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

on the moduli space of certain smooth codimension one foliations of the 5 sphere by complex surfaces in this paper we first determine the set of all possible integrable almost cr structures on the smooth foliation of s 5 constructed in m v we give a specific concrete model of each of these structures we show that this set can be naturally identified with c c c we then adapt the classical notions of coarse and fine moduli space to the case of a foliation by complex manifolds we prove that the previous set identified with c 3 defines a coarse moduli space for the foliation of m v but that it does not have a fine moduli space finally using the same ideas we prove that the standard lawson foliation on the 5 sphere can be endowed with almost cr structures but none of these is integrable this is a foliated analogue to the examples of almost complex manifolds without complex structure

perturbation expansions for a class of singular potentials harrell s modified perturbation theory ann phys n y 105 379 1977 is applied and extended to obtain nonpower perturbation expansions for a class of singular hamiltonians h d2 dx2 x2 a x2 x a 0 2 known as generalized spiked harmonic oscillators the perturbation expansions developed here are valid for small values of the coupling 0 and they extend the results which harrell obtained for the spiked harmonic oscillator a 0 formulas for the excited states are also developed

scalar curvatures on sn soit m n g une variete de riemann compacte de dimension n 3 et r x une fonction lisse sur m n on etudie si r x peut etre la courbure scalaire d une metrique g qui est conforme point par point a la metrique originale g

a basis for variational calculations in d dimensions in this paper we derive expressions for matrix elements i hj for the hamiltonian h qa q rq in d 2 dimensions the basis functions in each angular momentum subspace are of the form the matrix elements are given in terms of the gamma function for all d the significance of the parameters t and p and scale s are discussed applications to a variety of potentials are presented including potentials with singular repulsive terms of the form r 0 perturbed coulomb potentials d r br ar2 and potentials with weak repulsive terms such as r2 r4 0

kuranishi type moduli spaces for proper cr submersions fibering over the circle kuranishi s fundamental result 1962 associates to any compact complex manifold x 0 sub a finite dimensional analytic space which has to be thought of as a local moduli space of complex structures close to x 0 sub in this paper we give an analogous statement for levi flat cr manifolds fibering properly over the circle by describing explicitely an infinite dimensional kuranishi type local moduli space of levi flat cr structures we interpret this result in terms of kodaira spencer deformation theory making clear the likenesses as well as the differences with the classical case the article ends with applications and examples

a note on the problem of prescribing gaussian curvature on surfaces the problem of existence of conformal metrics with gaussian curvature equal to a given function k on a compact riemannian 2 manifold m of negative euler characteristic is studied let ko be any nonconstant function on m with max ko 0 and let ka ko a it is proved that there exists a a 0 such that the problem has a solution for k ka iff a e oo a moreover if a e 0 a then the problem has at least 2 solutions let m be a closed 2 dimensional smooth manifold and g be a riemannian metric on m let k denote the gaussian curvature of g if g e2ug is another riemannian metric conformal to g and has gaussian curvature k then it is well known that k e 2u k au where a is the laplacian of g given a function k e c m the problem of prescribing gaussian curvature asks whether one can find u e c m such that the metric g e2ug has the given k as its gaussian curvature obviously this is equivalent to the problem of solvability of the following elliptic equation 1 au k ke2u o onm if u is a solution of 1 then we have by integrating 1

a new geometric construction of compact complex manifolds in any dimension we consider holomorphic linear foliations of dimension m of mathbb c n with n 2m fulfilling a so called weak hyperbolicity condition and equip the projectivization of the leaf space for the foliation restricted to an adequate open dense subset with a structure of compact complex manifold of dimension n m 1 we show that except for the limit case n 2m 1 where we obtain any complex torus of any dimension this construction gives non symplectic manifolds including the previous examples of hopf calabi eckmann haefliger linear case loeb nicolau linear case and lopez de medrano verjovsky we study some properties of these manifolds that is to say meromorphic functions holomorphic vector fields forms and submanifolds for each manifold we construct an analytic space of deformations of dimension m n m 1 and show that under some additional conditions it is universal lastly we give explicit examples of new compact complex manifolds in particular of connected sums of products of spheres and show the existence of a momentum like map which classifies these manifolds up to diffeomorphism

conformal deformation of metrics on s 2 soit d un domaine lisse de s 2 et k une fonction lisse definie sur d alors pour que le probleme aux limites de neumann u k exp 2u 1 sur d u n 0 sur d ait une solution u on a a quand aire d max x d k x 0

