sort and match algorithm for soft decision decoding let a q ary linear n k code c be used over a memoryless channel we design a decoding algorithm spl psi sub n that splits the received block into two halves in n different ways first about spl radic n error patterns are found on either half then the left and right hand lists are sorted out and matched to form codewords finally the most probable codeword is chosen among at most n spl radic n codewords obtained in all n trials the algorithm can be applied to any linear code c and has complexity order of n sup 3 spl radic n for any n spl ges q sup n k the decoding error probability p sub n exceeds at most 1 q sup n k n times the probability p sub spl psi c of maximum likelihood decoding for code rates r spl ges 1 2 the complexity order q sup n k 2 grows as square root of general trellis complexity q sup min n k k when used on quantized additive white gaussian noise awgn channels the algorithm spl psi sub n can provide maximum likelihood decoding for most binary linear codes even when n has an exponential order of q sup n k

some new solitonary solutions of the modified benjamin bona mahony equation abstract in this paper we use the exp function method to construct some new soliton solutions of the benjamin bona mahony and modified benjamin bona mahony equations these equations have important and fundamental applications in mathematical physics and engineering sciences the exp function method is used to find the soliton solution of a wide class of nonlinear evolution equations with symbolic computation this method provides the concise and straightforward solution in a very easier way the results obtained in this paper can be viewed as a refinement and improvement of the previously known results

variational approach soliton solutions and singular solitons for new coupled zk system in this paper we obtain a variational principle for the new coupled zakharov kuznetsov zk system by the semi inverse method based on this formulation a new solitary wave solution can be easily obtained using ritz method we obtained the conditions which must remain valid for continuation of the new solitary solution and other solutions to exist we also studied the collision dynamics between waves in each case finally we give the numerical simulations to complete the study

new periodic wave and soliton solutions for system of coupled korteweg de vries equations the periodic wave solutions for the system of coupled korteweg de vries equations are obtained by using of jacobi elliptic function method in the limit cases the multiple soliton solutions are also obtained the properties of some periodic and soliton solution for this system are shown by some figures

numerical solitons of generalized korteweg de vries equations abstract we propose a numerical method for finding solitary wave solutions of generalized korteweg de vries equations by solving the nonlinear eigenvalue problem on an unbounded domain the artificial boundary conditions are obtained to make the domain finite we specially discuss the soliton solutions of the k m n equation and kdv k m n equation furthermore for the mixed models of linear and nonlinear dispersion the collision behaviors of soliton soliton and soliton antisoliton are observed

looping vs repeating in dynamic logic two extensions of propositional dynamic logic for dealing with infinite computations lpdl and rpdl are compared in expressive power the first is obtained by adding the assertion loop for any program meaning contains an infinite computation and the second by adding repeat meaning can be repeated indefinitely while repeat can be used to encode loop and hence lpdl rpdl it is shown here that the converse fails thus lpdl

all traveling wave exact solutions of two kinds of nonlinear evolution equations abstract in this article we employ the complex method to obtain all meromorphic solutions of complex korteweg de vries kdv equation and the modified benjamin bona mahony mbbm equation at first then find out all traveling wave exact solutions of the eqs kdv and mbbm the idea introduced in this paper can be applied to other nonlinear evolution equations our results show that all rational and simply periodic solutions of the eqs kdv and mbbm are solitary wave solutions the complex method is simpler than other methods and there exist some rational solutions w 2 r 2 z and simply periodic solutions w 2 s 1 z which are not only new but also not degenerated successively by the elliptic function solutions we give some computer simulations to illustrate our main results

solitary waves of the regularized long wave equation abstract a finite element solution of the regularised long wave equation based on galerkin s method using cubic splines as element shape functions is set up a linear stability analysis shows the scheme to be unconditionally stable test problems including the migration and interaction of solitary waves are used to validate the method which is found to be accurate and efficient the three invariants of the motion are evaluated to determine the conservation properties of the algorithm the temporal evolution of a maxwellian initial pulse is then studied

exact solutions of a third grade fluid flow on a porous plate in this paper the exact solutions for an unsteady flow of an incompressible fluid of third grade occupying space over an infinite porous plate are obtained for a given velocity component translational type symmetries are employed to reduce the non linear equations governing the flow under discussion to two ordinary differential equations with and without dispersion terms graphs representing the solutions are discussed and appropriate conclusions drawn

absorbing boundary conditions for the stationary forced kdv equation abstract in the present work we study the stationary korteweg de vries kdv equation with a forcing for a flow of an inviscid and incompressible fluid the stationary fkdv equation is defined in an infinite domain and it is reduced to a bounded domain by introducing absorbing boundary conditions a new numerical method is proposed to solve this boundary value problem new multiple numerical solitary wave solutions of the stationary kdv equation are discussed for various forcings numerical examples are provided to confirm and illustrate the accuracy and effectiveness of the method

