Effect of the chemical structure of the polymer matrix on the properties of foam polyurethanes at low temperatures

The dependence of physical and mechanical properties of oligoether-based foam polyurethanes on the molecular mass (M_c) of polymer chains between the nodes of the polymer network and on the content of rigid segments in the polymer is investigated at 293 and 98K. The values of M_c at which the foam plastics have the best mechanical properties at low temperatures are determined. The content of rigid segments in the polymer at which foam polyurethanes have the best combination of the linear thermal expansion coefficient and mechanical properties in tension at a temperature of 98K is found.Latvian State Institute of Wood Chemistry, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 517–526, July–August, 1999.     

Properties of Some Generalized Hypergeometric Functions Governing Coupling at Transition Points

Understanding of wave propagation problems is enhanced by consideringgeneralizations to differential equations of order 2n. In particular,reflection and coupling of waves at transition points can involvecertain types of generalized hypergeometric functions. In thispaper, properties of _oF_2n-1 functions are considered systematically,when the parameters are specially chosen for application totransition points; a wide range of interesting properties unfolds,which recall the properties of Bessel functions when n = 1.     

Six Kinds of Roughly Convex Functions

This paper considers six kinds of roughly convex functions, namely: δ-convex, midpoint δ-convex, ρ-convex, γ-convex, lightly γ-convex, and midpoint γ-convex functions. The relations between these concepts are presented. It is pointed out that these roughly convex functions have two optimization properties: each r-local minimizer is a global minimizer, and if they assume their maximum on a bounded convex domain D (in a Hilbert space), then they do so at least at one r-extreme point of D, where r denotes the roughness degree of these functions. Furthermore, analytical properties are investigated, such as boundedness, continuity, and conservation properties.     

Quasi-hereditary algebras with two simple modules and fibonacci numbers

Let K be an algebraically closed field. In [10] Happel showed that number-theoretic properties of the Fibonacci numbers are related to ho-mological properties of a family of finite-dimensional Ji-algebras An. In particular he showed that at least for n > 3 odd, An is not derived equiv alent to a quasi-hereditary algebra.Using well-known properties that are shared by two rings that are derived equivalent and deeper properties of the Fibonacci numbers we are able to show that for all n > 3, the algebra A_n is not derived equivalent to a quasi-hereditary algebra.     

Prosperity properties of TU-games

An important open problem in the theory of TU-games is to determine whether a game has a stable core (Von Neumann-Morgenstern solution (1944)). This seems to be a rather difficult combinatorial problem. There are many sufficient conditions for core-stability. Convexity is probably the best known of these properties. Other properties implying stability of the core are subconvexity and largeness of the core (two properties introduced by Sharkey (1982)) and a property that we have baptized extendability and is introduced by Kikuta and Shapley (1986). These last three properties have a feature in common: if we start with an arbitrary TU-game and increase only the value of the grand coalition, these properties arise at some moment and are kept if we go on with increasing the value of the grand coalition. We call such properties prosperity properties. In this paper we investigate the relations between several prosperity properties and their relation with core-stability. By counter examples we show that all the prosperity properties we consider are different. Received: June 1998/Revised version: December 1998     

On the global optimization properties of finite-difference local descent algorithms

The paper is devoted to the convergence properties of finite-difference local descent algorithms in global optimization problems with a special -convex structure. It is assumed that the objective function can be closely approximated by some smooth convex function. Stability properties of the perturbed gradient descent and coordinate descent methods are investigated. Basing on this results some global optimization properties of finite-difference local descent algorithms, in particular, coordinate descent method, are discovered. These properties are not inherent in methods using exact gradients.The paper was presented at the II. IIASA-Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Effect of mineral fillers on properties of composite matrix material

The influence of mineral fillers on thermomechanical properties of matrix material of composites is investigated. Different methods to determine elastic properties and thermal expansion coefficients of composite materials have been considered and compared. Injection moulded polyester samples containing varying concentrations of talc filler are tested and properties such as Young 's modulus, thermal expansion coefficients, and volumetric shrinkage during cure are measured. Results obtained by theoretical models and from experiments are compared and discussed.To be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 435–445, July–August, 1995.     

