves for the 3 1 dimensional jimbo miwa equation we analyze the dynamic behaviors of the constructed solutions in four special cases in detail and the dynamic characteristics of the obtained solutions are illustrated by some interesting figures with the help of maple

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

analytic programming in the task of evolutionary synthesis of a controller for high order oscillations stabilization of discrete chaotic systems this paper deals with the utilization of a symbolic regression tool which is analytic programming ap together with two evolutionary algorithms the self organizing migrating algorithm soma and differential evolution de for the synthesis of a new control law this synthesized chaotic controller secures the stabilization of higher periodic orbits which represent oscillations between several values of three selected discrete chaotic systems selected examples were an artificially evolutionary synthesized system logistic equation and henon map the paper consists of the description of analytic programming as well as chaotic systems used evolutionary techniques and the cost function

second order resolvability intrinsic randomness and fixed length source coding for mixed sources information spectrum approach the second order achievable asymptotics in typical random number generation problems such as resolvability intrinsic randomness and fixed length source coding are considered in these problems several researchers have derived the first order and the second order achievability rates for general sources using the information spectrum methods although these formulas are general their computations are quite hard hence an attempt to address explicit computation problems of achievable rates is meaningful in particular for i i d sources the second order achievable rates have earlier been determined simply by using the asymptotic normality in this paper we consider mixed sources of two i i d sources the mixed source is a typical case of nonergodic sources and whose self information does not have the asymptotic normality nonetheless we can explicitly compute the second order achievable rates for these sources on the basis of two peak asymptotic normality in addition extensions of our results to more general mixed sources such as a mixture of countably infinite i i d sources or markov sources and a continuous mixture of i i d sources are considered

distinct variants of the kdv equation with compact and noncompact structures in this paper we examine three distinct variants of the generalized kdv equation both the compact and the noncompact structures are treated for these variants we also emphasize the different physical structures of the two classes the focusing branch and the defocusing branch

quadratic model for reservoir management application to the central valley project a quadratic optimization model is applied to a large scale reservoir system to obtain operation schedules the model has the minimum possible dimensionality treats spillage and penstock releases as decision variables and takes advantage of system dependent features to reduce the size of the decision space an efficient and stable quadratic programming active set algorithm is used to solve for the optimal release policies the stability and convergence of the solution algorithm are ensured by the factorization of the reduced hessian matrix and the accurate computation of the lagrange multipliers the quadratic model is compared with a simplified linear model and it is found that optimal release schedules are robust to the choice of model both yielding an increase of nearly 27 in the total annual energy production with respect to conventional operation procedures although the quadratic model is more flexible and of general applicability the adequate fulfillment of other system functions such as flood control and water supply is guaranteed via constraints on storage and spillage variables

new solutions of distinct physical structures to high dimensional nonlinear evolution equations abstract in this work we employ the tanh coth method for a reliable treatment on nonlinear evolution equations three models namely the 3 1 dimensional jimbo miwa equation the 2 1 dimensional calogero bogoyavlenskii schiff equation and the 3 1 dimensional potential ytsf equation are use as vehicles to conduct the analysis new travelling wave solutions are formally derived the work shows the power of the proposed scheme and the variety of the obtained solutions

optimal multireservoir network control by the discrete maximum principle an optimal control algorithm based on the discrete maximum principle is applied to multireservoir network control variable metric techniques are used for direct solution of the resulting two point boundary value problem state variable constraints are considered by use of penalty functions computer time and storage requirements are moderate and increase roughly linearly with the problem dimension application to a 10 reservoir network demonstrates efficacy of the proposed algorithm

a constrained and non smooth hydrothermal problem this paper addresses a hydrothermal problem that simultaneously considers non regular lagrangian and non holonomic inequality constraints obtaining a necessary minimum condition it is further shown that the discontinuity of the lagrangian does not translate as discontinuity in the derivative of the solution finally a solution algorithm is developed and applied to an example

source resolvability and intrinsic randomness two random number generation problems with respect to a subclass of f divergences this paper deals with two typical random number generation problems in information theory one is the source resolvability problem resolvability problem for short and the other is the intrinsic randomness problem in the literature optimum achievable rates in these two problems with respect to the variational distance as well as the kullback leibler kl divergence have already been analyzed on the other hand in this study we consider these two problems with respect to f divergences the f divergence is a general non negative measure between two probabilistic distributions on the basis of a convex function f the class of f divergences includes several important measures such as the variational distance the kl divergence the hellinger distance and so on hence it is meaningful to consider the random number generation problems with respect to f divergences in this paper we impose some conditions on the function f so as to simplify the analysis that is we consider a subclass of f divergences then we first derive general formulas of the first order optimum achievable rates with respect to f divergences next we particularize our general formulas to several specified functions f as a result we reveal that it is easy to derive optimum achievable rates for several important measures from our general formulas the second order optimum achievable rates and optimistic optimum achievable rates have also been investigated

