Antiproximinal sets in spaces of continuous functions

Closed convex bounded antiproximinal bodies are constructed in the infinite-dimensional spacesC(Q), C ₀(T), L(S, S, ), andB(S), whereQ is a topological space andT is a locally compact Hausdorff space. It is shown that there are no closed bounded antiproximinal sets in Banach spaces with the Radon-Nikodym property.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 643–657, November, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00196.     

The influence of contact electrification on the adhesion of dielectric elastic spheres subjected to external loads before detachment

The influence of a static load on the adhesion of an elastic sphere to a rigid smooth surface has been investigated. The change in ratio of the electrostatic component of the adhesion force resulting from the formation of an electric double layer to the molecular one as a result of the contact pressure has been evaluated theoretically. The tearing-off force and the surface density of the charge forming in the contact between the silicone rubber sphere and a steel plate were determined simultaneously. It is shown that the observed increase in sticking force of the sphere after its compression may be explained by an increase in the electrostatic component of the adhesion force, which is proportional to the contact area.     

生物体中微量钛的测定——邻硝基苯基荧光酮直接光度法

研究了用邻硝基苯基荧光酮显色测酞时,酒石酸钾钠和氟化铵的影响。从而能直接测定生物体中微量钛。检出限为0.05μg.     

On models in the theory of stability of multiwalled carbon nanotubes in matrix

Models in the theory of stability of multiwalled carbon nanotubes in a polymer matrix are justified. Some results on the fracture mechanics of nanocomposites are presented. New areas of research in mechanics suggested by a group of well-known scientists are discussed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 3–21, June 2006.     

The extension of Beltrami's ellipsoid to anisotropic bodies

Summary The spectral decomposition of the compliance, stiffness, and failure tensors for transversely isotropic materials was studied and their characteristic values were calculated using the components of these fourth-rank tensors in a Cartesian frame defining the principal material directions. The spectrally decomposed compliance and stiffness or failure tensors for a transversely isotropic body (fiber-reinforced composite), and the eigenvalues derived from them define in a simple and efficient way the respective elastic eigenstates of the loading of the material. It has been shown that, for the general orthotropic or transversely isotropic body, these eigenstates consist of two double components, ₁ and ₂ which are shears (₂ being a simple shear and ₁, a superposition of simple and pure shears), and that they are associated with distortional components of energy. The remaining two eigenstates, with stress components ₃, and ₄, are the orthogonal supplements to the shear subspace of ₁ and ₂ and consist of an equilateral stress in the plane of isotropy, on which is superimposed a prescribed tension or compression along the symmetry axis of the material. The relationship between these superimposed loading modes is governed by another eigenquantity, the eigenangle .The spectral type of decomposition of the elastic stiffness or compliance tensors in elementary fourth-rank tensors thus serves as a means for the energy-orthogonal decomposition of the energy function. The advantage of this type of decomposition is that the elementary idempotent tensors to which the fourth-rank tensors are decomposed have the interesting property of defining energy-orthogonal stress states. That is, the stress-idempotent tensors are mutually orthogonal and at the same time collinear with their respective strain tensors, and therefore correspond to energy-orthogonal stress states, which are therefore independent of each other. Since the failure tensor is the limiting case for the respective _x, which are eigenstates of the compliance tensor S, this tensor also possesses the same remarkable property.An interesting geometric interpretation arises for the energy-orthogonal stress states if we consider the projections of _x in the principal₃D stress space. Then, the characteristic state ₂ vanishes, whereas stress states ₁, ₃ and ₄ are represented by three mutually orthogonal vectors, oriented as follows: The ₃ and ₄ lie on the principal diagonal plane (₃₁₂) with subtending angles equaling (–/2) and (-), respectively. On the positive principal ₃-axis, is the eigenangle of the orthotropic material, whereas the ₁-vector is normal to the (₃₁₂)-plane and lies on the deviatoric -plane. Vector ₂ is equal to zero.It was additionally conclusively proved that the four eigenvalues of the compliance, stiffness, and failure tensors for a transversely isotropic body, together with value of the eigenangle , constitute the five necessary and simplest parameters with which invariantly to describe either the elastic or the failure behavior of the body. The expressions for the _x-vector thus established represent an ellipsoid centered at the origin of the Cartesian frame, whose principal axes are the directions of the ₁-, ₃- and ₄-vectors. This ellipsoid is a generalization of the Beltrami ellipsoid for isotropic materials.Furthermore, in combination with extensive experimental evidence, this theory indicates that the eigenangle alone monoparametrically characterizes the degree of anisotropy for each transversely isotropic material. Thus, while the angle for isotropic materials is always equal to _i = 125.26° and constitutes a minimum, the angle || progressively increases within the interval 90–180° as the anisotropy of the material is increased. The anisotropy of the various materials, exemplified by their ratiosE _L/2G_L of the longitudinal elastic modulus to the double of the longitudinal shear modulus, increases rapidly tending asymptotically to very high values as the angle approaches its limits of 90 or 180°.     

拟L_p-混合相交体

1988年,Lutwak首次提出了相交体的概念.本文在相交体以及拟L_p-相交体的基础上,引入了拟L_p-混合相交体的概念.通过利用对偶L_p-混合均值积分理论和相关的不等式,给出了L_p型的Busemann相交不等式,建立了关于L_p径向组合和L_p-调和Blaschke组合的Brunn-Minkowski型不等式及其隔离形式,并且探讨了拟L_p-混合相交体的单调性问题.     

Jumping Platonic Solids on a Vibrating Plate

The mechanical excitation of solid bodies by a vibrating plate is not only an interesting fundamental problem, but also has relevance in many mechanical systems, for example, in the preparation of granular gases in microgravity. Herein, the energy input by an oscillating plate is numerically investigated as a function of the excitation parameters for selected Platonic solids and their behavior compared to that of a jumping sphere. The most important additional features, not relevant for spheres, are the excitation of body rotations and a permanent energy exchange between the rotational and translational degrees of freedom during the collisions with the plate. The distribution of kinetic energies is analyzed by a numerical simulation of the dynamics, using structures which emulate the mechanical behavior of regular polyhedra.