Properties of rigid polyurethane foams filled with milled carbon fibers

The effect of milled carbon fibers of two types (differing in length) on the properties of rigid polyurethane foams in the density range from 50 to 90 kg/m³ is investigated. The coefficient of thermal expansion and properties of the foams in tension and compression as functions of fiber content in them are determined. It is found that the long fibers are more efficient in improving the properties of the foams in their rise direction. The elongation at break of the foams decreases significantly with increasing fiber content.     

Elementary properties of optimal irrigation patterns

In this paper we follow the approach in Maddalena et al. (Interfaces and Free Boundaries 5, 391–415, 2003) to the study of the ramified structures and we identify some geometrical properties enjoyed by optimal irrigation patterns. These properties are “elementary” in the sense that they are not concerned with the regularity at the ending points of such structures, where the presumable selfsimilarity properties should take place. This preliminary study already finds an application in G. Devillanova and S. Solimini (Math. J. Univ. Padua, to appear), where it is used in order to discuss the irrigability of a given measure.     

Improper actions and higher connectivity at infinity

Given an improper action (= cell stabilizers are infinite) of a group G on a CW-complex , we present criteria, based on connectivity at infinity properties of the cell stabilizers under the action of G that imply connectivity at infinity properties for G. A refinement of this idea yields information on the topology at infinity of Artin groups, and it gives significant progress on the question of which Artin groups are duality groups. Received: October 30, 1998     

Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media

The Ginzburg-Landau-Allen-Cahn equation is a variational model for phase coexistence and for other physical problems. It contains a term given by a kinetic part of elliptic type plus a double-well potential. We assume that the functional depends on the space variables in a periodic way.We show that given a plane with rational normal, there are minimal solutions, satisfying the following properties. These solutions are asymptotic to the pure phases and are separated by an interface. The convergence to the pure phases is exponentially fast. The interface lies at a finite distance M from the chosen plane, where M is a universal constant. Furthermore, these solutions satisfy some monotonicity properties with respect to integer translations (namely, integer translations are always comparable to the function).We then show that all the interfaces of the global periodic minimizers satisfy similar monotonicity and plane-like properties.We also consider the case of possibly irrationally oriented planes. We show that either there is a one parameter family of minimizers whose graphs provide a field of extremals or there are at least two solutions, one which is a minimizer and another one which is not. These solutions also have interfaces bounded by a universal constant, they enjoy monotonicity properties with respect to integer translations and the nonminimal solutions are trapped inside a gap of the lamination induced by the minimizers.     

Structural approach to calculation of the effect of moisture on elastic characteristics of organoplastics

Data have been obtained for the structural calculation of the effect of moisture on the elastic characteristics of organoplastics from the properties of components. The distribution of moisture between the fiber and matrix — the components of a unidirectional composite — is considered. The elastic properties of the fiber are determined by an inverse calculation using the experimental dependences of the composite and matrix on moisture. The moisture effect on the properties of the materials is taken into account with influence functions, which differ by more than 25% for various characteristics. The results can be used for calculating the elastic properties of composites with various reinforcement schemes and at the nonequilibrium distribution of the moisture concentration in an actual environment.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Polymer Mechanics, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 525–530, July–August, 1998.     

Special Eccentric Vertices for the Class of Chordal Graphs and Related Classes

A vertex is simplicial if the vertices of its neighborhood are pairwise adjacent. It is known that, for every vertex v of a chordal graph, there exists a simplicial vertex among the vertices at maximum distance from v. Here we prove similar properties in other classes of graphs related to that of chordal graphs. Those properties will not be in terms of simplicial vertices, but in terms of other types of vertices that are used to characterize those classes.     

Effect of small additives of oligomer on the viscoelastic properties of carbon fiber plastics

The viscoelastic properties of carbon fiber composites whose phenol-formaldehyde matrix is modified by thermodynamically incompatible isocyanate derivatives have been investigated. Data are given on fiber wetting (Table 11), internal stress (Table 2), viscoelastic properties (Fig. 1), and tensile strength (Fig. 2). The modified composites are strengthened by the addition of 0.5–4% oligomer additive. This process involves the formation of a two-phase structure, in which the additive phase microparticles act as a polymer filler. Due to selective interactions, the intermediate layer formed at the fiber-binder interface leads to changes in the viscoelastic properties and tensile strength of the matrix and improved maintenance characteristics for the material as a whole.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 440–445, July–August, 1993.     

