Theory of the spontaneous polarization of the adsorbed monolayer of polar molecules. The collective variables method

The theory of the spontaneous polarization of the adsorbed monolayer of polar molecules is developed using the collective variables method. The total potential of the system is represented as the sum of the one-body and two-body interaction potentials. The one-body potential depends on the orientation of the molecular dipoles in the external electric field and on the interactions between the molecules and the substrate. The two-body potential consists of the sum of intermolecular potentials which can be separated into the short-range part describing the orientation-independent interaction at distances, and the long-range part dependent on both the coordinates and the orientations of the interacting species. The variation of the configurational Helmholtz free energy of the system related to the long-range orientational interactions is shown to consist of three terms describing different modes of interactions of density fluctuations: (a) neglect of particle's density fluctuation or self-consistent mean field approximation (SCMF), (b) harmonic oscillations of the particle's density-the random phases approximation (RPA), and (c) various unharmonic interactions of the fluctuation waves. In the SCMF approximation using the assumption of the multiplicative separation of the high-order distribution function the singlet distribution function is calculated and the polarization vector of the adsorbed monolayer is determined. The corrections to the singlet distribution function arising from the terms (b) and (c) of the free energy are calculated. It is shown that the spontaneous polarization of the adsorbed monolayer of polar molecules may be regarded as the first-order phase transition.     

Minimalities and Modules over Dedekind-Like Rings

We are interested in (right) modules M satisfying the following weak divisibility condition: If R is the underlying ring, then for every r ∈ R either Mr = 0 or Mr = M. Over a commutative ring, this is equivalent to say that M is connected with regular generics. Over arbitrary rings, modules which are “minimal” in several model theoretic senses satisfy this condition. In this article, we investigate modules with this weak divisibility property over Dedekind-like rings and over other related classes of rings.     

Total Synthesis of Mycinamicin IV as Integral Part of a Collective Approach to Macrolide Antibiotics

The total synthesis of the 16-membered macrolide mycinamicin IV is outlined, which complements our previously disclosed, largely catalysis-based route to the aglycone. This work must also be seen in the context of our recent conquest of aldgamycin N, a related antibiotic featuring a similar core but a distinctly different functionalization pattern. Taken together, these projects prove that the underlying blueprint is integrative and hence qualifies for a collective approach to this prominent class of natural products. In both cases, the final glycosylation phase mandated close attention and was accomplished only after robust de novo syntheses of the (di)deoxy sugars of the desosamine, chalcose, mycinose and aldgarose types had been established. Systematic screening of the glycosidation promoter was also critically important for success.     

Computational Hardness of Collective Coin-Tossing Protocols

Ben-Or and Linial, in a seminal work, introduced the full information model to study collective coin-tossing protocols. Collective coin-tossing is an elegant functionality providing uncluttered access to the primary bottlenecks to achieve security in a specific adversarial model. Additionally, the research outcomes for this versatile functionality has direct consequences on diverse topics in mathematics and computer science. This survey summarizes the current state-of-the-art of coin-tossing protocols in the full information model and recent advances in this field. In particular, it elaborates on a new proof technique that identifies the minimum insecurity incurred by any coin-tossing protocol and, simultaneously, constructs the coin-tossing protocol achieving that insecurity bound. The combinatorial perspective into this new proof-technique yields new coin-tossing protocols that are more secure than well-known existing coin-tossing protocols, leading to new isoperimetric inequalities over product spaces. Furthermore, this proof-technique’s algebraic reimagination resolves several long-standing fundamental hardness-of-computation problems in cryptography. This survey presents one representative application of each of these two perspectives.     

Asymptotic behavior of solutions to a class of nonlocal non‐autonomous diffusion equations

In this paper, we consider the nonlocal non‐autonomous evolution problems where Ω is a bounded smooth domain in , N≥1, β is a positive constant, the coefficient a is a continuous bounded function on , and K is an integral operator with symmetric kernel , being J a non‐negative function continuously differentiable on and . We prove the existence of global pullback attractor, and we exhibit a functional to evolution process generated by this problem that decreases along of solutions. Assuming the parameter β is small enough, we show that the origin is locally pullback asymptotically stable. Copyright © 2014 John Wiley & Sons, Ltd.     

一类非自治Brinkman-Forchheimer系统的拉回$\mathcal{D}$-吸引子

The asymptotic behavior of solutions of the three-dimensional nonautonomous Brinkman-Forchheimer equation is investigated. And the existence of pullback global attractors in L2 (Ω) and H01(Ω) is proved, respectively.     

Pullback attractors for non-autonomous porous elastic system with nonlinear damping and sources terms

In this paper, we study the asymptotic behavior of a non-autonomous porous elastic systems with nonlinear damping and sources terms. By employing nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions. We also prove the existence of minimal pullback attractors with respect to a universe of tempered sets defined by the sources terms. Finally, we prove the upper-semicontinuity of pullback attractors with respect to non-autonomous perturbations.     

Pullback attractors and invariant measures for the discrete Zakharov equations

This article studies the probability distributions of solutions in the phase space for the discrete Zakharov equations. The authors first prove that the generated process of the solutions operators possesses a pullback-${\mathcal D}$ attractor, and then they establish that there exists a unique family of invariant Borel probability measures supported by the pullback attractor.