a new conservation law constructed without using either lagrangians or hamiltonians a new conservation theorem is derived the conserved quantity is constructed in terms of a symmetry transformation vector of the equations of motion only without using either lagrangian or hamiltonian structures which may even fail to exist for the equations at hand one example and implications of the theorem on the structure of point symmetry transformations are presented

w symmetries of ito stochastic differential equations we discuss w symmetries of ito stochastic differential equations introduced in a recent paper by gaeta and spadaro j math phys 58 053503 2017 in particular we discuss the general form of acceptable generators for continuous lie point w symmetry arguing that they are related to the linear conformal group and how w symmetries can be used in the integration of ito stochastic equations along kozlov theory for standard deterministic or random symmetries it turns out that this requires in general considering more general classes of stochastic equations than just ito ones we discuss w symmetries of ito stochastic differential equations introduced in a recent paper by gaeta and spadaro j math phys 58 053503 2017 in particular we discuss the general form of acceptable generators for continuous lie point w symmetry arguing that they are related to the linear conformal group and how w symmetries can be used in the integration of ito stochastic equations along kozlov theory for standard deterministic or random symmetries it turns out that this requires in general considering more general classes of stochastic equations than just ito ones

random lie point symmetries of stochastic differential equations we study the invariance of stochastic differential equations under random diffeomorphisms and establish the determining equations for random lie point symmetries of stochastic differential equations both in ito and in stratonovich forms we also discuss relations with previous results in the literature

approximate symmetries and conservation laws for ito and stratonovich dynamical systems a new definition for the approximate symmetries of ito dynamical system is given determining systems of approximate symmetries for ito and stratonovich dynamical systems have been obtained it has been shown that approximate conservation laws can be found from the approximate symmetries of stochastic dynamical systems which do not arise from a hamiltonian the results have been applied to an example

the group classification of a scalar stochastic differential equation lie point group classification of a scalar stochastic differential equation sde with one dimensional brownian motion is presented the admitted symmetry group can be zero one two or three dimensional if an equation admits a three dimensional symmetry group it can be transformed into the equation of brownian motion by a change of variables with non random time transformation such equations can be integrated by quadratures there are described drift coefficients for which sdes with constant diffusion coefficients admit two and three dimensional symmetry groups

a remark on symmetry of stochastic dynamical systems and their conserved quantities the symmetry properties of stochastic dynamical systems described by a stochastic differential equation of stratonovich type and related conserved quantities are discussed extending previous results by misawa new conserved quantities are given by applying symmetry operators to known conserved quantities some detailed examples are presented

lagrangian variational principle in stochastic mechanics gauge structure and stability the lagrangian variational principle with the classical action leads in stochastic mechanics to madelung s fluid equations if only irrotational velocity fields are allowed while new dynamical equations arise if rotational velocity fields are also taken into account the new equations are shown to be equivalent to the gauge invariant system of a schrodinger equation involving a four vector potential a and the coupled evolution equation of magnetohydrodynamical type for the vector field a a general energy theorem can be proved and the stability properties of irrotational and rotational solutions investigated

surface critical exponents for models of polymer collapse and adsorption the universality of the theta and theta points the surface critical exponents are estimated both in ordinary and in special regimes from exact series expansions of up to 28 terms for a model of the theta point they are found to be in agreement with those derived for the theta point confirming the conjecture that the theta and theta points lie in the same universality class some essential features of the phase diagram for a self interacting self avoiding polymer in solution are also calculated to a higher degree of accuracy than previously obtained

differential methods in inverse scattering this paper discusses a new set of differential methods for solving the inverse scattering problem associated to the propagation of waves in an inhomogeneous medium by writing the medium equations in the form of a two component system describing the interaction of rightward and leftward propagating waves the causality of the propagation phenomena is exploited in order to identify the medium layer by layer the recursive procedure that we obtain constitutes a continuous version of an algorithm first derived by schur in order to test for the boundedness of functions analytic inside the unit circle it recovers the local reflectivity function of the medium using similar ideas some other differential methods can also be derived to reconstruct alternative parametrizations of the layered medium in terms of the local impedance or of the potential function the differential inverse scattering methods turn out to be very efficient since in some sense they let the medium perform the inversion by itself and thus

application of the schur algorithm to the inverse problem for a layered acoustic medium the schur algorithm is a signal processing algorithm which works on a layer stripping principle its time domain version the fast cholesky recursion is a fast and efficient algorithm well suited for high speed data processing in this paper these algorithms are applied to the inverse problem for a continuous layered acoustic medium three different excitations of the medium are considered impulsive plane waves at normal incidence impulsive plane waves at oblique incidence and spherical waves emanating from an impulsive point source the fast algorithms obtained for each of these problems seem to be computationally superior to past work done on these problems that employed gelfand levitan theory to reconstruct the potential of a schrodinger equation

