large order perturbation expansions for the charged harmonic oscillator the charged oscillator defined by the hamiltonian h d2 dr2 r2 lambda r in the domain 0 infinity is a particular case of the family of spike oscillators which does not behave as a supersingular hamiltonian this problem is analysed around the three regions lambda to infinity lambda to 0 and lambda to infinity by using rayleigh ritz large order perturbative expansions a path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda finally the riccati pade method is used to construct an implicit expansion around lambda to 0 which extends to very large values of mod lambda mod

precise determination of the energy levels of the anharmonic oscillator from the quantization of the angle variable using an ansatz motivated by the classical form of el phi where phi is the angle variable we construct operators which satisfy the commutation relations of the creation annihilation operators for the anharmonic oscillator the matrix elements of these operators can be expressed in terms of entire functions in the position complex plane these functions provide solutions of the ricatti equation associated with the time independent schrodinger equation we relate the normalizability of the eigenstates to the global properties of the flows of this equation these exact results yield approximations which complement the wkb approximation and allow an arbitrarily precise determination of the energy levels we give numerical results for the first 10 levels with 30 digits we address the question of the quantum integrability of the system

complete global stability for an sirs epidemic model with generalized non linear incidence and vaccination abstract this paper deals with global dynamics of an sirs epidemic model for infections with non permanent acquired immunity the sirs model studied here incorporates a preventive vaccination and generalized non linear incidence rate as well as the disease related death lyapunov functions are used to show that the disease free equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one and that there is an endemic equilibrium state which is globally asymptotically stable when it is greater than one

ergodicity of the stochastic fractional reaction diffusion equation abstract a stochastic reaction diffusion equation with fractional dissipation is considered the smaller the exponent of the equation is the weaker the dissipation of the equation is the equation is discussed in detail when the exponent changes the aim is to prove the well posedness existence and uniqueness of an invariant measure as well as strong law of large numbers and convergence to equilibrium without the analytic property of the semigroup some methods are used to overcome the difficulties to get the energy estimates the results in this paper can be applied to the classic reaction diffusion equation with wiener noise

polynomial solutions for a class of second order linear differential equations we analyze the polynomial solutions of the linear differential equation p 2 x y p 1 x y p 0 x y 0 where p j x is a jth degree polynomial we discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials p j x special cases are related to known differential equations of mathematical physics classes of new soluble problems are exhibited general results are obtained for weight functions and orthogonality relations

spin and pseudospin symmetry along with orbital dependency of the dirac hulthen problem abstract the role of the hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the dirac equation with attractive scalar s r and repulsive vector v r potentials the spin and pseudospin symmetry along with orbital dependency pseudospin orbit and spin orbit dependent couplings of the dirac equation are included to the solution by introducing the hulthen square approximation this effective approach is based on forming the spin and pseudo centrifugal kinetic energy term from the square of the hulthen potential the analytical solutions of the dirac equation for the hulthen potential with the spin orbit and pseudospin orbit dependent couplings are obtained by using the nikiforov uvarov nu method the energy eigenvalue equations and wave functions for various degenerate states are presented for several spin orbital pseudospin orbital and radial quantum numbers under the condition of the spin and pseudospin symmetry

asymptotic iteration method solutions to the relativistic duffin kemmer petiau equation a simple exact analytical solution of the relativistic duffin kemmer petiau equation within the framework of the asymptotic iteration method is presented exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the relativistic harmonic oscillator as well as the coulomb potentials as a nontrivial example the anharmonic oscillator is solved and the energy eigenvalues are obtained within the perturbation theory using the asymptotic iteration method

remarks on the solution of the position dependent mass schrodinger equation an approximate method is proposed to solve the position dependent mass pdm schrodinger equation the procedure suggested here leads to the solution of the pdm schrodinger equation without transforming the potential function to the mass space or vice versa the method based on the asymptotic taylor expansion of the function produces an approximate analytical expression for eigenfunction and numerical results for eigenvalues of the pdm schrodinger equation the results show that the pdm and constant mass schrodinger equations are not isospectral the calculations are carried out with the aid of a computer system of symbolic or numerical calculation by constructing a simple algorithm