long time bounds for the periodic benjamin ono bbm equation abstract we consider the periodic benjamin ono equation regularized in the same way as the benjamin bona mahony equation is found from the korteweg de vries one t b benjamin j l bona j j mahony model equations for long waves in nonlinear dispersive systems philos trans roy soc london ser a 272 1220 1972 47 78 namely the equation u t u x u u x h u x t 0 where h is the hilbert transform the quotient between the characteristic wave amplitude and the depth of the waves and the quotient between this depth and the wavelength we show that the solution starting from an initial datum of size e remains smaller than e for a time scale of order e 1 2 whereas the local well posedness gives only a time of order e 1

on a class of physically important integrable equations abstract a methodology introduced by fuchssteiner and the author is used to derive a class of physically important integrable evolution equations among these equations are integrable generalizations of the korteweg devries kdv of the modified kdv of the nonlinear schrodinger nls and of the sine gordon equations the modeling of water waves as well as general asymptotic considerations are used to illustrate the occurrence of the generalized modified kdv and nls equations respectively

extended jacobi elliptic function expansion solutions of variant boussinesq equations with the aid of symbolic computation maple an extended jacobi elliptic function expansion method is presented and successfully applied to variant boussinesq equations as a result abundant periodic wave solutions in terms of the jacobi elliptic functions are obtained when the modulus m 1 or m 0 exact solitary wave solutions and trigonometric function solutions are also derived the properties of four new solutions are graphically studied

multi soliton solution for the system of coupled korteweg de vries equations in this paper we consider the system of coupled korteweg de vries equations and establish the transformation which turns the coupled kdv equations into the single nonlinear partial differential equation then we obtain an auto backlund transformation and lax pairs by using the extended homogeneous balance method also we obtain the multi soliton solutions and the new trigonometric function periodic solutions by using the generalized tanh method

numerical study of three dimensional turing patterns using a meshless method based on moving kriging element free galerkin efg approach in this paper a numerical procedure is presented for solving a class of three dimensional turing system first we discrete the spatial direction using element free galerkin efg method based on the shape functions of moving kriging interpolation then to achieve a high order accuracy we use the fourth order exponential time differencing runge kutta etdrk4 method using this discretization for the temporal dimension we obtain an explicit scheme and do not need to solve nonlinear system of equations the efg method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the efg method test and trial functions are moving least squares approximation mls shape functions since the shape functions of moving least squares mls approximation do not have kronecker delta property we cannot implement the essential boundary condition directly also building shape functions of mls approximation is a time consuming procedure because of the mentioned reasons we employ the shape functions of moving kriging interpolation technique which have the mentioned property and less cpu time is required for building them for testing this method on three dimensional pdes we select some equations and system of pdes such as allen cahn gray scott ginzburg landau brusselator models predator prey model with additional food supply to predator several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme

on the undecidability of logics with converse nominals recursion and counting the evolution of description logics dls and propositional dynamic logics produced a hierarchy of decidable logics with multiple maximal elements it would be desirable to combine different maximal logics into one super logic but then inference may turn out to be undecidable then it is important to characterize the decidability threshold for these logics in this perspective an interesting open question pointed out by sattler and vardi proc ijcar 01 in lecture notes in artif intel vol 2083 springer 2001 pp 76 91 is whether inference in a hybrid calculus with restricted forms of graded modalities is decidable and which complexity class it belongs to in this paper we improve a previous result proc ijcai 03 morgan kaufmann 2003 pp 331 336 and prove that this calculus and the corresponding dl accio fa are undecidable we show also that nested fixpoints are not necessary for undecidability

the lie group method based on radial basis functions for solving nonlinear high dimensional generalized benjamin bona mahony burgers equation in arbitrary domains abstract the aim of this paper is to introduce a new numerical method for solving the nonlinear generalized benjamin bona mahony burgers gbbmb equation this method is combination of group preserving scheme gps with radial basis functions rbfs which takes advantage of two powerful methods one as geometric numerical integration method and the other meshless method thus we introduce this method as the lie group method based on radial basis functions lg rbfs in this method we use kansas approach to approximate the spatial derivatives and then we apply gps method to approximate first order time derivative one of the important advantages of the developed method is that it can be applied to problems on arbitrary geometry with high dimensions to demonstrate this point we solve nonlinear gbbmb equation on various geometric domains in one two and three dimension spaces the results of numerical experiments are compared with analytical solutions and the method presented in dehghan et al 2014 to confirm the accuracy and efficiency of the presented method

