相关论文: Potential theoretic approach to rendezvous numbers
For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation,…
We review some probabilistic properties of the sum-of-digits function of random integers. New asymptotic approximations to the total variation distance and its refinements are also derived. Four different approaches are used: a classical…
Resources and their use and consumption form a central part of our life. Many branches of science and engineering are concerned with the question of which given resource objects can be converted into which target resource objects. For…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
Point configurations have been widely used as model systems in condensed matter physics, materials science and biology. Statistical descriptors such as the $n$-body distribution function $g_n$ is usually employed to characterize the point…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
In science, as in life, `surprises' can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of…
The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail is reexamined from a fundamental statistical point of view making use of the division of particle orbits into waiting…
We extend the theory of discrete capacity to critical branching random walk. We introduce branching capacity for any finite subset of $\Z^d, d\geq5$. Analogous to the regular discrete capacity, branching capacity is closely related to the…
We consider the possibility of obtaining emergent properties of physical spaces endowed with structures analogous to that of collective models put forward by classical statistical physics. We show that, assuming that a so-called "metric…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
Given a finite and non-empty set $X$ and randomly selected specific functions and relations on $X$, we investigate the existence and non-existence of fixed points and reflexive points, respectively. First, we consider the class of…
For a compact $ d $-dimensional rectifiable subset of $ \mathbb{R}^{p} $ we study asymptotic properties as $ N\to\infty $ of $N$-point configurations minimizing the energy arising from a Riesz $ s $-potential $ 1/r^s $ and an external field…
Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time…
Markov numbers are integers that appear in the solution triples of the Diophantine equation, $x^2+y^2+z^2=3xyz$, called the Markov equation. A classical topic in number theory, these numbers are related to many areas of mathematics such as…
The orbits about Lagrangian equilibrium points are important for scientific investigations. Since, a number of space missions have been completed and some are being proposed by various space agencies. In light of this, we consider a more…
In this paper, we will develop a significantly more general notion of classical Ramsey numbers (extending most other graph-theoretic generalizations) and make some preliminary characterizations of these new Ramsey numbers using simple…
Noncommutativity lies in the heart of quantum theory and provides rich set of interesting questions in physics and mathematics. In this work I present some of them through the concept of Joint Numerical Range (JNR) - the set of…
In this work we demonstrate how different semi-classical methods can be combined in a novel way to reconstruct the perturbation potential of ultra compact stars. Besides rather general assumptions, the only specific information entering…
We review the hypothetical interactions predicted beyond the Standard Model which could be constrained by using the results of tabletop laboratory experiments. These interactions are described by the power-type potentials with different…