Combined bending and compression of circular cylindrically orthotropic plates with low shear strength

Equations are derived for the combined bending and compression of cylindrically orthotropic plates with allowance for shear and without postulating a shear distribution lawf/it(z). Solutions of the equations obtained are given for various boundary conditions. The error introduced by postulating the distribution lawf/it(z) is estimated. The effect of the ratio of the Young's moduli in the circumferential and radial directions E/E_r and the ratio of the Young's modulus E_r and the shear modulus G on the deflection w and the critical load T_cr is investigated. It is shown that for plates made of materials such as oriented glass-reinforced plastics the shear correction is very important. It is noted that buckling (due to shear) can occur even when the Young's moduli of the material are infinite.Mekhanika Polimerov, Vol. 4, No. 1, pp. 116–123, 1968     

Mechanical phenomena accompanying the structure formation of reinforced polymer materials

A systemic approach to the processing of reinforced polymers into articles is outlined. The structuralstate parameter of the polymer matrix is introduced, and used to model mechanical phenomena, taking into account that the conversion fields are frontal for the whole technological cycle as a continuous process. By postulating the principles of temperature-time analogy and homogeneous equivalence, the problem is reduced to coupled boundary problems of thermokinetics and hereditary viscoelasticity.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 31–36, 1987.     

Alpha-theory: An elementary axiomatics for nonstandard analysis

The methods of nonstandard analysis are presented in elementary terms by postulating a few natural properties for an infinite “ideal” number . The resulting axiomatic system, including a formalization of an interpretation of Cauchy's idea of infinitesimals, is related to the existence of ultrafilters with special properties, and is independent of ZFC. The Alpha-Theory supports the feeling that technical notions such as superstructure, ultrapower and the transfer principle are definitely not needed in order to carry out calculus with actual infinitesimals.     

Class of analytical closed-form polynomial solutions for clamped–guided inhomogeneous beams

New closed-form solutions for the natural frequency of a clamped–guided beam are derived in this investigation. By postulating the mode shape of the clamped–guided beam, whose material density and stiffness are taken as polynomial functions, one is able to calculate the closed-form solution for its natural frequency. A remarkable property of the suggested method is its extreme simplicity.     

Supersymmetry, transfinite neural networks, hyperbolic manifolds, quantum gravity and the Higgs

Connections between the transfinite extension of neural networks and hyperbolic manifolds are pointed out. The found relations are subsequently used to elucidate a certain quantum gravity equation that is reinterpreted via Spinor varieties. Finally it is shown how a definite picture of ^(∞) spacetime may be obtained from a transfinite extension of a certain four dimensional hyperbolic manifold based on Coxeter 120-cell polytop and how this helps in understanding the need of postulating the existence of not only one but three Higgs particles.     

Quasilinear theory of viscoelasticity

By postulating equal contributions the number of kernels in the principal cubic theory of viscoelasticity and in the theory with regular kernels of two arguments is reduced to three. For certain quasilinear relations all the kernels and functions are determined from creep, relaxation, and simple loading and deformation tests. In the case of simple loading and deformation the problems for a viscoelastic incompressible material reduce to problems of the theory of small elastoplastic deformations of an incompressible material. Several problems relating to this case are considered.Moscow M. V. Lomonosov State University. Translated from Mekhanika Polimerov, No. 4, pp. 603–611, July–August, 1969.     

Flexure of beams with low shear strength on an elastic foundation

The deflection of a beam on an elastic foundation is determined with allowance for shears and without postulating a law of shear-stress distribution. The accuracy of approximating this law with a quadratic parabola is estimated. The effect of shears on deflection is investigated in relation to beams of different length made of materials of the oriented glass-reinforced plastic type with low shear strength.Mekhanika Polimerov, Vol. 3, No. 5, pp. 881–887, 1967     

Melnikov’s method for chaos of the nanoplate postulating nonlinear foundation

In this brief communication, Melnikov’s method is adopted to investigate the chaotic behaviors of a nanoplate postulating nonlinear Winkler foundation. The critical curves separating the chaotic and non-chaotic regions are found. It is presented that the chaotic behaviors can occur when the parameters are chosen in the chaotic regions. Numerical simulations verify the theoretical analytical results. The results provide some inspiration and guidance for the analysis and dynamic design of this nanoplate.     

Static-arbitrage optimal subreplicating strategies for basket options

In this paper we investigate the possible values of basket options. Instead of postulating a model and pricing the basket option using that model, we consider the set of all models which are consistent with the observed prices of vanilla options of all strikes. In the case of basket options on two components we find, within this class, the model for which the price of the basket option is smallest. This price, as discovered by Rapuch and Roncalli, is associated to the lower Fréchet copula. We complement their result in this paper by describing an optimal subreplicating strategy. This strategy is associated with an explicit portfolio which consists of being long and short a series of calls with strikes chosen as the zeros of an auxiliary function.     

弹性动力学中的牵引力问题

在连续介质力学中不仅Cauchy六方程 是不完善的,而且著名的Cauchy运动定律(式中,,ρb,T及divT是连续的)也是不完善的[2].前六个方程的不完善是由于在空间给定点上变形的几何表示方法至今尚非完全[3],而后两个定律的不完善则Cauchy自己解释说ρb,T及divT是标架无关的,但则不是,且T是对称的[2].因此我们说后两个定律不可能满足广义标架上的非对称张量.本文的目的是在三维牵引力域的影响下用广义标架上的非对称张量来完善Cauchy运动定律.     

