Functions averages over the roots of unity,cauchy problems and addition formulas

An averaging operator over the roots of unity is defined on a class of analytic functions and its algebraic and analytic properties are investigated. A Cauchy like integral formula for this is obtained. This operator and its properties are then employed to solve higher order Cauchy problems, to derive addition formulas for hypergeometric functions and to obtain integral representations for special classes of hypergeometric functions.     

Cohomological uniqueness of the Cauchy problem solutions for the Einstein equation

In this paper we analyze the Cauchy problem for the Einstein equation in the case of a non-characteristic initial hypersurface. To find the correct notions for the characteristic and Cauchy data we introduce a complex, which we call the Einstein complex. Then the Cauchy problem acquires correctness in terms of the associated spectral sequence. We define the Cauchy data in such way that they allow us to reconstruct a cohomologously unique formal solution.     

Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator

The paper deals with second order nonlinear evolution inclusions and their applications. We study evolution inclusions involving a Volterra-type integral operator, which are considered within the framework of an evolution triple of spaces. First, we deliver a result on the unique solvability of the Cauchy problem for the inclusion by combining a surjectivity result for multivalued pseudomonotone operators and the Banach contraction principle. Next, we provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem. Finally, we consider a dynamic frictional contact problem of viscoelasticity for materials with long memory and indicate how the result on evolution inclusion is applicable to the model of the contact problem.     

Pseudochelin A,a siderophore of Pseudoalteromonas piscicida S2040

A new siderophore containing a 4,5-dihydroimidazole moiety was isolated from Pseudoalteromonas piscicida S2040 together with myxochelins A and B, alteramide A and its cycloaddition product, and bromo- and dibromoalterochromides. The structure of pseudochelin A was established by spectroscopic techniques including 2D NMR and MS/MS fragmentation data. In bioassays selected fractions of the crude extract of S2040 inhibited the opportunistic pathogen Pseudomonas aeruginosa. Pseudochelin A displayed siderophore activity in the chrome azurol S assay at concentrations higher than 50 μM, and showed weak activity against the fungus Aspergillus fumigatus, but did not display antibacterial, anti-inflammatory or anticonvulsant activity.     

Quantum Pfaffians and hyper-Pfaffians

The concept of the quantum Pfaffian is rigorously examined and refurbished using the new method of quantum exterior algebras. We derive a complete family of Plücker relations for the quantum linear transformations, and then use them to give an optimal set of relations required for the quantum Pfaffian. We then give the formula between the quantum determinant and the quantum Pfaffian and prove that any quantum determinant can be expressed as a quantum Pfaffian. Finally the quantum hyper-Pfaffian is introduced, and we prove a similar result of expressing quantum determinants in terms of quantum hyper-Pfaffians at modular cases.     

On solitary wave solutions to the nonlinear Schrödinger equations with two parameters

In this paper, we discuss the existence and multiplicity of positive solitary wave solutions for nonlinear Schrödinger equations with two parameters. The proof is based on the method of upper and lower solutions and the fixed point index.     

An evaluation of the CYP2D6 and CYP3A4 inhibition potential of metoprolol metabolites and their contribution to drug–drug and drug–herb interaction by LC‐ESI/MS/MS

The aim of the present study was to evaluate the contribution of metabolites to drug–drug interaction and drug–herb interaction using the inhibition of CYP2D6 and CYP3A4 by metoprolol (MET) and its metabolites. The peak concentrations of unbound plasma concentration of MET, α‐hydroxy metoprolol (HM), O‐desmethyl metoprolol (ODM) and N‐desisopropyl metoprolol (DIM) were 90.37 ± 2.69, 33.32 ± 1.92, 16.93 ± 1.70 and 7.96 ± 0.94 ng/mL, respectively. The metabolites identified, HM and ODM, had a ratio of metabolic area under the concentration–time curve (AUC) to parent AUC of ≥0.25 when either total or unbound concentration of metabolite was considered. In vitro CYP2D6 and CYP3A4 inhibition by MET, HM and ODM study revealed that MET, HM and ODM were not inhibitors of CYP3A4‐catalyzed midazolam metabolism and CYP2D6‐catalyzed dextromethorphan metabolism. However, DIM only met the criteria of >10% of the total drug related material and <25% of the parent using unbound concentrations. If CYP inhibition testing is solely based on metabolite exposure, DIM metabolite would probably not be considered. However, the present study has demonstrated that DIM contributes significantly to in vitro drug–drug interaction. Copyright © 2016 John Wiley & Sons, Ltd.     

海蛎壳粉废弃物负载CuCl_2作为高效、廉价以及可回收催化剂合成炔胺类化合物(英文)

发展了一种经济、简单的海蛎壳粉负载的CuCl2异相催化剂OSP-CuCl2,用来催化醛-炔-胺之间的A3偶联反应.OSP-CuCl2容易通过简单的方法从海蛎壳粉以及CuCl2制备,且显示出高的催化活性以及良好的可循环回收性.在微波辅助以及无溶剂条件下,以OSP-CuCl2为催化剂,能够以高产物收率制备出一系列炔胺类化合物.OSP-CuCl2可通过简单的过滤方式进行回收,并至少可循环使用6次.初步放大实验表明,炔胺类化合物能够以150 mmol的规模制备(87%收率).     

Nuklearpharmaka — Ihre Entwicklung,Präparation und Anwendungsmöglichkeiten

Radioaktiv markierte Präparate haben in denletzten Jahren in schnell zunehmendem Maße Eingang in die klinische Medizin gefunden. Sie sind beieiner Reihe von Indikationen schon jetzt außerordentlich wertvolle Hilfsmittel bei der Diagnose, besonders bei der Prüfung von Organfunktionen.     

Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.