Related papers: A Generalization of Monotonicity Condition and App…
In this paper we establish some results concerning the existence, regularity and concentration phenomenon of nontrivial solitary waves for a Generalized Kadomtsev-Petviashvili (GKP) equation in $\mathbb{R}^2.$ Variational methods are used…
We consider the problem of birationally modifying a morphism of complete varieties to make it a morphism from a nonsingular variety to a normal variety. Our main result is to give a counterexample to this problem. This example also is a…
Despite the celebrated popularity of Graph Neural Networks (GNNs) across numerous applications, the ability of GNNs to generalize remains less explored. In this work, we propose to study the generalization of GNNs through a novel…
We show that Gabbay's nonmonotonic consequence relations can be reduced to a new family of relations, called entrenchment relations. Entrenchment relations provide a direct generalization of epistemic entrenchment and expectation ordering…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…
Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so…
In this letter, by regarding finite-time stability as an inverse problem, we reveal the essence of finite-time stability and fixed-time stability. Some necessary and sufficient conditions are given. As application, we give a new approach…
WE derive exact and more general solutions of the two coupled Gross-Pitaevskii equation with suitable parameters by demonstrating two analytical methods. In the first method, equations are analysed and inferred some of their mathematical…
We generalise classical reconstruction results in algebra, using the language of monads, monoidal categories, module categories, as well as various notions of duality, such as closedness, Grothendieck--Verdier duality (also known as…
This is an overview of the present-day versions of monadology with some applications to vector lattices and linear inequalities.
Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still…
We study the symmetries enjoyed by the Newtonian equations of motion of the non-relativistic dark matter fluid coupled to gravity which give rise to the phenomenon of gravitational instability. We also discuss some consistency relations…
A modification of general relativity is presented in which Newton's constant and the cosmological constant become a conjugate pair of dynamical variables.
Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…
General Relativity is the modern theory of gravitation. It has replaced the newtonian theory in the description of the gravitational phenomena. In spite of the remarkable success of the General Relativity Theory, the newtonian gravitational…
In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves as well as stationary fields like…
This paper uses a generalization of symplectic geometry, known as $n$-symplectic geometry and developed by Norris, to find observables on three-dimensional manifolds. It will be seen that for the cases considered, the $n$-symplectic…
We classify non-dilatonic NS-NS type II supergravity backgrounds admitting a consistent absolute parallelism. They are all given by parallelised Lie groups admitting scalar flat bi-invariant lorentzian metrics. There are seven different…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
In this article, we make a generalization of classical fixed point theorems by using the concept of half-continuity and then apply it to improve the nonuniqueness result for solutions to the vacuum Einstein conformal equations shown by the…