Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then C*max(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.
Let A(z) be an entire function with $\mu (A) < \tfrac{1}{2}$ such that the equation f (k) + A(z)f = 0, where k ≥ 2, has a solution f with λ(f) < μ(A), and suppose that A 1 = A + h, where h ≢ 0 is an entire function with ρ(h) < μ(A). Then g (k) + A 1(z)g = 0 does not have a solution g with λ(g) < ∞.
The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in ℂ n, which are natural extensions to higher dimensions of some Fekete and Szegö inequalities for subclasses of the normalized univalent functions in the unit disk.
Let F be an algebraically closed field of prime characteristic, and W(m, n, 1) be the simple restricted Lie superalgebra of Witt type over F, which is the Lie superalgebra of superderivations of the superalgebra $\mathfrak{A}(m;1)\otimes\wedge(n)$, where $\mathfrak{A}(m;1)$ is the truncated polynomial algebra with m indeterminants and ∧(n) is the Grassmann algebra with n indeterminants. In this paper, the author determines the character formulas for a class of simple restricted modules of W(m, n, 1) with atypical weights of type I.
In this paper, the authors introduce a class of functionals. This class forms a Banach algebra for the special cases. The main purpose of this paper is to investigate some properties of the modified analytic function space Feynman integral of functionals in the class. Those properties contain various results and formulas which were not obtained in previous papers. Also, the authors establish some relationships involving the first variation via the translation theorem on function space. In particular, the authors establish the Fubini theorem for the modified analytic function space Feynman integral which was not obtained in previous researches yet.
Let L = −Δ + V(x) be a Schrödinger operator, where Δ is the Laplacian on ℝ n, while nonnegative potential V(x) belonging to the reverse Hölder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schrödinger operator and their commutators. Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schröodinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schroödinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood (H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.
Let Ω ∈ L s(S n−1) (s > 1) be a homogeneous function of degree zero and b be a BMO function or Lipschitz function. In this paper, the authors obtain some boundedness of the Calderón-Zygmund singular integral operator T Ω and its commutator [b, T Ω] on Herz-Morrey spaces with variable exponent.
An initial boundary-value problem for the Hirota equation on the half-line, 0 < x < ∞, t > 0, is analysed by expressing the solution q(x, t) in terms of the solution of a matrix Riemann-Hilbert (RH) problem in the complex k-plane. This RH problem has explicit (x, t) dependence and it involves certain functions of k referred to as the spectral functions. Some of these functions are defined in terms of the initial condition q(x, 0) = q 0(x), while the remaining spectral functions are defined in terms of the boundary values q(0, t) = g 0(t), q x(0, t) = g 1(t) and q xx(0, t) = g 2(t). The spectral functions satisfy an algebraic global relation which characterizes, say, g 2(t) in terms of {q 0(x), g 0(t), g 1(t)}. The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.
The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition $\tilde Z(\xi ,Y) \cdot \tilde S = 0$, where $\tilde Z, \tilde S$ are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.
Let E be the Engel group and D be a bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, the author constructs a parametrization of a quasi-pendulum equation by Jacobi functions, and then gets the space-like Hamiltonian geodesics in the Engel group with a sub-Lorentzian metric.