Application of the Asymptotic Iteration Method to a Perturbed Coulomb Model

We show that the asymptotic iteration method converges and yields accurate energies for a perturbed Coulomb model. We also discuss alternative perturbation approaches to that model.Comment: 9 pages, 2 figures, 1 tabl

Exact solutions for vibrational levels of the Morse potential via the asymptotic iteration method

Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in excellent agreement with the ones obtained before. Without any loss of generality, other states and molecules could be treated in a similar way

Distal Recurrence of Periosteal Osteosarcoma After Complete Excision of Proximal Primary Tumour With Good Excision Margins

We present this case of an unusual recurrence of a periosteal osteosarcoma in the distal right tibia 2 years after a successful proximal right tibia primary periosteal osteosarcoma excision with a successful fibular graft. This recurrence lead to a right below-knee amputation

Homalg: A meta-package for homological algebra

The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. The paper describes a way allowing one to realize such functors, e.g. Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra system. Once this is achieved, one can compose and derive functors and even iterate this process without the need of any specific knowledge of these functors. These ideas are realized in the ring independent package homalg. It is designed to extend any computer algebra software implementing the arithmetics of a computable ring R, as soon as the latter contains algorithms to solve inhomogeneous linear equations with coefficients in R. Beside explaining how this suffices, the paper describes the nature of the extensions provided by homalg.Comment: clarified some points, added references and more interesting example

Criterion for polynomial solutions to a class of linear differential equation of second order

We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1}\hbox{and}\quad s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1},\quad n=1,2,.... Conversely (ii) if \lambda_n\lambda_{n-1}\ne 0 and \delta_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 kind), 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.Comment: 12 page

Any ll-state solutions of the Hulth\'en potential by the asymptotic iteration method

In this article, we present the analytical solution of the radial Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any $l$ states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different $\delta$ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.Comment: 14 pages and 1 figur

The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

The asymptotic iteration method is applied, to calculate the angular spheroidal eigenvalues $\lambda^{m}_{\ell}(c)$ with arbitrary complex size parameter $c$. It is shown that, the obtained numerical results of $\lambda^{m}_{\ell}(c)$ are all in excellent agreement with the available published data over the full range of parameter values $\ell$, $m$, and $c$. Some representative values of $\lambda^{m}_{\ell}(c)$ for large real $c$ are also given.Comment: 15 pages, 1 figur

Roles of binding elements, FOXL2 domains, and interactions with cJUN and SMADs in regulation of FSHβ.

We previously identified FOXL2 as a critical component in FSHβ gene transcription. Here, we show that mice deficient in FOXL2 have lower levels of gonadotropin gene expression and fewer LH- and FSH-containing cells, but the same level of other pituitary hormones compared to wild-type littermates, highlighting a role of FOXL2 in the pituitary gonadotrope. Further, we investigate the function of FOXL2 in the gonadotrope cell and determine which domains of the FOXL2 protein are necessary for induction of FSHβ transcription. There is a stronger induction of FSHβ reporter transcription by truncated FOXL2 proteins, but no induction with the mutant lacking the forkhead domain. Specifically, FOXL2 plays a role in activin induction of FSHβ, functioning in concert with activin-induced SMAD proteins. Activin acts through multiple promoter elements to induce FSHβ expression, some of which bind FOXL2. Each of these FOXL2-binding sites is either juxtaposed or overlapping with a SMAD-binding element. We determined that FOXL2 and SMAD4 proteins form a higher order complex on the most proximal FOXL2 site. Surprisingly, two other sites important for activin induction bind neither SMADs nor FOXL2, suggesting additional factors at work. Furthermore, we show that FOXL2 plays a role in synergistic induction of FSHβ by GnRH and activin through interactions with the cJUN component of the AP1 complex that is necessary for GnRH responsiveness. Collectively, our results demonstrate the necessity of FOXL2 for proper FSH production in mice and implicate FOXL2 in integration of transcription factors at the level of the FSHβ promoter

On the dilaton and the axion potentials

We extend the Vecchia-Veneziano-Witten (VVW) model of QCD in the chiral limit and for large colour number $N_c$, by introducing an effective dilaton-gluon coupling from which we derive both the axion and dilaton potentials. Furthermore, using a string inspired model, we determine a new interquark potential as a perturbative series in terms of the interquark distance $r$. Our potential goes beyond Dick one obtained in [8] and shares the same features as the Bian-Huang-Shen potential $V_{BHS}$ which depends only on odd powers of $r$ [22].Comment: 15 pages, Late