Infinite-dimensional diffusions as limits of random walks on partitions

Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n → ∞, a family of infinite-dimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the so-called z-measures, appeared earlier in the problem of harmonic analysis for the infinite symmetric group. The generators of the processes are explicitly described.     

Application of hysteresis functions in vibration problems

In the paper, the notion of the hysteresis function introduced by the author is developed further and applied in some vibration problems for hysteretic materials. The stress–strain relation is built on the basis of well-known extended Masing's rules in which the scaled backbone curve used in the second rule is replaced by a more general function called the hysteresis function. This modification allows us to regulate the dependence of the damping ratio on the strain amplitude in the process of cycle deforming of a material with further extending to arbitrary deformation processes. The three cases of hysteretic systems are considered: the system with limited stress when strain increases without bound, the system with linear backbone curve, and the system with the backbone curve having increasing stiffness for increasing strain. For a number of dynamic examples, a comparison of different hysteresis functions is carried out.     

Effect of aromatic substitution on phase behavior of blends of halogenated polystyrene and conventional polystyrene

Miscibility phase behavior in blends of poly(bromostyrene) with polystyrene (PS) has been investigated by means of time‐resolved light scattering, optical microscopy, and DSC. Cloud point phase diagrams of blends of conventional PS with poly‐(2‐bromostyrene) (P2BrS), poly‐(3‐bromostyrene), and poly‐(4‐bromostyrene) of comparable molecular weights were established by light scattering. Of particular interest is the fact that ortho, meta, and para substitutions in the styrenic aromatic rings of poly(bromostyrene) show profound effects on the composition–temperature phase diagrams of their blends with PS, exhibiting a lower critical‐solution temperature (LCST), an upper critical solution temperature (UCST), and combined LCST/UCST diagrams, respectively. Poly‐(2‐chlorostyrene) exhibits an LCST behavior very close to that of the P2BrS blend, suggesting that these types of halogen atoms may be inconsequential to phase behavior. A similar study has been extended to a PS blend containing commercial brominated PS (66 mol % bromine substitution) to determine what location of bromine substitution is crucial for miscibility enhancement in the flame‐retardant brominated PS blends. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1605–1615, 2001     

General procedure for the synthesis of ortho-vinylbenzyl-substituted amines, ethers, and sulfides

A convenient procedure has been proposed for the synthesis ortho-vinylbenzyl-substituted ethers, amines, and sulfides via reaction of o-(2-bromoethyl)benzyl bromide with various nucleophiles.     

A critical analysis of the effect of crosslinking on the linear viscoelastic behavior of styrene–butadiene rubber and other elastomers

The linear viscoelastic behavior in dynamic shear and tensile creep at temperatures from −30 to 70 °C is measured for an styrene–butadiene rubber (SBR) elastomer cured with dicumyl peroxide to crosslinking densities between 0 and 23.5 × 10⁻⁵ mol/cm³. The G′, G″, and tan δ isotherms are analyzed by time–temperature superposition (TTS), where the tan δ master curves are consistent with those of Mancke and Ferry. However, to achieve the TTS in the lightly crosslinked SBR systems, an anomalous vertical shift is required in the narrow temperature region from 10 to 30 °C. The vertical shift factor in this temperature region is not the standard from rubber elasticity. No anomalous behavior is detected in the equilibrium modulus, which is a linear function of temperature in accordance with the classical theory of rubber elasticity. In contrast to SBR, standard vertical shifts are required to effect TTS for uncrosslinked polybutadiene and an ethylene propylene diene monomer elastomer. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Topologically Complete Representations of Inverse Semigroups

A representation of an inverse semigroup by means of partial open homeomorphisms of a topological T ₀ -space is called topologically complete if the domains of these partial homeomorphisms form a base of the topology. It is shown how to construct topologically complete representations on the base of a ternary relation satisfying some elementary axioms. This result makes it possible to obtain a pseudo-elementary axiomatization for inverse semigroups that have faithful topologically complete representations in T ₁ ,T ₂ and T ₃ -spaces. A topology is introduced on any antigroup; this topology is a concomitant of the algebraic structure and every topologically complete representation is continuous with respect to this topology.