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

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

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

Antiproliferative, antimicrobial, and antifungal activities of polyphenol extracts from Ferocactus species

Polyphenols, obtained from natural resources, may possess important pharmacological effects. The polyphenolic profiles of the stem extracts of six Ferocactus species (sp.): F. gracilis, F. pottsii, F. herrerae, F. horridus, F. glaucescens, and F. emoryi, were measured using high-performance liquid chromatography (HPLC) with diode-array detection (DAD). Additionally, anticancer, antibacterial, and antifungal activities were examined. Results showed the presence of high to moderate amounts of polyphenols in the extracts (phenolic acids: Protocatechuic acid, 3,4-dihydroxyphenylacetic acid, cffeic acid, and vanillic acid; flavonoids: Rutoside and quercitrin). The highest amounts of 3,4-dihydroxyphenylacetic acid were found in F. glaucescens ((132.09 mg 100 $g^{-1}$ dry weight (DW)), F. pottsii (75.71 mg 100 $g^{-1}$ DW), and F. emoryi (69.14 mg 100 $g^{-1}$ DW) while rutoside content was highest in F. glaucescens (107.66 mg 100 $g^{-1}$ DW). Maximum antiproliferative activities were observed against HeLa and Jurkat cancer cells, with F. glaucescens, F. emoryi, and F. pottsii showing the highest anticancer activity. Most bacteria were sensitive to Ferocactus sp. stem extracts. Escherichia coli and Staphylococcus aureus were the most sensitive. Excellent antifungal effects were observed against Aspergillus ochraceus and A. niger. However, Penicillium funiculosum, P. ochrochloron, and Candida albicans were relatively resistant. This is the first study reporting novel sources of polyphenols in Ferocactus sp. with anticancer and antimicrobial activities

Analysis of CLDN14 gene in deaf Moroccan patients with non-syndromic hearing loss

Mutations in the CLDN14 gene, encoding the tight junction claudin 14 protein has been reported to date in an autosomal recessive form of isolated hearing loss DFNB29. In order to identify the contribution of CLDN14 to inherited deafness in Moroccan population, we performed a genetic analysis of this gene in 80 Moroccan familial cases. Our results show the presence of 7 mutations: 6 being conservative and one leading to a missense mutation (C11T) which was found at heterozygous and homozygous states, with a general frequency of 6.87%. The pathogenicity of the resulting T4M substitution is under discussion. Finally, our study suggests that CLDN14 gene can be implicated in the development of hearing loss in the Moroccan population

Part of the D - dimensional Spiked harmonic oscillator spectra

The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge

The Klein-Gordon equation with the Kratzer potential in d dimensions

We apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact solutions for S(r)=V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.Comment: 13 page

Molecular analysis of the TMPRSS3 gene in Moroccan families with non-syndromic hearing loss

Autosomal recessive non-syndromic hearing impairment (ARNSHI) is the most common type of inherited hearing impairment, accounting for approximately 80% of inherited prelingual hearing impairment. Hearing loss is noted to be both phenotypically and genetically heterogeneous. Mutations in the TMPRSS3 gene, which encodes a transmembrane serine protease, are known to cause autosomal recessive non-syndromic hearing impairment DFNB8/10. In order to elucidate if the TMPRSS3 gene is responsible for ARNSHI in 80 Moroccan families with non-syndromic hearing impairment, the gene was sequenced using DNA samples from these families. Nineteen TMPRSS3 variants were found, nine are located in the exons among which six are missense and three are synonymous. The 10 remaining variations are located in non-coding regions. Missense variants analysis show that they do not have a significant pathogenic effect on protein while pathogenicity of some variant remains under discussion. Thus we show that the TMPRSS3 gene is not a major contributor to non-syndromic deafness in the Moroccan population

Mammillaria species : polyphenols studies and anti-cancer, anti-oxidant, and anti-bacterial activities

Discovering new natural resources of polyphenols is the aim of many recent studies in the field of natural product research. This study tentatively investigated the polyphenols profile of the stems of seven Mammillaria species (M. rhodantha, M. spinosissima, M. hahniana, M. crucigera, M. candida, M. albilanata, and M. muehlenpfordtii) using high performance liquid chromatography with DAD detector (HPLC-DAD) method. Furthermore, the anti-cancer, anti-oxidant, and anti-bacterial potentials of these extracts as well as major identified phenols were explored. The HPLC-DAD study confirmed the availability of six phenolic acids, including gentisic acid, chlorogenic acid, caffeic acid, protocatechuic acid, sinapic acid, and p-hydroxybenzoic acid. The dominant compounds were: gentisic acid in M. rhodantha and M. spinosissima; chlorogenic acid in M. muehlenpfordtii, M. crucigera, and M. rhodantha; and caffeic acid in M. rhodantha, M. crucigera, and M. spinosissima. Stems of Mammillaria sp. showed antiproliferative e ects against HeLa, MCF-7, and Jurkat cells. In HeLa and MCF-7 cells, the best antiproliferative activities were found in the treatments with M. rhodantha, M. spinosissima, and M. muehlenpfordtii. The apoptotic assay of M. rhodantha, M. spinosissima, and M. muehlenpfordtii showed accumulation of necrotic cells in the early and late apoptotic phase. M. rhodantha, M. spinosissima, and M. muehlenpfordtii showed the highest anti-oxidant activities using 2,2-diphenyl-1-picrylhydrazyl (DPPH), -carotene bleaching, and ferric reducing anti-oxidant power (FRAP) assays. M. rhodantha was the best source of antioxidants. Mammillaria sp. showed moderate anti-bacterial effects against bacteria and the highest effects were found using the extracts of M. rhodantha, M. spinosissima, M. crucigera and M. muehlenpfordtii against most bacteria. The anti-bacterial activities were attributed to other phenolic compounds (e.g., chlorogenic acid) than gentisic acid, which was not active against most bacteria. Mammillaria sp. could be considered to be an important natural source of phenolic acids with anti-cancer, anti-bacterial, and anti-oxidant activities