new bounds for the first inequality of ostrowski gruss type and applications abstract some new bounds for the first inequality of ostrowski gruss type are derived these new bounds can be much better than some recently obtained bounds applications in numerical integration are also given

error bounds in approximating the riemann stieltjes integral of c n 1 class integrands and nonsmooth integrators in the present paper we investigate the problem of approximating the riemann stieltjes integral a b f du in the case when the integrand f is n 1 time differentiable n 0 and the derivative f n 1 is continuous on a b while the integrator u is riemann integrable on a b a priory error bounds for different classes of functions are provided

fractional equivalent lagrangian densities for a fractional higher order equation in this communication we show that the equivalent lagrangian densities elds of a fractional higher order nonlinear schrodinger equation with stable soliton like solutions can be related in a hitherto unknown way this new relationship is described in terms of a new fractional operator that includes both left and right sided fractional derivatives using this operator it is possible to generate new elds that contain different fractional parts in addition to the already known elds which only differ by a sum of first order partial derivatives of two arbitrary functions

three point rules in numerical integration identities and inequalities are obtained involving evaluations at an interior and at the end points it is shown how previous work and rules in numerical integration are recaptured as particular instances of the current development explicit a priori bounds are provided allowing the determination of the partition required for achieving a prescribed error tolerance in the main ostrowski gruss type inequalities are used to obtain bounds on the rules in terms of a variety of norms

large deviations and nontrivial exponents in coarsening systems we investigate the statistics of the mean magnetization of its large deviations and persistent large deviations in simple coarsening systems in particular we consider more specifically the case of the diffusion equation of the ising chain at zero temperature and of the two dimensional voter model for the diffusion equation at large times the mean magnetization has a limit law which is studied analytically using the independent interval approximation the probability of persistent large deviations defined as the probability that the mean magnetization was for all previous times greater than some level x decays algebraically at large times with an exponent continuously varying with x when x 1 is the usual persistence exponent similar behaviour is found for the glauber ising chain at zero temperature for the two dimensional voter model large deviations of the mean magnetization are algebraic while the probability of persistent large deviations seem to behave as the usual persistence probability

on sharp inequalities of simpson type and ostrowski type in two independent variables in this paper two sharp inequalities are derived the first is a sharp simpson inequality and the second is a sharp inequality of ostrowski type in two independent variables

the inverse of a singular linear transformation and some applications in constrained mechanics we extend the notion of the moore penrose inverse of a matrix to the case of a morphism between vector bundles and a more general concept is used to develop the geometric theory of udwadia and kalaba s approach to constrained lagrangian mechanics

approximating the finite hilbert transform via a companion of ostrowski s inequality for function of bounded variation and applications the finite hilbert transform plays an important role in scientific and engineering computing by using a companion of ostrowski s inequality for function of bounded variation we give some new approximations of the finite hilbert transform which may have the better error bounds than the known results obtained via ostrowski type inequality some numerical experiments are also presented

dynamical critical behaviours of the ising spin chain swendsen wang and wolff algorithms we study the zero temperature ising chain evolving according to the swendsen wang dynamics we determine analytically the domain length distribution and various historical characteristics e g the density of unreacted domains is shown to scale with the average domain length as l with 3 2 for the q state potts model 1 q 1 we also compute the domain length distribution for the ising chain endowed with the zero temperature wolff dynamics

new error bounds for the simpson s quadrature rule and applications new error bounds for the well known simpson s quadrature rule are derived if we use these bounds then we can apply the simpson s rule to functions whose first second or third derivatives are unbounded below or above furthermore these error bounds can be much better than some recently obtained bounds applications in numerical integration are also given

on the optimal constants of ostrowski like inequalities involving n knots we compute the optimal constants of ostrowski like inequalities involving n knots given by huy and ngo

generalized canonical transformations for time dependent systems we introduce the concept of generalized canonical transformations as symplectomorphisms of the extended phase space we prove that any such transformation factorizes in a standard canonical transformation times another one that changes only the time variable the theory of generating functions as well as that of hamilton jacobi is developed some further applications are developed

lax formalism for a family of integrable toda related n particle systems this article can be divided in two parts first a lax representation is obtained for a family of integrable three particle toda related systems the second part contains the generalization to the case of n particles

non noether constants of motion mathematical tools of modern differential geometry are used to derive in an intrinsic formulation more general results about non noether constants of motion a relation between two different ways of obtaining such constants is found by making use of leverrier s method of determining the characteristics polynomial of a matrix in terms of the traces of its increasing powers

