Supporting and separating subsets for invex bodies

Invex bodies represent an important class of bodies which are considered as a generalization of convex bodies.In this article,the author studies the supporting for this class of bodies as well as the separating subsets of two bodies.     

Inequalities for dual quermassintegrals of mixed intersection bodies

In this paper, we first introduce a new concept ofdual quermassintegral sum function of two star bodies and establish Minkowski’s type inequality for dual quermassintegral sum of mixed intersection bodies, which is a general form of the Minkowski inequality for mixed intersection bodies. Then, we give the Aleksandrov-Fenchel inequality and the Brunn-Minkowski inequality for mixed intersection bodies and some related results. Our results present, for intersection bodies, all dual inequalities for Lutwak’s mixed prosection bodies inequalities.     

Modeling Creep and Continuous Fracture Process Zones in Spatial Prismatic Bodies

The semianalytic finite-element method is used to develop a method for solving problems of creep and continuous fracture of complex spatial bodies. The method allows modeling the variation of the stress-strain state during creep, accompanying accumulation of dispersed microdamages, and development of macroscopic effects—continuous fracture process zones. The growth of a continuous fracture process zone is modeled. A criterion is formulated for determination of the applicability limits of continuum damage mechanics. The method is exemplified by the problem of deformation and continuous fracture of a gas turbine blade __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 70–86, September 2005.     

Supramolecular Protein Assemblies in the Nucleus of Human Cells

Genetically encoded supramolecular protein assemblies (SMPAs) are induced to form in living cells by combination of distinct self‐assembly properties. A single fusion construct contains genes encoding the heavy chain (H) of human ferritin and the citrine fluorescent protein, the latter exposing a weak dimerization interface, as well as a nuclear localization signal. Upon expression in HeLa cells, in vivo confocal fluorescence and differential interference contrast imaging revealed extended SMPA structures exclusively in the nuclei. Assemblies were typically round and took alveolar, shell‐like, or hybrid structure. Transmission electron microscopy revealed a crystalline packing. Site‐specific mutagenesis of the citrine dimerization interface clarified the mechanism of SMPA formation. The constituent proteins retained their activity in iron binding and fluorescence emission, thus suggesting a general strategy for formation of synthetic cellular bodies with specific biochemical function.     

Prebiotic Potential of Oligosaccharides Obtained by Acid Hydrolysis of α-(1→3)-Glucan from Laetiporus sulphureus: A Pilot Study

Increasing knowledge of the role of the intestinal microbiome in human health and well-being has resulted in increased interest in prebiotics, mainly oligosaccharides of various origins. To date, there are no reports in the literature on the prebiotic properties of oligosaccharides produced by the hydrolysis of pure fungal α-(1→3)-glucan. The aim of this study was to prepare α-(1→3)-glucooligosaccharides (α-(1→3)-GOS) and to perform initial evaluation of their prebiotic potential. The oligosaccharides were obtained by acid hydrolysis of α-(1→3)-glucan isolated from the fruiting bodies of Laetiporus sulphureus and then, characterized by HPLC. Fermentation of α-(1→3)-GOS and reference prebiotics was compared in in vitro pure cultures of Lactobacillus, Bifidobacterium, and enteric bacterial strains. A mixture of α-(1→3)-GOS, notably with a degree of polymerization of 2 to 9, was obtained. The hydrolysate was utilized for growth by most of the Lactobacillus strains tested and showed a strong bifidogenic effect, but did not promote the growth of Escherichia coli and Enterococcus faecalis. α-(1→3)-GOS proved to be effective in the selective stimulation of beneficial bacteria and can be further tested to determine their prebiotic functionality.     

Linearization as a method for determining parameters of relaxation spectra

A new method for determining parameters of a relaxation spectrum of visco-elastic bodies is proposed. The basic idea of the method consists of presenting measured frequency dependencies of the dynamic modules components by the power series. The coefficients of these series are found by comparing varying values with experimental data by linear functional of errors. The parameters of a spectrum are then calculated from the coefficients of the series. This procedure allows us to overcome the main problem of finding relaxation times, i.e. to pass from non-linear to linear functional of errors. It gives us the unique possibility of unambiguously estimating weights (partial moduli) of lines in a discrete relaxation spectrum and relaxation times because there is only a single minimum in the functional of errors. Received: 8 December 1999/Accepted: 10 December 1999     

An explicit transient algorithm for predicting incompressible viscous flows in Arbitrary Geometry

A numerical method for predicting viscous flows in complex geometries has been presented. Integral mass and momentum conservation equations are deploved and these are discretized into algebraic form through numerical quadrature. The physical domain is divided into a number of non-orthogonal control volumes which are isoparametrically mapped on to standard rectangular cells. Numerical integration for unsteady mementum equations is performed over such non-orthogonal cells. The explicitly advanced velocity components obtained from unsteady momentum equations may not necessarily satisfy the mass conservation condition in each cell. Compliance of the mass conservation equation and the consequent evolution of correct pressure distribution are accomplished through an iterative correction of pressure and velocity till divergence-free condition is obtained in each cell. The algorithm is applied on a few test problems, namely, lid-driven square and oblique cavities, developing flow in a rectangular channel and flow over square and circular cylinders placed in rectangular channels. The results exhibit good accuracy and justify the applicability of the algorithm. This Explicit Transient Algorithm for Flows in Arbitrary Geometry is given a generic name EXTRAFLAG.     

Random Motion of a Rigid Body

We study the random motion of a rigid body through a stochastic differential equation on the special orthogonal group SO(d).     

Convective heat transfer from a rotating or nonrotating axisymmetric body

An analysis of steady laminar mixed-convection heat transfer from a rotating or nonrotating axisymmetric body is presented. A mixed-convection parameter is proposed to serve as a controlling parameter that determines the relative importance of the forced and the free convection. In addition, a rotation parameter is introduced to indicate the relative contributions of the flow forced convection and the rotational forced convection. The values of both these two parameters lie between 0 and 1. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection from the forced-convection limit (rotating or nonrotating bodies) to the pure free-convection limit (non-rotating bodies) and the entire regime of forced convection from the pure flow forced-convection limit (nonrotating bodies) to pure rotational forced-convection limit (rotating bodies). The effects of mixed-convection intensity, body rotation, fluid suction or injection, and fluid Prandtl number on the velocity profiles, the temperature profiles, the skin-friction parameter, and heat transfer parameter are clearly illustrated for both cases of buoyancy assisting and opposing flow conditions.