In this paper, we investigate the problem of electromagnetic wave propagation in hyperbolic nonlinear media. To address this problem, we consider the scalar hyperbolic nonlinear Schrödinger system and its coupled version, namely hyperbolic Manakov t...
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Magneto conductance oscillations periodic in flux with periodicity $Φ_{0}$ and $Φ_{0}/2$ are seen in asymmetric Aharonov-Bohm rings as a function of density of electrons or Fermi wave vector. Dephasing of these oscillations is incorporated using...
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) ) = ∇ ( ∇ 2 ψ ) {\displaystyle \nabla ^{2}(\nabla \psi )=\nabla (\nabla \cdot (\nabla \psi ))=\nabla \left(\nabla ^{2}\psi \right)} ∇ 2 ( ∇ ⋅ A ) =
Oct 17, 2019 · To give an example, in the derivation of the wave equation from maxwell's equations, the following identity is used: $$ \nabla\times (\nabla\times \mathbf f)=\nabla (\nabla\cdot \mathbf f) …
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Mixture of Experts (MoE) models have achieved great success by significantly improving performance while maintaining computational efficiency through sparse expert activation. However, their enormous parameter sizes and memory demands pose major chal...
Translation-based knowledge graph embedding has been one of the most important branches for knowledge representation learning since TransE came out. Although many translation-based approaches have achieved some progress in recent years, the performan...
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Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the scattering and in...
We have recently solved the inverse scattering problem for one parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations conne...
The Pavlov equation is one of the simplest integrable systems of vector fields arising from various problems of mathematical physics and differential geometry which are intensively studied in recent literature. In this report, solving a nonlinear Rie...
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There exist two issues among popular lattice reduction (LR) algorithms that should cause our concern. The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovasz (LLL) algorithms may increase the lengths of basis vectors. The other is KZ reduc...