equivalent lagrangians multidimensional case we generalize a theorem known for one dimensional nonsingular equivalent lagrangians l and to the multidimensional case in particular we prove that the matrix which relates the left hand sides of the euler lagrange equations obtained from l and is such that the trace of all its integer powers are constants of the motion we construct several multidimensional examples in which the elements of are functions of position velocity and time and prove that in some cases equivalence prevails even if det 0

invariance of second order ordinary differential equations under two dimensional affine subalgebras of ermakov pinney lie algebra abstract using the only admissible rank two realisations of the lie algebra of the affine group in one dimension in terms of the lie algebra of lie symmetries of the ermakov pinney ep equation some classes of second order nonlinear ordinary differential equations solvable by reduction method are constructed one class includes the standard ep equation as a special case a new ep equation with a perturbed potential but admitting the same solution formula as ep itself arises the solution of the dissipative ep equation is also discussed

alternative lagrangians for spherically symmetric potentials a new geometrical account of the existence of alternative s equivalent lagrangians is given for a particle moving in three dimensional euclidean space under the influence of a central force the fact that the lagrangian for this familiar problem is not unique was pointed out by henneaux and shepley j math phys 23 2101 1982 the present analysis makes the reasons for the phenomenon more transparent than theirs

a note on some ostrowski like type inequalities abstract error estimate plays an important role for numerical integration some ostrowski like type inequalities concerning a new type of quadrature formula are established recently by huy and ngo 2009 2010 6 7 in this note improvement and extension to these inequalities are given

the action principle for a system of differential equations we consider the problem of constructing an action functional for physical systems whose classical equations of motion cannot be directly identified with euler lagrange equations for an action principle two ways of constructing the action principle are presented from simple consideration we derive the necessary and sufficient conditions for the existence of a multiplier matrix which can endow a prescribed set of second order differential equations with the structure of the euler lagrange equations an explicit form of the action is constructed if such a multiplier exists if a given set of differential equations cannot be derived from an action principle one can reformulate such a set in an equivalent first order form which can always be treated as the euler lagrange equations of a certain action we construct such an action explicitly there exists an ambiguity not reduced to a total time derivative in associating a lagrange function with a given set of equations we present a complete description of this ambiguity the general procedure is illustrated by several examples

coarsening in the 1d ising model evolving with swendsen wang dynamics an unusual scaling we consider a simple model of domain growth the zero temperature 1d ising model evolving according to the swendsen wang dynamics we find that in the long time limit the pair correlation function scales with a characteristic length increasing as the square of the average domain size in that limit a few large domains occupy almost all the space with many small domains between them in contrast to the usual picture of coarsening the average domain size here is not a characteristic length of the growth problem instead one finds a power law distribution for the sizes of large domains with a cut off at a length which grows as the square of the average size of the domains

some recent results on symmetries of lagrangian systems re examined hojman s results 1984 on alternative lagrangians and first integrals related to symmetries of lagrangian systems are shown to be covered by previous treatments in a more geometrical setting it is argued that the use of lagrangians linear in the accelerations for second order systems does not widen the spectrum of results

improvement of some inequalities of euler gruss type abstract we prove an inequality of gruss type and use it to improve strictly some general euler gruss type inequalities all improved inequalities are sharp

fluctuations in coagulating systems ii in this paper we consider coagulation processes in large but finite systems and study the time dependent behavior of the nonequilibrium fluctuations in the cluster size distribution for this purpose we apply van kampen s expansion to a master equation describing coagulation processes and derive an approximate fokker planck equation for the probability distribution of the fluctuations first we consider two exactly soluble models corresponding to the choicesk i j i jandk i j 1 for the rate constants in the fokker planck equation for these models and monodisperse initial conditions we calculate the probability distribution of the fluctuations and the equal time and two time correlation functions for general initial conditions we study the behavior of the fluctuations at large cluster sizes and in the scaling limit next we consider in general homogeneous rate constants with the propertyk i j a k ai aj for alla 0 and we give asymptotic expressions for the equal time correlation functions at large cluster sizes and in the scaling limit in the scaling limit we find that the fluctuations show relatively simple scaling behavior for all homogeneous rate constantsk i j