a bolza problem in hydrothermal optimization abstract this paper studies the optimization of large scale hydrothermal power systems for the general problem with n hydro plants we present an algorithm using a particular strategy related to the gauss southwell method of nonlinear optimization the algorithm offers a constructive method for producing sequences of problems with one hydro plant for this simple problem we use pontryagin s minimum principle to prove a condition for the extremals of the functional we set out our problem in terms of optimal control in continuous time with the bolza type functional finally we present one example employing a program developed with the mathematica package and analyze the convergence of the algorithm

application of the g g expansion method to 3 1 dimensional nonlinear evolution equations in this paper the g g expansion method is employed to solve the 3 1 dimensional kadomtsev petviashvili kp equation the 3 1 dimensional potential ytsf equation and the 3 1 dimensional jimbo miwa jm equation exact traveling wave solutions are obtained the traveling wave solutions are expressed in terms of hyperbolic functions the trigonometric functions and the rational functions

the solitonic features of a nonintegrable 3 1 dimensional jimbo miwa equation abstract we investigate a nonintegrable 3 1 dimensional jimbo miwa equation by truncating the painleve expansion and performing computerized symbolic computation we obtain a new auto backlund transformation and a new family of the exact solitonic solutions sample solutions of this family are presented

nonasymptotic and second order achievability bounds for coding with side information we present a novel nonasymptotic or finite blocklength achievability bounds for three side information problems in network information theory these include 1 the wyner ahlswede korner wak problem of almost lossless source coding with rate limited side information 2 the wyner ziv wz problem of lossy source coding with side information at the decoder and 3 the gel fand pinsker gp problem of channel coding with noncausal state information available at the encoder the bounds are proved using ideas from channel simulation and channel resolvability our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the wak wz and gp problems in particular those derived by verdu using our novel nonasymptotic bounds we recover the general formulas for the optimal rates of these side information problems finally we also present achievable second order coding rates by applying the multidimensional berry esseen theorem to our new nonasymptotic bounds numerical results show that the second order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds

two new wronskian conditions for the 3 1 dimensional jimbo miwa equation abstract in this paper we obtain two kinds of sufficient conditions consisting of systems of linear partial differential equations which guarantee that the corresponding wroskian determinant solves the 3 1 dimensional jimbo miwa equation in the hirota bilinear form our results suggest that more general conditions could be derived by further study

extended gram type determinant wave and rational solutions to two 3 1 dimensional nonlinear evolution equations new exact grammian determinant solutions to two 3 1 dimensional nonlinear evolution equations are derived extended set of sufficient conditions consisting of linear partial differential equations with variable coefficients is presented moreover a systematic analysis of linear partial differential equations is used for solving the representative linear systems the bilinear backlund transformations are also constructed for the equations also as an application of the bilinear backlund transforms a new class of wave and rational solutions to the equations are explicitly computed

utilization of soma and differential evolution for robust stabilization of chaotic logistic equation this paper deals with the utilization of two evolutionary algorithms self organizing migrating algorithm soma and differential evolution de for the optimization of the control of chaos this paper is aimed at an explanation on how to use evolutionary algorithms eas and how to properly define the advanced targeting cost function cf securing fast precise and mainly robust stabilization of selected chaotic system on a desired state for any initial conditions the role of ea here is as a powerful tool for an optimal tuning of control technique input parameters as a model of deterministic chaotic system the one dimensional discrete logistic equation was used the four canonical strategies of soma and six canonical strategies of de were utilized for each ea strategy repeated simulations were conducted to outline the effectiveness and robustness of used method and targeting cf securing robust solution satisfactory results obtained by both heuristic and the two proposed cost functions are compared with previous research given by different cost function designs

the extended tanh method for abundant solitary wave solutions of nonlinear wave equations the extended tanh method is used to establish abundant solitary wave solutions of nonlinear wave equations the obtained solutions include solitons kinks and plane periodic solutions the study is an extension to the remarkable development by malfliet 1 the extended tanh method presents a wider applicability for handling nonlinear wave equations

targeting chaos through adaptive control we describe adaptive control algorithms whereby a chaotic dynamical system can be steered to a target state with desired characteristics a specific implementation considered has the objective of directing the system to a state which is more chaotic or mixed than the uncontrolled one this methodology is easy to implement in discrete or continuous dynamical systems it is robust and efficient and has the additional advantage that knowledge of the detailed behavior of the system is not required

a new method for the real time operation of reservoir systems this paper introduces a new method for the real time operation of reservoir systems the system is represented by a set of stochastic differential equations describing the reservoir and river dynamics in state space form the formulated reservoir operation problem calls for finding policies which maximize the expected benefits of one system s objective while satisfying the remaining objectives at prespecified reliability levels the solution is obtained by a new method named extended linear quadratic gaussian elqg controller elqg draws on and extends stochastic control theory results and it is well suited for the optimization of constrained dynamical systems it is a trajectory iteration algorithm theoretically expected to exhibit reliability and computational efficiency the new method is tested and evaluated in a real world case study

