Subjects -> MATHEMATICS (Total: 1118 journals)     - APPLIED MATHEMATICS (92 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (819 journals)    - MATHEMATICS (GENERAL) (45 journals)    - NUMERICAL ANALYSIS (26 journals)    - PROBABILITIES AND MATH STATISTICS (113 journals) MATHEMATICS (819 journals)                  1 2 3 4 5 | Last

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 Acta Mathematica Sinica, English SeriesJournal Prestige (SJR): 0.379 Citation Impact (citeScore): 1Number of Followers: 6      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1439-8516 - ISSN (Online) 1439-7617 Published by Springer-Verlag  [2658 journals]
• Engel Condition and p-nilpotency of Finite Groups

Abstract: Let G be a finite group, and let P be a Sylow p-subgroup of G. Under the hypothesis that NG(P) is p-nilpotent, we provide some conditions to give a p-nilpotency criterion of finite groups by Engel condition, which improves some recent results.
PubDate: 2021-09-01

• Scattering Versus Blowup Beyond the Mass-Energy Threshold for the
Davey-Stewartson Equation in ℝ3

Abstract: We study the Cauchy problem for the Davey-Stewartson equation $${\rm{i}}{\partial _t}u + \Delta u + {\left u \right ^2}u + {E_1}({\left u \right ^2})u = 0,\,\,\,\,\,\,(t,x) \in \mathbb{R} \times {\mathbb{R}^3}.$$ The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u0)E(u0) above the ground state threshold M(Q)E(Q).
PubDate: 2021-09-01

• Toeplitz Products on Bergman-Sobolev Spaces over the Unit Polydisk

Abstract: In this paper, we characterize the compactness and Fredholmness of Toeplitz operators and Toeplitz products on Bergman-Sobolev spaces over the unit polydisk. We also calculate the essential norm of finite sums of finite Toeplitz products on these spaces.
PubDate: 2021-09-01

• Variational Principle for Topological Pressure on Subsets of Free
Semigroup Actions

Abstract: We investigate the relations between Pesin-Pitskel topological pressure on an arbitrary subset and measure-theoretic pressure of Borel probability measures for finitely generated semigroup actions. Let (X, $${\cal G}$$ ) be a system, where X is a compact metric space and $${\cal G}$$ is a finite family of continuous maps on X. Given a continuous function f on X, we define Pesin-Pitskel topological pressure $${P_{\cal G}}(Z,f)$$ for any subset Z ⊂ X and measure-theoretical pressure $${P_{\mu ,{\cal G}}}(X,f)$$ for any $$\mu \in {\cal M}(X)$$ , where $${\cal M}(X)$$ denotes the set of all Borel probability measures on X. For any non-empty compact subset Z of X, we show that $${P_{\cal G}}(Z,f) = \sup \{ {P_{\mu ,{\cal G}}}(X,f):\mu \in {\cal M}(X),\mu (Z) = 1\} .$$
PubDate: 2021-09-01

• Asymptotic Distributions for Power Variation of the Solution to a
Stochastic Heat Equation

Abstract: Let u = {u(t,x),t ∈ [0,T],x ∈ ℝ} be a solution to a stochastic heat equation driven by a space-time white noise. We study that the realized power variation of the process u with respect to the time, properly normalized, has Gaussian asymptotic distributions. In particular, we study the realized power variation of the process u with respect to the time converges weakly to Brownian motion.
PubDate: 2021-09-01

• Difference of Composition Operators on Some Analytic Function Spaces

Abstract: For two analytic self-maps φ and ψ defined on the unit disk ⅅ, we characterize completely the boundedness and compactness of the difference Cφ − Cψ of the composition operators Cφ and Cψ from Bloch space B into Besov space $$B_\nu ^\infty$$ . Moreover, we also give a complete characterization of the compactness of the difference Cφ − Cψ on BMOA space.
PubDate: 2021-09-01

• The Neumann Problem for Parabolic Hessian Quotient Equations

Abstract: In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of elliptic Hessian quotient equations. Also solutions of the classical Neumann problem converge to a translating solution.
PubDate: 2021-09-01

• On the Distribution of Hecke Eigenvalues over Piatetski-Shapiro Prime
Twins

Abstract: Let λf (n) be the normalized n-th Fourier coefficient of holomorphic eigenform f for the full modular group and ℙc(x): = {p ≤ x ∣ [pc]prime}, c ∈ ℝ+. In this paper, we show that for all 0 < c < 1 the mean value of λf(n) in ℙc(x) is ≪x log−Ax assuming the Riemann Hypothesis. Unconditionally, in the sense of Lebesgue measure, it holds for almost all c ∈ (ε, 1 − ε).
PubDate: 2021-09-01