sl 3 r as the group of symmetry transformations for all one dimensional linear systems the converse problem of similarity analysis is solved in general for the finite symmetry transformations of any inhomogeneous ordinary linear differential equation of the second order x f2 t x f1 t x f0 t the eight parameter realizations of the symmetry group are obtained in the form f 1p2 f where f stands for transformations of t x that depend exclusively on the fundamental solutions of the equation and where p2 is an arbitrary projective transformation in the plane thus it is shown that the full point symmetry group corresponds to sl 3 r indeed without recourse to the lie algebra also a technique is obtained for calculating the finite point symmetry realization of sl 3 r for any given one dimensional linear system some miscellaneous examples are given

a separability theorem for dynamical systems admitting alternative lagrangian descriptions by generalising earlier results the authors prove that whenever a lagrangian dynamical system can be associated with a 1 1 type tensor field which is left invariant by the dynamics satisfies the nijenhuis condition and is compatible with the tangent bundle structure the system necessarily decomposes into a collection of lower dimensional mutually non interacting lagrangian subsystems

tangent bundle geometry lagrangian dynamics various aspects of the differential geometry of the tangent bundle of a differentiable manifold are examined and the results applied to time independent lagrangian dynamics it is shown that a certain type 1 1 tensor field which is part of the intrinsic geometry of a tangent bundle being a tensorial equivalent of the projection map of tangent vectors plays a role in lagrangian theory scarcely less important than that of the canonical one form on a cotangent bundle in hamiltonian theory recent results in lagrangian theory are interpreted from this new viewpoint

remarks on ostrowski like inequalities abstract we show the error inequalities on quadrature formulas obtained by huy and ngo can be improved if m is even

geometric theory of the equivalence of lagrangians for constrained systems the lagrangian description of a system is analysed from a geometric viewpoint in order to find a concept for equivalence of singular lagrangians generalising that of the regular case geometric and gauge equivalence of singular lagrangians are studied and the authors also give some conditions in which second order differential equations exist satisfying the dynamical equation on the final constraint submanifold

new classes of conversed quantities associated with non noether symmetries a result of hojman and harleston 1981 has been used to extend the known relationship between conserved quantities and non noether symmetries it is shown that n constants of the motion may be derived from each non noether symmetry of an n dimensional lagrangian system this applies whether the symmetry is continuous or discrete in addition the properties of the cartan form are utilised to to give a new proof of the hojman harleston theorem

several error inequalities for a quadrature formula with a parameter and applications in this paper we will derive several error inequalities for a quadrature formula with a parameter which will not only provide some generalizations of the known results but also give some other interesting quadrature formulae as special cases furthermore sharp upper and lower error bounds for the double error inequalities are obtained applications in numerical integration are also given

a generalization of two sharp inequalities in two independent variables a generalization of two sharp inequalities of simpson type and ostrowski type in two independent variables is established

improvement of some ostrowski gruss type inequalities abstract in this paper we improve and further generalize some ostrowski gruss type inequalities involving bounded once and twice differentiable mappings

blow up regularization of singular lagrangians we propose a method for regularizing singular lagrangians by adding new degrees of freedom we illustrate this regularization method with some particular examples this procedure is shown to be very useful when the lagrangian is homogeneous of degree one in the velocities giving rise to an identically vanishing hamiltonian

equivalent lagrangians in field theory a theorem by hojman and harleston 1981 for multidimensional equivalent lagrangians l and l in the realm of newtonian mechanics is generalised to field theory equivalent lagrangians for some set of field equations are found

a representation of the peano kernel for some quadrature rules and applications a general interpolating formula is established from this formula all newton cotes quadrature rules of the closed type can be derived some corrected interpolating polynomials are also derived and used for obtaining corresponding quadrature rules a new effective representation of the peano kernel is derived estimation of errors for these quadrature rules is established

a note to inequalities of euler gruss type following the main ideas of wang 1 we generalize matie s results and establish our inequalities for functions with n t h derivatives of bounded p variation all of our error bounds are sharp in the sense that they cannot be replaced by smaller ones

new inequalities of ostrowski type for mappings whose derivatives are s convex in the second sense via fractional integrals a new identity similar to an identity proved in alomari et al 2010 15 for fractional integrals is established then by making use of the established identity some new ostrowski type inequalities for riemann liouville fractional integral are established our results have some relationships with the results of alomari et al 2010 proved in 15 and the analysis used in the proofs is simple

