iterated collocation methods for volterra integral equations with delay arguments in this paper we give a complete analysis of the global convergence and local superconvergence properties of piecewise polynomial collocation for volterra integral equations with constant delay this analysis includes continuous collocation based volterra runge kutta methods as well as iterated collocation methods and their discretizations

schwinger terms from geometric quantization of field theories geometric quantization is applied to infinite countable dimensional linear kahler manifolds to obtain a closed expression for the anomalous commutator of arbitrary polynomial observables examples for the physical relevance of the result are given including the polarization dependence of schwinger terms in bilinear constraint algebras the central terms of virasoro and kac moody algebras and the determination of the critical dimension of the bosonic string

two dimensional tensor function representation for all kinds of material symmetry all kinds of physically possible material symmetry in two dimensional space were investigated in a recent work of q s zheng and j p boehler in this paper we establish the complete and irreducible representations with respect to every kind of material symmetry for scalar vector and second order tensor valued functions in two dimensional space of any finite number of vectors and second order tensors these representations allow general invariant forms of physical and constitutive laws of anisotropic materials to be developed in plane problems

fluid films with curvature elasticity the phenomenology of surfactant fluid film microstructures interspersed in bulk fluids poses significant challenges to continuum theory by using simple models of elastic surfaces chemical physicists have been partially successful in describing the qualitative features of

on anisotropic scalar functions of a single symmetric tensor irreducible functional bases for anisotropic scalar functions of a single symmetric secord order tensor under all 32 crystal classes are presented for the first time for most cases the presented results are more compact and simpler than the well known results for integrity bases

the brs method and geometric quantization some examples we recall the method of quantization of constraints as outlined by kostant and sternberg we discuss various examples to test compatibility between geometric quantization and this procedure in almost all cases reduction and quantization commute

stability analysis of product t methods for abel integral equations of the second kind stability analysis of product methods for abel integral equations of the second kind based on the test equation y t 1 lambda int limits 0 1 frac y s t s alpha ds t geqq 0 0 0 and we investigate whether this property is inherited by numerical approximations toy

existence theorems for an integral equation of the chandrasekhar h equation with perturbation abstract we prove existence of positive solutions in thaces c 0 1 and c c 0 1 of an integral equation of the chandrasekhar h equation with perturbation

variable transformations in the numerical solution of second kind volterra integral equations with continuous and weakly singular kernels extensions to fredholm integral equations abstract a number of techniques that use variable transformations in numerical integration have been developed recently cf sidi numerical integration iv h brass g hammerlin eds birkhauser basel 1993 pp 359 373 laurie j comput appl math 66 1996 337 344 the use of these transformations resulted in increasing the order of convergence of the trapezoidal and the midpoint quadrature rule in this paper the application of variable transformation techniques of sidi and laurie type to the numerical solution of second kind volterra integral equations with continuous and weakly singular kernels is considered since the transformations are such that the end points of integration need not be used as mesh points the methods introduced can be used for vie with both continuous and weakly singular kernel in a uniform way the methods have also the advantages of simplicity of application and of achieving high order of convergence the application of the idea to fredholm integral equations with continuous and weakly singular equations is also considered numerical results are included and they verify the expected increased order of convergence they were obtained by using the trapezoidal formula for the evaluation of the transformed integrals

mathematical programming methods in the numerical solution of volterra integral and integro differential equations with weakly singular kernel abstract nonlinear volterra integral and integro differential equations with weakly singular kernel are considered and solved numerically using nonlinear mathematical programming methods based on minimax approximations in both cases polynomial and multiquadric approximation are used

product integration for volterra integral equations of the second kind with weakly singular kernels we introduce a new numerical approach for solving volterra integral equations of the second kind when the kernel contains a mild singularity we give a convergence result we also present numerical examples which show the performance and efficiency of our method

collocation and continuous implicit runge kutta methods for a class of delay volterra integral equations abstract in this paper we present an analysis of the global convergence properties of certain piecewise polynomial collocation methods for a class of volterra integral equations with constant delay this analysis also encompasses continuous implicit m stage volterra runge kutta methods based on collocation techniques

a survey of recent advances in the numerical treatment of volterra integral and integro differential equations abstract the present survey paper samples recent advances in the numerical analysis of volterra integral equations of the first and second kind and of integro differential equations including equations with weakly singular kernels except for some important earlier references the discussion focuses on the development which has taken place during the last dozen years a fairly extensive bibliography selected to be representative rather than comprehensive complements the paper

