conformal invariance and integrable models usually an integrable nonlinear partial differential equation can be transformed to its conformal invariant form schwartz form using the conformal invariance of the integrable models we can obtain many interesting results in this paper we will focus mainly in obtaining new symmetries and new integrable models starting from the conformal invariance of an integrable model one can obtain infinitely many non local symmetries many types of 1 1 and 2 1 dimensional new sine gordon or sinh gordon extensions are obtained from the conformal flow equations of the koerteweg de vries type equations many other kinds of integrable models can be obtained from the conformal constraints of the known integrable models

a note on time reversibility of multivariate linear processes we derive some readily verifiable necessary and sufficient conditions for a multivariate non gaussian linear process to be time reversible under two sets of conditions on the contemporaneous dependence structure of the innovations one set of conditions concerns the case of independent component innovations in which case a multivariate non gaussian linear process is time reversible if and only if the coefficients consist of essentially asymmetric columns with column specific origins of symmetry or symmetric pairs of columns with pair specific origins of symmetry on the other hand for dependent component innovations plus other regularity conditions a multivariate non gaussian linear process is time reversible if and only if the coefficients are essentially symmetric about some origin

some new periodic solitary wave solutions of 3 1 dimensional generalized shallow water wave equation by lie symmetry approach abstract many important physical situations such as fluid flows marine environment solid state physics and plasma physics have been represented by shallow water wave equations in this article we construct new solitary wave solutions for the 3 1 dimensional generalized shallow water wave gsww equation by using optimal system of lie symmetry vectors the governing equation admits twelve lie dimension space a variety of analytic closed form solutions such as new periodic solitary wave cross kink soliton and doubly periodic breather type solutions have been obtained by using invariance of the concerned 3 1 dimensional gsww equation under one parameter lie group of transformations lie symmetry transformations have applied to generate the different forms of invariant solutions of the 3 1 dimensional gsww equation for different lie algebra lie symmetry method reduces 3 1 dimensional gsww equation into various ordinary differential equations odes while one of the lie algebra it is transformed into the well known 2 1 dimensional blmp equation it is affirmed that the proposed techniques are convenient genuine and powerful tools to find the exact solutions of nonlinear partial differential equations pdes under the suitable choices of arbitrary functions and parameters 2d 3d and contour graphics to the obtained results of gsww equation are also analyzed

an application of symmetry groups to nonlocal continuum mechanics in this study the symmetry group properties of the one dimensional elastodynamics problem in nonlocal continuum mechanics is discussed by using an approach developed for symmetry group analysis of integro differential equations with general form this approach is based on the modification of the invariance criterion of the differential equations which include nonlocal variables and integro differential operators lie point symmetries of the nonlocal elasticity equation are obtained based on solving nonlocal determining equations by using a new approach the symmetry groups for different types of kernel function and the free term including the classical linear elasticity case are presented

thermodynamics of the general diffusion process time reversibility and entropy production we introduce an axiomatic thermodynamic theory for the general diffusion process and prove a theorem concerning entropy and irreversibility the equivalence among time reversibility zero entropy production symmetricity of the stationary diffusion process and a potential condition

on detailed balance and reversibility of semi markov processes and single molecule enzyme kinetics semi markov processes have found increasing applications in modeling the kinetics of single enzyme molecules detailed balance is a widely accepted condition for markov models of closed chemical systems and well known to be equivalent to the reversibility of a stationary markov process we show that for a semi markov process detailed balance is only a necessary condition but not sufficient for its time reversibility the statistical independence between the transition direction and the sojourn time is also necessary we show that the direction time independence naturally arises from the exit problem of markov models for enzyme kinetics with detailed balance detailed balance and the direction time independence together are equivalent to the time reversibility of a stationary semi markov process applications of the present theory to single molecule enzymology are also presented

on time reversibility and the uniqueness of moving average representations for non gaussian stationary time series a recent result by findley 1986 on the uniqueness of moving average representations for non gaussian time series is shown to establish a conjecture by weiss 1975 on the time reversibility of general linear processes 1988 biometrika trust

group classification for isothermal drift flux model of two phase flows in this paper a full symmetry group classification for isothermal multiphase drift flux model is presented all invariant functions are developed for the lie algebra which play a vital role in construction of optimal systems further with the help of one dimensional optimal classification group invariant solutions are obtained which describe the asymptotic behavior of general solution

miscellanea on time reversibility of linear processes summary a necessary and sufficient condition for time reversibility of stationary linear processes is given which contrary to previous results does not require existence of moments of order higher than two

solitary wave solutions of 3 1 dimensional extended zakharov kuznetsov equation by lie symmetry approach abstract in this paper the solitary wave solutions of 3 1 dimensional extended zakharov kuznetsov ezk equation are constructed which appear in the magnetized two ion temperature dusty plasma and quantum physics lie group of transformation method is proposed to investigate the solution of 3 1 dimensional ezk equation via lie symmetry method the optimal system of one dimensional lie subalgebra is constructed by using lie point symmetries the three dimensional ezk equation reduced into number of ordinary differential equations odes by applying similarity reductions consequently solutions so extracted are more general than erstwhile known results we have obtained twenty one solutions in the explicit form some of them are likewise general and some are new for the best study of us eventually single soliton quasi periodic soliton multisoliton lump type soliton traveling wave and solitary wave interaction behavior are illustrated graphically through numerical simulation for physical affirmation of the results please check whether the affiliations are correct

