Positive and Nontrivial Solutions for the Urysohn Integral Equation

We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.     

Effect of the paste molding pressure on the mechanical strength of an iron oxide catalyst in the dehydrogenation of methylbutenes

The effect of the paste molding pressure on the physicomechanical and texture characteristics of catalysts was studied. An indirect criterion is suggested to evaluate the molding pressure in industrial extruders, whose optimal value ensures good physicomechanical properties of the catalysts and kinetic control over the catalyzed reaction. The results obtained were verified in paste molding on various industrial extruders, and this enabled the optimal choice of the molding equipment.     

Joint detection of a given number of reference fragments in a quasi-periodic sequence and its partition into segments containing series of identical fragments

The problem of joint a posteriori detection of reference fragments in a quasi-periodic sequence and its partition into segments containing series of recurring fragments from the reference tuple is solved. It is assumed that (i) an ordered reference tuple of sequences to be detected is given, (ii) the number of desired fragments is known, (iii) the index of the sequence term corresponding to the beginning of a fragment is a deterministic (not random) value, and (iv) a sequence distorted by an additive uncorrelated Gaussian noise is available for observation. It is established that the problem consists in testing a set of hypotheses about the mean of a random Gaussian vector. The cardinality of the set grows exponentially as the vector dimension (i.e., the sequence length) increases. An efficient a posteriori algorithm producing a maximum-likelihood optimal solution to the problem is substantiated. Time and space complexity bounds related to the parameters of the problem are derived. The results of numerical simulation are presented.     

Structural phase transformations and physical properties of intercalation compounds in the Cr0.5Ti(Se1−x Tex)2 system

The atomic structure and magnetic and electric properties of the Cr_0.5TiSe₂-Cr_0.5TiTe₂ system of intercalated phases were studied in detail by gradually replacing selenium by tellurium. It was revealed that this replacement changes the crystalline structure from monoclinic in the initial compounds to hexagonal in the compounds containing various types of chalcogen atoms; this is accompanied by disordering of chromium atoms in the van der Waals gaps. The electrical resistance and magnetic characteristics vary nonmonotonically on replacement of selenium by tellurium, which is associated with a change in the degree of atomic disordering during the transition from Cr_0.5TiSe₂ to Cr_0.5TiTe₂.     

Conformational characteristics of polycaproamide in dimethylacetamide containing lithium chloride

The viscosity behavior, index of refraction, and density of dilute polycaproamide solutions in DMAc containing lithium chloride have been studied. On the basis of temperature dependences of the index of refraction and the density of solutions, the θ-condition of polycaproamide solutions in DMAc containing 2.5% lithium chloride is estimated as 21.3°C. From intrinsic viscosity [η] measurements, the coefficients of swelling of a polymer coil, the mean-square distance between chain ends, and other parameters of macromolecules in solution are calculated.     

Recovered-voltage phenomenon and prospects for its use for assessment of the condition of polymers

A general theory of the phenomenon of recovered voltage in polymers was considered on the basis of representation of an actual poling process by a discrete set of Debye relaxators. Examples of numerical solution of the direct and inverse problems are given. A correlation expression between intentionally aged polymer specimens and recovered-voltage curves was proposed for use in the assessment of the material state of a polymer under actual service conditions. It was shown that it is sufficient to restrict consideration to three relaxation processes in analysis of the phenomenon.     

Laser-induced breakdown threshold and fracture versus the nanostructure of two-phase glass

The radiation hardness and mechanical strength of single-and two-phase glasses are studied for the case when nanosecond laser pulses (λ= 1.06 μm, τ_0.5 ≈ 12.5 ns) are focused inside the material. Laser interferometry is applied to measure the displacement of the free surface, find optical breakage thresholds, and carry out the fractographic analysis of damaged regions. It is shown that breakdown channels and damage regions develop in a nonlinear manner according to optical breakdown mechanisms, changing each other with an increase in the laser energy. The strength of the two-phase glass is found to be more than four times that of the single-phase glass, although their elastic properties differ insignificantly. Such a considerable difference in the hardness of these materials with chemically similar constitutents is attributed to the presence of the double-lattice nanometer-scale structure of the two-phase glass.     

Variation of supramolecular structure of heat-resistant polyimide films during thermal treatment

Variation of the supramolecular structure of heat-resistant polymide films in the course of high-temperature treatment was studied by X-ray diffraction analysis and NMR spectroscopy in solids.     

Chemisorption of vapors of organic substances on a modified silica gel

Experimental data on the equilibrium and dynamics of chemisorption of vapors of organic substances on a silica gel modified with color reagents are presented.     

Reaction of furan-2(3H)-ones with 1,2-binucleophiles

Reactions of 5-substituted furan-2(3H)-ones with ethylenediamine, 2-aminoethanol, and o-aminophenol do not stop at the stage of formation of the corresponding 4-oxoalkanoic acid amides but lead to new bi-and tricyclic structures as a result of double intramolecular cyclodehydration.