In this paper, the authors systematically discuss orbit braids in M × I with regards to orbit configuration space F _G(M, n), where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G. These orbit braids form a group, named orbit braid group, which enriches the theory of ordinary braids.

The authors analyze the substantial relations among various braid groups associated to those configuration spaces F _G(M, n), F(M/G, n) and F(M, n). They also consider the presentations of orbit braid groups in terms of orbit braids as generators by choosing M = ℂ with typical actions of ℤ _p and (ℤ₂)².

The purpose is to introduce the notions of 3-Bihom-ρ-Lie algebras and 3-pre-Bihom-ρ-Lie algebras. The authors describe their constructions and express the related lemmas and theorems. Also, they define the 3-Bihom-ρ-Leibniz algebras and show that a 3-Bihom-ρ-Lie algebra is a 3-Bihom-ρ-Leibniz algebra with the ρ-Bihom-skew symmetry property. Moreover, a combination of a 3-Bihom-ρ-Lie algebra bracket and a Rota-Baxer operator gives a 3-pre-Bihom-ρ-Lie algebra structure.

In this paper, the authors consider the zero-viscosity limit of the three dimensional incompressible steady Navier-Stokes equations in a half space ℝ⁺ × ℝ². The result shows that the solution of three dimensional incompressible steady Navier-Stokes equations converges to the solution of three dimensional incompressible steady Euler equations in Sobolev space as the viscosity coefficient going to zero. The method is based on a new weighted energy estimates and Nash-Moser iteration scheme.

The authors study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus (KE for short) equation and construct the long time asymptotic expansion of its solution in fixed space-time cone with C(x ₁, x ₂, v ₁, v ₂) = {(x, t) ∈ ℝ² : x = x ₀ + vt, x ₀ ∈ [x ₁, x ₂], v ∈ [v ₁, v ₂]}. By using the inverse scattering transform, Riemann-Hilbert approach and $\overline{\partial}$ steepest descent method, they obtain the lone time asymptotic behavior of the solution, at the same time, they obtain the solitons in the cone compare with the all N-soliton the residual error up to order $\cal{O}(t^{-{3\over 4}})$.

In this article, the refined Schwarz-Pick estimates for positive real part holomorphic functions $p(x)=p(0)+\sum\limits_{m=k}^{\infty}{{D^{m}p(0)(x^{m})}\over{m!}}:G\rightarrow\mathbb{C}$ are given, where k is a positive integer, and G is a balanced domain in complex Banach spaces. In particular, the results of first order Fréchet derivative for the above functions and higher order Fréchet derivatives for positive real part holomorphic functions $p(x)=p(0)+\sum\limits_{s=1}^{\infty}{{D^{sk}p(0)(x^{sk})}\over{(sk)!}}:G\rightarrow\mathbb{C}$ are sharp for G = B, where B is the unit ball of complex Banach spaces or the unit ball of complex Hilbert spaces. Their results reduce to the classical result in one complex variable, and generalize some known results in several complex variables.

In this paper, the authors consider the range of a certain class of ASH algebras in [An, Q., Elliott, G. A., Li, Z. and Liu, Z., The classification of certain ASH C*-algebras of real rank zero, J. Topol. Anal., 14(1), 2022, 183–202], which is under the scheme of the Elliott program in the setting of real rank zero C^*-algebras. As a reduction theorem, they prove that all these ASH algebras are still the AD algebras studied in [Dadarlat, M. and Loring, T. A., Classifying C ^*-algebras via ordered, mod-p K-theory, Math. Ann., 305, 1996, 601–616].

Let $\mathbb{B}_{E}$ be a bounded symmetric domain realized as the unit open ball of JB*-triples. The authors will characterize the bounded weighted composition operator from the Bloch space $\cal{B}(\mathbb{B}_{E})$ to weighted Hardy space $H_{v}^{\infty}(\mathbb{B}_{E})$ in terms of Kobayashi distance. The authors also give a sufficient condition for the compactness, and also give the upper bound of its essential norm. As a corollary, they show that the boundedness and compactness are equivalent for composition operator from $\cal{B}(\mathbb{B}_{E})$ to $H^{\infty}(\mathbb{B}_{E})$, when E is a finite dimension JB*-triple. Finally, they show the boundedness and compactness of weighted composition operators from $H_{v}^{\infty}(\mathbb{B}_{E})$ to $H_{v,0}^{\infty}(\mathbb{B}_{E})$ are equivalent when E is a finite dimension JB*-triple.

Infinite game is a power tool in studying various objects and finding descriptions of some properties of filters in mathematics. Game-theoretic characterizations for meager filters, Q-filters and Ramsey filters were obtained by Tomek Bartoszynski, Claude Laflamme and Marion Scheepers. In this paper, the authors obtain two game-theoretic characterizations for rapid filters on ω.

In this paper, the authors extend the Roper-Suffridge operator on the generalized Hartogs domains. They mainly research the properties of the extended operator. By the characteristics of Hartogs domains and the geometric properties of subclasses of spirallike mappings, they obtain the extended Roper-Suffridge operator preserving almost starlikeness of complex order λ, almost spirallikeness of type β and order α, parabolic spirallikeness of type β and order ρ on the Hartogs domains in different conditions. They conclude that the corresponding extension operator preserves the same geometric invariance on the unit ball B ⁿ in ℂ ⁿ. The conclusions provide a new approach to study these geometric mappings in ℂ ⁿ.