the homogeneous balance method and its application to the benjamin bona mahoney bbm equation abstract we make use of the homogeneous balance method and symbolic computation to construct new exact traveling wave solutions for the benjamin bona mahoney bbm equation many new exact traveling wave solutions are successfully obtained which contain rational and periodic like solutions this method is straightforward and concise and it can also be applied to other nonlinear evolution equations

an artificial boundary method for the hull white model of american interest rate derivatives abstract the hull white hw model is a widely used one factor interest rate model because of its analytical tractability on liquidly traded derivatives super calibration ability to the initial term structure and elegant tree building procedure as an explicit finite difference scheme lattice method is subject to some stability criteria which may deteriorate the computational efficiency for early exercisable derivatives this paper proposes an artificial boundary method based on the partial differential equations pdes to price interest rate derivatives with early exercise american feature under the hw model we construct conversion factors to extract the market information from the zero coupon curve and then reduce the infinite computational domain into a finite one by using an artificial boundary on which an exact boundary condition is derived we then develop an implicit scheme with unconditional stability to solve the pde in the reduced bounded domain with a finite computational domain the optimal exercise strategy can be determined efficiently our numerical examples show that the proposed scheme is accurate robust to the truncation size and more efficient than the popular lattice method for accurate derivative prices in addition the singularity separating technique is incorporated into the artificial boundary method to enhance accuracy and flexibility of the numerical scheme

self similar radiation from numerical rosenau hyman compactons the numerical simulation of compactons solitary waves with compact support is characterized by the presence of spurious phenomena as numerically induced radiation which is illustrated here using four numerical methods applied to the rosenau hyman k p p equation both forward and backward radiations are emitted from the compacton presenting a self similar shape which has been illustrated graphically by the proper scaling a grid refinement study shows that the amplitude of the radiations decreases as the grid size does confirming its numerical origin the front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters the amplitude of the radiations decreases exponentially in time being characterized by a nearly constant scaling exponent an ansatz for both the backward and forward radiations corresponding to a self similar function characterized by the scaling exponent is suggested by the present numerical results

a locally conservative eulerian lagrangian finite difference method for the forced kdv equation abstract we propose a locally conservative eulerian lagrangian finite difference method fdlcelm for approximating the solution of the forced korteweg de vries equation the new numerical method employs an operator splitting scheme that solves the nonlinear transport equation and the linear dispersive equation sequentially in order to conserve mass in the transport fractional step we trace back each grid cell in time along the integral curve the dispersive fractional step will be solved using a cell centered finite difference method numerical examples are provided to confirm and illustrate the accuracy and mass conservation property of the new method we also study the numerical stability and time evolution of various stationary solitary wave solutions in the presence of one or two bumps

exp function method for traveling wave solutions of nonlinear evolution equations in this paper we apply the exp function method to construct generalized solitary and periodic solutions of nonlinear evolution equations the proposed technique is tested on the modified zakharov kuznetsov zk and zakharov kuznetsov modified equal width zk mew equations these equations play a very important role in mathematical physics and engineering sciences the suggested algorithm is quite efficient and is practically well suited for use in these problems numerical results clearly indicate the reliability and efficiency of the proposed exp function method

new multi soliton solutions of a 3 1 dimensional nonlinear evolution equation in this paper applying homoclinic test approach to a 3 1 dimensional nonlinear evolution equation new kink breather soliton solutions are obtained in addition some new multi soliton solutions are obtained via three wave method it is shown that the homoclinic test approach and the three wave method can be used for constructing multi soliton solutions of nonlinear evolution equations in mathematical physics

ellipsoidal lists and maximum likelihood decoding we study an interrelation between the coverings generated by linear n k codes and complexity of their maximum likelihood ml decoding first discrete ellipsoids in the hamming spaces e sub 1 sup n are introduced these ellipsoids represent the sets of most probable error patterns that need to be tested in soft decision ml decoding we show that long linear n k codes surrounded by ellipsoids of exponential size 2 sup n k can cover the whole space e sub 2 sup n then it is proven that ml decoding of most long n k codes needs only about 2 sup n k most probable error patterns to be tested on any quantized memoryless channel finally ml decoding complexity is bounded from above by 2 sup k n k n this substantially reduces the general trellis complexity 2 sup min n k k

solitary solutions periodic solutions and compacton like solutions using the exp function method in this paper the exp function method is used for seeking solitary solutions periodic solutions and compacton like solutions of nonlinear differential equations the combined kdv mkdv equation and the liouville equation are chosen to illustrate the effectiveness and convenience of the proposed method

