Related papers: A Physical Approach to Polya's Conjecture
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…
It is well recognized that in auxiliary equation methods, the exact solutions of different types of auxiliary equations may produce new types of exact travelling wave solutions to nonlinear partial differential equations in hand. In this…
We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…
We consider exact solutions generated by the inverse scattering technique, also known as the soliton transformation. In particular, we study the class of simple real pole solutions. For quite some time, those solutions have been considered…
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
We consider noncommutative theory of a compact scalar field. The recently discovered projector solitons are interpreted as classical vacua in the model considered. Localized solutions to the projector equation are pointed out and their…
While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex…
We consider the problem of distance between two particles in the universe, where space is taken to be Liebnizian rather than Newtonian, this being the present day approach. We then argue that with latest inputs from physics, it is possible…
We introduce different notions of polynomial convexity with bounds on degrees of polynomials in $\mathbb C^n$. We provide some examples in higher dimensions and show necessary and sufficient conditions for polynomial convexity with degree…
The concept of walking wave is introduced from classical relativistic positions. One- and three-dimensional walking waves considered with their wave equations and dispersion equations. It is shown that wave characteristics (de Broglie's and…
The Hamiltonian defines the dynamical properties of the universe. Evidence from particle physics shows that there is a different version of the Hamiltonian for each direction of time. As there is no physical basis for the universe to be…
The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.
The phenomenology of MOND (flat rotation curves of galaxies, baryonic Tully-Fisher relation, etc.) is a basic set of phenomena relevant to galaxy dynamics and dark matter distribution at galaxy scales. Still unexplained today, it enjoys a…
The main purpose of this paper is to present the generalization of the inequalities between the modulus of the polar derivative and the polynomial itself, depending on consideration of the zeros inside and outside of a closed disk and the…
The aim of this paper is to show that the concept of probability is best understood by dividing this concept into two different types of probability, namely physical probability and analogical probability. Loosely speaking, a physical…
Astrophysical bounds on the cosmological constant are examined for spherically symmetric bodies. Similar limits emerge from hydrostatical and gravitational equilibrium and the validity of the Newtonian limit. It is argued that the bound…
Using an effective one body approach we describe in detail gravitational waves from classical three body problem on a non-rotating straight line and derive their basic physical characteristics. Special attention is paid to the irregular…
The confrontation between general relativity (and its theoretically most plausible deviations) and experimental or observational results is summarized. Some discussion is devoted to the various methodologies used in confronting theory and…
We prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection, then the polynomials have a common iterate. We also prove a special case of a conjectured dynamical analogue of the Mordell-Lang…
It seems reasonable that a toroid can be thought of approximately as a solenoid bent into a circle. The correspondence of the inductances of these two objects gives an approximation for the natural logarithm in terms of the average of two…