RESTRICTION RESPECTUEUSE ET RECONSTRUCTION DES CHAINES ET DES RELATIONS INFINITES

We show a faithful restriction theorem among infinite chains which implies a reconstructibility conjecture of Halin. This incite us to study the reconstructibility in the sense of Fraïssé and to prove it for orders of cardinality infinite or ≥ 3 and for multirelations of cardinality infinite or ≥ 7, what improves the theory obtained by G. Lopez in the finite case. For this work we had to study the infinite classes of difference which have to be a linear order of type ω, ω* or ω* + ω; this complete the theory made by G. Lopez for the finite case ([13]). We show also Ulam-reconstructibility for linear orders which have a fixed point.     

Generalisation of the Viterbi algorithm

The Viterbi algorithm, derived using dynamic programming techniques,is a maximum a posteriori (MAP) decoding method which was developedin the electrical engineering literature to be used in the analysisof hidden Markov models (HMMs). Given a particular HMM, theoriginal algorithm recovers the MAP state sequence underlyingany observation sequence generated from that model. This paperintroduces a generalization of the algorithm to recover, forarbitrary L, the top L most probable state sequences, with specialreference to its use in the area of automatic speech recognition.     

On generalized gradients

In this paper we present a concept of the construction of generalized gradients by considering a development of directional derivatives into spherical harmonics. This leads to a derivation system as a system of generalized partial derivatives. Necessary conditions for local extrema for a broad class of not necessarily differentiable function can be given and a characterization of points of differentiability can be proved by using generalized gradients.     

The automatic conversion of spinor equations to dyad form in MAPLE

A new package in the symbolic algebra system MAPLE is presented for the conversion of complicated spinor equations to their expansions with respect to a normalized spinor dyad. By following a simple index convention, we obtain a powerful computational tool with a straightforward and easy to use syntax. A number of examples, including nontrivial applications of the package to recent research, are provided.     

Periodic solutions of second-order quasilinear hyperbolic equations

We study a periodic boundary-value problem for a quasilinear equation with the d'Alembert operator on the left-hand side and a nonlinear operator on the right-hand side and establish conditions under which the solution of the indicated problem is unique.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 10, pp. 1370–1375, October, 1995.     

Conditions for the onset of sliding in a plane system with friction

The problem of the plane motion of a rigid body along a fixed surface in the presence of dry (Coulomb) friction is considered. The constraint is assumed to be non-restraining. It is shown that the validity of a certain system of two inequalities of the same type guarantees that the surfaces maintain contact and that the body will continue to roll without sliding. These conditions are analysed in a few specific cases of mechanical systems.     

Application of the variation principle for the problem of buckling of a nonlinearly elastic ring nonuniform along its thickness

There has been considerable recent attention given to the stressed and buckled states of items with complicated configuration made of different nonlinearly elastic materials joined by complete adhesion. However, effective analytical solutions for such problems have been hindered by mathematical difficulties. Approximate methods have thus been developed for such problems. A variational combined principle has been formulated in this communication. A nonlinear geometrical approach has been used for formulating a mixed-type functional with physical relationships given by Euler equations, nonlinear equilibrium equations, and nonlinear boundary conditions for a piecewise-nonuniform nonlinearly elastic body composed of finite elements (particles). As an example, buckling along the nonuniform thickness of nonlinearly elastic rings was analyzed hypothetically assuming plane cross-sections. Options for two-, three-, four-, five-, and six-layered rings in a periodical structure have been reviewed. The critical buckling forces for an even number of layers have been found to be equal to each other. The ratios of the critical forces, elasticity moduli, and proportionality levels were determined for all five variants by the Runge-Kutta method.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 262–268, March–April, 1995.     

Rheology of a mixture of liquid-crystal polymers in solution

The rheological behavior of a mixture of two liquid-crystal polymers, hydroxypropyl cellulose and ethyl cellulose, in acetone solution is studied. The total polymer concentration in the solvent is held constant (40%) as the ratio of the two polymers is varied. The mixtures are anisotropic, isotropic, or biphasic (isotropic/anisotropic), depending on the concentration. Curves of viscosity vs shear rate for all the mixtures studied show three regions of viscosity, as described by Onogi and Asada for liquid-crystal polymers. The viscosity as a function of the weight ratio of the two polymers at constant shear rate exhibits deviations from additivity of viscosities of the two components at all concentrations. In mixtures of two polymers in the melt, deviations are also observed; the negative ones are attributed to phase separation and the positive ones to homogenous mixing (comparison with the phase diagram). All the mixtures studied (anisotropic, isotropic, or biphasic), show ranges of shear rates where the first normal-stress difference is negative, as is generally observed for anisotropic liquid-crystal polymers. It is concluded that the isotropic solutions become anisotropic under shear, as they are not far from the critical concentration. © 1994 John Wiley & Sons, Inc.     

Properties of polystyrene-poly(methylmethacrylate) random and diblock copolymers in dilute and semidilute solutions

Solution properties for random and diblock copolymers of polystyrene (PS) and poly(methyl methacrylate) (PMMA) have been measured by dynamic and total intensity light scattering in solvents of differing quality. The results are compared with the corresponding properties for PS and PMMA homopolymers of similar molecular weight, in order to determine if interactions between unlike monomers are significant. The hydrodynamic radius (R_h) and diffusion second virial coefficient (k_d) for the random copolymer are found to be larger than the corresponding values for the homopolymers in a solvent which is near-theta for the two homopolymers, whereas no such effect is observed for the block copolymer. This suggests that most intrachain interactions occur a relatively short distance along the chain backbone. In a mutual good solvent R_h and k_d of the random copolymer are comparable to the average of the values for the homopolymers, indicating that in a good solvent monomer/solvent interactions dominate over monomer/monomer interactions. For an isolated diblock copolymer in a mutual good solvent, there is no evidence that interactions between unlike monomers lead to additional expansion of the entire molecule, as measured by R_h, nor expansion of the individual blocks as probed by light scattering with one block optically masked. However, at low but finite concentration there is evidence (the coefficients of the binary interaction terms in the viscosity and the mutual diffusion coefficient, and the second and third virial coefficients) that a weak ordering effect may exist in block copolymer solutions, far from the conditions where microphase separation occurs. Finally, measurements of ternary polymer-polymer-solvent solutions show no dependence on monomer composition or monomer distribution for the tracer diffusion of probe PS-PMMA copolymers in a PMMA/toluene matrix. This indicate that the frictional interaction is largely unaffected by interactions between unlike monomers. However, there is evidence that the thermodynamic interaction is more unfavorable between a random copolymer and the homopolymer matrix than between a diblock and the matrix. © 1994 John Wiley & Sons, Inc.