Calculating singular integrals as an ill-posed problem

Summary Applying numerical quadrature to singular integrals in a straightforward way leads to uncontrolled instability with respect to data errors. In this paper we describe how to control this instability.Dedicated to Professor G. Hämmerlin on the occasion of his 60th birthday.     

The jump operation for structure degrees

One of the main problems in effective model theory is to find an appropriate information complexity measure of the algebraic structures in the sense of computability. Unlike the commonly used degrees of structures, the structure degree measure is total. We introduce and study the jump operation for structure degrees. We prove that it has all natural jump properties (including jump inversion theorem, theorem of Ash), which show that our definition is relevant. We study the relation between the structure degree jump (in the sense of Soskov) and the jump degrees of a structure (in the sense of Jockusch) and give necessary and sufficient conditions for their existence in the terms of structure degrees. We show some properties, distinguishing the structure degrees from the enumeration degrees.     

On a Serrin-Type Regularity Criterion for the Navier–Stokes Equations in Terms of the Pressure

We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result of Zhou [28].     

飞机起落架活塞杆断裂原因分析

针对飞机起落架活塞杆在外场使用过程中裂纹失效问题,利用扫描电子显微镜对其断裂面微观形貌进行观察,研究其断裂机理.结果表明:该活塞杆断裂性质为服役过程中循环应力作用下的疲劳断裂.应力使活塞杆件表面出现微裂纹,在其内部形成微孔.随着应力循环次数增加,微孔的数量和大小都不断增加,最终导致了钢的疲劳断裂.通过优化其热处理工艺,使活塞杆获得良好的强韧配比,提高了抗疲劳性能.     

Nanostructure development in nylon 6-Cloisite® 30B composites. Effects of the preparation conditions

PA6 composites with Cloisite® 30B (30B), prepared by different procedures, i.e., melt compounding, static annealing and solution blending, have been characterized by X-ray diffraction and microscopic analyses (TEM, SEM, POM) in order to shed more light on the mechanism of nanostructure development. It has been demonstrated that intercalation of the PA6 chains within the 30B galleries takes place very rapidly, in the absence of applied stresses, even when the size of the clay particles is relatively large (tens of microns) and the clay loading is very high (even 50 wt.%). It has also been shown that, if, conversely, the filler content is low (∼10 wt.% or less) and the particles are tiny (e.g., as for polymer/clay mixtures prepared by precipitation from a common solution), intercalation continues, under quiescent conditions, and leads in reasonable times to complete destruction of the silicate platelets stacking order. The composites with higher filler contents display a mixed exfoliated/intercalated morphology, with the intercalated silicate stacks characterized by an interlayer distance of about 3.7 nm. Contrary to statically annealed composites, the melt kneaded ones are characterized by a homogeneous dispersion of the filler particles and a local parallel orientation of the silicate platelets that induces, during polymer crystallization, an orientation of the polymer crystallites parallel to the faces of the compression molded specimens. Experiments carried out using 30B samples previously treated at 250 °C for 4 h under vacuum (30Bdegr) indicate that this treatment, probably due to the collapsed interlayer spaces, lowers the extent of PA6 chains intercalation. Thus, the relevant PA6/30Bdegr composites are characterized by the coexistence of unintercalated clay tactoids/agglomerates and individual silicate layers formed as result of intercalation on the edges of the filler particles.     

Mononuclear and dinuclear chiral vanadium(V) complexes with tridentate Schiff bases derived from R(−)-1,2-diaminopropane: Synthesis,structure, characterization and catalytic properties