Dynamics of local groups of conformal mappings and generic properties of differential equations on ℂ2

This paper is a survey of the present state of the problems related to the generic properties of foliations defined on ?² by algebraic differential equations. We prove that the properties of density, absolute rigidity, and existence of a countable set of complex limit cycles are inherent in all equations except possibly for the union of some real algebraic set and real analytic set of codimension at least two in the space of coefficients.     

Dispersive properties of a viscous numerical scheme for the Schrödinger equation

In this Note we study the dispersive properties of the numerical approximation schemes for the free Schrödinger equation. We consider finite-difference space semi-discretizations. We first show that the standard conservative scheme does not reproduce at the discrete level the properties of the continuous Schrödinger equation. This is due to spurious high frequency numerical solutions. In order to damp out these high-frequencies and to reflect the properties of the continuous problem we add a suitable extra numerical viscosity term at a convenient scale. We prove that the dispersive properties of this viscous scheme are uniform when the mesh-size tends to zero. Finally we prove the convergence of this viscous numerical scheme for a class of nonlinear Schrödinger equations with nonlinearities that may not be handeled by standard energy methods and that require the so-called Strichartz inequalities. To cite this article: L.I. Ignat, E. Zuazua, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Overconvergence properties of quintic interpolatory splines

Let Q be a quintic spline with equi-spaced knots on [a, b] interpolating a given function y at the knots. The parameters which determine Q are used to construct a piecewise defined polynomial P of degree six. It is shown that P can be used to give at any point of [a, b] better orders of approximation to y and its derivatives than those obtained from Q. It is also shown that the superconvergence properties of the derivatives of Q, at specific points of [a, b], are all simple consequences of the properties of P.     

Van Gulick’s solution of the exclusion problem revisited

The anti-reductionist who wants to preserve the causal efficacy of mental phenomena faces several problems in regard to mental causation, i.e. mental events which cause other events, arising from her desire to accept the ontological primacy of the physical and at the same time save the special character of the mental. Psychology tries to persuade us of the former, appealing thereby to the results of experiments carried out in neurology; the latter is, however, deeply rooted in our everyday actions and beliefs and despite the constant opposition of science still very much alive. Difficulties, however, arise from a combination of two claims that are widely accepted in philosophy of mind, namely, physical monism and mental realism, the acceptance of which leads us to the greatest problem of mental causation: the problem of causal exclusion. Since physical causes alone are always sufficient for physical effects mental properties are excluded from causal explanations of our behaviour, which makes them “epiphenomenal”. The article introduces Van Gulick’s solution to the exclusion problem which tries to prove that physical properties, in contrast to mental properties, do not have as much of a privileged status with respect to event causation as usually ascribed. Therefore, it makes no sense to say that physical properties are causally relevant whereas mental properties are not. This is followed by my objection to his argument for levelling mental and physical properties with respect to causation of events. I try to show that Van Gulick’s argument rests on a premise that no serious physicalist can accept. Also called The Problem of Causal Exclusion.     

The composite Milstein methods for the numerical solution of Stratonovich stochastic differential equations

In this paper, we present two composite Milstein methods for the strong solution of Stratonovich stochastic differential equations driven by d-dimensional Wiener processes. The composite Milstein methods are a combination of semi-implicit and implicit Milstein methods. The criterion for choosing either the implicit or the semi-implicit method at each step of the numerical solution is given. The stability and convergence properties of the proposed methods are analyzed for the linear test equation. It is shown that the proposed methods converge to the exact solution in Stratonovich sense. In addition, the stability properties of our methods are found to be superior to those of the Milstein and the composite Euler methods. The convergence properties for the nonlinear case are shown numerically to be the same as the linear case. Hence, the proposed methods are a good candidate for the solution of stiff SDEs.