Automorphisms of flag systems

We first discuss the problems in the theory of ordinary differential equations that gave rise to the concept of a flag system and illustrate these with the Cartan criterion for Monge equations (1st order) as well as the Cartan statement concerning the local equivalence of Monge–Ampère type equations (2nd order). Next, we describe a prolongation functor operating on the infinitesimal symmetries (automorphisms) of the Darboux flag and extending these, isomorphically, to all the symmetries of any other flag. Hence, flag systems cannot be distinguished by their symmetry algebras and the local classification of these objects is approached by considering higher order isotropies of these algebras as well as the groupoids of k-th order formal equivalences since the differential equations defining the latter provide precious information for the application of flag systems to differential equations (e.g., Cartan's criterion for non-linear Monge equations). In examining the behavior of the isotropy algebras, that can either diminish or remain the same, when passing from a derived system $S_{\nu }$ to the consecutive system $S_{\nu +1}$, we obtain a full set of numerical invariants for the elementary flag systems that moreover specifies the local models.     

Next-generation NATO reference mobility model complex terramechanics – Part 2: Requirements and prototype

In part 2 of this paper, the Complex Terramechanics (CT) software tools requirements recommended by the NATO research task group RTG-248 are presented along with example simulations from a CT prototype software tool which attempts to satisfy the requirements.     

Computer-aided design of formulated products

Formulated products represent a particular class of complex chemical products, and their design is typically based on experience and extensive experimentation. Although still at an early stage, and despite that their potential is not fully accessed and not fully used by the industry, computer-aided design (CAD) methods and tools offer many possibilities in the design of formulated products. The CAD methodology based on computerized models enables the formulation chemists to speed up the design process, without completely replacing experiments.In this work, we summarize previous studies in the field and present important elements of the CAD framework, emphasizing estimation methods for key target properties, link to specifications, and finally, some case studies will illustrate how the CAD framework can be used in practice for formulated products.     

A New Thiolate-Bound Dimanganese Cluster as a Structural and Functional Model for Class Ib Ribonucleotide Reductases

In class Ib ribonucleotide reductases (RNRs) a dimanganese(II) cluster activates superoxide (O₂⋅⁻) rather than dioxygen (O₂), to access a high valent Mn^III−O₂−Mn^IV species, responsible for the oxidation of tyrosine to tyrosyl radical. In a biomimetic approach, we report the synthesis of a thiolate-bound dimanganese complex [Mn^II₂(BPMT)(OAc)₂](ClO)₄ (BPMT=(2,6-bis{[bis(2-pyridylmethyl)amino]methyl}-4-methylthiophenolate) ( 1 ) and its reaction with O₂⋅⁻ to form a [(BPMT)MnO₂Mn]²⁺ complex 2 . Resonance Raman investigation revealed the presence of an O−O bond in 2 , while EPR analysis displayed a 16-line S_t=1/2 signal at g=2 typically associated with a Mn^IIIMn^IV core, as detected in class Ib RNRs. Unlike all other previously reported Mn−O₂−Mn complexes, generated by O₂⋅⁻ activation at Mn₂ centers, 2 proved to be a capable electrophilic oxidant in aldehyde deformylation and phenol oxidation reactions, rendering it one of the best structural and functional models for class Ib RNRs.     

Multiple Statistical models for simulation and prediction of nonlinear processes

The paper describes a parameterisation procedure for multiple nonlinear equations with intercepts. These equations may consist of numerous members with few practical limitations on their structure. Examples are given on the application of the procedure to simulation in the areas of chemical technology and hydrology. Advantages of the proposed method are simplicity of the fitting procedure, high accuracy of simulations and more reliable simulations beyond the calibration range     

Models of expansions of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb N}$\end{document} with no end extensions

We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of ${\mathbb N}$ such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of ${\mathbb N}$ such that expanding ${\mathbb N}$ by any uncountably many of them suffice. Also we find arithmetically closed ${\mathcal A}$ with no ultrafilter on it with suitable definability demand (related to being Ramsey). © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

MICROEMULSION SYSTEMS WITH A NONIONIC COSURFACTANT

The conditions to obtain W/0 microemulsions using ionic surfactants and a nonionic cosurfactant, a polyoxyethylene alkyl ether, were investigated. The length of the polyoxyethylene chain was critical to obtain the typical water solubilization maximum

The variation of the W/0 microemulsion region with hydrocarbon content was different from that of the usual type of microemulsions having a medium chain length alcohol as cosurfactant. In the present systems the W/0 microemulsion region was not a direct continuation of the inverse micellar area at zero content of hydrocarbon. Addition of hydrocarbon was necessary for the formation of inverse micelles

The microemulsion regions were sensitive to the kind of hydrocarbon used; a sign of the importance of the nonionic surfactant for the stability of this kind of microemulsions.     

THE ADSORPTION OF AN ANIONIC SURFACTANT AT THE OIL WATER INTERFACE DURING EMULSION HOMOGENIZATION

Adsorption of sodium dodecylbenzene sulfonate (NaDBS) on the surfaces of dispersed oil globules during homogenization of paraffin oil in water emulsions has been studied. NaDBS concentration was changed over a wide interval comprising critical micelle concentration. For the emulsions homogenized for different time intervals the total quantity and the percentage of NaDBS adsorbed, the amount and number of NaDBS molecules adsorbed per unit inter-facial area, as well as the specific surface area of dispersed phase and the area per emulsifier molecule have been determined.

The amount adsorbed and density of the emulsifier layer, I.e., the area per NaDBS molecule adsorbed on the oil globule surfaces, depend not only on Initial NaDBS concentration but also, on the homogenization time and the homogenization action. This makes a difference between the adsorption behaviour under the conditions of emulsion formation and its subsequent homogenization, and the adsorption behaviour of the emulsifier at a plane quiescent Interface.     

Dynamics of surface reactions: from “hot” precursors to conventional thermal activation

Heterogeneous catalytic reactions usually contain steps, e.g., adsorption, generating energy-rich (“hot”) precursors for other steps. With increasing the rate of energy relaxation one can observe a transition from the reaction regime dominated by “hot” precursors to conventional thermal activation. To illustrate this transition in detail and to show what may happen in various situations, I present an analytical model based on the Fokker-Planck equation for energy relaxation.     

上海证券市场回报率分析——基于ARIMA模型和GARCH模型

本文分析中国上海证券市场回报率。分别通过APdMA模型和GARCH模型，发现若用APdMA模型分析和建立时间序列模型，一次自回归项是不够的，需要高次项，在大多数情形，若运用GARCH模型，则GARCH（1，1）就能够很好的拟合数据。