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

Wilson’s Disease and Autoimmune Hepatitis Coexistence: A Cause of Diagnostic Delay

This case report describes a 27-year-old housewife who presented with a progressive and insidious onset of abdominal distension, loss of appetite, and fatigue which started 3 months before her presentation. The physical assessment showed moderate ascites and small liver size, and no other peripheral evidence of chronic liver disease was observed. A diagnosis of liver cirrhosis and was confirmed by investigations and imaging, where ascites responded well to therapy with diuretics. Investigations for the cause of cirrhosis was established through the diagnosis of autoimmune hepatitis, and she was started on steroids and azathioprine with partial improvement in liver biochemistry. She presented 8 months later with neuropsychiatric symptoms in the form of slurred speech and difficulty walking. Accordingly, Wilson’s disease was suspected to be the cause and further investigations confirmed this. A chelating agent, D penicillamine, was added to her immunosuppressive treatment. Nine months later she showed slow improvement in her neurological symptoms and was referred for assessment for liver transplantation. Wilson’s disease, although rare, should be suspected in patients with decompensated liver disease. The dominance of clinical and epidemiological features of autoimmune hepatitis as a common causative pathology for chronic liver disease in young and middle-aged ladies may hide the presence of other serious different pathologies such as Wilson’s disease

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

Palladate precatalysts for the formation of C-N and C-C bonds

A series of imidazolium-based palladate precatalysts has been synthesized and the catalytic activity of these air- and moisture-stable complexes evaluated as a function of the nature of the imidazolium counterion. These precatalysts can be converted under catalytic conditions to Pd-NHC species capable of enabling the Buchwald-Hartwig aryl amination and the alpha-arylation of ketones. Both reactions can be carried out efficiently under very mild operating conditions. The effectiveness of the protocol was tested on functionality-laden substrates

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

Radio Astronomical Polarimetry and the Lorentz Group

In radio astronomy the polarimetric properties of radiation are often modified during propagation and reception. Effects such as Faraday rotation, receiver cross-talk, and differential amplification act to change the state of polarized radiation. A general description of such transformations is useful for the investigation of these effects and for the interpretation and calibration of polarimetric observations. Such a description is provided by the Lorentz group, which is intimately related to the transformation properties of polarized radiation. In this paper the transformations that commonly arise in radio astronomy are analyzed in the context of this group. This analysis is then used to construct a model for the propagation and reception of radio waves. The implications of this model for radio astronomical polarimetry are discussed.Comment: 10 pages, accepted for publication in Astrophysical Journa

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 role of pressure anisotropy in the turbulent intracluster medium

In low-density plasma environments, such as the intracluster medium (ICM), the Larmour frequency is much larger than the ion-ion collision frequency. In such a case, the thermal pressure becomes anisotropic with respect to the magnetic field orientation and the evolution of the turbulent gas is more correctly described by a kinetic approach. A possible description of these collisionless scenarios is given by the so-called kinetic magnetohydrodynamic (KMHD) formalism, in which particles freely stream along the field lines, while moving with the field lines in the perpendicular direction. In this way a fluid-like behavior in the perpendicular plane is restored. In this work, we study fast growing magnetic fluctuations in the smallest scales which operate in the collisionless plasma that fills the ICM. In particular, we focus on the impact of a particular evolution of the pressure anisotropy and its implications for the turbulent dynamics of observables under the conditions prevailing in the ICM. We present results from numerical simulations and compare the results which those obtained using an MHD formalism.Comment: 7 pages, 14 figures, Journal of Physics: Conference Serie

A New Quantitative Classification of the Extrahepatic Biliary Tract Related to Cystic Duct Implantation

Background: Knowledge regarding biliary anatomy and its variations, including the cystic duct (CD), is important in the pre-surgical setting and for predicting biliary diseases. However, no large series has focused on CD evaluation using a quantitative analysis. The primary aim of this prospective study was to create a ‘taxonomic’ classification of CD anatomy in a large cohort of subjects who underwent magnetic resonance cholangiopancreatography (MRCP). The secondary aim was to evaluate the correlations between extrahepatic bile duct (EHBD) variants and biliary diseases. Methods: We enrolled patients who underwent MRCP for different clinical indications from January 2017 to May 2019. Demographical, anatomical and clinical data were evaluated using statistical analyses, as appropriate. The anatomical assessment of EHBD was performed using the standard classification for CD in low, medium, and high insertions, and the lengths of CD to the duodenal papilla (DP), and EHBD was determined to conduct a new quantitative analysis. Results: The final study population comprised 1004 subjects. A new classification for EHBD as per the percentile distribution of the ratio CDDP/EHBD was designed, and the following categories were obtained: type 1 (below the 25th percentile) for CDDP/EHBD ratio ≤ 50%; type 2 (25th to 75th percentile) for CDDP/EHBD ratio 51–75% and type 3 (above the 75th percentiles) for CDDP/EHBD ratio > 75%. Type 1 of the new classification of CD implantation was significantly superior in terms of the detection of low, medial and intra-pancreatic CD that was significantly correlated with a high risk of choledochal lithiasis in comparison with the standard classification (P < 0.001). Conclusions: The new classification of CD implantation enables identification of the vast majority of intra-pancreatic CDs that are correlated with a high risk of choledochal lithiasis in a single category (type 1) that is easy to identify using imaging