On heat conductors with a stationary hot spot

We consider a heat conductor having initial constant temperature and zero boundary temperature at every time.The hot spot is the point at which temperature attains its maximum at each given time. For convex conductors, if the hot spot does not move in time, we prove symmetry results for planar triangular and quadrangular conductors.Then, we examine the case of a general conductor and, by an asymptotic formula, we prove that, if there is a stationary critical point, not necessarily the hot spot, then the conductor must satisfy a geometric condition. In particular, we show that there is no stationary critical point inside planar non-convex quadrangular conductors. Mathematics Subject Classification (2000) Primary 35K05, 35K20, 35J05; Secondary 35J25, 35B38, 35B40     

Korn’s Inequalities for Junctions of Elastic Bodies with Thin Plates

We prove the anisotropic Korn inequalities for an elastic junction of a massive body with thin plates clamped along parts of the lateral surfaces. The distribution of the weight factors in the norms under consideration depends essentially on the disposition of the plates, the way they are clamped to the body, and their relative rigidity (as compared with the body).Original Russian Text Copyright © 2005 Nazarov S. A.The author was supported by the Russian Foundation for Basic Research (Grant 03-01-00835).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 876–889, July–August, 2005.     

Central limit theorems for random polytopes

Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is to determine the precise asymptotic order of the occurring variances. Research was supported in part by the European Network PHD, MCRN-511953.     

Post-Newtonian perturbed theory of elastic astronomical bodies in rotating spherical coordinates

In this paper the dynamical equations for an elastic deformable body in the first post-Newtonian approximation of Einstein theory of gravity are derived in rotating spherical coordinates. The unperturbed rotating body (the relaxed ground state) is described as uniformly rotating, stationary and axisymmetric configuration in an asymptotically flat space-time manifold. Deviations from the equilibrium configuration are described by means of a displacement field. By making use of the schemes developed by Damour, Soffel and Xu, and by Carter and Quintana we calculate the post-Newtonian Lagrangian strain tensor and symmetric trace-free shear tensor. Considering the Euler variations of Einstein's energy-momentum conservation law, we derive the post- Newtonian energy equation and Euler equations of elastic deformable bodies in rotating spherical coordinates.     

CLT and the Volume of Intersections of ℓp n-Balls

An asymptotic formula for the volume of the intersection of multiples of the unit balls of _p ⁿ and _q ⁿ is proved.     

Helly-Type Theorems on Common Supporting Lines for Nonoverlapping Families of Convex Bodies in the Plane

Helly-type results are established relating to the existence of a line supporting a family of nonoverlapping convex bodies in the plane.     

High-level expression of acidic partner-mediated antimicrobial peptide from tandem genes inEscherichia coli

A novel strategy for constructing multiple joined genes of acidic partner-mediated antimicrobial peptide is described. This strategy allows the expression of antimicrobial peptide byEscherichia coli in a stable form and with high yield. Cecropin A (1–8)-melittin (1–10) (CAME) hybrid peptide was selected as a model of antimicrobial peptide. An acidic fragment from magainin intervening sequence was fused to the antimicrobial peptide as a partner to neutralize the lethal effects on the host cells. Multiple copies of the fusion peptide gene were tandemly linked and cloned into the expression vector pET21a. Multimers were expressed at high levels, reaching up to 36% of total cell proteins, and expression levels were proportional to the degree of multimerization. The fusion proteins were mainly expressed as inclusion bodies, probably owing to cysteine residues in the multimers. The target CAME peptide was obtained by cleaving the multimers with cyanogen bromide and purified by cation-exchange chromatography. Recombinant CAME peptide showed strong antimicrobial activities against both Gram-negative and -positive bacteria. These results might provide an efficient solution for high-level expression of various kinds of antimicrobial peptides that are toxic to the host.     

一个与投影体相关的锥体积不等式

本文研究了一个与投影体相关的锥体积不等式.利用凸函数的梯度性质,获得了n维欧氏空间中关于任意原点对称凸体的一个锥体积不等式,推进了Schneider投影问题的解决.     

Studies on the Structure and Properties of Membrane Phospholipase A1 Inclusion Bodies Formed at Low Growth Temperatures Using GFP Fusion Strategy

The effect of cultivation temperatures (37, 26, and 18 °C) on the conformational quality of Yersinia pseudotuberculosis phospholipase A₁ (PldA) in inclusion bodies (IBs) was studied using green fluorescent protein (GFP) as a folding reporter. GFP was fused to the C-terminus of PldA to form the PldA-GFP chimeric protein. It was found that the maximum level of fluorescence and expression of the chimeric protein is observed in cells grown at 18 °C, while at 37 °C no formation of fluorescently active forms of PldA-GFP occurs. The size, stability in denaturant solutions, and enzymatic and biological activity of PldA-GFP IBs expressed at 18 °C, as well as the secondary structure and arrangement of protein molecules inside the IBs, were studied. Solubilization of the chimeric protein from IBs in urea and SDS is accompanied by its denaturation. The obtained data show the structural heterogeneity of PldA-GFP IBs. It can be assumed that compactly packed, properly folded, proteolytic resistant, and structurally less organized, susceptible to proteolysis polypeptides can coexist in PldA-GFP IBs. The use of GFP as a fusion partner improves the conformational quality of PldA, but negatively affects its enzymatic activity. The PldA-GFP IBs are not toxic to eukaryotic cells and have the property to penetrate neuroblastoma cells. Data presented in the work show that the GFP-marker can be useful not only as target protein folding indicator, but also as a tool for studying the molecular organization of IBs, their morphology, and localization in E. coli, as well as for visualization of IBs interactions with eukaryotic cells.     

Numerical modeling of flow past a volumeless and thin rigid body using direct forcing immersed boundary method

The new capability has been added as the numerical method for modeling volumeless and thin rigid bodies to the direct forcing immersed boundary (DFIB) method. The DFIB approach is based on adding a virtual force to the Navier–Stokes equations of incompressible flow to account for the interaction between the fluid and structures. The volume of a solid function (VOS) identifies the stationary or moving solid structures in a given fluid domain. A new VOS-based algorithm was developed to identify thin, rigid structure boundary points in fluid flow and ensure that the fluid cannot cross through the boundary of a thin rigid structure while moving or stationary. The DFIB method was first validated in a three-dimensional (3D) turbulent flow over a circular cylinder. The large-eddy simulation simulated the turbulent flow scales. The proposed algorithm was tested using a 3D turbulent flow past a stationary and rotating Savonius wind turbine that functions as a thin, rigid body. The validation results showed that the selected DFIB approach, combined with the novel algorithm, could simulate a thin, volumeless, rigid structure that is stationary and rotating in incompressible turbulent flows. The current method is also applicable for two-way fluid-structure interaction problems.