On a q-gamma and a q-beta matrix functions

The main goal of this article is to extend the concept of q-special functions of complex variable to q-special matrix functions through the study of a q-gamma and a q-beta matrix function. The q-shifted factorial, q-gamma and q-beta matrix functions are defined and some of their properties are investigated.     

Classification of finite Morse index solutions for Hénon type elliptic equation -\Delta u = |x|^{\alpha } u_{+}^{p}

In this paper we investigate the non-autonomous elliptic equations \(-\Delta u = |x|^{\alpha } u_{+}^{p}\) in \( \mathbb{R }^{N}\) and in \( \mathbb{R }_+^{N}\) with the Dirichlet boundary condition, with \(N \ge 2\) , \(p>1\) and \(\alpha >-2\) . We consider the weak solutions with finite Morse index and obtain some classification results.     

Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

High performance liquid chromatographic analysis of tetroxoprim and sulphadiazine in serum and urine.

Quantitative determination of tetroxoprim and sulphadiazine in serum and urine was performed using reversed phase high performance liquid chromatography. Protein precipitation using 10% perchloric acid was utilized for purification of serum samples while urine samples were diluted prior to analysis. The mobile phase consisted of triethylammonium acetate buffer (85%), acetonitrile (12%) and methanol (3%), with a final pH of 4.2. The eluent was monitored at 280 nm. Benzoic acid was used as an internal standard. Standardization, validation and application of the method is described.     

Iphiona mucronata (Forssk.) Asch. & Schweinf. A Comprehensive Phytochemical Study via UPLC-Q-TOF-MS in the Context of the Embryo- and Cytotoxicity Profiles

Iphiona mucronata (Family Asteraceae) is widely distributed in the Eastern desert of Egypt. It is a promising plant material for phytochemical analysis and pharmacologic studies, and so far, its specific metabolites and biological activity have not yet been thoroughly investigated. Herein, we report on the detailed phytochemical study using UPLC-Q-TOF-MS approach. This analysis allowed the putative annotation of 48 metabolites belonging to various phytochemical classes, including mostly sesquiterpenes, flavonoids, and phenolic acids. Further, zebrafish embryotoxicity has been carried out, where 100 µg/mL extract incubated for 72 h resulted in a slow touch response of the 10 examined larvae, which might be taken as a sign of a disturbed peripheral nervous system. Results of in vitro testing indicate moderate cytotoxicity towards VERO, FaDu, and HeLa cells with CC₅₀ values between 91.6 and 101.7 µg/mL. However, selective antineoplastic activity in RKO cells with CC₅₀ of 54.5 µg/mL was observed. To the best of our knowledge, this is the first comprehensive profile of I. mucronata secondary metabolites that provides chemical-based evidence for its biological effects. A further investigation should be carried out to precisely define the underlying mechanisms of toxicity.     

Koordinationschemie von Dinitroresorcin mit Kupfer-, Kobalt-, Nickel-, Eisen- und Zinksalzen

The reactions of the bidentate dinitrosoresorcinol (DNR) with copper, cobalt, nickel, iron and zinc salts were investigated. This ligand was found to react with these metal salts in aqueous media where hydrogen ion was confirmed to be liberated except in case of iron. The solid complexes were prepared in alcoholic media. Chemical analyses, magnetic and spectral data were compatible to determine the structure of these complexes and their mode of chelation.

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Mit 2 Abbildungen     

Spectrum of relaxation times for ising spin clusters in random fields

Summary Exact results on the single-spin-flip Glauber dynamics of six-coupled random field Ising spins with the coordination number of four are presented. Two distributions of random fields (RF), binary (BD) and Gaussian (GD) ones, are investigated. The effects of the static magnetic field are discussed. In the zero-magnetic-field case, the number of diverging relaxation times is equal to the number of energy minima minus one. This rule breaks in the presence of a magnetic field. The longest relaxation times in the absence of the field verify the Arrhenius law with the energy barrier determined by the energy needed to invert the ground-state spin configuration. At low temperature, according to the Arrhenius law, the spectrum of relaxation times shows a two-peaked distribution on a logarithmic scale. In the GD case of RF, the energy barrier distribution is continuous, while it is quasi-discrete in the BD case.     

Two-electron,one-photon transitions in nickel

The two emission lines, Kα₁α₃^h and Kα₂α₃^h resulting from the two-electron transitions $\text{1s}{}^{\mathrm{?2}}\text{→ 2s}{}^{\mathrm{?1}}\text{2p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ and $\text{1s}{}^{\mathrm{?2}}\text{→ 2s}{}^{\mathrm{?1}}\text{2p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ were resolved for elemental nickel. Their measured energies agree well with calculations. Their relative intensity $\text{I(Kα}{}_1\text{α}{}_3{}^{\mathrm{h}}\text{)/I(Kα}{}_2\text{α}{}_3{}^{\mathrm{h}}\text{) ≈}\text{3}\text{4}$ and their intensity relative to that of the Kα diagram lines is about 10^?4. This is some 10⁴ times larger than both theoretical results and the results of ion-atom collision experiments.