a new ostrowski gruss inequality involving 3n knots abstract this is the fifth and last in our series of notes concerning some classical inequalities such as the ostrowski simpson iyengar and ostrowski gruss inequalities in r in the last note we propose an improvement of the ostrowski gruss inequality which involves 3 n knots where n 1 is an arbitrary numbers more precisely suppose that x k k 1 n 0 1 y k k 1 n 0 1 and k k 1 n 0 n are arbitrary sequences with k 1 n k n and k 1 n k x k n 2 the main result of the present paper is to estimate 1 n k 1 n k f a b a y k 1 b a a b f t d t f b f a n k 1 n k y k x k in terms of either f or f unlike the standard ostrowski gruss inequality and its known variants which basically estimate f x a b f t d t b a in terms of a correction term as a linear polynomial of x and some derivatives of f our estimate allows us to freely replace f x and the correction term by using 3 n knots x k k 1 n y k k 1 n and k k 1 n as far as we know this is the first result involving the ostrowski gruss inequality with three sequences of parameters

sharp inequalities of simpson type and ostrowski type two sharp inequalities are derived the first is a sharp simpson s inequality and the second is a sharp inequality of ostrowski type the mentioned inequalities give error bounds for some known quadrature rules these results enlarge applicability email protected the corresponding quadrature rules with respect to the obtained error bounds applications in numerical integration are also given

note on equivalent lagrangians and symmetries shows that every ordered pair of equivalent lagrangians determines an equivalence class of dynamical symmetries of non noether type its explicit construction merely requires a particular solution of a single partial differential equations various related aspects are discussed

on some generalizations of an ostrowski gruss type integral inequality in this paper we improve and extend a new ostrowski gruss type integral inequality obtained recently by feng and meng 2012 26 to be precise we show that a condition imposed on the inequality can be removed furthermore we provide a two dimensional generalization of this ostrowski gruss type inequality which is sharp

bounds for the chebyshev functional and applications to the weighted integral formulae the aim of this paper is to provide some error estimates for the general weighted n point quadrature formulae by using some inequalities for the chebyshev functional the above results are applied to obtain some new bounds for the gauss chebyshev formulae of the first and the second kind

another demonstration of the theorem by hojman and harleston another demonstration of a theorem on the calculus of variations derived recently by hojman and harleston 1981 using helmholtz conditions is presented

quantization of non standard hamiltonian systems the quantization of classical theories that admit more than one hamiltonian description is considered this is done from a geometrical viewpoint both at the quantization level geometric quantization and at the level of the dynamics of the quantum theory a spin system is taken as an example in which all the steps can be completed it is shown that the geometry of the quantum theory imposes restrictions on the physically allowed non standard quantum theories

on certain canonoid transformations and invariants for the parametric oscillator in classical mechanics a transformation in phase space is said to be canonoid if it maps only some hamiltonian systems into hamiltonian systems once canonoid transformations are considered these systems can be classically described by means of lagrangians or hamiltonians other than the conventional ones in this context a basic role is played by the dynamical invariants generated through the poisson brackets of the new independent variables in phase space here we obtain the explicit form of special canonoid transformations of the polynomial type for systems which can be classically described by an equation of the parametric oscillator type and discuss some algebraic properties shown by the associated dynamical invariants

sharp inequalities of ostrowski type for convex functions defined on linear spaces and application an ostrowski type inequality for convex functions defined on linear spaces is generalised some inequalities which improve the hermite hadamard type inequality for convex functions defined on linear spaces are derived using the obtained result the results in normed linear spaces are used to obtain some inequalities which are related to the given norm and associated semi inner products and to prove the sharpness of the constants in those inequalities

an inequality of ostrowski gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules abstract in this paper we derive a new inequality of ostrowski gruss type and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules

some new error inequalities for a generalized quadrature rule of open type some new error inequalities for a generalized quadrature rule of open type are established especially two sharp inequalities are derived when n is an odd and an even integer respectively

equivalence and s equivalence of vector tensor lagrangians it will be proven that if a gauge invariant lagrangian density having the local form l l gij ai ai j is such that its euler lagrange equations ei l 0 have the same set of solutions as ei l0 0 where l0 g1 2fijfij then l and cl0 are equivalent for same constant c i e ei l ei cl0 from a previous result it follows that l cl0 d eg1 2 where d is a divergence and e is a constant

lagrangian formalism for nonlinear second order riccati systems one dimensional integrability and two dimensional superintegrability the existence of a lagrangian description for the second order riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized riccati equation the lagrangians are non natural and the forces are not derivable from a potential the constant value e of a preserved energy function can be used as an appropriate parameter for characterizing the behavior of the solutions of these two systems in the second part the existence of two dimensional versions endowed with superintegrability is proved the explicit expressions of the additional integrals are obtained in both cases finally it is proved that the orbits of the second system that represents a nonlinear oscillator can be considered as nonlinear lissajous figures

