Properties of excited BcB_c states in QCD

The mass and leptonic decay constants of recently observed two new excited $B_c$ states at LHC are studied within the QCD sum rules. Considering the contributions of the ground and radially excited states, the mass and residues of the excited states of pseudoscalar and vector mesons are calculated in the framework of two different approaches of the QCD sum rules, namely, linear combinations of the corresponding sum rules and its derivatives as well as QCD sum rules with the incorporation of the least square fitting method. The obtained results on mass $m_{B_c^+}(2S) = 6.88 \pm 0.03~\rm{GeV}$ and $m_{B_c^{*+}}(2S) = 6.94 \pm 0.03~\rm{GeV}$ are in good agreement with the experimental data. Our predictions for the decay constants of these states are: $f_{B_c^+}(2S) = 0.42 \pm 0.02~\rm{GeV}$ and $f_{B_c^{*+}}(2S) = 0.46 \pm 0.01~\rm{GeV}$, which can be checked at future experiments to be conducted at the LHC. Comparison of our results with the predictions of the other approaches on mass and residues is also presented.Comment: 11 pages, 4 figures Misprints are corrected and reference list has been update

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

γ∗N→Δ+(1600)\gamma^* N \rightarrow \Delta^{+}(1600) transition form factors in light-cone sum rules

The form factors of $\gamma^* N \rightarrow \Delta(1600)$ transition is calculated within the light-cone sum rules assuming that $\Delta^+(1600)$ is the first radial excitation of $\Delta(1232)$. The $Q^2$ dependence of the magnetic dipole $\tilde{G}_M(Q^2)$, electric quadrupole $\tilde{G}_E(Q^2)$, and Coulomb quadrupole $\tilde{G}_c(Q^2)$ form factors are investigated. Moreover, the $Q^2$ dependence of the ratios $R_{EM} = -\frac{\tilde{G}_E(Q^2)}{\tilde{G}_M{Q^2}}$ and $R_{SM} = - \frac{1}{4 m_{\Delta(1600)}^2} \sqrt{4 m_{\Delta(1600)}^2 Q^2 + (m_{\Delta(1600)}^2 - Q^2 - m_N^2)^2} \frac{\tilde{G}_c(Q^2)}{\tilde{G}_M(Q^2)}$ are studied. Finally, our predictions on $\tilde{G}_M(Q^2)$, $\tilde{G}_E(Q^2)$, and $\tilde{G}_C(Q^2)$ are compared with the results of other theoretical approaches.Comment: 19 pages, 5 figure

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 expansion of 300 CTG repeats in myotonic dystrophy transgenic mice does not induce sensory or motor neuropathy

Summary: Although many studies have been carried out to verify the involvement of the peripheral nervous system (PNS) in dystrophia myotonica (DM1) patients, the results remain controversial. The generation of DM1 transgenic mice displaying the human DM1 phenotype provides a useful tool to investigate the type and incidence of structural abnormalities in the PNS. In the present study, the morphological and morphometric analysis of semi-thin sections of sciatic and sural nerves, lumbar dorsal root ganglia (DRG) and lumbar spinal cords revealed that in DM1 transgenic mice carrying 300 CTG repeats, there is no change in the number and diameter of myelinated axons compared to wild type. Only a non-significant reduction in the percentage of thin myelinated axons was detected in electron micrographs of ultra-thin sciatic nerve sections. Analysis of the number of neurons did not reveal a loss in number of either sensory neurons in the lumbar DRG or motor neurons in the lumbar spinal cord in these DM1 mice. Furthermore, in hind limb muscle sections, stained with a neurofilament antibody and α-bungarotoxin, the intramuscular axon arborization appeared normal in DM1 mice and undistinguishable from that in wild-type mice. Moreover, in DM1 mice, there was no irregularity in the structure or an increase in the endplate area. Also statistical analysis did not show an increase in endplate density or in the concentration of acetylcholine receptors. Altogether, these results suggest that 300 CTG repeats are not sufficient to induce axonopathy, demyelination or neuronopathies in this transgenic mouse mode