A series of vanadium(V) complexes with unsymmetrical tridentate Schiff base ligands, obtained by the single condensation of R(−)-1,2-diaminopropane with salicylaldehyde and its derivatives, 2-hydroxy-1-naphthaldehyde, 2-hydroxyacetophenone, 1-hydroxy-2-acetonaphthone and 2-hydroxybenzophenone, were prepared. The complexes were characterized by elemental analysis and by their IR, CD, UV–Vis, 1D (¹H, ⁵¹V) and 2D (COSY, NOESY, gHSQC) NMR spectra. Crystal structures of the mononuclear complex {R(−)-2-amino-1-N-[(2′-oxido-κO-4′,6′-dimethoxyphenyl)methylene]aminopropane-κ²N}dioxidovanadium(V), VO₂(C₁₂H₁₇N₂O₃), 4, and of the dinuclear complex, di-μ-oxido-bis({R(−)-2-[1-(2-aminopropylimino)ethyl]-4-methylphenolato-κ³N,N′,O}oxidovanadium(V)), V₂O₄(C₁₁H₁₅N₂O)₂, 5, have been obtained by X-ray diffraction studies. The structure of 4 was revealed to be a distorted trigonal–bipyramidal coordination geometry, rarely encountered in VO₂(tridentate Schiff base) complexes. Complexes 2 and 3 have the ability to catalyze the oxidation of prochiral sulfide substrates PhSR (R = Me, Bz) utilizing hydrogen peroxide or cumene hydroperoxide (CHPO) as the oxidant.     

SE‐30 Graphite Composite Electrode: An Alternative for the Development of Electrochemical Biosensors

A new graphite composite electrode was constructed by mixing graphite powder with chromatography stationary phase, SE‐30, as the binder. The electrochemical behavior of the new electrode has been evaluated and compared with that of traditional carbon paste electrode (CPE). The proposed electrode provides a remarkable increase in the rate of electron transfer of biomolecules such as nicotinamide adenine dinucleotide (NADH), cysteine, ascorbic acid and catechol and shows a low surface fouling effects. The electrode shows highly promising results when used as an amperometic sensor for biocompounds such as NADH.     

First isolation of a flavonoid from Juniperus procera using ethyl acetate extract

Phytochemical investigation of the ethyl acetate extract of the leaves of Juniperus procera growing in south Saudi Arabia Enemas region led to the isolation of a new flavonoid using different chromatographic methods (i.e. paper, thin layer and column chromatography). The isolated flavonoid was identified and established by m.p., ¹H-NMR, ¹³C-NMR, UV and MS spectral analysis. The isolated compound was identified as 3′,4′,3,7-tetrahydroxyflavone.     

Electrochemical hydrogen storage properties of melt-spun Ti0.9Zr0.1V0.2Ni1.5La0.5 alloy

The Ti_0.9Zr_0.1V_0.2Ni_1.5La_0.5 alloy samples were synthesized by melt-spinning technique at the different wheel velocity (cooling rate), and the structure and electrochemical hydrogen storage properties were investigated. The result indicated that the structure of the melt-spun ribbons mainly contains C14 Laves phase and V-based solid solution phase. The discharge capacity, cyclic stability, high-rate discharge ability and electrochemical kinetic of the alloy electrodes are correlated with the cooling rate (wheel velocity), and the maximum discharge capacity is over 200 mA·h/g at the wheel velocity of 20 m/s.     

Investigation of the voltage and time effects on the formation of hydroxyapatite-containing titania prepared by plasma electrolytic oxidation on Ti-6Al-4V alloy and its corrosion behavior

Producing titania and hydroxyapatite (HA) bioceramic coating on titanium alloys increases corrosion resistance and biocompatibility of these alloys. Plasma electrolytic oxidation (PEO) is one of the effective techniques for producing this type of coating. This method produces coatings with enough thickness and appropriate adhesion. In this study, titania and HA were directly produced on Ti-6Al-4V by applying PEO process in a Ca- and P-containing electrolyte by changing voltage and time parameters. Morphology and cross section, chemical composition and elements of coatings were investigated by scanning electron microscope, X-ray diffraction and energy dispersive spectroscopy, respectively. Corrosion behavior of the samples was also examined by potentiodynamic polarization and electrochemical impedance spectroscopy. The results indicated that the formation of HA phase with titania needs a minimum voltage below which HA is not formed. By increasing the operation time, the amount of the formed HA increased. Also, the sample coated at 500 V and 15 min showed the best corrosion behavior in Ringer's solution.