soliton solutions of kd system using similarity transformations method abstract present article deals with some exact solutions of 2 1 dimensional system of coupled konopelchenko dubrovsky equations similarity transformations method is proposed to seek the solution of the system using lie group theory the lie group theory is a very strong tool by which complicated nonlinear partial differential equations under the group transformations remains invariant a brief review of lie symmetries of a system of partial differential equations has been described during the process method reduces the number of independent variables by one hence the system of partial equations reduces into a new system of ordinary differential equations in addition the infinitesimals after first reductions are more general than the previous established results by us kumar et al 2016 consequently solutions so derived are more general than previously known results we have obtained nine solutions in the explicit form some of them are more general and some are new for the best knowledge of us ultimately single solitons multi solitons and shocks behaviour is represented graphically through the numerical simulation for physical validation of the results

invariant solutions and conservation laws to nonconservative fp equation we generate conservation laws for the one dimensional nonconservative fokker planck fp equation also known as the kolmogorov forward equation which describes the time evolution of the probability density function of position and velocity of a particle and associate these where possible with lie symmetry group generators we determine the conserved vectors by a composite variational principle and then check if the condition for which symmetries associate with the conservation law is satisfied as the fokker planck equation is evolution type no recourse to a lagrangian formulation is made moreover we obtain invariant solutions for the fp equation via potential symmetries

invariant solutions of integro differential vlasov maxwell equations in lagrangian variables by lie group analysis the lie point symmetries of the vlasov maxwell system in lagrangian variables are investigated by using a direct method for symmetry group analysis of integro differential equations with emphasis on solving nonlocal determining equations all similarity reduction forms for the system are obtained by using different approaches and some analytical and numerical solutions are presented

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

some more similarity solutions of the 2 1 dimensional blp system some more similarity solutions of the coupled boiti leon pempinelli system have been obtained by using similarity transformations method via lie group theory the solutions are attained under the restrictions imposed on the functions involved in infinitesimals then solutions are investigated through the graphical representation in different cases the cases depend upon some suitable choice of arbitrary functions involved there i e in the solutions to get physically meaningful structures analytical solutions are supplemented by numerical simulations with appropriate choice of arbitrary functions and constants eventually profiles show single soliton elastic multisolitons quasi periodic parabolic and asymptotic nature of solutions

similarity solutions of the konopelchenko dubrovsky system using lie group theory this research deals with the similarity solutions of 2 1 dimensional konopelchenko dubrovsky kd system solutions so obtained are derived by using similarity transformations method based on lie group theory the method reduces the number of independent variables by one exploiting lie symmetries and using invariance property thus the kd system can further be reduced to a new system of ordinary differential equations under a suitable choice of functions and the arbitrary constants these new equations yield the explicit solutions of the kd system which are discussed in the similarity solutions section of the article moreover the physical analysis of the solutions is illustrated graphically in the analysis and discussions section based on numerical simulations in order to highlight the importance of the study

application of lie groups to compressible model of two phase flows this paper presents some exact solutions for the drift flux model of two phase flows using lie group analysis the analysis involves an isentropic no slip conservation of mass for each phase and the conservation of momentum for the mixture the present analysis employs a complete lie algebra of infinitesimal symmetries subsequent to these theoretical analysis a symmetry group is established the symmetry generators are used for constructing similarity variables which reduce the model equations to a system of ordinary differential equations odes in particular a general framework is discussed for solving the model equations analytically as a consequence of this new classes of exact group invariant solutions are developed this provides new insights into the fundamental properties of weak discontinuities and helps one to understand better on existence of solutions

optimal kernel weights under a power criterion abstract we develop an approach to choosing optimal kernel weights for nonparametric estimation of the slope of the regression function which uses maximization of power rather than minimization of integrated mean squared error imse as its optimality criterion this power criterion leads to optimal kernel weights whose derivation is simpler than under other criteria and which provides an intuitive understanding of the nature of the optimality

on the reversibility of the observed process of three state hidden markov model for the continuous time and the discrete time three state hidden markov model the flux of the likelihood function up to 3 dimensional of the observed process is shown explicitly as an application the sufficient and necessary condition of the reversibility of the observed process is shown

soliton solutions of blmp equation by lie symmetry approach abstract shallow water wave equations are usually described by korteweg de vries kdv type equations in this paper we have used lie transformation group theory to solve 2 1 dimensional boiti leon manna pempinelli blmp equation we have obtained some exact solutions of blmp equation in the explicit form through similarity reduction all the reported results are expressed in closed form and analysed physically through their evolution profiles the physical analysis reveals that the nature of solutions is parabolic quasi periodic multisoliton and asymptotic