fixed point results for generalized quasicontraction mappings in abstract metric spaces in this paper we introduce the concept of generalized quasicontraction mappings in an abstract metric space by using this concept we construct an iterative process which converges to a unique fixed point of these mappings the result presented in this paper generalizes the banach contraction principle in the setting of metric space and a recent result of huang zhang for contractions we also validate our main result by an example

the one dimensional inverse problem of reflection seismology an impulsive normal traction is applied uniformly over the surface of a perfectly stratified plane layered earth the ensuing particle velocity at the surface is assumed to be measured the problem of calculating the subsurface characteristic impedance from knowledge of the input pulse and the measured data is the one dimensional inverse problem of reflection seismology the problem is set up mathematically as an inverse problem for a first order 2 times 2 hyperbolic system the role of propagation of singularities is explained and the relation between the solution of the inverse problem and the cholesky factorization of certain matrices constructed from the data is elaborated for both the continuum problem and the related discrete problem it is found that recursive numerical techniques such as the levinson algorithm and certain other fast methods for cholesky factorization are intimately related to explicit finite difference schemes for solving hyperbolic systems the order of approximation between the

inverse scattering for a layered acoustic medium using the first order equations of motion the inverse scattering problem for a layered acoustic medium is considered from the first order differential equations of motion resulting in a vector formulation of the problem and using a vector form of the schrodinger inverse scattering methods the result is a vector marchenko equation the differentiability constraints on the acoustic impedance are somewhat relaxed compared to the more standard approach of beginning with the wave equation the solution for plane waves at normal incidence is given along with a good approximate solution which is easily obtainable and takes into account transmission losses not included in the normal wkbj born approximation a new solution for extracting separately the velocity and density of the medium using the reflection response for two different angles of incidence is given which involves a nonlinear integral equation to relate the apparent traveltimes to depth

basic representations of a2l 2 and dl 1 2 and the polynomial solutions to the reduced bkp hierarchies basic representations of a2l 2 and dl 1 2 are studied the weight vectors are represented in terms of schur s q functions the method to get the polynomial solutions to the reduced bkp hierarchies is shown to be equivalent to a certain rule in the maya game

new conserved quantities derived from symmetry for stochastic dynamical systems recently the author has proposed an elementary theory of conserved quantities and symmetry for stochastic dynamical systems described by stochastic differential equations of stratonovich type within the framework a new method for deriving conserved quantities from symmetry is developed in a similar manner to that of hojman s work 1992 which gives a new conservation law constructed without using either lagrangians or hamiltonians for deterministic dynamical systems some examples of the conserved quantities obtained through the new method are given

on the definition of an admitted lie group for stochastic differential equations with multi brownian motion the definition of an admitted lie group of transformations for stochastic differential equations has been already presented for equations with one dimensional brownian motion the transformation of the dependent variables involves time as well and it has been proven that brownian motion is transformed to brownian motion in this paper we will discuss this concept for stochastic differential equations involving multi dimensional brownian motion and present applications to a variety of stochastic differential equations

common fixed points in best approximation for banach operator pairs with ciric type i contractions abstract the common fixed point theorems similar to those of ciric lj b ciric on a common fixed point theorem of a gregus type publ inst math beograd n s 49 1991 174 178 lj b ciric on diviccaro fisher and sessa open questions arch math brno 29 1993 145 152 lj b ciric on a generalization of gregus fixed point theorem czechoslovak math j 50 2000 449 458 fisher and sessa b fisher s sessa on a fixed point theorem of gregus internat j math math sci 9 1986 23 28 jungck g jungck on a fixed point theorem of fisher and sessa internat j math math sci 13 1990 497 500 and mukherjee and verma r n mukherjee v verma a note on fixed point theorem of gregus math japon 33 1988 745 749 are proved for a banach operator pair as applications common fixed point and approximation results for banach operator pair satisfying ciric type contractive conditions are obtained without the assumption of linearity or affinity of either t or i our results unify and generalize various known results to a more general class of noncommuting mappings

lie point symmetries of stratonovich stochastic differential equations this paper considers lie point symmetries of stochastic differential equations sdes in stratonovich form first we derive the determining equations of the random symmetries which correspond to lie group transformations acting in the space of the independent variable time the dependent variables and the brownian motion then the determining equations of the random symmetries are used to obtain the determining equations of the deterministic symmetries which correspond to lie group transformations acting in the space of the independent variable and dependent variables in the case of the deterministic symmetries the transformation of the brownian motion is induced by the random time change it is proved that the corresponding ito and stratonovich sdes admit the same random symmetries and the same deterministic symmetries