construction of exact solutions to the jimbo miwa equation through backlund transformation and symbolic computation based on a simple transformation and with the aid of symbolic computation a backlund transformation relating the jimbo miwa equation and a system of linear partial differential equations is obtained which enables us to construct exact solutions of the jimbo miwa equation through the wronskian determinants of independent solutions of the linear system particularly explicit wronskian form n soliton solutions for the jimbo miwa equation are presented moreover the introduced transformation also helps to construct bi soliton like solutions of the jimbo miwa equation due to the arbitrary functions they contain the bi soliton like solutions can represent various waves such as classical cross line bi solitons curved bi solitons and bi soliton like breathers

grammian type determinant solutions to generalized kp and bkp equations abstract grammian type determinant identities of the bilinear kp hierarchy and a useful property on the derivatives of grammians are proposed based on these grammian type determinant identities three grammian structures are furnished to a large class of generalized nonlinear kp and bkp type equations all the generating functions for matrix entries satisfy a system of combined linear partial differential equations in the first case of the class of generalized kp and bkp equations general rational solutions are given making use of its grammian formulation

generating random bits from an arbitrary source fundamental limits suppose we are given a random source and want to use it as a random number generator at what rate can we generate fair bits from it we address this question in an information theoretic setting by allowing for some arbitrarily small but nonzero deviation from ideal random bits we prove our results with three different measures of approximation between the ideal and the obtained probability distributions the variational distance the d bar distance and the normalized divergence two different contexts are studied fixed length and variable length random number generation the fixed length results of this paper provide an operational characterization of the inf entropy rate of a source defined in han and verdu see ibid vol 39 no 3 p 752 772 1993 and the variable length results characterize the liminf of the entropy rate thereby establishing a pleasing duality with the fundamental limits of source coding a feature of our results is that we do not restrict ourselves to ergodic or to stationary sources

new solutions of the 3 1 dimensional jimbo miwa equation we find new exact solutions of the 3 1 dimensional jimbo miwa equation by applying the extended homogeneous balance method we also get an iterative formula of finding exact solutions this paper shows that there exist a lot of solutions for the 3 1 dimensional jimbo miwa equation

are all the equations of the kadomtsev petviashvili hierarchy integrable the kadomtsev petviashvili kp hierarchy is an infinite set of nonlinear partial differential equations in which the number of independent variables increases indefinitely as one proceeds down the hierarchy since these equations were obtained as part of a group theoretical approach to soliton equations it would appear that the kp hierarchy provides integrable scalar equations with an arbitrary number of independent variables it is shown by investigating a specific equation in 3 1 dimensions that the higher equations in the kp hierarchy are only integrable in a conditional sense the equation under study taken in isolation does not pass certain well known and reliable integrability tests thus applying painleve analysis we find that solutions exist allowing movable critical points furthermore solitary wave solutions are shown to exist that do not behave like solitons in multiple collisions on the other hand if the dependence of a solution on the first 2 1 variables is restricted by the fact that it should also satisfy the kp equation itself then the integrability conditions in the other dimensions are satisfied conditional integrability thus means that linear techniques will provide only those solutions of equations in the hierarchy that simultaneously satisfy lower equations in the same hierarchy

rational solutions to a kdv like equation two classes of rational solutions to a kdv like nonlinear differential equation are constructed the basic object is a generalized bilinear differential equation based on a prime number p 3 a conjecture is made that the two presented classes of rational solutions contain all rations solutions to the considered kdv like equation which are generated from polynomial solutions to the corresponding generalized bilinear equation

optimization of local control of chaos by an evolutionary algorithm an evolutionary algorithm for optimizing local control of chaos is presented based on a lyapunov approach a linear control law and the state space region in which this control law is activated are determined in addition we study a relation between certain adjustable design parameters and a particular measure of the uncontrolled chaotic attractor in the state space region of control ssrc from this relation the objective function to be optimized is derived in that context we assume a linear control law to be given and optimize size and shape of the ssrc using an evolutionary algorithm it is shown by examples how the algorithm can also be applied to higher dimensional systems with possibly more than one positive lyapunov exponent 2000 elsevier science b v all rights reserved

real time forecasting and daily operation of a multireservoir system during floods by linear quadratic gaussian control the problem of short term daily operation of a multireservoir system during floods is examined the problem is how to use all available real time information to solve the tactical problem of regulating reservoirs to minimize the expected value of flood damage during a relatively short operating horizon and to do so consistently with the long term operating strategy a state space mathematical model is presented for short term forecasting of river flows and description of the dynamics of a multireservoir system the model includes reduced order state space unit hydrographs to forecast storm runoff from effective rainfall and state space representations of linear flood routing the optimization problem is solved in the framework of discrete time linear quadratic gaussian lqg control lqg control is a computationally efficient and flexible method of solving the large dimensional optimization problems associated with the solution of the tactical problem of short term operation of reservoirs for application of the lqg control methodology the system must be represented in state space form with quadratic cost functions subject to linear equality constraints given by the state transition equations the scheme was found to be suitable for operation under moderate flood conditions when capacity constraints are not likely to become binding the methodology has been applied and tested in a real world case