• Symmetry of Positive Solutions to the Coupled Fractional System with
Isolated Singularities

Abstract: In this paper, we consider the following two-coupled fractional Laplacian system with two or more isolated singularities $$\left\{ {\begin{array}{*{20}{c}} {{{( - \Delta )}^s}u}&{ = {\mu _1}{u^{2q + 1}} + \beta {u^{p1 - 1}}{v^{p2}},}&\; \\ {{{( - \Delta )}^s}u}&{ = {\mu _2}{v^{2q + 1}} + \beta {u^{p1}}{v^{p2 - 1}}}&{\text{in}\;{\mathbb{R}^n}\backslash \Lambda ,} \\ {u > 0,}&{v > 0,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}&\; \end{array}} \right.$$ where s ∈ (0, 1), n > 2s and n ≥ 2. μ1, μ2 and β are all positive constants. p1, p2 > 1 and $${p_1} + {p_2} = 2q + 2 \in \left( {{{2n - 2s} \over {n - 2s}},\left. {{{2n} \over {n - 2s}}} \right]} \right.$$ . Λ ⊂ ℝn contains finitely many isolated points. By the method of moving plane, we obtain the symmetry results for positive solutions to above system.
PubDate: 2021-09-01

• Derivations of the Positive Part of the Two-parameter Quantum Group of
Type G2

Abstract: In this paper, we compute the derivations of the positive part of the two-parameter quantum group of type G2 by embedding it into a quantum torus. We also show that the first Hochschild cohomology group of this algebra is a two-dimensional vector space over the complex field.
PubDate: 2021-09-01

• Higher Genus FJRW Theory for Fermat Cubic Singularity

Abstract: In this paper, we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Givental formalism. As results, we prove the finite generation property and holomorphic anomaly equation for the associated FJRW theory. Via general LG-LG mirror theorem, our results also hold for the Saito-Givental theory of the Fermat cubic singularity.
PubDate: 2021-08-01

• Banach Spaces Which are Isometric to Subspaces of c0(Γ)

Abstract: In this paper, we give a number of characterizations for a Banach space X which is isometric to a subspace of c0, or, c0(Γ), successively, in terms of extreme points of its dual unit ball BX*, Fréchet and Gâteaux derivatives of its norm, or, in terms of w*-strongly exposed points and w*-exposed points of BX*.
PubDate: 2021-08-01

• Dirac Operators on Quadratic Lie Superalgebras

Abstract: Assume that $$\mathfrak{r}$$ is a finite dimensional complex Lie superalgebra with a non-degenerate super-symmetric invariant bilinear form, $$\mathfrak{p}$$ is a finite dimensional complex super vector space with a non-degenerate super-symmetric bilinear form, and $$\nu : \mathfrak{r}\to \mathfrak{osp}(\mathfrak{p})$$ is a homomorphism of Lie superalgebras. In this paper, we give a necessary and sufficient condition for $$\mathfrak{r} \oplus \mathfrak{p}$$ to be a quadratic Lie superalgebra. Then, we define the cubic Dirac operator $$D(\mathfrak{g},\mathfrak{r})$$ on $$\mathfrak{g}$$ and give a formula of $${\left( {D\left( {\mathfrak{g},\mathfrak{r}} \right)} \right)^2}$$ . Finally, we get the Vogan’s conjecture for quadratic Lie superalgebras by $$D(\mathfrak{g},\mathfrak{r})$$ .
PubDate: 2021-08-01

• Characterizations of Weighted BMO Space and Its Application

Abstract: In this paper, we prove that the weighted BMO space $${\rm{BM}}{{\rm{O}}^p}(\omega ) = \left\{ {f \in L_{{\rm{loc}}}^1:\mathop {\sup }\limits_Q \left\ {{\chi _Q}} \right\ _{{L^p}(\omega )}^{ - 1}{{\left\ {(f - {f_Q}){\omega ^{ - 1}}{\chi _Q}} \right\ }_{{L^p}(\omega )}} < \infty } \right\}$$ is independent of the scale p ∈ (0, ∞) in sense of norm when ω ∈ A1. Moreover, we can replace Lp(ω) by Lp,∞(ω). As an application, we characterize this space by the boundedness of the bilinear commutators [b, T]j(j = 1, 2), generated by the bilinear convolution type Calderón-Zygmund operators and the symbol b, from $${L^{{p_1}}}(\omega ) \times {L^{{p_2}}}(\omega )$$ to Lp(ω1−p) with 1 < p1,p2 < ∞ and 1/p =1/p1 + 1/p2. Thus we answer the open problem proposed by Chaffee affirmatively.
PubDate: 2021-08-01

