Criteria for assessing the leveling effect of agents used for batch dyeing of synthetic fibrous materials

Various methods for assessing the performance of levelers in batch dyeing of synthetic fibrous materials were analyzed. Criteria most suitable for technological and scientific applications were chosen.     

Changes in the supramolecular structure of heat-resistant polyimide fibers in the course of thermal treatment

Changes in the supramolecular structure of heat-resistant fibers based on polyimide PM were studied by X-ray diffraction analysis and NMR spectroscopy.     

Dependence of the driving current on the harmonic behavior of giant magneto-impedance voltage of Co-based amorphous wires

The frequency and the amplitude of the driving AC current dependence on the harmonic behavior of the giant magneto-impedance (GMI) voltage of Co-rich amorphous wire have been studied. Single-peak, two-peak and three-peak behavior in the GMI characteristics was studied with the change of amplitude and frequency of the AC current. GMI ratio was calculated from the first harmonic signals which were initially increased and then decreased monotonically with the increase of frequency (f) and the amplitude (I_AC) of the driving current. The response of the GMI voltage was found non-linear with the generation of higher harmonics at higher amplitude of the driving current. The second and third harmonic signals were also evaluated and their dependence on the driving current amplitude and frequency were presented in the paper. The experimental results were analyzed using single domain rotational model. The voltage harmonics were calculated through Fourier transform of the time derivative of the estimated circular magnetization of the sample.     

Atomic configurations in close-packed lennard-jones systems

Conclusions DS provide a convenient means of researching local atomic configurations in disordered systems. On the one hand, a DS is a strictly defined geometrical structure, while on the other hand the shapes of the simplexes directly reflect the atomic disposition.New characteristics T and O have been proposed for DS shape and allow one to distinguish the corresponding configurations reliably. It is evident that a close-packed system of spherical atoms contains considerable proportions of slightly distorted tetrahedral and octahedral configurations. In a disordered close packing of soft spheres, such configurations form distinct classes similar to those occurring in an FCC crystal.Institute of Chemical Kinetics and Combustion, Siberian Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 28, No. 2, pp. 62–69, March–April, 1987.     

Regularity of Bunimovich’s stadia

Stadia are popular models of chaotic billiards introduced by Bunimovich in 1974. They are analogous to dispersing billiards due to Sinai, but their fundamental technical characteristics are quite different. Recently many new results were obtained for various chaotic billiards, including sharp bounds on correlations and probabilistic limit theorems, and these results require new, more powerful technical apparatus. We present that apparatus here, in the context of stadia, and prove “regularity” properties.      

A compactification of the moduli variety of stable vector 2-bundles on a surface in the Hilbert scheme

A new compactification of the variety of moduli of stable vector 2-bundles with Chern classes c ₁ and c ₂ is constructed for the case in which the universal family of stable sheaves with given values of invariants is defined and there are no strictly semistable sheaves. The compactification is a subvariety in the Hilbert scheme of subschemes of a Grassmann manifold with fixed Hilbert polynomial; it is obtained from the variety of bundle moduli by adding points corresponding to locally free sheaves on surfaces which are modifications of the initial surface. Moreover, a morphism from the new compactification of the moduli space to its Gieseker-Maruyama compactification is constructed.     

Optimal reconstruction of the solution of the wave equation from inaccurate initial data

In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from l ₂, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors.     

On multiple integrals of special form

Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples.