We study the synchronization of a generalized Kuramoto system in which coupling weights are determined by phase differences between oscillators. employ fast-learning regime Hebbian-like plasticity rule so that interaction oscillators is enhanced approach phases. First, we well-posedness problem for singular weighted systems Lipschitz continuity deprived. present dynamics equipped with all subcr...

Abstract We consider the EBT algorithm (a particle method) for nonlocal equation with a discontinuous interaction kernel. The main difficulty lies in low regularity of kernel, which is not Lipschitz continuous, thus preventing application standard arguments. Therefore, we use radial symmetry problem instead and transform it using spherical coordinates. resulting has kernel only one singularity ...

We study the properties of a future singularity encountered by a perfect fluid observer in tilting spatially homogeneous Bianchi cos-mologies. We derive the boost formulae for the Weyl tensor to establish that, for two observers that are asymptotically null with respect to each other, their respective Weyl parameters generally both tend to zero, constant, or infinity together. We examine three ...

In this paper, we first present the complete list of the singularity types of the Picard number one Gorenstein log del Pezzo surface and the number of the isomorphism classes with the given singularity type. Then we give out a method to find out all singularity types of Gorenstein log del Pezzo surface. As an application, we present the complete list of the Dynkin type of the Picard number two ...

Singularity based on fractal and multifractal is a technique for detection of depletion and enrichment for geochemical exploration, while the index of vertical geochemical zonality (Vz) of Pb.Zn/Cu.Ag is a practical method for exploration of blind porphyry copper mineralization. In this study, these methods are combined for recognition, delineation, and enrichment of Vz in Jebal- Barez in the s...

We study analytically the Cauchy horizon singularity inside spherically-symmetric charged black holes, coupled to a spherical self-gravitating, minimally-coupled, massless scalar field. We show that all causal geodesics terminate at the Cauchy horizon at a null singularity, which is weak according to the Tipler classification. The singularity is also deformationally-weak in the sense of Ori. Ou...