半平面双材料角界面应力奇异性分布规律的探究

论文对半平面双材料角受集中力问题的界面应力场作了深入的探究,特别着重于双材料角端点附近的界面应力的奇异性分布规律.论文通过对界面应力的严格解和渐近解[16]的比较,发现在双材料角界面端点邻近,严格解和渐近解的差是一个向端点衰减的微幅震荡分布的应力.这个向端点衰减的微幅震荡应力的起始点,称为转换点.自界面端点到转换点,严...     

弹性大变形问题中的应力状态描述、奇异性问题和余能原理

对弹性大变形理论中的3方面问题进行了综述.首先,对各种应变度量的共轭应力进行综述.大变形问题引起的应力状态描述的复杂性引起了许多学者的兴趣,对这个问题的研究也促进了大变形弹性理论的发展.在各种特定问题中,人们提出了不同的应力张量来描述应力状态,如Caucby应力张量、第一类和第一二类Piola-Kirchhoff应力张...     

Stress singularity analysis of anisotropic multi-material wedges under antiplane shear deformation using the symplectic approach

Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities. However, anisotropic material problem under polar coordinate system is still a bottleneck. This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation. Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually. In this way, approximate solutions of the stress and displacement can be obtained. Numerical examples show that the present method is very accurate and efficient for such wedge problems. Besides, this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material.     

Convergence of Calabi–Yau manifolds

In this paper, we study the convergence of Calabi–Yau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of Calabi–Yau manifolds.     

Gorenstein正则环、奇点范畴和Ding模

本文证明了任意环的整体Ding投射维数和整体Ding内射维数一致,研究了奇点范畴和相对于Ding模的稳定范畴间的关系,并刻画了Gorenstein (正则)环以及环的整体维数的有限性.     

Optimal estimates of the field enhancement in presence of a bow-tie structure of perfectly conducting inclusions in two dimensions

This paper deals with the field enhancement due to insertion of a bow-tie structure of perfectly conducting inclusions into the two-dimensional space with a given field. The field enhancement is represented by the gradient blow-up of a solution to the conductivity problem. The bow-tie structure consists of two disjoint bounded domains which have corners with possibly different aperture angles. The domains are parts of cones near the vertices which are nearly touching to each other. We construct functions explicitly which characterize the field enhancement. As consequences, we derive optimal estimates of the gradient in terms of the distance between two inclusions and aperture angles of the corners. The estimates show in quantitatively precise way that the field is enhanced beyond the corner singularities due to the interaction between two inclusions, and the blow-up rate is much higher than the one for the case of inclusions with smooth boundaries.     

Fractional Hardy–Hénon equations on exterior domains

In this paper, we consider the fractional Hardy–Hénon equations with an isolated singularity. If the isolated singularity is located at the origin, we give a classification of solutions to this equation. If the isolated singularity is located at infinity, in the case of exterior domains, we provide decay estimates of solutions and their gradients at infinity. Our results are an extension of the classical work by Caffarelli, Gidas et al.     

Activity of Compounds from Temperate Propolis against Trypanosoma brucei and Leishmania mexicana

Ethanolic extracts of samples of temperate zone propolis, four from the UK and one from Poland, were tested against three Trypanosoma brucei strains and displayed EC₅₀ values < 20 µg/mL. The extracts were fractionated, from which 12 compounds and one two-component mixture were isolated, and characterized by NMR and high-resolution mass spectrometry, as 3-acetoxypinobanksin, tectochrysin, kaempferol, pinocembrin, 4′-methoxykaempferol, galangin, chrysin, apigenin, pinostrobin, cinnamic acid, coumaric acid, cinnamyl ester/coumaric acid benzyl ester (mixture), 4′,7-dimethoxykaempferol, and naringenin 4′,7-dimethyl ether. The isolated compounds were tested against drug-sensitive and drug-resistant strains of T. brucei and Leishmania mexicana, with the highest activities ≤ 15 µM. The most active compounds against T. brucei were naringenin 4′,7 dimethyl ether and 4′methoxy kaempferol with activity of 15–20 µM against the three T. brucei strains. The most active compounds against L. mexicana were 4′,7-dimethoxykaempferol and the coumaric acid ester mixture, with EC₅₀ values of 12.9 ± 3.7 µM and 13.1 ± 1.0 µM. No loss of activity was found with the diamidine- and arsenical-resistant or phenanthridine-resistant T. brucei strains, or the miltefosine-resistant L. mexicana strain; no clear structure activity relationship was observed for the isolated compounds. Temperate propolis yields multiple compounds with anti-kinetoplastid activity.     

A construction of singular overlapping asymmetric self-similar measures

Summary In [8] we found a class of overlapping asymmetric self-similar measures on the real line, which are generically absolutely continuous with respect to the Lebesgue measure. Here we construct exceptional measures in this class being singular.