Magnetothermal instabilities in magnetized anisotropic plasmas

Using the transport equations for an ideal anisotropic collisionless plasma derived from the Vlasov equation by the 16-moment method, we analyse the influence of pressure anisotropy exhibited by collisionless magnetized plasmas on the magnetothermal (MTI) and heat-flux-driven buoyancy (HBI) instabilities. We calculate the dispersion relation and the growth rates for these instabilities in the presence of a background heat flux and for configurations with static pressure anisotropy, finding that when the frequency at which heat conduction acts is much larger than any other frequency in the system (i.e. weak magnetic field) the pressure anisotropy has no effect on the MTI/HBI, provided the degree of anisotropy is small. In contrast, when this ordering of timescales does not apply the instability criteria depend on pressure anisotropy. Specifically, the growth time of the instabilities in the anisotropic case can be almost one order of magnitude smaller than its isotropic counterpart. We conclude that in plasmas where pressure anisotropy is present the MTI/HBI are modified. However, in environments with low magnetic fields and small anisotropy such as the ICM the results obtained from the 16-moment equations under the approximations considered are similar to those obtained from ideal MHD.Comment: v3: 16 pages, 2 figures, fixed typos, added references and a final note on related wor

Prolonging Vase Life of Carnation Flowers Using Natural Essential Oils and its Impact on Microbial Profile of Vase Solutions

Abstract: This experiment was conducted during the two summer seasons; 2008 and 2009. Two cultivars of Dianthus caryphyllus L. were used; Farida and Madam Collate. Four essential oil treatments were used versus two controls; Tap water and 8-Hydroxyquinoline (8-HQ). These essential oils were extracted from mandarin, coriander, dill and clove. The maximum vase-life over the two seasons was recorded with dill oil followed by coriander in cv. Farida and with 8-HQ in cv. Madam Collate. The essential oils treatments showed accumulative significant reduction percentages in flower fresh weight, which increased by decreasing the used oil concentrations. The accumulative reduction percentage in flower fresh weight and the average flower dry weight showed negative significant correlation coefficients. The relative increased percentages in net water uptake were 10.93 and 7.95% in 8-HQ for both cultivars. The net water uptake had the greatest values with those flowers kept in solution containing dill followed by clove oils in cv. M adam Collate and by mandarin oil in cv. Farida. The highest positive correlation coefficient was recorded between vase life and net water uptake. The highest pH value was observed in vase containing tap water for both cultivars. In comparison, due to different treatments application, the pH values were significantly changed to a fairly acidic. These treatments were ranked, in this respect, at descending order as follows; dill oil, 8-HQ, mandarin, coriander and clove with both cultivars. The highest mean count of total sporeforming bacteria was recorded in the tap water vase solutions, while the lowest counts were with coriander oil. In vase solution containing dill oil, the log count of molds decreased as the dose concentration increased. The same trend was observed in cv. Madam Collate during the seasons. Counts of cellulose decomposing microorganisms were increased by extending the life of the carnation cut flowers in the vase solutions. All the examined preservatives, in particular 8-HQ, and the oils of dill, clove and coriander greatly suppressed proliferation of cellulose decomposers and resulted in flower densities compared with control solutions. The anatomical study indicated that, cv. Farida flower stalks greatly severe from more exposure to microorganisms attack in vase solution, especially cellulose decomposing microorganisms which penetrate tissues as lethal and blockage parasites. These negative influences on cv. Farida could be an evidence for explaining its rapid senescence and the longevity of the flowers of cv. Madam Collate

An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of computability need to be turned into constructive ones. We do this explicitly for the often-studied example Abelian category of finitely presented modules over a so-called computable ring $R$, i.e., a ring with an explicit algorithm to solve one-sided (in)homogeneous linear systems over $R$. For a finitely generated maximal ideal $\mathfrak{m}$ in a commutative ring $R$ we show how solving (in)homogeneous linear systems over $R_{\mathfrak{m}}$ can be reduced to solving associated systems over $R$. Hence, the computability of $R$ implies that of $R_{\mathfrak{m}}$. As a corollary we obtain the computability of the category of finitely presented $R_{\mathfrak{m}}$-modules as an Abelian category, without the need of a Mora-like algorithm. The reduction also yields, as a by-product, a complexity estimation for the ideal membership problem over local polynomial rings. Finally, in the case of localized polynomial rings we demonstrate the computational advantage of our homologically motivated alternative approach in comparison to an existing implementation of Mora's algorithm.Comment: Fixed a typo in the proof of Lemma 4.3 spotted by Sebastian Posu