matrix elements for a generalized spiked harmonic oscillator closed form expressions for the singular potential integrals m x n are obtained with respect to the gol dman and krivchenkov eigenfunctions for the singular potential bx2 a x2 b 0 a 0 the formulas obtained are generalizations of those found earlier by use of the odd solutions of the schrodinger equation with the harmonic oscillator potential aguilera navarro et al j math phys 31 99 1990

variational analysis for a generalized spiked harmonic oscillator a variational analysis is presented for the generalized spiked harmonic oscillator hamiltonian operator d2 dx 2 bx 2 a x 2 x where is a real positive parameter the formalism makes use of a basis provided by exact solutions of schrodinger s equation for the gol dman and krivchenkov hamiltonian and the corresponding matrix elements that were previously found for all the discrete eigenvalues the method provides bounds which improve as the dimension d of the basis set is increased extension to the n dimensional case in arbitrary angular momentum subspaces is also presented by minimizing over the free parameter a we are able to reduce substantially the number of basis functions needed for a given accuracy

strong solutions of stochastic equations with singular time dependent drift we prove existence and uniqueness of strong solutions to stochastic equations in domains with unit diffusion and singular time dependent drift b up to an explosion time we only assume local l q l p integrability of b in g with d p 2 q 1 we also prove strong feller properties in this case if b is the gradient in x of a nonnegative function blowing up as g x g we prove that the conditions 2d t k 2d t ke 0 2 imply that the explosion time is infinite and the distributions of the solution have sub gaussian tails

orientation of particle attachment and local isotropy in diffusion limited aggregation dla we simulate 50 off lattice diffusion limited aggregation dla clusters of one million particles each the probability distribution of the angle of attachment of arriving particles with respect to the local radial direction is obtained numerically for increasing cluster size n the distribution crosses over extremely accurately to a cosine with an amplitude which decreases towards zero as a power law in n from this specific viewpoint asymptotically large dla clusters are locally isotropic

sir model with general distribution function in the infectious period abstract the susceptible infected removed or sir model as it was formulated by kermack and mckendrick is the key model for epidemic dynamics most applications of such a basic scheme use a constant rate for the removal term however that assumption corresponds to the rather unrealistic exponential distribution of infectious times on the other hand recent approaches like numerical simulations frequently assume a fixed and uniform duration for the infectious state which is unrealistic too the extreme assumptions in those different schemes are a hurdle that can frustrate any intention of drawing comparison between results from them in the present contribution we study the delay equations for the sir model comparing the solutions for many typical cases with the simulation counterpart and with the standard sir model using delay equations where each infected individual is removed at a specific time after being infected the dynamics for the infected and susceptible agree almost exactly with the numerical implementation even in the general case of distributed infective periods the agreement is excellent

gradient estimates and applications for sdes in hilbert space with multiplicative noise and dini continuous drift abstract consider the stochastic evolution equation in a separable hilbert space h with a nice multiplicative noise and a locally dini continuous drift we prove that for any initial data the equation has a unique possibly explosive mild solution under a reasonable condition ensuring the non explosion of the solution the strong feller property of the associated markov semigroup is proved gradient estimates and log harnack inequalities are derived for the associated semigroup under certain global conditions which are new even in finite dimensions

spiked harmonic oscillators a complete variational treatment is provided for a family of spiked harmonic oscillator hamiltonians h d2 dx2 bx2 x b 0 0 for arbitrary 0 a compact topological proof is presented that the set s n of known exact solutions for 2 constitutes an orthonormal basis of the hilbert space l2 0 closed form expressions are derived for the matrix elements of h with respect to s these analytical results and the inclusion of a further free parameter facilitate optimized variational estimation of the eigenvalues of h to high accuracy

well posedness of semilinear stochastic wave equations with holder continuous coefficients abstract we prove that semilinear stochastic abstract wave equations including wave and plate equations are well posed in the strong sense with an holder continuous drift coefficient if 2 3 1 the uniqueness may fail for the corresponding deterministic pde and well posedness is restored by adding an external random forcing of white noise type this shows a kind of regularization by noise for the semilinear wave equation to prove the result we introduce an approach based on backward stochastic differential equations we also establish regularizing properties of the transition semigroup associated to the stochastic wave equation by using control theoretic results

comment on the asymptotic iteration method for polynomial potentials it is shown that polynomial potentials can be treated by a method which cuts out most of the complications of the popular aim approach several examples are given to show how expectation values and resonance energies can be calculated using the simplified approach

