Related papers: Application of Morse index in weak force $N$-body …
A quantum transition can be seen as a result of interference between various pathways(e.g. Feynman paths) which can be labelled by a variable $f$. An attempt to determine the value of f without destroying the coherence between the pathways…
For a Gaussian process $X$ and smooth function $f$, we consider a Stratonovich integral of $f(X)$, defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on $X$ such that the sequence converges…
Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…
When we use variational methods to study the Newtonian $N$-body problem, the main problem is how to avoid collisions. C.Marchal got a remarkable result, that is, a path minimizing the Lagrangian action functional between two given…
In this communication we discuss the Weak Field Approach, and in particular the Newtonian limit, applied to f(R)-Gravity. Particular emphasis is placed on the spherically symmetric solutions and finally, it is clearly shown that General…
The paper is concerned with the weak convergence of $n$-particle processes to deterministic stationary paths as $n\to\infty$. A Mosco type convergence of a class of bilinear forms is introduced. The Mosco type convergence of bilinear forms…
In this paper, we consider periodic solutions of the $n$-body problem that satisfy symmetry constraints, expressed through invariance under finite group actions. We focus on their stability properties and present algorithms specifically…
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and…
We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third…
We present some improvements in the method of the weakly conjugate operator, one variant of the Mourre theory. When applied to certain two-body Schroedinger operators, this leads to a limiting absorption principle that is uniform on the…
Existence and uniqueness of weak solutions to the collision-induced breakage and coag-ulation equation are shown when coagulation is the dominant mechanism for small volumes. The collision kernel may feature a stronger singularity for small…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…
We count the number of critical points of a modular form with real Fourier coefficients in a $\gamma$-translate of the standard fundamental domain $\mathcal{F}$ (with $\gamma\in \mathrm{SL}_2(\mathbb{Z})$). Whereas by the valence formula…
In the systems showing critical behavior, various response functions have a singularity at the critical point. Therefore, as the driving field is tuned towards its critical value, the response functions change drastically, typically…
We investigate an initial-(periodic-)boundary value problem for a continuum equation, which is a model for motion of grain boundaries based on the underlying microscopic mechanisms of line defects (disconnections) and integrated the effects…
Many-body interactions in effective field theories for disordered interacting electrons are considered. It is shown that three-body and higher interaction terms are generated in perturbation theory, and some of the physical consequences of…
This paper studies the parabolic $p$-Laplace equation with $p>2$ in a moving domain under a Neumann type boundary condition corresponding to the total mass conservation. We establish the existence and uniqueness of a weak solution by the…
In the spirit of Morse homology initiated by Witten and Floer, we construct two $\infty$-categories $\mathcal{A}$ and $\mathcal{B}$. The weak one $\mathcal{A}$ comes out of the Morse-Samle pairs and their higher homotopies, and the strict…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
The classical gravitational two-body problem is generalized in order to be applicable also to weak gravitational fields. The equation of motion holds both for terrestrial and large cosmic scales, the Newtonian gravitational law represents a…