Stability for the Dirichlet Problem under Continuous Steiner Symmetrization

In this paper we prove the existence of a deformation transforming an arbitrary open set into the ball, which has the following properties: it keeps constant the measure, the kth eigenvalue of Laplace–Dirichlet operator is continuous from the left and the first eigenvalue is decreasing. The deformation is given by a sequence of continuous Steiner symmetrizations, and the behavior of the eigenvalues is related to the stability of the Dirichlet problem.     

Simple General Neron Desingularization in local Q-algebras

We give here an easier proof of the so-called General Neron Desingularization in the frame of local algebras.     

Betti numbers for p -stable ideals

Abstract

All Riemannian algebras of dimension ≤3 are classified in this paper.     

On the Beurling dimension of exponential frames

We study Fourier frames of exponentials on fractal measures associated with a class of affine iterated function systems. We prove that, under a mild technical condition, the Beurling dimension of a Fourier frame coincides with the Hausdorff dimension of the fractal.     

Synthesis,characterization, molecular docking studies and in vitro screening of new metal complexes with Schiff base as antimicrobial and antiproliferative agents

A series of Cu(II), Co(II), Pd(II), Pt(II), Zn(II), Cd(II) and Fe(III) complexes were designed and synthesized using Schiff base 1‐phenyl‐2,3‐dimethyl‐4‐(N‐3‐formyl‐6‐methylchromone)‐3‐pyrazolin‐5‐one (HL). The new metal complexes were investigated using various physicochemical techniques including elemental and thermal analyses, molar electric conductivity and magnetic susceptibility measurements, as well as spectroscopic methods. Also, the crystal structures of ligand HL and the Pd(II) complex were determined using single‐crystal X‐ray diffraction analysis. For all compounds, the antimicrobial activity was studied against a series of standard strains: Staphylococcus aureus, Bacillus cereus, Enterococcus faecalis, Escherichia coli, Acinetobacter baumannii, Candida albicans, Candida krusei and Cryptococcus neoformans. The in vitro antiproliferative activity of the ligand and complexes was evaluated against ten cancer cell lines: MSC, A375, B16 4A5, HT‐29, MCF‐7, HEp‐2, BxPC‐3, RD, MDCK and L20B. At 10 μM concentration a significant cytotoxic effect of the Co(II), Pd(II) and Cd(II) complexes was observed against B16 4A5 murine melanoma cells. The Zn(II) complex is active against HEp‐2, RD and MDCK cancer cell lines, where IC₅₀ values vary between 1.0 and 77.6 and for BxPC‐3 the activity index versus doxorubicin is 3.7 times higher.     

Multilayered catalysts for fatty acid ester hydrotreatment into fuel range hydrocarbons

This study aims to investigate Ni–Mo/γAl₂O₃ and Ni–La/Zn-ZSM-5–γAl₂O₃ catalysts, which convert methyl esters into various compounds with a similar composition to those found in diesel fuels. The catalysts were synthesized by impregnation using two different routes and characterized by atomic absorption spectrometry, Brunauer–Emmett–Teller, and scanning electron microscopy. The acid strength distribution indicates a relatively high concentration of weak acid centers for both materials. The disposal of the catalysts into the reactor system is an important factor for driving the process toward the desired reaction products. The hydrodeoxygenation becomes important and paraffins are formed as intermediaries when Ni–Mo/γAl₂O₃ is first disposed into the reactor, whereas hydrocracking is poor and the dehydrocyclization does not occur in the case of Ni–La/Zn-ZSM-5–γAl₂O₃ as first layer. Triple-layered catalytic systems enhance the production of n-paraffins with high carbon number, mainly C17 and C18, which are important as diesel component. The effect of temperature was also studied and it was found that aromatics are mainly formed over double-layered catalytic systems by varying the temperature. In the case of triple-layered catalysts, the change in the product composition from saturated hydrocarbons with 12–18 carbon atoms to aromatics was observed by increasing the temperature from 420 to 445 °C. An interesting finding by the addition of n-octane in the feed was observed and the considerable increase in C8 aromatics involved the dehydrocyclization that occurred faster than hydrocracking.     

Constructive Néron Desingularization of algebras with big smooth locus

An algorithmic proof of the General Néron Desingularization theorem and its uniform version is given for morphisms with big smooth locus. This generalizes the results for the one-dimensional case (cf. [10 Pfister, G., Popescu, D. (2017). Constructive General Neron Desingularization for one dimensional local rings. J. Symbolic Comput. 80:570–580.[Crossref], [Web of Science ®] , [Google Scholar]], [7 Khalid, A., Pfister, G., Popescu, D. (2018). A uniform General Neron Desingularization in dimension one. J. Algebra Appli. 16. arXiv:AC/1612.03416. [Google Scholar]]).     

Ordered mesoporous silicon carbide (OM-SiC) via polymer precursor nanocasting

Ordered mesoporous SiC with high specific surface area (650-800 m(2) g(-1)) and well ordered pore structure was obtained via nanocasting of polycarbosilanes into SBA-15 and subsequent conversion of the polymer at 1300 degrees C.     

On the Asymptotic Limit of Flows Past a Ribbed Boundary

We consider a stationary Navier–Stokes flow in a bounded domain supplemented with the complete slip boundary conditions. Assuming the boundary of the domain is formed by a family of unidirectional asperities, whose amplitude as well as frequency is proportional to a small parameter ε, we shall show that in the asymptotic limit the motion of the fluid is governed by the same system of the Navier–Stokes equations, however, the limit boundary conditions are different. Specifically, the resulting boundary conditions prevent the fluid from slipping in the direction of asperities, while the motion in the orthogonal direction is allowed without any constraint. The work of Š. N. supported by Grant IAA100190505 of GA ASCR in the framework of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503.