nonsingular spiked harmonic oscillator a perturbative study of a class of nonsingular spiked harmonic oscillators defined by the hamiltonian h d2 dr 2 r 2 r in the domain 0 is carried out in the two extremes of a weak coupling and a strong coupling regimes a path has been found to connect both expansions for near 2

anharmonic oscillator constructing the strong coupling expansions two novel approaches to construction of the strong coupling expansion for the anharmonic oscillator with the potential v x 1 2 x2 g 4 x4 are proposed the first one is simply a straightforward solution of the schrodinger equation via the nonlinearization technique resulting in the rapidly convergent perturbation series the second one is a version of the path integral perturbation theory but with an unconventional choice of the zeroth approximation action nine leading coefficients of the strong coupling expansion are computed they decrease rapidly the ninth one being of the order of 10 9 three leading corrections of the nonlinearization approach provide the ground state energy within a relative accuracy of 10 7 10 9 at an arbitrary coupling g the explicit formulas for corrections enable one to study the analyticity properties of the energy as a function of the coupling g in the second approach the strong coupling expansion coefficients are computed as an infinite linear series of the weak

study of anharmonic singular potentials a simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a hamiltonian h with singular potentials closed form analytic expressions in n dimensions are obtained for the matrix elements of h with respect to the eigenfunctions of a soluble singular problem with two free parameters a and b the matrix eigenvalues are then optimized with respect to a and b for a given n applications convergence rates and comparisons with earlier work are discussed in detail

how do supersingular perturbations generate non taylor series we show that a suitable choice of the zero order problem can lead directly to the emergence of non taylor expansions in for the ground state energies of the hamiltonian family h 2 r2 r in regions 3 the discussion includes the role of dimension and the right order parameter the effect of choosing a more general potential of the form r r is also considered

spiked oscillators exact solution a procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented the originality of the method lies in an adequate use of asymptotic expansions of wronskians of algebraic solutions of the schrodinger equation the procedure is applied to three familiar examples of spiked oscillators

summation of strongly divergent perturbation series a new method for summing strongly divergent perturbation series is presented it is based on the change of the power series into a convergent sequence by means of an order dependent mapping obtained from a simple scaling relation the perturbation expansions for a one dimensional integral and for the ground states of the anharmonic oscillator and of the linear confining potential model are accurately summed in the most unfavorable strong coupling limit

tight bounds to the schrodinger equation eigenvalues increasing tight upper and lower bounds to the schrodinger equation eigenvalues are obtained from the riccati equation for the logarithmic derivative of the wavefunction the solution of this non linear equation is written as a pade approximant and the bounds are given by the roots of a sequence of determinants numerical results are shown for the anharmonic and quartic oscillators

the equation on a positive current we study the induced equation on a positive current in a complex manifold we extend the l 2 estimates for the equation to harmonic currents of bidimension 1 1 satisfying a frobenius type condition we also show that the l 2 estimates are satisfied for the equation on a positive closed current of bidegree 1 1 on a pseudoconvex domain in n

kazdan warner equation on graph in the negative case abstract let g v e be a connected finite graph in this short paper we reinvestigate the kazdan warner equation u c h e u with c 0 on g where h defined on v is a known function grigor yan lin and yang 3 showed that if the kazdan warner equation has a solution then h the average value of h is negative conversely if h 0 then there exists a number c h 0 such that the kazdan warner equation is solvable for every 0 c c h and it is not solvable for c c h moreover if h 0 and h 0 then c h inspired by chen and li s work 1 we ask naturally is the kazdan warner equation solvable for c c h in this paper we answer the question affirmatively we show that if c h then h 0 and h 0 moreover if c h then there exists at least one solution to the kazdan warner equation with c c h

accurate eigenvalues and eigenfunctions for quantum mechanical anharmonic oscillators the representation of the taylor expansion of the logarithmic derivative of the wavefunction by means of a pade approximant followed by an appropriate quantization condition proves a powerful way of obtaining accurate eigenvalues of the schrodinger equation in this paper we investigate in detail some of the interesting features of this approach termed riccati pade method rpm by means of its application to anharmonic oscillators we analyse the occurrence of many roots in the neighborhoods of the physical eigenvalues in the weak coupling regime and also obtain accurate coefficients of the strong coupling expansion we finally investigate the global and the local accuracy of the rpm eigenfunctions

elementary bound states for the power law potentials the author shows how the exact polynomial exp polynomial bound state solutions to the radial schrodinger equation may be constructed for any potential of the form v r sigma delta in d gdelta rdelta where d is a finite set of arbitrary rational numbers and some of the couplings gdelta are not independent

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

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