closed form sums for some perturbation series involving hypergeometric functions infinite series of the type are investigated closed form sums are obtained for a positive integer 1 2 3 the limiting case of b after y is replaced with x2 b leads to this type of series appears in the first order perturbation correction for the wavefunction of the generalized spiked harmonic oscillator hamiltonian these results have immediate applications to perturbation series for the energy and wavefunction of the spiked harmonic oscillator hamiltonian

criterion for polynomial solutions to a class of linear differential equations of second order we consider the differential equations y 0 x y s0 x y where 0 x s0 x are c functions we prove i if the differential equation has a polynomial solution of degree n 0 then n nsn 1 n 1sn 0 where n n 1 sn 1 0 n 1andsn s n 1 s0 k 1 n 1 2 conversely ii if n n 1 0 and n 0 then the differential equation has a polynomial solution of degree at most n we show that the classical differential equations of laguerre hermite legendre jacobi chebyshev first and second kinds gegenbauer and the hypergeometric type etc obey this criterion further we find the polynomial solutions for the generalized hermite laguerre legendre and chebyshev differential equations

pathwise uniqueness for a class of sde in hilbert spaces and applications abstract an abstract evolution equation in hilbert spaces is considered in the deterministic case it includes several examples of non uniqueness it is proved that pathwise uniqueness is restored by means of a suitably non degenerate additive noise the proof is based on the associated infinite dimensional kolmogorov equation

well posedness of the transport equation by stochastic perturbation we consider the linear transport equation with a globally holder continuous and bounded vector field with an integrability condition on the divergence while uniqueness may fail for the deterministic pde we prove that a multiplicative stochastic perturbation of brownian type is enough to render the equation well posed this seems to be the first explicit example of a pde of fluid dynamics that becomes well posed under the influence of a multiplicative noise the key tool is a differentiable stochastic flow constructed and analyzed by means of a special transformation of the drift of ito tanaka type

on the elementary schrodinger bound states and their multiplets the problem of the existence of elementary bound states is discussed a trivial observation that every elementary wave function i r is an exact bound state for an appropriate potential v r v i r r is shown to lead to a very transparent form of the quasiexact qe solvability condition v i v j for doublets and multiplets of the s in this sense the particular class of elementary ansatze i r r polynomial r2 exp r polynomial r2 also defines the particular class of qe solvable potentials they have an elementary nonpolynomial rational form possibly also with a strongly singular repulsive core at the origin the properties of these forces are discussed in detail

asymptotic behavior and stability of a stochastic model for aids transmission a stochastic model for aids transmission is presented in this paper the existence and uniqueness of its solution is proved and the solution belongs to an interval satisfying the actual condition furthermore the disease equilibrium can be demonstrated to be existent and both its almost surely exponential stability and its pth moment exponential stability can be concluded based on parameter analysis the first quadrant can be integrated into several parts according to the comparison between almost surely exponential stability and pth moment exponential stability and the potential meaning of the stability is further demonstrated finally based on the above theoretical analysis some conditions for aids to decrease and then to die out are obtained by computer simulation

on the eigenvalues of the s state radial equation of a spiked harmonic oscillator eigenvalues of the ground state of the radial schrodinger equation for a spiked harmonic oscillator potential have been evaluated employing two methods numerically via the lanczos grid technique and by means of standard pade approximants constructed from an expansion of large coupling parameter series for the energy numerical results are compared for several values of the parameters characterizing the spiked singular potential

simple bound state energy spectra solutions of dirac equation for hulthen and eckart potentials within the framework of simple similarity transformation method we present simple schrodinger like equation for dirac equation with hulthen and eckart lorentz vectors potentials using the asymptotic iteration method we have managed to obtain the explicit analytical solution of the bound state energy spectra as well as the eigenfunctions for both potentials discussion related to the eigenfunction for both cases is also considered we have shown that the wave function is sensitive for both potentials as well as the parameter

degenerate sdes with singular drift and applications to heisenberg groups abstract by using the ultracontractivity of a reference diffusion semigroup krylov s estimate is established for a class of degenerate sdes with singular drifts which leads to existence and pathwise uniqueness by means of zvonkin s transformation the main result is applied to singular sdes on generalized heisenberg groups