the helmholtz conditions in terms of constants of motion in classical mechanics the helmholtz conditions are the necessary and sufficient conditions for a set of second order differential equations to be equivalent to a variational principle in this work an alternative approach to the inverse problem in classical mechanics is described it is proven that the helmholtz conditions can be transformed into a set of conditions for a nonsingular antisymmetric matrix whose entries are constants of motion of the problem in question

on the inverse problem of the calculus of variations in field theory the inverse problem of the calculus of variations is investigated in the case of field theory uniqueness of the action principle is demonstrated for the vector laplace equation in a non decomposable riemannian space as well as for the harmonic map equation

error inequalities for a quadrature formula and applications an optimal two point quadrature formula of open type is derived it is shown that the optimal quadrature formula has a better error bound than the well known two point gaus quadrature formula various error inequalities for this formula are established applications in numerical integration are given

improvement and further generalization of inequalities of ostrowski gruss type abstract we improve some inequalities of ostrowski gruss type and further generalize them we apply the obtained results to the estimation of error bounds for some numerical quadrature rules also some bounds for the differences of some special means are discussed

a unified approach to some inequalities of ostrowski gruss type based on the euler maclaurin formula in the spirit of 1 we provide a unified approach to some inequalities of ostrowski gruss type which include some existing results as special cases some illustrative examples are also included

a new way to think about ostrowski like type inequalities in this present paper by considering some known inequalities of ostrowski like type we propose a new way to treat a class of ostrowski like type inequalities involving n points and m th derivative to be precise the following inequality email protected a bf x email protected i 1nf a x i b a 2m 54 b a m 1 m 1 s s holds where email protected sup a x bf m x email protected inf a x bf m x and for suitable x 1 x 2 x n it is worth noticing that n m are arbitrary numbers this means that the estimate in is more accurate when m is large enough our approach is also elementary

construction of alternative hamiltonian structures for field equations we use symmetry vectors of nonlinear field equations to build alternative hamiltonian structures we construct such structures even for equations which are usually believed to be non hamiltonian such as heat burger and potential burger equations we improve on a previous version of the approach using recursion operators to increase the rank of the poisson bracket matrices cole hopf and miura type transformations allow the mapping of these structures from one equation to another

on the generalization of ostrowski and gruss type discrete inequalities abstract the main purpose of this paper is to establish a generalization of discrete inequalities of the ostrowski and gruss type involving two functions the analysis used in the proofs is fairly elementary

a unified generalization of some quadrature rules and error bounds by introducing a parameter we give a unified generalization of some quadrature rules which not only unify the recent results about error bounds for generalized mid point trapezoid and simpson s rules but also give some new error bounds for other quadrature rules as special cases especially two sharp error inequalities are derived when n is an odd and an even integer respectively

non symplectic symmetries and bi hamiltonian structures of the rational harmonic oscillator the existence of bi hamiltonian structures for the rational harmonic oscillator non central harmonic oscillator with rational ratio of frequencies is analysed by making use of the geometric theory of symmetries we prove that these additional structures are a consequence of the existence of dynamical symmetries of non symplectic non canonical type the associated recursion operators are also obtained

gruss and ostrowski type inequalities abstract in this paper we use a method originated in s s dragomir some gruss type inequalities in inner product spaces j inequal pure appl math 4 2 2003 article 42 to establish some gruss and ostrowski type inequalities

sl 3 r as the group of symmetry transformations for all one dimensional linear systems iii equivalent lagrangian formalisms the sl 3 r theory of projective transformations of the plane is applied to the lagrangians of all one dimensional newtonian linear systems noether and non noether equivalent lagrangians as well as the associated noether and non noether constants of motion are thus obtained in a completely general and systematic way complete unification is achieved by this group theoretic approach to lagrangians of one dimensional linear systems

canonoid transformations from a geometric perspective the concept of canonoid transformation for a locally hamiltonian vector field is introduced and its relation with the existence of non noether constants of the motion is shown from a geometrical viewpoint the equations determining generating functions for such canonoid transformations are obtained and applications to some particular problems given

a sharp estimate for the peano error representation we provide a sharp estimate of the peano error representation formula for linear functionals as applications we obtain sharp estimates for the remainder term in general quadrature formulae and expand some ostrowski like type inequalities to linear functionals the new approach extends and unifies many earlier results on the subject dragomir and wang 1997 cheng 2001 matic 2003 vong 2011 gonska et al 2012