symmetries of systems of stochastic differential equations with diffusion matrices of full rank lie point symmetries of a system of stochastic differential equations sdes with diffusion matrices of full rank are considered it is proved that the maximal dimension of a symmetry group admitted by a system of n sdes is n 2 in addition such systems cannot admit symmetry operators whose coefficients are proportional to a nonconstant coefficient of proportionality these results are applied to compute the lie group classification of a system of two sdes the classification is obtained with the help of non equivalent realizations of real lie algebras by fiber preserving vector fields in 1 2 variables possibilities of using symmetries for integration of sdes by quadratures are discussed

backscattering and inverse problem in random media with use of the invariant imbedding method and markov process approximation the statistical characteristics of the backscattering field from the impulse point source in a nonstationary multidimensional random medium are considered the equations for the characteristic function and the density of the probability in the functional space of the backscattering are obtained the equations for the statistical moments of the field are yielded and then solutions are presented in the matrix form the additional averaging of the fast field variations is used for the simplification of the statistical equations the procedures for the investigation of the direct and inverse statistical problem are proposed the role of the phenomenological transfer theory is discussed from the statistical point of view

random lie symmetries of ito stochastic differential equations lie point symmetries of stochastic differential equations sdes which include transformations depending on the brownian motion are considered the corresponding lie group transformations acting in the space of the independent variable time the dependent variables and the brownian motion preserve the differential form of sdes and the properties of the brownian motion such symmetries are called random symmetries the focus of the paper is a definition of the random symmetries and their properties it is shown that the random symmetries form a lie algebra we also investigate relations between the random symmetries and the conserved quantities of sdes for several stochastic differential equations we find their random symmetries and compare them with the deterministic symmetries which correspond to lie group transformations in the space of the independent and dependent variables

inverse problem in nonstationary multidimensional medium the problem of a scalar wave propagation from the point impulsive source in the layer of a nonstationary multidimensional medium is considered the boundary problem for the wave equation is reformulated in the problem with the initial condition using the invariant imbedding method the integral differential inverse procedures of the various orders were obtained from the imbedding equations using the singularities method the order of inverse procedure is defined by the degree of a polynomial in the analytical representation of the medium characteristic near the layer boundary it was shown that the coefficients of the polynomial are calculated with the help of the differential characteristics of the point impulsive source in the inhomogeneous medium the cause and character of the multidimensional inverse problem overdefiniteness are considered the application of the proposed procedure for a statistical problem is discussed

a new type of fixed point theorem in metric spaces abstract we prove a generalization of edelstein s fixed point theorem though there are thousands of fixed point theorems in metric spaces our theorem is a new type of theorem

common fixed points for banach operator pairs with applications the existence of common fixed point results for a banach operator pair under certain generalized contractions is established the invariant best approximation results are proved as applications and the existence of solutions of variational inequalities is obtained we also study the solution of functional equations arising from dynamic programming 2007 elsevier ltd all rights reserved

symmetries of stochastic differential equations a geometric approach a new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations sdes the correspondence between an algebra of weak symmetries for a given sde and an algebra of strong symmetries for a modified sde is proved under suitable regularity assumptions this general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional brownian motion

fixed points for generalized contractions and applications to control theory the concepts of weak strong topological contraction and a generalization of banach contraction mappings called p contraction are introduced and used to prove fixed point theorems for self mappings from a topological metric space into itself satisfying topological contraction metric p contraction respectively certain non linear integral equations defined on c a b satisfying generalized lipschitzian conditions can easily be solved by applying these theorems in the sequel we shall study the possibility of optimally controlling the solution of the ordinary differential equation via dynamic programming

direct and inverse scattering in the time domain via invariant imbedding equations this paper examines the implementation of a new approach to direct and inverse scattering problems in the time domain which is applied here to the case of a one dimensional lossless medium the method is based on an integro differential equation which is satisfied by the reflection kernel and has been derived elsewhere using invariant imbedding techniques an example of an exact solution to this equation is given numerical schemes for solving the direct and inverse problems are derived by discretizing this equation the behavior of the resulting algorithms is then tested on several examples the results suggest that the inversion method is stable in the presence of additive noise

on maximal lie point symmetry groups admitted by scalar stochastic differential equations it is proved that the lie point symmetry group admitted by a scalar stochastic differential equation sde of order n 3 is at most n 2 dimensional this result supplements those for first and second order sdes maximal dimensionality can be used to carry out lie group classifications lie point group classification of the third order sdes is provided