generalized bergman kernels and geometric quantization in geometric quantization it is well known that if f is an observable and f a polarization on a symplectic manifold m then the condition xf leaves f invariant where xf denotes the hamiltonian vector field associated to f is sufficient to guarantee that one does not have to compute the bks kernel explicitly in order to know the corresponding quantum operator it is shown in this paper that this condition on f can be weakened to xf leaves f f invariant and the corresponding quantum operator is then given implicitly by formula 4 8 in particular when f is a positive kahler polarization all observables can be quantized directly and moreover an explicit formula for the corresponding quantum operator is derived theorem 5 8 applying this to the phase space r2n one obtains a quantization prescription which ressembles the normal ordering of operators in quantum field theory when we translate this prescription to the usual position representation of quantum mechanics the result i

numerical solution of non linear volterra integral equations this paper deals with non linear volterra integral equations of the type y x f x 0x h t x y t y x dt convergence criteria are given in the same sense of the maximum and ca norms for the numerical solution of this type of volterra integral equation several numerical methods are compared

quantization scheme based on the extension of phase space a new quantization scheme is proposed the similarity of geometric and covariant quantization of a certain class of constrained dynamical systems is shown a method to calculate anomalies is developed

numerical solutions of volterra integral equations with a solution dependent delay on demontre l existence et l unicite des solutions pour l equation ainsi qu une limitation a priori de la solution on definit une solution numerique et on demontre que la solution numerique converge vers la solution de l equation integrale

brst cohomology in classical mechanics the classical non quantum cohomology of the becchi rouet stora tyutin brst symmetry in phase space is defined and worked out no group action for the gauge transformations is assumed the results cover therefore the general case of an open algebra and are valid off shell each cohomology class contains all brst invariant functions with fixed ghost number an integer which differ from each other by a brst variation if the ghost number is negative there is only the trivial class whose elements are equivalent to zero if the ghost number is positive or zero there is a bijective correspondence between the brst classes and those of the exterior derivative along the gauge orbits these gauge orbits lie in the phase space surface on which the gauge generators are constrained to vanish the brst invariant functions of ghost numberp are then related to closedp forms along the orbits the addition of a brst variation corresponds to the addition of an exact form some comments about the quantum case are included the physical meaning of the classes with ghost number greater than zero is not discussed

yang mills and dirac fields in a bag constraints and reduction the structure of the constraint set in the yang mills dirac theory in a contractible bounded domain is analysed under the bag boundary conditions the gauge symmetry group is identified and it is proved that its action on the phase space is proper and admits slices the reduced phase space is shown to be the union of symplectic manifolds each of which corresponds to a definite mode of symmetry breaking

on anisotropic invariants of n symmetric second order tensors crystal classes and quasi crystal classes as subgroups of the cylindrical group dh this paper is concerned with anisotropic invariants of n symmetric second order tensors relative to crystal classes and quasi crystal classes as subgroups of the cylindrical group d h simple irreducible functional bases for the latter are derived in unified forms by means of a simple procedure based upon recent development in isotropic extension of anisotropic functions as a particular case a new simple derivation is available for the corresponding results on anisotropic invariants of a single symmetric second order tensor presented in a paper by xiao

quantization towards a comparison between methods in this paper it is shown that the procedure of geometric quantiztion applied to kahler manifolds gives the following result the hilbert space h consists roughly speaking of holomorphic functions on the phase space m and to each classical observable f i e a real function on m is associated an operator f on h as follows first multiply by f 1 4 drf dr being the laplace de rham operator on the kahler manifold m and then take the holomorphic part see g m tuynman j math phys 27 573 1987 this result is correct on compact kahler manifolds and correct modulo a boundary term md on noncompact kahler manifolds in this way these results can be compared with the quantization procedure of berezin math ussr izv 8 1109 1974 9 341 1975 commun math phys 40 153 1975 which is strongly related to quantization by products e g see c moreno and p ortega navarro amn inst h poincare sec a 38 215 1983 lett math phys 7 181 1983 c moreno lett math phys 11 3