on the solution of a class of the reduced wave equation and the riccati differential equation in this paper we present an iteration technique for a class of differential equation having the form z email protected where l is a function in c we show that we can construct not only the general solution of the reduced wave equation but also the general solution of the riccati differential equation by using this iteration technique if the given function l is satisfies the condition l 2 n email protected 2 n email protected 2 n email protected 2 n email protected email protected then we give a simple application of this technique to inverse conductive scattering problem for an inhomogeneous spherical medium

non relativistic treatment of diatomic molecules interacting with a generalized kratzer potential in hyperspherical coordinates we investigate solutions of a non relativistic wave equation in hyperspherical coordinates for a diatomic molecule system interacting with a generalized kratzer potential rovibrational eigenvalues and corresponding wavefunctions of non relativistic diatomic molecules have been determined within the framework of the asymptotic iteration method certain fundamental conditions for the applications of the asymptotic iteration method such as a suitable asymptotic form for the wave function and the termination condition for the iteration process are discussed n dimensional bound state eigenfunction solutions used in studying the dynamical variables of diatomic molecules are obtained in terms of a confluent hypergeometric function and a generalized laguerre polynomial this systematic approach is tested by calculating the rovibrational energy spectra of hydrogen and sodium chloride molecules

energy spectrum of a generalized scarf potential using the asymptotic iteration method and the tridiagonal representation approach the well known trigonometric scarf potential is generalized by adding a sinusoidal term and then treated using the asymptotic iteration method aim and the tridiagonal representation approach tra the energy spectrum of the associated bound states is computed for the aim we have improved convergence of the quantization condition that terminates the iterations asymptotically this is accomplished by looking for the range of initial values of the space variable in the terminating condition that produces stable results plateau of convergence we have shown that with increasing iteration this plateau of convergence grows up rapidly to an optimal iteration number and then shrinks slowly to a point the value of this point or points may depend on the physical parameters the numerical results have been compared favorably with those resulting from the tra the well known trigonometric scarf potential is generalized by adding a sinusoidal term and then treated using the asymptotic iteration method aim and the tridiagonal representation approach tra the energy spectrum of the associated bound states is computed for the aim we have improved convergence of the quantization condition that terminates the iterations asymptotically this is accomplished by looking for the range of initial values of the space variable in the terminating condition that produces stable results plateau of convergence we have shown that with increasing iteration this plateau of convergence grows up rapidly to an optimal iteration number and then shrinks slowly to a point the value of this point or points may depend on the physical parameters the numerical results have been compared favorably with those resulting from the tra

global stability of a delayed sirs epidemic model with a non monotonic incidence rate in this paper we investigate a disease transmission model of sirs type with latent period 0 and the specific nonmonotone incidence rate k exp d s t i t 1 i 2 t for the basic reproduction number r0 1 applying monotone iterative techniques we establish sufficient conditions for the global asymptotic stability of endemic equilibrium of system which become partial answers to the open problem in hai feng huo and zhan ping ma dynamics of a delayed epidemic model with non monotonic incidence rate commun nonlinear sci numer simulat 15 2010 459 468 moreover combining both monotone iterative techniques and the lyapunov functional techniques to an sir model by perturbation we derive another type of sufficient conditions for the global asymptotic stability of the endemic equilibrium

the effect of impulsive vaccination on an sir epidemic model in this paper an sir epidemic model is constructed and analyzed we get the result that if the parameters satisfy the condition b a c b then the disease will be ultimately permanent under this condition we consider how the impulsive vaccination affects the original system the sufficient condition for the global asymptotical stability of the disease eradication solution is obtained we also get that if the impulsive vaccination rate is less than some value the disease will be permanent and the disease cannot be controlled people can select appropriate vaccination rate according to our theoretical result to control diseases

a solution of the bosonic and algebraic hamiltonians by using an aim we apply the notion of an asymptotic iteration method aim to determine the eigenvalues of the bosonic hamiltonians that include a wide class of quantum optical models we consider the solutions of the hamiltonians which are even the polynomials of the fourth order with respect to the boson operators we also demonstrate the applicability of the method for obtaining the eigenvalues of the simple lie algebraic structures the eigenvalues of the multi boson hamiltonians have been obtained by transforming them into the form of the single boson hamiltonian in the framework of the aim

