Thermal stability and combustibility of rubbers and sealing plates

The present paper describes the test results concerning the thermal properties and flammability of the selected sealing plates and rubbers that may become components of plates. The thermal analysis methods (DTA, DSC, TG, and DTG) and flammability methods (OI, rate of burning in air, and ignition temperature) were used in this study. The thermal analysis of plates was also performed under isothermal conditions. It was stated that investigated sealing plates belong to the group of flame-retardant materials and type of rubber included in plate influences its thermal stability and combustibility.     

An essay on model theory

Some basic ideas of model theory are presented and a personal outlook on its perspectives is given.     

M-gap conjecture and m-normal theories

We find a small weakly minimal theory with an isolated weakly minimal type ofM-rank ∞ and an isolated weakly minimal type of arbitrarily large finiteM-rank. These examples lead to the notion of an m-normal theory. We prove theM-gap conjecture for m-normalT. In superstable theories with few countable models we characterize traces of complete types as traces of some formulas. We prove that a 1-based theory with few countable models is m-normal. We investigate generic subgroups of small superstable groups. We compare the notions of independence induced by measure (μ-independence) and category (m-independence). Research supported by KBN grant 2 P03A 006 09.     

On solving the dual for portfolio selection by optimizing Conditional Value at Risk

This note is focused on computational efficiency of the portfolio selection models based on the Conditional Value at Risk (CVaR) risk measure. The CVaR measure represents the mean shortfall at a specified confidence level and its optimization may be expressed with a Linear Programming (LP) model. The corresponding portfolio selection models can be solved with general purpose LP solvers. However, in the case of more advanced simulation models employed for scenario generation one may get several thousands of scenarios. This may lead to the LP model with huge number of variables and constraints thus decreasing the computational efficiency of the model. To overcome this difficulty some alternative solution approaches are explored employing cutting planes or nondifferential optimization techniques among others. Without questioning importance and quality of the introduced methods we demonstrate much better performances of the simplex method when applied to appropriately rebuilt CVaR models taking advantages of the LP duality.     

An effective Hamiltonian for sulfur adsorption at Au(1 0 0) surface

Adsorption of sulfur at the (1 0 0) surface of gold is analyzed with the help of the density functional theory (DFT). Potential energy surface for a single S atom at the Au(1 0 0) surface is computed and a simple analytical formula was found to reproduce the ab initio results to a good accuracy. Vibration frequencies of the adsorbed S atom are computed using the harmonic approximation and the contribution of zero-point motion to the adsorption energy is evaluated. The effects of surface Au atoms relaxation in the sulfur adsorption is analyzed. The interactions between S atoms adsorbed at the nearest and the next nearest equivalent adsorption sites are computed and used to define the effective Hamiltonian describing the interactions between the adsorbed sulfur atoms.     

Thermal stability of elastomers

Thermal transitions of elastomers are classified and problems concerning their stability are discussed. It is concluded that in the case of general-purpose elastomers no simple correlation exists between the energy of the bonds in the skeleton of a chain and their thermal stability. This also holds for the parameters of the physical structure of the chains. A high tendency to cross-linking, a high concentration of cross-links and their chemical structure give rise to a more perceptible effect.

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Zusammenfassung Thermische Umwandlungen von Elastomeren werden klassifiziert und mit der StabilitÄt von Elastomeren zusammenhÄngende Probleme diskutiert. Es wird gefolgert, da\ bei Elastomeren für allgemeine Verwendungszwecke keine einfache Korrelation zwischen der Energie der Bindungen im Kettengerüst und der thermischen StabilitÄt besteht. Das gilt auch für die Parameter der physikalischen Struktur der Ketten. Der Effekt einer starken Neigung zur Vernetzung, der Netwerkdichte und der chemischen Konstitution der Netzwerkbrücken ist dagegen augenscheinlicher.

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Very simple theories without forking

We prove Vaught's conjecture for minimal trivial simple theories satisfying the generalized independence theorem. Research supported by KBN grant 2 P03A 006 09     

Viscosity Solutions of Dynamic-Programming Equations for the Optimal Control of the Two-Dimensional Navier-Stokes Equations

In this paper we study the infinite-dimensional Hamilton-Jacobi equation associated with the optimal feedback control of viscous hydrodynamics. We resolve the global unique solvability problem of this equation by showing that the value function is the unique viscosity solution.     

Approximations and Mittag-Leffler conditions the applications

A classic result by Bass says that the class of all projective modules is covering if and only if it is closed under direct limits. Enochs extended the if-part by showing that every class of modules C, which is precovering and closed under direct limits, is covering, and asked whether the converse is true. We employ the tools developed in [18] and give a positive answer when C = A, or C is the class of all locally A^≤ω-free modules, where A is any class of modules fitting in a cotorsion pair (A, B) such that B is closed under direct limits. This setting includes all cotorsion pairs and classes of locally free modules arising in (infinite-dimensional) tilting theory. We also consider two particular applications: to pure-semisimple rings, and Artin algebras of infinite representation type.     

Bounded orbits and measures on a group

We consider a definable group G acting on the space of complete types over G, in a monster model of a theory T. We discuss the notion of a bounded orbit of this action. We prove that some boundedness assumptions imply definable amenability of G.