Recently, many novel and exotic phases have been proposed by considering the role of topology in non-Hermitian systems, their emergent properties are wide current interest. In this work we propose generalization semi-Dirac semimetals, which feature a linear dispersion along one momentum direction quadratic other. We study topological phase transitions such two-dimensional semimetals presence pa...

in this paper, we have de ned and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are de ned by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

We prove that Lipschitz learning on graphs is consistent with the absolutely minimal Lipschitz extension problem in the limit of infinite unlabeled data and finite labeled data. In particular, we show that the continuum limit is independent of the distribution of the unlabeled data, which suggests the algorithm is fully supervised (and not semisupervised) in this setting. We also present some n...

In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type ( Dn − n−1 ∑ i=1 aiD αi ) x(t) ∈ F (t, x(φ(t))), a.e. on (0, 1), I1−αnx(0) = c, αn ∈ (0, 1), where F (t, ·) is lower semicontinuous from R into R and F (·, ·) is measurable. The corresponding single-valued problem will be considered first.

where x stands for the three coordinate functions, ^(w , u)} ff (#\ u), x{u, u), and X stands for their three Jacobians. Various theorems of the following general type have been proved by McShane, Caccioppoli, Cimmino, and Radó: If (i) the triples of functions xn{u , u), i = 1, 2; n = 0, 1, 2, • • • , satisfy certain conditions; (ii) the surfaces defined by x = xn(u , u), i = l,2;n = l,2, • • •...