Separation of variables in anisotropic models and non-skew-symmetric elliptic <Emphasis Type="Italic">r</Emphasis>-matrix

We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic \(so(3)\otimes so(3)\)-valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the “separating functions” B(u) and A(u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Euler’s top, Steklov–Lyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and “spin” generalization of Steklov–Lyapunov model.     

Classifying homeomorphism groups of infinite graphs

In this paper, we classify topologically the homeomorphism groups H(Γ) of infinite graphs Γ with respect to the compact-open and the Whitney topologies.     

On functors preserving skeletal maps and skeletally generated compacta

A map $f:X\to Y$ between topological spaces is skeletal if the preimage $f^{?1}(A)$ of each nowhere dense subset $A?Y$ is nowhere dense in X. We prove that a normal functor $F:\mathbf{Comp}\to \mathbf{Comp}$ is skeletal (which means that F preserves skeletal epimorphisms) if and only if for any open surjective map $f:X\to Y$ between metrizable zero-dimensional compacta with two-element non-degeneracy set $N^f=\{x\in X:|f^{?1}(f(x))|>1\}$ the map $Ff:FX\to FY$ is skeletal. This characterization implies that each open normal functor is skeletal. The converse is not true even for normal functors of finite degree. The other main result of the paper says that each normal functor $F:\mathbf{Comp}\to \mathbf{Comp}$ preserves the class of skeletally generated compacta. This contrasts with the known ??epin?s result saying that a normal functor is open if and only if it preserves the class of openly generated compacta.     

Low-power,phase-preserving 2R amplitude regenerator

We propose a modification of a NALM-based 2R regenerator of phase-encoded signals which operates at considerably lower input powers than was studied earlier. Our modification consists of replacing the core-matched and lossless fiber coupler in the NALM by a coupler with a propagation constant mismatch and loss asymmetrically distributed between the two cores. The performance of the modified regenerator and the one studied earlier is approximately the same.     

Heterogeneous oligomerization catalysts: properties and efficiency

A number of heterogeneous acid type catalysts of silica-alumina nature, which are proposed to be used for petrochemistry by-product oligomerization, have been investigated. Particularly, such key indicators as active site concentration and strength have been determined. These parameters have been determined by the method based on potentiometric titration that is relatively seldom used in heterogeneous catalysis. The number of active site types present in investigated catalysts, as well as concentrations of each type of site, has been determined by mathematical processing of potentiometric titration data. The sequence of mathematical processing of titration data is described. The relationship between the properties of the investigated catalysts and their effectiveness in heterogeneous catalytic cooligomerization of the C₉ fraction of liquid products of diesel fuel pyrolysis has been analyzed. The relationships between yields achieved in the presence of various catalysts and the properties of these catalysts have been defined. Namely, it was determined that the product yield is almost proportional to the active site??s concentration of the catalysts (activated clay materials). The relationship between the strength of active sites and average molecular weight of the cooligomers has been found. The causes of obtained regularities have been analyzed and explained.      

Nanostructured diamine-fullerene derivatives: computational density functional theory study and experimental evidence for their formation via gas-phase functionalization

Nanostructure derivatives of fullerene C(60) are used in emerging applications of composite matrices, including protective and decorative coating, superadsorbent material, thin films, and lightweight high-strength fiber-reinforced materials, etc. In this study, quantum chemical calculations and experimental studies were performed to analyze the derivatives of diamine-fullerene prepared by the gas-phase solvent-free functionalization technique. In particular, the aliphatic 1,8-diamino-octane and the aromatic 1,5-diaminonaphthalene, which are diamines volatile in vacuum, were studied. We addressed two alternative mechanisms of the amination reaction via polyaddition and cross-linking of C(60) with diamines, using the pure GGA BLYP, PW91, and PBE functionals; further validation calculations were performed using the semiempirical dispersion GGA B97-D functional which contains parameters that have been specially adjusted by a more realistic view on dispersion contributions. In addition, we looked for experimental evidence for the covalent functionalization by using laser desorption/ionization time-of-flight mass spectrometry, thermogravimetric analysis, and atomic force microscopy.     

Enrichment of low-abundant serum proteins by albumin/immunoglobulin G immunoaffinity depletion under partly denaturing conditions

We present a simple protocol for affinity depletion to remove the two most abundant serum proteins, albumin and immunoglobulin G (IgG). Under native conditions, albumin/IgG were efficiently removed and several proteins were enriched as shown by two-dimensional electrophoresis (2-DE). Besides that, partly denaturing conditions were established by adding 5 or 20% acetonitrile (ACN) in order to disrupt the binding of low-molecular-weight (LMW) proteins to the carrier proteins albumin/IgG. 2-DE results showed that the total number of detected LMW proteins increased under denaturing conditions when compared to native conditions. Interestingly, the presence of 5% ACN in serum revealed better enrichment of LMW proteins when compared to 20% ACN condition. Seven randomly distributed spots in albumin/IgG depleted serum samples under 5% ACN condition were picked from the 2-DE gels and identified by mass spectrometry (MS). The intensity of five LMW protein spots increased under denaturing conditions when compared to native conditions. Three of the seven identified spots (serum amyloid P, vitamin D-binding protein, and transthyretin) belong to a group of relatively low-abundant proteins, which make up only 1% of all serum proteins. The method presented here improves the resolution of the serum proteome by increasing the number of visualized spots on 2-D gels and allowing the detection and MS identification of LMW proteins and proteins of lower abundance.