相关论文: Anholonomic Transformations of Mechanical Action P…
Social physics is the application of ideas, concepts and tools from physics to study social phenomena. In this article, we present a mechanical theory underlying a mathematical treatment of social physics. We explore the possibility of…
Starting from the Lovelock action and its supplementation by the relevant Gibbons-Hawking-York boundary term, the curvature action corresponding to second-order General Relativity is stated in accordance to the topological properties of the…
By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to…
We present the set of axioms for topological space with the operation of boundary as primitive notion.
A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the…
Angular momentum and torque are important principles for basic and applied physics on any spatial scales, for example, in elementary particles, cold gases, optical tweezers, quantum information technology, metamaterials, gyroscopes or…
We postulate the applicability of the general form-invariance principle in special relativity. It is shown that this principle holds in classical mechanics. Some examples of transformations between the reference frames which satisfy this…
We draw attention to a novel type of geometric gauge invariance relating the autoparallel equations of motion in different Riemann-Cartan spacetimes with each other. The novelty lies in the fact that the equations of motion are invariant…
A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools are based on the well-known de Rham-Kodaira decomposing theorem on harmonic…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…
The possibility of the fundamental interactions unification arises at the consideration of the field equation of the energy conservation if one takes into account Salam's effect. Such account results in the functional division between…
The technique of transformation optics (TO) is an elegant method for the design of electromagnetic media with tailored optical properties. In this paper, we focus on the formal structure of TO theory. By using a complete covariant…
Systems of equations are invariant under "polydimensional transformations" which reshuffle the geometry such that what is a line or a plane is dependent upon the frame of reference. This leads us to propose an extension of Clifford calculus…
Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism. Firstly, the case of canonoid transformations is studied with great detail and…
In this paper, we embed metric space endowed with a convex combination operation, named convex combination space, into a Banach space and the embedding preserves the structures of metric and convex combination. For random element taking…
We provide frequency probabilistic analysis of perturbations of physical systems by preparation procedures. We obtained the classification of possible probabilistic transformations connecting input and output probabilities that can appear…
We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.
Study on a rectified current induced by active particles has received a great attention due to its possible application to a microscopic motor in biological environments. Insertion of an {\em asymmetric} passive object amid many active…
We introduce a new approach to build microscopic engines on the atomic scale that move translationally or rotationally and can perform useful functions such as pulling of a cargo. Characteristic of these engines is the possibility to…
Various complexes of differential operators are constructed on complex projective space via the Penrose transform, which also computes their cohomology.