error exponents for entanglement concentration consider entanglement concentration schemes that convert n identical copies of a pure state into a maximally entangled state of a desired size with success probability being close to one in the asymptotic limit we give the distillable entanglement the number of bell pairs distilled per copy as a function of an error exponent which represents the rate of decrease in failure probability as n tends to infinity the formula fills the gap between the least upper bound of distillable entanglement in probabilistic concentration which is the well known entropy of entanglement and the maximum attained in deterministic concentration the method of types in information theory enables the detailed analysis of the distillable entanglement in terms of the error rate in addition to the probabilistic argument we consider another type of entanglement concentration scheme where the initial state is deterministically transformed into a possibly mixed final state whose fidelity to a maximally entangled state of a desired size converges to one in the asymptotic limit we show that the same formula as in the probabilistic argument is valid for the argument on fidelity by replacing the success probability with the fidelity furthermore we also discuss entanglement yield when optimal success probability or optimal fidelity converges to zero in the asymptotic limit strong converse and give the explicit formulae for those cases

analyzing the combined multi waves polynomial solutions in a two layer liquid medium abstract in this work we investigate the behavior of mixed wave solutions in two layer liquid with dispersive waveguide these combined multi wave solutions were obtained in polynomial types for the 3 1 dimensional yu toda sasa fukuyama ytsf equation with variable coefficients by virtue of the generalized unified method and symbolic computations we formally derive polynomial solutions for this equation the obtained solutions include multi soliton solutions multi periodic solutions and multi elliptic solutions furthermore the physical insight and the movement role of the waves in the two layers are discussed and analyzed graphically for different selections of the arbitrary functions of the obtained solutions

soliton solution to bkp equation in wronskian form we find out a group of identities named wronskian identities of bilinear kp hierarchy here as well as two useful properties of d operator this makes it possible to easily search for some new wronskian solutions for pde which owns bilinear form and to simplify the process of the proof as an application of this new method we propose the first wronskian condition for the bkp i equation and for the bkp ii equation respectively in addition we also discuss several generalized bkp equations and obtain their wronskian conditions

optimal short term hydro scheduling from the principle of progressive optimality this paper presents an algorithm based on the principle of progressive optimality for determining the optimal short term scheduling of multireservoir power systems the method takes into account water head variations spilling and time delays between upstream and downstream reservoirs the method is computationally efficient and has minimal storage requirements the convergence is monotonic and a global solution is reached contrary to dynamic programing the state variables do not have to be discretized with this method an example consisting of four hydroplants in series is solved and the results are presented

wronskian determinant solutions of the 3 1 dimensional jimbo miwa equation abstract a set of sufficient conditions consisting of systems of linear partial differential equations is obtained which guarantees that the wronskian determinant solves the 3 1 dimensional jimbo miwa equation in the bilinear form upon solving the linear conditions the resulting wronskian formulations bring solution formulas which can yield rational solutions solitons negatons positons and interaction solutions

general formulas for fixed length quantum entanglement concentration in this paper we derive general formulas for the amount of entanglement that can be concentrated from general sequences of partially entangled bipartite pure states the formulas are obtained by using an information spectrum approach the formulas obtained express the optimal rate under constant error constraints or exponential error constraints in the asymptotic framework since the formulas treat general sequences they can be applied to i i d sequences as well as sequences with correlations

the tanh coth method for solitons and kink solutions for nonlinear parabolic equations abstract the tanh coth method is used to derive solitons and kink solutions for some of the well known nonlinear parabolic partial differential equations the equations include the fisher equation newell whithead equation allen cahn equation fitzhugh nagumo equation fisher s equation and the burgers fisher equation the new tanh coth approach provides abundant solitons and kink solutions in addition to the existing ones the power of this manageable method is confirmed

algebraic geometrical solutions of some multidimensional nonlinear evolution equations the known 2 1 dimensional breaking soliton equation the coupled kp equation with three potentials and a new 3 1 dimensional nonlinear evolution equation are decomposed into systems of solvable ordinary differential equations with the help of the 1 1 dimensional akns equations the abel jacobi coordinates are introduced to straighten out the associated flows from which algebraic geometrical solutions of the 2 1 dimensional breaking soliton equation the coupled kp equation and the 3 1 dimensional evolution equation are explicitly given in terms of the riemann theta functions

point symmetries of conditionally integrable nonlinear evolution equations the lie point symmetries of the first two equations in the kadomtsev petviashvili kp hierarchy introduced by jimbo and miwa are investigated the first is the potential kp equation the second involves four independent variables and is called the jimbo miwa jm equation the joint symmetry algebra for the two equations is shown to have a kac moody virasoro structure whereas the symmetry algebra of the jm equation alone does not subgroups of the joint symmetry group are used to perform symmetry reduction and to obtain invariant solutions

second order analysis for joint source channel coding with general channel and markovian source we derive the optimal second order rates in joint source channel coding when the channel is a general discrete memoryless channel and the source is an irreducible and ergodic markov process in contrast previous studies solved it only when the channel satisfies a certain unique variance condition and the source is subject to an independent and identical distribution we also compare the joint source channel scheme with the separation scheme in the second order regime while a previous study made a notable comparison with numerical calculation to discuss these two topics we introduce two kinds of new distribution families switched gaussian convolution distribution and product distribution which are defined by modifying the gaussian distribution

