Conditions for Choquet integral representation of the comonotonically additive and monotone functional

If the universal set X is not compact but locally compact, a comonotonically additive and monotone functional (for short c.m.) on the class of continuous functions with compact support is not represented by one Choquet integral, but represented by the difference of two Choquet integrals. The conditions for which a c.m. functional can be represented by one Choquet integral are discussed.     

Existence of periodic solutions

An apparatus for proving existence theorems for periodic solutions of equations with discontinuous right-hand side and differential inclusions is developed. Translated fromMatematischeskie Zametki, Vol. 61, No. 5, pp. 769–784, May, 1997. Translated by V. N. Dubrovsky     

New free‐volume‐related activity model for polymer solutions

A new activity model was developed with the use of the Gibbs–Helmholtz relation at constant pressure and composition. This model consists of combinatorial and residual terms. The residual term is the same as that in the UNIQUAC method, but the total area fraction of molecules is introduced on account of the hole effect. The combinatorial part takes into account the free volume (FV) effect, which plays a significant role in polymer systems. The validity of this model is demonstrated by calculating the solvent activities in 36 polymer solutions in comparison with Entropic‐FV (EFV) and UNIFAC‐FV methods. The total average absolute deviations (AAD) from the experimental observations are 8.27, 6.38, and 1.64 for EFV, UNIFAC‐FV, and the present method, respectively. It is found that the fit to these experimental data by the present model is quite good over a wide range of concentration. An estimation of the infinite dilution activity coefficients also proves the validity of the new method. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3299–3307, 2005     

ON A PERIODIC DELAY LOGISTIC TYPE POPULATION MODEL

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｏｗｉｎｇｐｅｒｉｏｄｉｃｄｅｌａｙＬｏｇｉｓｔｉｃｔｙｐｅｐｏｐｕｌａｔｉｏｎｄＮ（ｔ）ｄｔ＝ｒ（ｔ）Ｎ（ｔ）１－ｘ（ｔ－τ（ｔ）Ｋ（ｔ）θ，（１．１）ｗｉｔｈａｎｉｎｉｔｉａｌｃｏｎｄｉｔｉｏ...     

二阶多时滞非线性微分方程的周期解

研究二阶系数非线性多时滞微分方程ω周期解的存在性，得到了ω周期解存在的充分条件。     

Gibbs measures for the SOS model with four states on a Cayley tree

We analyze the SOS (solid-on-solid) model with spins 0, 1, 2, 3 on a Cayley tree of order k ≥ 1. We consider translation-invariant and periodic splitting Gibbs measures for this model. The majority of the constructed Gibbs measures are mirror symmetric. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 1, pp. 18–31, October, 2006.     

The nature of the bufferness phenomenon in weakly dissipative systems

We propose a mechanism for accumulating attractors in finite-dimensional weakly dissipative systems. The essence of this mechanism is that if a Hamiltonian or a conservative system with one and a half or more degrees of freedom is perturbed by small additional terms ensuring that it is dissipative, then under certain conditions, the number of its attractors appearing in small neighborhoods of different elliptic equilibriums or cycles of the nonperturbed system can increase without bound as the perturbations tend to zero. We consider meaningful examples from mechanics and radio physics: models of the bouncing ball dynamics, Fermi accelerations, the linear oscillator with impacts, and the self-excited oscillator with a discrete sequence of RLC circuits in the feedback circuit. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 447–466, March, 2006.     

Activity coefficients at infinite dilution for surfactants

A new alternative is presented for activity coefficients at infinite dilution determination via surface tension data of low vapour pressure substances. It was found that experimental data for surfactants follows Volmer's surface equation of state behaviour over the diluted region until the critical micelle concentration. The key operations are: the choice of the same standard conditions for the bulk and the surface phases, the combination of Gibbs and Volmer equations and the use of the symmetric activity coefficients convention. An exact relation between the activity coefficient at infinite dilution and the reciprocal of the critical micelle mole fraction was found which allowed us the verification of the model.     

On Weyl almost periodic selections of multivalued maps

We prove that Weyl almost periodic multivalued maps R∋t→F(t)∈clU have Weyl almost periodic selections, where clU is the collection of non-empty closed sets of a complete metric space U.