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A problem about the present structure of dimensional analysis, and another one about the differences between solids and fluids are suggested. Both problems appear to have certain foundational aspects.
In this note we explain two transitions known for moment generating functions of local times by means of properties of the renewal measure of a related renewal equation. The arguments simplify and strengthen results on the asymptotic…
Identifying temporal relations between events is an essential step towards natural language understanding. However, the temporal relation between two events in a story depends on, and is often dictated by, relations among other events.…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, these extraordinarily small effects may in fact have a real and significant influence on our world. A calculation suggests that the minute…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
We define a truncated Euler polynomial $E_{m,n}(x)$ as a generalization of the classical Euler polynomial $E_n(x)$. In this paper we give its some properties and relations with the hypergeometric Bernoulli polynomial.
For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
The main purpose of this paper is to propose some interesting number theory problems related to the Legendre's symbol and the two-term exponential sums.
We consider the classical response in a chaotic system. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in a chaotic system vanishes at long times. The response also reveals certain…
In this article, the existence of global classical solutions to the discrete coagulation equations with collisional breakage is established for collisional kernel having linear growth whereas the uniqueness is shown under additional…
In this paper we consider two related objects: singular positive semidefinite Hankel block--matrices and associated degenerate truncated matrix Hamburger moment problems. The description of all solutions of a degenerate matrix Hamburger…
A time-variant analogue of an interpolation problem equivalent to the relaxed commutant lifting problem is introduced and studied. In a somewhat less general form the problem already appears in the analysis of the set of all solutions to…
The idea that the electron is an extended charged object the spinning of which is responsible for its magnetic moment is shown to require a sizable portion of the electron to spin at speeds very close to the speed of light, and in fact to…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
We derive new solutions of the Schr\"odinger equation which describe the motion of particles in the Penning trap. These solutions are direct counterparts of classical orbits. They are obtained by injection of classical trajectories into the…
In this paper we show an alternative approach to the concentration of truncated variation for stochastic processes on a real line. Our method is based on the moments control and can be used to generalize the results to the case of processes…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which…