dynamical survey of the dual power zakharov kuznetsov burgers equation with external periodic perturbation abstract we investigate the dynamical behavior of the newly introduced dual power zakharov kuznetsov burgers equation using bifurcation theory of planar dynamical systems we study bifurcations of traveling wave solutions of the dual power zakharov kuznetsov burgers equation in presence and absence of viscosity effect in presence of an external periodic perturbation we discuss the periodic and chaotic motions of the perturbed dual power zakharov kuznetsov burgers equation by analyzing phase projection analysis time series analysis poincare section and sensitivity analysis the effect of viscosity plays an important role in the transition from chaotic motion to periodic motion of the perturbed dual power zakharov kuznetsov burgers equation

an enhanced differential evolution algorithm for daily optimal hydro generation scheduling the daily optimal hydro generation scheduling problem dohgsb is a complicated nonlinear dynamic constrained optimization problem which plays an important role in the economic operation of electric power systems this paper proposes a new enhanced differential evolution algorithm to solve dohgsb in the proposed method chaos theory was applied to obtain self adaptive parameter settings in differential evolution de in order to handle constraints effectively three simple feasibility based selection comparison techniques embedded into de are devised to guide the process toward the feasible region of the search space the feasibility of the proposed method is demonstrated for the daily generation scheduling of a hydro system with four interconnected cascade hydro plants and the test results are compared with those obtained by the conjugate gradient and two phase neural network method in terms of solution quality the simulation results show that the proposed method is able to obtain higher quality solutions

on the dispersions of three network information theory problems we analyze the dispersions of distributed lossless source coding the slepian wolf problem the multiple access channel and the asymmetric broadcast channel for the two encoder slepian wolf problem we introduce a quantity known as the entropy dispersion matrix which is analogous to the scalar dispersions that have gained interest recently we prove a global dispersion result that can be expressed in terms of this entropy dispersion matrix and provides intuition on the approximate rate losses at a given blocklength and error probability to gain better intuition about the rate at which the nonasymptotic rate region converges to the slepian wolf boundary we define and characterize two operational dispersions 1 the local dispersion and 2 the weighted sum rate dispersion the former represents the rate of convergence to a point on the slepian wolf boundary whereas the latter represents the fastest rate for which a weighted sum of the two rates converges to its asymptotic fundamental limit interestingly when we approach either of the two corner points the local dispersion is characterized not by a univariate gaussian but a bivariate one as well as a subset of off diagonal elements of the aforementioned entropy dispersion matrix finally we demonstrate the versatility of our achievability proof technique by providing inner bounds for the multiple access channel and the asymmetric broadcast channel in terms of dispersion matrices all our proofs are unified by a so called vector rate redundancy theorem which is proved using the multidimensional berry esseen theorem

resonant soliton and complexiton solutions for 3 1 dimensional boiti leon manna pempinelli equation abstract in this letter the linear superposition principle is used to discuss the 3 1 dimensional boiti leon manna pempinelli equation with bilinear derivatives as a result we obtain new resonant soliton and complexiton solutions by discussing two different cases involved the parameters these solutions are a class of n wave solutions of linear combinations of exponential traveling waves

an algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations an algebraic method is devised to uniformly construct a series of exact solutions for general integrable and nonintegrable nonlinear evolution equations compared with most existing tanh methods the jacobi function expansion method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters the solutions obtained in this paper include a polynomial solutions b exponential solutions c rational solutions d triangular periodic wave solutions e hyperbolic and solitary wave solutions and f jacobi and weierstrass doubly periodic wave solutions the efficiency of the method can be demonstrated on a large variety of nonlinear equations such as those considered in this paper new 2 1 dimensional calogero kdv equation 3 1 dimensional jimbo miwa equation symmetric regular long wave equation drinfel d sokolov wilson equation 2 1 dimensional generalized dispersive long wave equation double sine gordon equation calogero degasperis fokas equation and coupled schrodinger boussinesq equation in addition the links among our proposed method the tanh method the extended method and the jacobi function expansion method are also clarified generally

new solitary wave solutions for two nonlinear evolution equations abstract in this paper multiple exp function method is employed to investigate exact multiple wave solutions for 2 1 dimensional potential kadomtsev petviashvili equation and 3 1 dimensional jimbo miwa equation not only already known multiple wave solutions are recovered but also several new or more general multiple wave solutions are obtained

random number conversion and locc conversion via restricted storage we consider random number conversion rnc through random number storage with restricted size we clarify the relation between the performance of rnc and the size of storage in the framework of the first and second order asymptotics and derive their rate regions then we show that the results for rnc with restricted storage recover those for conventional rnc without storage in the limit of storage size to treat rnc via restricted storage we introduce a new kind of probability distributions named generalized rayleigh normal distributions using the generalized rayleigh normal distributions we can describe the second order asymptotic behavior of rnc via restricted storage in a unified manner as an application to quantum information theory we analyze locc conversion via entanglement storage with restricted size moreover we derive the optimal locc compression rate under a constraint of conversion accuracy

