In this paper, the authors introduce the notion of generalized squeezing function and study the basic properties of generalized squeezing functions and Fridman invariants. They also study the comparison of these two invariants, in terms of the so-called quotient invariant.

Recently, some concepts such as Hom-algebras, Hom-Lie algebras, Hom-Lie admissible algebras, Hom-coalgebras are studied and some classical properties of algebras and some geometric objects are extended on them. In this paper by recalling the concept of Hom-ρ-commutative algebras, the authurs intend to develop some of the most classical results in Riemannian geometry such as metric, connection, torsion tensor, curvature tensor on it and also they discuss about differential operators and get some results of differential calculus by using them. The notions of symplectic structures and Poisson structures are included and an example of ρ-Poisson bracket is given.

This paper characterizes the limits of a large system of interacting particles distributed on the real line. The interaction occurring among neighbors involves two kinds of independent actions with different rates. This system is a generalization of the voter process, of which each particle is of type A or a. Under suitable scaling, the local proportion functions of A particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wright white noise. To obtain the convergence, the tightness of these functions is derived from the moment estimate method.

In this paper the author establishes the sufficiency of Kalman’s rank condition on the approximate boundary controllability at a finite time for diagonalizable systems on an annular domain in higher dimensional case.

The main purpose of this paper is to study the differential geometrical objects on tangent bundle corresponding to dual-holomorphic objects of dual-holomorphic manifold. As a result of this approach, the authors find a new class of lifts (deformed complete lifts) in the tangent bundle.

This paper is concerned with the large time behavior of solutions to the Cauchy problem for a one-dimensional compressible non-isentropic Navier-Stokes/Allen-Cahn system which is a combination of the classical Navier-Stokes system with an Allen-Cahn phase field description. Motivated by the relationship between Navier-Stokes/Allen-Cahn and Navier-Stokes, the author can prove that the solutions to the one dimensional compressible non-isentropic Navier-Stokes/Allen-Cahn system tend time-asymptotically to the rarefaction wave, where the strength of the rarefaction wave is not required to be small. The proof is mainly based on a basic energy method.

Almansi-type decomposition theorem for bi-k-regular functions defined in a star-like domain Ω ⊆ ℝ ⁿ⁺¹ × ℝ ⁿ⁺¹ centered at the origin with values in the Clifford algebra Cl _2n+2,0(ℝ) is proved. As a corollary, Almansi-type decomposition theorem for biharmonic functions of degree k is given.

The authors give the condition that the Bergman kernel function on the first type of Cartan-Hartogs domain exists zeros. If the Bergman kernel function of this type of domain has zeros, the zero set is composed of several path-connected branches, and there exists a continuous curve to connect any two points in the non-zero set.

In this paper, the authors obtain the Dunkl analogy of classical L ^p Hardy inequality for p > N + 2γ with sharp constant ${\left({{{p - N - 2\gamma} \over p}} \right)^p}$, where 2γ is the degree of weight function associated with Dunkl operators, and L ^p Hardy inequalities with distant function in some G-invariant domains. Moreover they prove two Hardy-Rellich type inequalities for Dunkl operators.

This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system, and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products. Also, the authors show that if the locally compact group is amenable, then the crossed product and the reduced crossed product are isometrically isomorphic.

In this paper, the authors show that there exists infinitely many family of pairs of quadratic fields $\mathbb{Q} (\sqrt D)$ and $\mathbb{Q} (\sqrt {D + n})$ with D,n ∈ ℤ whose class numbers are both divisible by 3.