existence of strong solutions for ito s stochastic equations via approximations given strong uniqueness for an ito s stochastic equation with discontinuous coefficients we prove that its solution can be constructed on any probability space by using for example euler s polygonal approximations stochastic equations in d and in domains in d are considered

variational sturmian approximation a nonperturbative method of solving time independent schrodinger equation a variationally improved sturmian approximation for solving time independent schrodinger equation is developed this approximation is used to obtain the energy levels of a quartic anharmonic oscillator a quartic potential and a gaussian potential the results are compared with those of the perturbation theory the wkb approximation and the accurate numerical values

the asymptotic iteration method revisited the asymptotic iteration method is a technique for solving analytically and approximately the linear second order differential equation especially the eigenvalue problems that frequently appear in theoretical and mathematical physics the analysis and mathematical justifications of the success and failure of the asymptotic iteration method are detailed in this work a theorem explaining why the asymptotic iteration method works for the eigenvalue problem is presented as a byproduct a new procedure to generate unlimited classes of exactly solvable differential equations is also introduced

stability analysis of a novel epidemics model with vaccination and nonlinear infectious rate in this paper by considering pathogen evolution and human interventions behaviors with vaccines or drugs we build up a novel seirw model with the vaccination to the newborn children the stability of the seirw model with time varying perturbation to predict the evolution tendency of the disease is analyzed furthermore we introduce a time varying delay into the susceptible and infective stages in the model and give some global exponential stability criteria for the time varying delay system finally numerical simulations are presented to verify the results

on the stochastic burgers equation in the real line this is the publisher s version also available electronically from http projecteuclid org euclid aop 1022677386 abstract

on the regularization effect of space time white noise on quasi linear parabolic partial differential equations we show that an existence and uniqueness and a comparison theorem hold if we add a space time white noise to a quasi linear parabolic equation in one space dimension even if the nonlinearity is only measurable and not even locally bounded

comment on an application of the asymptotic iteration method to a perturbed coulomb model we discuss a recent application of the asymptotic iteration method aim to a perturbed coulomb model contrary to what was argued before we show that the aim converges and yields accurate energies for that model we also consider alternative perturbation approaches and show that one of them is equivalent to that recently proposed by another author

sobolev differentiable flows of sdes with local sobolev and super linear growth coefficients by establishing a characterization for sobolev differentiability of random fields we prove the weak differentiability of solutions to stochastic differential equations with local sobolev and super linear growth coefficients with respect to the starting point moreover we also study the strong feller property and the irreducibility to the associated diffusion semigroup

reply to the comment on a solution of the bosonic and algebraic hamiltonians by using an aim we reply to the comment made by fernandez 2011 j phys a math theor 44 228001 on our recent paper koc et al 2010 j phys a math theor 43 395208 we have shown that the main equations are consistent and the results can be applied for solving a significant number of problems we admit that one or two steps missing in the original paper may lead to a different interpretation

variational and perturbative schemes for a spiked harmonic oscillator a variational analysis of the spiked harmonic oscillator hamiltonian operator d2 dx2 x2 l l 1 x2 x where is a real positive parameter is reported in this work the formalism makes use of the functional space spanned by the solutions of the schrodinger equation for the linear harmonic oscillator hamiltonian supplemented by a dirichlet boundary condition and a standard procedure for diagonalizing symmetric matrices the eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system valid for positive and relatively large values of the coupling parameter additionally a large coupling perturbative expansion is carried out and the contributions up to fourth order to the ground state energy are explicitly evaluated numerical results are compared for the special case 5 2

large order shifted 1 n expansions through the asymptotic iteration method the perturbation technique within the framework of the asymptotic iteration method is used to obtain large order shifted 1 n expansions where n is the number of spatial dimensions this method is contrary to the usual rayleigh schrodinger perturbation theory no matrix elements need to be calculated the method is applied to the schrodinger equation and the non polynomial oscillator potential is discussed as an illustrative example

asymptotic iteration method for eigenvalue problems an asymptotic iteration method for solving second order homogeneous linear differential equations of the form y 0 x y s0 x y is introduced where 0 x 0 and s0 x are c functions applications to schrodinger type problems including some with highly singular potentials are presented