gradient dynamic programming for stochastic optimal control of multidimensional water resources systems a new computational algorithm is presented for the solution of discrete time linearly constrained stochastic optimal control problems decomposable in stages the algorithm designated gradient dynamic programming is a backward moving stagewise optimization the main innovations over conventional discrete dynamic programming ddp are in the functional representation of the cost to go function and the solution of the single stage problem the cost to go function assumed to be of requisite smoothness is approximated within each element defined by the discretization scheme by the lowest order polynomial which preserve its values and the values of its gradient with respect to the state variables at all nodes of the discretization grid the improved accuracy of this hermitian interpolation scheme reduces the effect of discretization error and allows the use of coarser grids which reduces the dimensionality of the problem at each stage the optimal control is determined on each node of the discretized state space using a constrained newton type optimization procedure which has quadratic rate of convergence the set of constraints which act as equalities is determined from an active set strategy which converges under lenient convexity requirements this method of solving the single stage optimization is much more efficient than the conventional way based on enumeration or iterative methods with linear rate of convergence once the optimal control is determined the cost to go function and its gradient with respect to the state variables is calculated to be used at the next stage the proposed technique permits the efficient optimization of stochastic systems whose high dimensionality does not permit solution under the conventional ddp framework and for which successive approximation methods are not directly applicable due to stochasticity results for a four reservoir example are presented the purpose of this paper is to present a new computational algorithm for the stochastic optimization of sequential decision problems one important and extensively studied class of such problems in the area of water resources is the discrete time optimal control of multireservoir systems under stochastic inflows other applications include the optimal design and operation of sewer systems e g mays and wenzel 1976 labadie et al 1980 the optimal conjunctive utilization of surface and groundwater resources e g buras 1972 and the minimum cost water quality maintenance in rivers e g dracup and fogarty 1974 chang and yeh 1973 to mention only a few of the water resources applications and pertinent references an extensive review of dynamic programming applications in water resources can be found in the works by yakowitz 1982 and yeh 1985 before we proceed with the

the painleve property for partial differential equations ii backlund transformation lax pairs and the schwarzian derivative in this paper we investigate the painleve property for partial differential equations by application to several well known partial differential equations burgers kdv mkdv bousinesq higher order kdv and kp equations it is shown that consideration of the singular manifold leads to a formulation of these equations in terms of the schwarzian derivative this formulation is invariant under the moebius group acting on dependent variables and is shown to obtain the appropriate lax pair linearization for the underlying nonlinear pde

unified view of quantum and classical correlations we discuss the problem of the separation of total correlations in a given quantum state into entanglement dissonance and classical correlations using the concept of relative entropy as a distance measure of correlations this allows us to put all correlations on an equal footing entanglement and dissonance whose definition is introduced here jointly belong to what is known as quantum discord our methods are completely applicable for multipartite systems of arbitrary dimensions we investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states

new traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized big frac g prime g big expansion method in this paper we construct new traveling wave solutions of some nonlinear evolution equations in mathematical physics via the 3 1 dimensional potential ytsf equation the 3 1 dimensional modified kdv zakharov kuznetsev equation the 3 1 dimensional kadomtsev petviashvili equation and the 1 1 dimensional kdv equation by using a generalized expansion method where g g satisfies the jacobi elliptic equation g 2 p g here we assume that p g is a polynomial of fourth order many new exact solutions in terms of the jacobi elliptic functions are obtained

extended linear quadratic gaussian control further extensions the extended linear quadratic gaussian elqg control method georgakakos and marks 1987 is a stochastic control algorithm for the optimal operation of multiobjective reservoirs mathematically this method optimizes a general functional of a stochastic system in state space form with upper and lower release constraints and probabilistic storage bounds elqg is a sequential algorithm which accounts for stochastic effects by preserving the first two statistical moments of the system s inputs and storages in this paper the method is first extended to handle nongaussian features which frequently characterize reservoir inputs second elqg s efficiency with respect to reliability storage constraints is discussed and a new barrier function method is researched these modifications are tested in case studies with the savannah river system

generalized wronskian solutions for the 3 1 dimensional jimbo miwa equation abstract more general wronskian conditions are constructed for the 3 1 dimensional jimbo miwa equation as a result the generalized wronskian solutions including rational solutions positons negatons solitons and interaction solutions are obtained moreover some new solutions together with some known solutions given by other solving methods are derived from these wronskian solutions

corrections to random number conversion and locc conversion via restricted storage in the captioned paper 3 fig 3 and fig 4 are based on incorrect numerical calculation the corrected plots in 3 fig 3 look as follows

exact solutions of the two dimensional burgers equation soliton like solutions of the two dimensional burgers equation are obtained some new solutions from soliton like solutions are also presented

