Current Issue : October-December Volume : 2021 Issue Number : 4 Articles : 5 Articles
In this paper, the conformal super-biderivations of two classes of Lie conformal superalgebras are studied. By proving some general results on conformal super-biderivations, we determine the conformal super-biderivations of the loop super-Virasoro Lie conformal superalgebra and Neveu–Schwarz Lie conformal superalgebra. Especially, any conformal super-biderivation of the Neveu–Schwarz Lie conformal superalgebra is inner....
In this paper, we initiate the concept of α-multiplier on almost distributive lattices. We prove some useful results by using the notion of α-multiplier and generalize the idea of multiplier on almost distributive lattices....
In this study, we define new semigroup structures using the set SS � {a ∈ S|aSa � 0} which is called the source of semiprimeness for a semigroup S with zero element. |SS|−idempotent semigroup, |SS|−regular semigroup, |SS|−reduced semigroup, and |SS|−nonzero divisor semigroup which are generalizations of idempotent, regular, reduced, and nonzero divisor semigroups in semigroup theory are investigated, and their basic properties are determined. In addition, we adapt some well-known results in semigroup theory to these new semigroups....
&e rototranslation group RT is the group comprising rotations and translations of the Euclidean plane which is a 3-dimensional Lie group. In this paper, we use the Riemannian approximation scheme to compute sub-Riemannian limits of the Gaussian curvature for a Euclidean C2-smooth surface in the rototranslation group away from characteristic points and signed geodesic curvature for Euclidean C2-smooth curves on surfaces. Based on these results, we obtain a Gauss–Bonnet theorem in the rototranslation group....
We prove the uniform Lipschitz bound of solutions for a nonlinear elliptic system modeling the steady state of populations that compete in a heterogeneous environment. This extends known quasi-optimal regularity results and covers the optimal case for this problem. The proof relies upon the blow-up technique and the almost monotonicity formula by Caffarelli, Jerison and Kenig....
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