• Equitable Vertex Arboricity Conjecture Holds for Graphs with Low
Degeneracy

Abstract: The equitable tree-coloring can formulate a structure decomposition problem on the communication network with some security considerations. Namely, an equitable tree-k-coloring of a graph is a vertex coloring using k distinct colors such that every color class induces a forest and the sizes of any two color classes differ by at most one. In this paper, we show some theoretical results on the equitable tree-coloring of graphs by proving that every d-degenerate graph with maximum degree at most Δ is equitably tree-k-colorable for every integer k ≥ (Δ + 1)/2 provided that Δ ≥ 9.818d, confirming the equitable vertex arboricity conjecture for graphs with low degeneracy.
PubDate: 2021-08-01

• The Uniqueness of Knieper Measure on Non-compact Rank 1 Manifolds of
Non-positive Curvature

Abstract: We study the Knieper measures of the geodesic flows on non-compact rank 1 manifolds of non-positive curvature. We construct the Busemann density on the ideal boundary, and prove that if there is a Knieper measure on T1M with finite total mass, then the Knieper measure is unique, up to a scalar multiple. Our result partially extends Paulin-Pollicott-Shapira’s work on the uniqueness of finite Gibbs measure of geodesic flows on negatively curved non-compact manifolds to non-compact manifolds of non-positive curvature.
PubDate: 2021-08-01

• Property (ω) and the Single-valued Extension Property

Abstract: By the new spectrum originated from the single-valued extension property, we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property (ω) holds. Meanwhile, the relationship between hypercyclic property (or supercyclic property) and property (ω) is discussed.
PubDate: 2021-08-01

• On Weak Well-posedness of the Nearest Point and Mutually Nearest Point
Problems in Banach Spaces

Abstract: Let G be a nonempty closed subset of a Banach space X. Let $${\cal B}(X)$$ be the family of nonempty bounded closed subsets of X endowed with the Hausdorff distance and $${{\cal B}_G}(X) = \overline {\{ A \in {\cal B}(X):A \cap G\emptyset \} }$$ , where the closure is taken in the metric space $$({\cal B}(X),H)$$ . For x ∈ X and $$F \in {{\cal B}_G}(X)$$ , we denote the nearest point problem inf{∥x − g∥: g ∈ G} by min(x, G) and the mutually nearest point problem inf{∥f − g∥: f ∈ F,g ∈ G} by min(F, G). In this paper, parallel to well-posedness of the problems min(x, G) and min(F, G) which are defined by De Blasi et al., we further introduce the weak well-posedness of the problems min(x, G) and min(F, G). Under the assumption that the Banach space X has some geometric properties, we prove a series of results on weak well-posedness of min(x, G) and min(F, G). We also give two sufficient conditions such that two classes of subsets of X are almost Chebyshev sets.
PubDate: 2021-08-01

• On Li-Yau Heat Kernel Estimate

Abstract: We present some improvements of the Li-Yau heat kernel estimate on a Riemannian manifold with Ricci curvature bounded below. As a consequence we prove a gradient estimate to the heat kernel with an optimal leading term.
PubDate: 2021-08-01

• Quasi-normal Family of Meromorphic Functions Whose Certain Type of
Differential Polynomials Have No Zeros

Abstract: Define the differential operators ϕn for n ∈ ℕ inductively by ϕ1 [f](z)= f (z) and $${\phi _{n + 1}}[f](z) = f(z){\phi _n}[f](z) + {d \over {dz}}{\phi _n}[f](z)$$ . For a positive integer k ≥ 2 and a positive number δ, let $${\cal F}$$ be the family of functions f meromorphic on domain D ⊂ ℂ such that ϕk[f](z) ≠ 0 and ∣Res(f, a) − j∣ ≥ δ for all j ∈{0, 1,…,k − 1} and all simple poles a of f in D. Then $${\cal F}$$ is quasi-normal on D of order 1.
PubDate: 2021-08-01

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