Time-temperature superposition for partially crystalline polymers (polytetrafluoroethylene)

Time-temperature superposition in the \(\mathop \varepsilon \limits^.\) = const regime can be applied to partially crystalline fluoroplastics with different specific volumes. There is a correlation between the variation of the specific volume and the relaxation processes in fluoroplastics. Time-temperature superposition is valid only in the temperature regions between transitions. The master curves are theoretically described by means of a nonlinear equation.     

Time-temperature superposition and the relaxation flow mechanism of rubbers and rubber compounds

It is shown that there is a universal relaxation spectrum for all rubbers and rubber compounds. The relaxation spectra of different rubbers and rubber compounds differ only with respect to the extent and location of the region of existence and the absolute value of the area bounded by the curve of the spectrum in H()- coordinates.Mekhanika Polimerov, Vol. 4, No. 3, pp. 523–530, 1968     

Time-temperature superposition applied to crosslinked polymers in creep with superimposed hydrostatic pressure

The creep of an epoxy composition under combined tension and hydrostatic pressure (up to 800 kgf/cm²) has been investigated. The applicability of time-temperature superposition to a complex state of stress is demonstrated. Hydrostatic pressure is shown to affect the deformability of crosslinked polymers in tension.Leningrad Technological Institute of the Refrigeration Industry. Plastpolimer Research-Production Association, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 541–544, May–June, 1976.     

Time-temperature superposition applied to the relaxation properties of a glass-reinforced plastic and its matrix

The relaxation behavior in compression of an unsaturated polyester resin and the corresponding glass-reinforced plastic has been investigated. The time-temperature superposition principle is shown to be applicable to the cross-linked polyester resin and the glass-reinforced plastic. The temperature dependences of the shift functionsa _T of the resin and the glass-reinforced plastic are found to satisfy an Arrhenius equation with the constant equal to 21–25 kcal/mole.Scientific-Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 360–363, March–April, 1972.     

Chebyshev approximation by discrete superposition. Application to neural networks

In this paper, we develop two algorithms for Chebyshev approximation of continuous functions on [0, 1] ⁿ using the modulus of continuity and the maximum norm estimated by a given finite data system. The algorithms are based on constructive versions of Kolmogorov's superposition theorem. One of the algorithms we apply to neural networks.     

Time — Moisture superposition

The results of creep tests on PN-3 polyester resin are given for various values of the temperature and moisture content of the material. It is shown that moisture content and time, like temperature and time, have an interchangeable effect on creep; i.e., in addition to a time-temperature (T-t) there is also a time-moisture (w-t) analogy. The (w-t) analogy can be used to predict the long-time creep from accelerated test data.Institute of Polymer Mechanics, Academy of Sciences of the Latian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 780–786, September–October, 1972.     

Multivalued superposition operators in ideal spaces of vector functions.I

The paper is concerned with boundedness properties of nonlinear superposition operators generated by multi-valued functions between ideal spaces (Banach lattices) of vector functions. In particular, sufficient conditions on the spaces X and Y are given under which any superposition operator from X into (Y) is locally bounded or bounded on bounded sets.     

Time-stress superposition in nonlinear viscoelasticity

Using low-density polyethylene, whose viscoelastic properties are nonlinear at high stresses, within reasonable limits of stress and time it is possible (under certain conditions) to use time-stress superposition, as well as time-temperature superposition, to predict the long-term creep of polymer materials. A variant of the compact approximation of nonlinear vicoelasticity effects in polymers is proposed.Mekhanika Polimerov, Vol. 4, No. 2, pp. 379–381, 1968Instantaneous elastic strains excluded.     

Weak convergence of inner superposition operators

The equivalence of the weak (pointwise) and strong convergence of a sequence of inner superposition operators is proved as well as the criteria for such convergence are provided. Besides, the problems of continuous weak convergence of such operators and of representation of a limit operator are studied.

