The Zeroth Law of Thermodynamics in Special Relativity

We critically revisit the definition of thermal equilibrium, in its operational formulation, provided by standard thermodynamics. We show that it refers to experimental conditions which break the covariance of the theory at a fundamental level and that, therefore, it cannot be applied to the case of moving bodies. We propose an extension of this definition which is manifestly covariant and can be applied to the study of isolated systems in special relativity. The zeroth law of thermodynamics is, then, proven to establish an equivalence relation among bodies which have not only the same temperature, but also the same center of mass four-velocity.

The Operational Choi–Jamiołkowski Isomorphism

In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.

WAVELET-BASED DISCRETE-CONTINUAL FINITE ELEMENT PLATE ANALYSIS WITH THE USE OF DAUBECHIES SCALING FUNCTIONS

The distinctive paper is detoded to special version of wavelet-based discrete-continual finite element method of plate analysis. Daubechies scaling functions are used within this version. Its field of application comprises plates with constant (generally piecewise constant) physical and geometrical parameters along one direction (so-called “basic” direction). Modified continual operational formulation of the problem with the use of the method of extended domain (proposed by A.B. Zolotov) is presented. Corresponding discrete-continual formulation is given as well. Brief information about computer implementation of the method with the use of MATLAB software is provided. Besides numerical sample of analysis of thin plate is considered.

Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Deep Beam Analysis

High-accuracy solution of the problem of deep beam analysis is normally required in some pre-known domains (regions with the risk of significant stresses that could potentially lead to the destruction of structure, regions which are subject to specific operational requirements). The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual finite element method for local analysis of deep beams with regular (in particular, constant or piecewise constant) physical and geometrical parameters (properties) in one direction. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.

Correct Direct Discrete-Continual Boundary Element Method of Structural Analysis

This paper is devoted to so-called direct discrete-continual boundary element method of structural analysis. Operational formulation of the problem is given. Using fundamental operational relations of direct approach after construction of corresponding fundamental matrix-function in a special form convenient for problems of structural mechanics and its application resolving set of differential equations with operational coefficients is obtained. The discrete-continual design model for structures with constant physical and geometrical parameters in one direction is offered on the basis of discrete-continual boundary elements. Basic pseudodifferential operators are approximated discretely by Fourier series. Fourier transformations and Wavelet analysis can be applied as well.

Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Plate Analysis

High-accuracy solution of the problem of plate analysis is normally required in some pre-known domains (regions with the risk of significant stresses that could potentially lead to the destruction of structure, regions which are subject to specific operational requirements). The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual finite element method for local analysis of plates with regular (in particular, constant or piecewise constant) physical and geometrical parameters (properties) in one direction. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.

Correct Wavelet-based Multilevel Discrete-Continual Methods for Local Solution of Boundary Problems of Structural Analysis

The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual methods for local solution of boundary problems of structural analysis. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.