the numerical solution of nonlinear high dimensional generalized benjamin bona mahony burgers equation via the meshless method of radial basis functions in this paper a numerical technique is proposed for solving the nonlinear generalized benjamin bona mahony burgers equation firstly we obtain a time discrete scheme by approximating the first order time derivative via forward finite difference formula then we use kansa s approach to approximate the spatial derivatives we prove that the time discrete scheme is unconditionally stable and convergent in time variable using the energy method also we show that convergence order of the time discrete scheme is o t we solve the two dimensional version of this equation using the method presented in this paper on different geometries such as the rectangular triangular and circular domains and also the three dimensional case is solved on the cubical and spherical domains the aim of this paper is to show that the meshless method based on the radial basis functions and collocation approach is also suitable for the treatment of the nonlinear partial differential equations also several test problems including the three dimensional case are given numerical examples confirm the efficiency of the proposed scheme

on soliton solutions of the 2 1 dimensional boussinesq equation abstract the repeated homogeneous balance method is used to construct exact traveling wave solutions of the 2 1 dimensional boussinesq equation in which the homogeneous balance method is applied to solve the riccati equation and the reduced nonlinear ordinary differential equation respectively many new exact traveling wave solutions are successfully obtained this method is straightforward and concise and it can be also applied to other nonlinear evolution equations

determinism and looping in combinatory pdl abstract in this paper some propositional modal logics of programs are considered based on the system cpdl combinatory pdl an extension of pdl with proper names for states these proper names are atomic formulae which are satisfied at exactly one state in each model among other things e g decidability and finite model property results a version of streett s conjecture that his axioms do axiomatize the infinite repeating construct repeat is established with respect to cpdl

suboptimal decoding of linear codes partition technique general symmetric channels are introduced and near maximum likelihood decoding in these channels is studied first we define a class of suboptimal decoding algorithms based on an incomplete search through the code trellis it is proved that the decoding error probability of suboptimal decoding is bounded above for any q ary code of length n and code rate r by twice the error probability of its maximum likelihood decoding and tends to the latter as n grows second we design a suboptimal trellis like algorithm which reduces the known decoding complexity of the order of q sup n min r 1 r operations to that of q sup nr i r operations for all cyclic codes and virtually all long linear codes we also consider the corresponding bounds for concatenated codes an important corollary is that this suboptimal decoding can provide complexity below the lower bounds on trellis complexity at a negligible expense in terms of decoding error probability

propositional dynamic logic of looping and converse is elementarily decidable propositional dynamic logic is a formal system for reasoning about the before after behavior of regular program schemes an extension of propositional dynamic logic which includes both an infinite looping construct and a converse or backtracking construct is considered and it is proved that the satisfiability problem for this logic is elementarily decidable in order to establish this result deterministic two way automata on infinite trees are defined and it is shown how they can be simulated by nondeterministic one way automata the satisfiability problem for propositional dynamic logic of looping and converse is then reduced to the emptiness problem for these two way automata

new soliton solutions for a kadomtsev petviashvili kp like equation coupled to a schrodinger equation abstract the repeated homogeneous balance is used to construct a new exact traveling wave solution of the kadomtsev petviashvili kp like equation coupled to a schrodinger equation in which the homogeneous balance method is applied to solve the riccati equation and the reduced nonlinear ordinary differential equation respectively many new exact traveling wave solutions are successfully obtained which contain rational and periodic like solutions this method is straightforward and concise and it can be applied to other nonlinear evolution equations

new periodic and soliton solutions for the generalized bbm and burgers bbm equations abstract in this paper we consider the benjamin bona mahony equation bbm and we obtain new exact solutions for it by using a generalization of the well known tanh coth method new periodic and soliton solutions for the generalized bbm and burgers bbm equations are formally derived

numerical methods based on modified equations for nonlinear evolution equations with compactons abstract compactons are traveling wave solutions with compact support resulting from the balance of both nonlinearity and nonlinear dispersion numerical methods with second fourth sixth and eighth order approximations to the spatial derivatives obtained by means of the method of modified equations applied to the ismail taha finite difference scheme for the rosenau hyman equation are developed the whole set of methods is compared among them in accuracy invariant conservation and in compacton collisions the best method among those studied in terms of the tradeoff between accuracy and computational cost is determined

the jacobi elliptic function method and its application for two component bkp hierarchy equations the periodic wave solutions for the two component bkp hierarchy are obtained by using of jacobi elliptic function method in the limit cases the multiple soliton solutions are also obtained the properties of some periodic and soliton solution for this system are shown by some figures

a modal logic for cyclic repeating abstract a simplified fragment of pdl denoted by mlcr a modal logic for cyclic repeating is introduced in which a cyclic repeating of a program can be expressed a completeness theorem for mlcr with respect to the intended standard semantics is given it is proved that mlcr does not possess the finite model property with respect to its standard models but nevertheless it possesses this property with respect to some nonstandard models and consequently is decidable