1,720,964 research outputs found
On non-topological solutions for planar Liouville Systems of Toda-type
No full textMotivated by the study of non-abelian Chern Simons vor- tices of non-topological type in Gauge Field Theory we analyse the solvability of some Liouville-type system in presence of singular sources We identify necessary and sufficient conditions which ensure the radial solvability of this system.Non UBCUnreviewedAuthor affiliation: Ben Gurion UniversityFacult
Asymptotic behavior of the <i></i>-norm of mollified <i></i> functions and applications to singular perturbation problems
No full text
Upper bounds for a class of energies containing a non-local term
No full textIn this paper we construct upper bounds for families of
functionals of the form
where Δ = div { u}. Particular cases of such functionals arise in
Micromagnetics. We also use our technique to construct upper bounds
for functionals that appear in a variational formulation of
the method of vanishing viscosity for conservation laws
Approximations in Besov Spaces and Jump Detection of Besov Functions with Bounded Variation
Full text linkIn this paper, we provide a proof that functions belonging to Besov spaces
, , ,
satisfy the following formula under a certain condition:
\begin{equation} \label{eq:main result in abstract} \lim_{{\epsilon}\to
0^+}\frac{1}{|\ln{\epsilon}|}\left[u_{\epsilon}\right]^q_{W^{r,q}(\mathbb{R}^N,\mathbb{R}^d)}=N\lim_{{\epsilon}\to
0^+}\int_{\mathbb{R}^N}\frac{1}{{\epsilon}^N}\int_{B_{\epsilon}(x)}\frac{|u(x)-u(y)|^q}{|x-y|^{rq}}dydx.
\end{equation} Here, represents the Gagliardo
seminorm, and denotes the convolution of with a mollifier
,
. Furthermore, we
prove that every function in satisfies
\begin{multline} \lim_{\epsilon\to
0^+}\frac{1}{|\ln{\epsilon}|}\left[u_{\epsilon}\right]^q_{W^{1/q,q}(\mathbb{R}^N,\mathbb{R}^d)}=N\lim_{{\epsilon}\to
0^+}\int_{\mathbb{R}^N}\frac{1}{{\epsilon}^N}\int_{B_{\epsilon}(x)}\frac{|u(x)-u(y)|^q}{|x-y|}dydx
=\left(\int_{S^{N-1}}|z_1|~d\mathcal{H}^{N-1}(z)\right)\int_{\mathcal{J}_u}
\Big|u^+(x)-u^-(x)\Big|^q d\mathcal{H}^{N-1}(x), \end{multline} for every
. Here are the one-sided approximate limits of along the
jump set
Non-relativistic model of the laws of gravity and electromagnetism, invariant under the change of inertial and non-inertial coordinate systems
Full text linkUnder the classical non-relativistic consideration of the space-time we propose the model of the laws of gravity and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian coordinate system. Being in the frames of non-relativistic model of the space-time, we adopt some general ideas of the General Theory of Relativity, like the assumption of invariance of the most general physical laws in every inertial and non-inertial coordinate system and equivalence of factious forces in non-inertial coordinate systems and the force of gravity. Moreover, in the frames of our model, we obtain that the laws of Non-relativistic Quantum Mechanics also invariant under the change of inertial or non-inertial cartesian coordinate system.This is a preprint of the following work: Arkady Poliakovsky, The Laws of Gravity and Electromagnetism: A Non-relativistic Model Invariant Under the Change of Inertial and Non-inertial Coordinate Systems , 2024, Springer Cham, reproduced with permission of Springer Nature Switzerland AG 2024. The final authenticated version is available online at: https://doi.org/10.1007/978-3-031-61407-
Lorentzian geometrical structures with global time, Gravity and Electrodynamics
No full textWe investigate Lorentzian structures in the four-dimensional space-time, supplemented either by a covector field of the time-direction or by a scalar field of the global time. Furthermore, we propose a new metrizable model of the gravity. In contrast to the usual Theory of General Relativity where all ten components of the symmetric pseudo-metrics are independent variables, the presented here model of the gravity essentially depend only on single four-covector field, restricted to have only three-independent components. However, we prove that the Gravitational field, ruled by the proposed model and generated by some massive body, resting and spherically symmetric in some coordinate system, is given by a pseudo-metrics {Kmn}m,n=0,1,2,3, which coincides with the well known Schwarzschild metric from the General Relativity. The Maxwell equations and Electrodynamics are also investigated in the frames of the proposed model. In particular, we derive the covariant formulation of Electrodynamics of moving dielectrics and para/diamagnetic mediums
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