elastic surface substrate interactions a theory for three dimensional finite deformations of elastic solids with conforming elastic films attached to their bounding surfaces is described the gurtin murdoch theory incorporating elastic resistance of the film to strain is generalized to account for the effects of intrinsic flexural resistance this modification yields a model that can be used to describe equilibrium deformations in the presence of compressive surface stress fields an associated variational theory is given and material symmetry considerations are discussed the theory is illustrated by examples

on anisotropic invariants of a symmetric tensor crystal classes quasi crystal classes and others this paper is concerned with invariants of a symmetric second order tensor relative to crystal classes and quasicrystal classes and some non continuous infinite orthogonal subgroups simple irreducible functional bases in unified forms each of which consists of eight polynomial invariants only are presented for all kinds of finite subgroups of the maximal transverse isotropy group d h except the subgroups of the orthotropy group d 2 h results are also provided for other kinds of orthogonal subgroups including icosahedral quasicrystal classes etc for the trigonal tetragonal and hexagonal crystal classes without two fold axis the results given here are even more compact than the corresponding results recently derived by this author xiao 1996 a for all non crystal classes except the transverse isotropy groups the presented results are the first ones

haar wavelet method for some nonlinear volterra integral equations of the first kind we present here a simple efficient haar wavelet method for numerical solution of a class of nonlinear volterra integral equations of the first kind the present method is based on converting nonlinear volterra integral equations of the first kind into linear volterra integral equations of the second kind numerical examples are given to illustrate efficiency and accuracy of the present method comparison with numerical methods in the past has also been done solving some nonlinear first kind volterra integral equations using haar wavelet haar wavelet method is simple and fast solved examples demonstrate the accuracy and efficiency of the present method present method gives better results than the numerical methods described in past necessary accuracy may be obtained by increasing the number of calculation points

resolvents for weakly singular kernels and fractional differential equations the solution r t s of the resolvent equation 1 r t s b t s stb t u r u s du where b t s denotes a given weakly singular matrix is obtained by means of fixed point mappings the result is a series that begins with some singular terms after which the remainder of the terms defines a continuous function in particular the resolvent is calculated for the kernel b t s t s q 1 of the scalar abel integral equation of the second kind 2 x t a t 0t1 t s 1 qx s ds where 0 q 1 it is then used to derive closed form formulas for the resolvents corresponding to q 1 2 and 1 3 furthermore a closed form formula for the resolvent for b t s s t2 s2 q 1 is derived thereby demonstrating that the results of this paper apply not only to kernels of convolution type but also to those of non convolution type as well finally the resolvent for the kernel of 2 is used to find a general solution of a linear fractional differential equation of caputo type

numerical solutions of a perturbed chandrasekhar h equation abstract numerical solutions of perturbed chandrasekhar h type integral equations are analysed convergence criteria in the sense of the maximum norm and the c norm are studied several numerical methods are compared

solutions to eshelby s problems of non elliptical thermal inclusions and cylindrical elastic inclusions of non elliptical cross section eshelby s inclusion problem is solved for non elliptical inclusions in the context of twodimensional thermal conduction and for cylindrical inclusions of non elliptical cross section within the framework of generalized plane elasticity first we consider a twodimensional infinite isotropic or anisotropic homogeneous medium with a non elliptical inclusion subjected to a prescribed uniform heat flux free temperature gradient eshelby s conduction tensor field and its area average are first expressed compactly in terms of two boundary integrals avoiding the usual singularity and then specified analytically for arbitrary polygonal inclusions and for inclusions characterized by the finite laurent series next we are interested in a three dimensional infinite isotropic or transversely isotropic homogeneous medium with a cylindrical inclusion of a non elliptical cross section that undergoes uniform generalized plane eigenstrains the solution to this problem is obtained by decomposing a generalized plane eigenstrain tensor into a plane strain part and an anti plane strain part exploiting the mathematical similarity between two dimensional thermal conduction and anti plane elasticity and combining the relevant results of zou et al zou et al 2010 j mech phys solids 58 346 372 doi 10 1016 j jmps 2009 11 008 with those derived in the present work for eshelby s conduction tensor field and its area average

product integration methods for second kind abel integral equations the construction and convergence of high order product integration methods for the second kind abel equation are discussed and the results of de hoog and weiss are generalised backward difference methods are introduced and numerical results are presented which verify the theoretical rates of convergence