new solitary wave and periodic wave solutions to the 2 1 dimensional nizhnik novikov veselov system in this work the 2 1 dimensional nizhnik novikov veselov nnv system is studied the tanh method the extended tanh method and the cosh sinh method are used to investigate this system by means of these methods new solitary wave and periodic wave solutions are determined

second order asymptotics of conversions of distributions and entangled states based on rayleigh normal probability distributions we discuss the asymptotic behavior of conversions between two independent and identical distributions up to the second order conversion rate when the conversion is produced by a deterministic function from the input probability space to the output probability space to derive the second order conversion rate we introduce new probability distributions named rayleigh normal distributions the family of rayleigh normal distributions includes a rayleigh distribution and coincides with the standard normal distribution in the limit case using this family of probability distributions we represent the asymptotic second order rates for the distribution conversion as an application we also consider the asymptotic behavior of conversions between the multiple copies of two pure entangled states in quantum systems when only local operations and classical communications locc are allowed this problem contains entanglement concentration entanglement dilution and a kind of cloning problem with locc restriction as special cases

optimization of hydropower systems operation with a quadratic model abstract this paper is devoted to the development and application of a reservoir optimization model that yields monthly release policies the generalization consists of the capability to handle nonlinear energy generation rates in the objective function maximization of system annual energy generation a quadratic model for the elevation storage average storage curve is used the optimization problem is described and formulated as the optimal control of a multivariable state space model in which the state and control vectors are constrained by sets of equality and inequality relations lagrange and kuhn tucker multipliers are used to adjoin these equality and inequality constraints to the objective functions the resulting cost functional is maximized by using the minimum norm formulation of the functional analysis numerical results are reported for a real system in operation consisting of three rivers each river has two series reservoirs

higher dimensional targeting this paper describes a procedure to steer rapidly successive iterates of an initial condition on a chaotic attractor to a small target region about any prespecified point on the attractor using only small controlling perturbations such a procedure is called targeting previous work on targeting for chaotic attractors has been in the context of one and two dimensional maps here it is shown that targeting can also be done in higher dimensional cases the method is demonstrated with a mechanical system described by a four dimensional mapping whose attractor has two positive lyapunov exponents and a lyapunov dimension of 2 8 the target is reached by making very small successive changes in a single control parameter in one typical case 35 iterates on average are required to reach a target region of diameter 10 sup minus 4 as compared to roughly 10 sup 11 iterates without the use of the targeting procedure

complexiton solutions to integrable equations abstract complexiton solutions or complexitons for short are exact solutions newly introduced to integrable equations are newly introduced starting with the solution classification for a linear differential equation the korteweg de vries equation and the toda lattice equation are considered as examples to exhibit complexiton structures of nonlinear integrable equations the crucial step in the solution process is to apply the wronskian and casoratian techniques for hirota s bilinear equations correspondence between complexitons of the korteweg de vries equation and complexitons of the toda lattice equation is provided

meromorphic exact solutions of two extended 3 1 dimensional jimbo miwa equations abstract in this work abundant meromorphic exact solutions of two kinds of extended 3 1 dimensional jimbo miwa equations are obtained by making use of the complex method which contain rational solutions exponential function solutions and elliptic function solutions the properties of the results are also shown by some figures

a study of lump type and interaction solutions to a 3 1 dimensional jimbo miwa like equation abstract using generalized bilinear equations we construct a 3 1 dimensional jimbo miwa like equation which possesses the same bilinear type as the standard 3 1 dimensional jimbo miwa equation classes of lump type solutions and interaction solutions between lump type and kink solutions to the resulting jimbo miwa like equation are generated through maple symbolic computation we discuss the conditions guaranteeing analyticity and positiveness of the solutions by taking special choices of the involved parameters 3d plots are presented to illustrate the dynamical features of the solutions

complexiton solutions of the toda lattice equation a set of coupled conditions consisting of differential difference equations is presented for casorati determinants to solve the toda lattice equation one class of the resulting conditions leads to an approach for constructing complexiton solutions to the toda lattice equation through the casoratian formulation an analysis is made for solving the resulting system of differential difference equations thereby providing the general solution yielding eigenfunctions required for forming complexitons moreover a feasible way is presented to compute the required eigenfunctions along with examples of real complexitons of lower order

multiple soliton solutions and multiple singular soliton solutions for two higher dimensional shallow water wave equations two 3 1 dimensional shallow water wave equations are studied for complete integrability the hirota s bilinear method is used to determine the multiple soliton solutions for these equations moreover multiple singular soliton solutions will also be determined for each model the analysis highlights the capability of the direct method in handling completely integrable equations

new solitons and kinks solutions to the sharma tasso olver equation abstract in this work the sharma tasso olver sto equation is investigated the tanh method the extended tanh method and other ansatze involving hyperbolic and exponential functions are efficiently used for analytic study of this equation new solitons and kinks solutions are formally derived the proposed schemes are reliable and manageable

new kink multi soliton solutions for the 3 1 dimensional potential yu toda sasa fukuyama equation by means of transformation of unknown function the non integrable system of 3 1 dimensional potential yu toda sasa fukuyama ytsf equation is converted into the combined equation of differently two bilinear forms by the darvishi s idea some new kink multi soliton solutions are obtained by using homoclinic test approach and three wave method respectively