How to Derive a ‘Not’ from an ‘Is’: A Defense of the Incompatibility View of Negative Truths

Truthmaker maximalism is the claim that every truth has a truthmaker. The case of negative truths leads some philosophers to postulate negative states of affairs or to give up on truthmaker maximalism. This paper defends a version of the incompatibility view of negative truths. Negative truths can be made true by positive facts, and thus, truthmaker maximalism can be maintained without postulating negative states of affairs.     

Sensitivity Statistical Estimates for Local A Posteriori Inference Matrix-Vector Equations in Algebraic Bayesian Networks over Quantum Propositions

An approach to the sensitivity analysis of local a posteriori inference equations in algebraic Bayesian networks is proposed in this paper. Some basic definitions and formulations are briefly given and the development of the matrix-vector a posteriori inference approach is considered. Some cases of the propagation of deterministic and stochastic evidence in a knowledge pattern with scalar estimates of component truth probabilities over quantum propositions are described. For each of the considered cases, the necessary metrics are introduced, and some transformations resulting in four linear programming problems are performed. The solution of these problems gives the required estimates. In addition, two theorems postulating the covering estimates for the considered parameters are formulated. The results obtained in this work prove the correct application of models and create a basis for the sensitivity analysis of local and global probabilistic-logic inference equations.     

A remarkable nature of the effect of boundary conditions on closed-form solutions for vibrating inhomogeneous Bernoulli–Euler beams

In this paper three sets of boundary conditions are considered for reconstructing the stiffness of the inhomogeneous Bernoulli–Euler beams. The essence of the paper consists in postulating the mode shape of the vibrating beam as a static deflection of associated uniform, homogeneous beam. This unconventional way of problem formulation turns out to lead to series of new closed-form solutions. For each combination of the boundary conditions several cases of the inertial coefficients are considered. All exact solutions for natural frequencies are represented as rational expressions of the involved coefficients. Solutions are written in terms of two positive integers: `m' representing the degree of the polynomial in the inertial term and `n' indicating power in the postulated mode shape. A remarkable conclusion is reached: For specified `m' and `n', the natural frequencies of the inhomogeneous beams with different boundary conditions coalesce. This remarkable nature does not imply that these beams share the same frequencies. In fact, these are different beams for each set of boundary conditions the expression for the stiffness is different. The paper should be considered as a first step towards analysis of uncertainty, inherently present in structures.     

Individual Essence: gibt es solche?

Two arguments are offered here for postulating individual essences of concrete individuals on top of their sortal essences. One is the explanatory gap argument, the other draws on the analogy with the individual essences of events presupposed in single causal explanations. These arguments support qualitative individual essences with explanatory goals as opposed to hybrid impure relational essences accounting for origin and numerical identity. It is highlighted why origin properties as parts of impure relational essences do not yield genuine de re constructions. The distinction between the two types of individual essences is traced back to the ambiguity of the very notion of individuation.     

Towards thermomechanics of fractal media

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius–Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.     

Towards thermomechanics of fractal media

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius–Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.     

The notion of a production function

Summary The mathematical notion of the production function is developed to relate input and output rates for unconstrained technological possibilities. It is shown that the structure of production may be expressed interchangeably, either by postulating the existence of a production function (X) satisfying certain properties or by a family of production possibility setsL (U), whenU is output rate,X is a vector of input rates,L (U) is the set of input rate vectors yielding at leastU, and . A class of production functions called homothetic is defined. This class is particularly useful in economic studies.

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Zusammenfassung In der vorliegenden Arbeit wird ein mathematischer Begriff der Produktionsfunktion entwickelt, um im Falle unbeschränkter technologischer Möglichkeiten Faktor- und Produktquantitäten zucinander in Beziehung zu setzen. Es wird gezeigt, daß die Produktionsstruktur wechselweise ausgedrückt werden kann, entweder durch Postulierung der Existenz einer Produktionsfunktion (X) mit gewissen Eigenschaften oder mit Hilfe einer Familie von MengenL (U) von Produktionsmöglichkeiten, wobeiU eine Produktquantität,X ein Vektor von Faktorquantitäten,L (U) die Menge der Faktorvektoren, die mindestensU erzeugen, und ist. Ferner wird eine Klasse sogenannter homothetischer Produktionsfunktionen definiert, die bei ökonomischen Untersuchungen besonders nützlich ist.

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This research was supported in part by the National Science Foundation Grant GP-4593 with the University of California, Berkeley; and the Logistics Research Project at Princeton University sponsored by the Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the United States Government.

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Vorgel. v.:W. Wittmann.     

Covariance in linearized elasticity

In this paper we covariantly obtain all the governing equations of linearized elasticity. Our motivation is to see if one can make a connection between invariance (covariance) properties of the (global) balance of energy in nonlinear elasticity and those of its counterpart in linear elasticity. We start by proving a Green-Naghdi-Rivilin theorem for linearized elasticity. We do this by first linearizing energy balance about a given reference motion and then by postulating its invariance under isometries of the Euclidean ambient space. We also investigate the possibility of covariantly deriving a linearized elasticity theory, without any reference to the local governing equations, e.g. local balance of linear momentum. In particular, we study the consequences of linearizing covariant energy balance and covariance of linearized energy balance. We show that in both cases, covariance gives all the field equations of linearized elasticity.