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Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
Time-asymmetric spacetime structures, in particular those representing black holes and the expansion of the universe, are intimately related to other arrows of time, such as the second law and the retardation of radiation. The nature of the…
We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of divergence-controlled positive symmetric tensors in…
An overview of recent developments in the renormalization and in the implementation of spacetime symmetries of noncommutative field theory is presented, and argued to be intimately related.
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with…
We study the relation between the intrinsic and the spatial numerical ranges with the recently introduced "approximated" spatial numerical range. As main result, we show that the intrinsic numerical range always coincides with the convex…
We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also…
In this paper, using 1+1D models as examples, we study symmetries and anomalous symmetries via multi-component partition functions obtained through symmetry twists, and their transformations under the mapping class group of spacetime. This…
We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…
Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.
The role of symmetries in formation of quantum dynamics is discussed. A quantum version of the d'Alambert's principle is proposed to take into account symmetry constrains for quantum case. It is noted that in this approach one can find, in…
We show that parity-time and partial parity-time symmetries are particular cases of antiunitary symmetry. This point is illustrated by means of a recently discussed system of non-Hermitian coupled harmonic oscillators that also exhibits…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
Mass of singularity is defined, and its relation to whether the singularity is spacelike, timelike or null is discussed for spherically symmetric spacetimes. It is shown that if the mass of singularity is positive (negative) the singularity…
Within an axiomatic framework, we investigate the possible structures of numbers (as physical quantities) in different theories of relativity.
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
In this thesis we study classical aspects of superconformal field theory via symmetry principles. Specifically, by employing the powerful setup of conformal superspace, we obtain a plethora of new results in the fields of geometric and…
We investigate a conformal-like transformation for which the spacetime interval is invariant.
This paper outlines a possibility for spacetime dynamics and structure, without postulating a metric ab initio. In this model, the closer an object is to a mass or energy source, the more paths through spacetime might be available to the…