second order asymptotics in fixed length source coding and intrinsic randomness there is a difference between the optimal rates of fixed length source coding and intrinsic randomness when we care about the second order asymptotics we prove this difference for general information sources and then investigate independent and identically distributed i i d random variables and markovian variables as examples the difference is demonstrated through an investigation of the second order asymptotic behavior of the rates a universal fixed length source code attaining the second order optimal rate is also proposed the difference between the rates of fixed length source coding and intrinsic randomness proves that the outputs of fixed length source codes are not uniformly distributed

dynamical survey of a generalized zakharov equation and its exact travelling wave solutions we investigate the dynamical behavior of a generalized zakharov equation for the complex envelope of the high frequency wave and the real low frequency field by analyzing its phase portraits following a dynamical system approach in different parameter regions we depict phase portraits of a travelling wave system through discussing the bifurcation of phase portraits we unwrap explicit miscellaneous travelling waves including localized and periodic ones

n soliton solutions to the bogoyavlenskii schiff equation and a quest for the soliton solution in 3 1 dimensions we study the integrable systems in higher dimensions which can be written by the trilinear form instead of by the hirota s bilinear form we explicitly discuss the bogoyavlenskii schiff equation in 2 1 dimensions its analytical proof of multisoliton solution and a new feature are given being guided by the strong symmetry we also propose a new equation in 3 1 dimensions

new solitonic solutions to a 3 1 dimensional jimbo miwa equation abstract performing computerized symbolic computation we are able to present new analytic solutions of a 3 1 dimensional jimbo miwa equation which does not pass any of the conventional integrability tests applying the generalized tanh method we have found such exact solutions as both the nontraveling solitonic and traveling solitary waves

multiple soliton solutions for the calogero bogoyavlenskii schiff jimbo miwa and ytsf equations abstract in this work we employ the hirota s bilinear method to derive multiple front solutions for nonlinear evolution equations three models namely the 2 1 dimensional calogero bogoyavlenskii schiff equation the 3 1 dimensional jimbo miwa equation and the 3 1 dimensional potential ytsf equation are used as vehicles to conduct the analysis the work shows the power of the bilinear method and the variety of the obtained front solutions

new extended rational expansion method and exact solutions of boussinesq equation and jimbo miwa equations abstract by means of an extended rational expansion method and symbolic computation we consider the exact solutions of boussinesq equation and jimbo miwa equations as a result we can construct many new exact solutions the solutions obtained here include the soliton wave solutions periodic wave solutions

a binary state dp algorithm for operation problems of multireservoir systems reservoir operation problems are complicated by the nonlinearities in the objective functions the dynamic programing dp procedure is often used to solve this problem because of the sequential nature of the decisions involved but for simultaneous operations of multireservoir systems other dp based techniques are frequently found to be more efficient in overcoming the curse of dimensionality problem caused by the interdependencies of the decisions in this paper another dp based procedure is proposed which performs better than the other well known techniques the applications of this technique are presented in two different formulations for four reservoir operation problems the convergence properties of the algorithm are investigated as revealed from the systematic solutions of a control problem with various dimensions

lie symmetry analysis and exact solutions of 3 1 dimensional yutodasasafukuyama equation in mathematical physics in this paper the lie symmetry analysis method has been proposed for finding similarity reduction and exact solutions of nonlinear evolution equation here for illustrating the effectiveness and accuracy of proposed method we have taken 3 1 dimensional yutodasasafukuyama ytfs equation also by using symmetry reduction method we have reduced nonlinear partial differential equation npde to nonlinear ordinary differential equation which has advantage to provide semi analytical solution we have obtained infinitesimal generators the entire geometric vector field commutator table of lie algebra and symmetry group by using lie symmetry analysis method then we have used tanh method for finding new analytical exact solutions of some reduced transform equations

hirota bilinear equations with linear subspaces of solutions we explore when hirota bilinear equations possess linear subspaces of solutions first we establish a sufficient and necessary criterion for the existence of linear subspaces of exponential traveling wave solutions to hirota bilinear equations second we show that multivariate polynomials whose zeros form a vector space can generate the desired hirota bilinear equations with given linear subspaces of solutions and formulate such multivariate polynomials by using multivariate polynomials which have one and only one zero third applying an algorithm using weights we present parameterizations of wave numbers and frequencies achieved by using one parameter to compute the desired hirota bilinear equations

exact solutions of the generalized 2 1 dimensional nonlinear evolution equations via the modified simple equation method in this paper the modified simple equation method msem is applied to construct exact solutions of the generalized 2 1 dimensional nonlinear evolution equations nlees involving parameters via the 2 1 dimensional calogero bogoyavlenskii schiff cbs equation the 2 1 dimensional breaking soliton equation and the 2 1 dimensional bogoyavlenskii s breaking soliton equation the solitary wave solutions are derived from the exact solutions by assigning special values of the parameters