In this paper, the authors study the elliptic system arising from the study of Maxwell-Chern-Simons model. They show that there exists a family of non-topological solutions with magnetic field concentrated at some of the vortex points as the two physical parameters satisfying almost optimal conditions where the limiting profile is the singular Liouville equation.

The authors show that ra-almost divisibility and weak (m, n)-divisibility of C*-algebras in a class $\cal{P}$ are preserved to the simple unital C*-algebras which are asymptotically tracially in $\cal{P}$.

The number of singular points on a klt Fano surface X is less than or equal to 2ρ(X) + 2.

Applying Singh’s quadratic transformation and the “creative microscoping” method (introduced by the author and Zudilin in 2019), the author proves several new q-supercongruences for truncated 4ϕ3 series. Some related conjectures on q-supercongruences are also presented.

For a conjugation C on a separable, complex Hilbert space $\cal{H}$, the set ${\cal{S}}_{C}$ of C-symmetric operators on $\cal{H}$ forms a weakly closed, selfadjoint, Jordan operator algebra. In this paper, the authors study ${\cal{S}}_{C}$ in comparison with the algebra $\cal{B}(H)$ of all bounded linear operators on $\cal{H}$, and obtain ${\cal{S}}_{C}$-analogues of some classical results concerning $\cal{B}(H)$. The authors determine the Jordan ideals of ${\cal{S}}_{C}$ and their dual spaces. Jordan automorphisms of ${\cal{S}}_{C}$ are classified. The authors determine the spectra of Jordan multiplication operators on ${\cal{S}}_{C}$ and their different parts. It is proved that those Jordan invertible ones constitute a dense, path connected subset of ${\cal{S}}_{C}$.

In this paper, the authors obtain two kinds of Kastler-Kalau-Walze type theorems for conformal perturbations of twisted Dirac operators and conformal perturbations of signature operators by a vector bundle with a non-unitary connection on six-dimensional manifolds with (respectively without) boundary.

Let Δ₁(x; φ) denote the error term in the classical Rankin-Selberg problem. In this paper, the authors consider the higher power moments of Δ₁(x; φ) and derive the asymptotic formulas for 3-rd, 4-th and 5-th power moments, which improve the previous results.