     

Generalized cofactors and nonlinear superposition principles

It is known from Lie's works that the only ordinary differential equation of first order in which the knowledge of a certain number of particular solutions allows the construction of a fundamental set of solutions is, excepting changes of variables, the Riccati equation. For planar complex polynomial differential systems, the classical Darboux integrability theory exists based on the fact that a sufficient number of invariant algebraic curves permits the construction of a first integral or an inverse integrating factor. In this paper, we present a generalization of the Darboux integrability theory based on the definition of generalized cofactors.     

Dimension and superposition of continuous functions

We give a relatively short proof of the following theorem of Sternfeld: LetX be a compact metric space with dimX ≧ 2, and letX ?R ^m be an embedding such that everyf ∈C(X) can be represented as $$f(x_1 ,x_2 ,...,x_m ) = \sum\limits_{i = 1}^m {g_i (x_i ),} (x_1 ,x_2 ,...,x_m ) \in X,g_i \in $$ Thenm ≧ 2 dimX + 1.     

Certain theorems of the theory of superposition of large deformations. Indifferent quantities

Certain theorems are proved about the indifference of strain and stress tensors that are in the governing relationships used in the theory of multiple superposition of large deformations.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 25–31, 1989.     

Regularizability of superposition of inverse linear operators

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 55, pp. 96–100, 1991.     

Nonlinear superposition formula of the Boussinesq hierarchy

In this paper, a Boussinesq hierarchy in the bilinear form is proposed. A Backlund transformation for this hierarchy is presented and the nonlinear superposition formula is proved rigorously.     

Discrete matrix Riccati equations with superposition formulas

An ordinary differential equation is said to have a superposition formula if its general solution can be expressed as a function of a finite number of particular solution. Nonlinear ODE's with superposition formulas include matrix Riccati equations. Here we shall describe discretizations of Riccati equations that preserve the superposition formulas. The approach is general enough to include q-derivatives and standard discrete derivatives.     

A note on superposition in Mindlin's problem

The problem of a half-space subjected to an interior concentrated force is posed as a superposition problem. For a free plane boundary it is shown that the boundary condition of traction may be expressed directly through the normal derivative of a harmonic Green's function by means of a linear operator. These circumstances at once generate the classical result. For a clamped boundary such a procedure becomes cumbersome and direct integration, in a manner proposed by Sanders, is performed.

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Zusammenfassung Das Problem eines Halbraumes, der von einer inneren konzentrierten Kraft beeinflußt ist, wird als ein Überlagerungsproblem betrachtet. Für einen freien Rand wird so gezeigt, daß die Randbedingung des Spannungsvektors durch die Ableitung in der normalen Richtung einer harmonischen Greenschen Funktion mittels eines linearen Operators ausgedrückt werden kann. Diese Umstände ermöglichen sofort die Lösung des klassischen Problems. Für einen eingespannten Rand ist eine solche Lösungsmethode umständlich und eine direkte Integration, in einem Verfahren wie von Sanders vorgeschlagen, wird durchgeführt.

     

Constructions of some exact vortex superposition solutions

In theoretical ways to solve the N-S equation, we will confront many difficulties. For example, the complex mathematical calculation, the 3D velocity components and the nonlinear terms, etc. We find that from the basis of Stokes-Helmholtz decomposition and after some processing, we can get a method of constructing the vortex superposition solutions. We get a set of exact solutions in different coordinates and we hope these solutions will be helpful to a clearer understanding of the vortex in Fluid Mechanics.     

The debate between Peletier and Clavius on superposition

This article considers the sixteenth-century debate between Jacques Peletier du Mans and Christoph Clavius over the admissibility of superposition as a means to demonstrate the equality of figures in Euclidean geometry. It notably aims to determine, in the first part, which understanding of superposition motivated its rejection by Peletier, especially whether and to which extent his critical position towards this method was related to its kinematic implications. In the second part, the article presents the critical response Clavius addressed to Peletier in order to defend the legitimacy of superposition in Euclid's Elements.