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Let H2(ⅅ2) be the Hardy space over the bidisk ⅅ2, and let Mψ,ϕ = [(ψ(z) − ϕ(w))2] be the submodule generated by (ψ(z) − ϕ(w))2, where ψ(z) and ϕ(w) are nonconstant inner functions. The related quotient module is denoted by Nψ,ϕ = H2(ⅅ2) ⊖ Mψ,ϕ. In this paper, we give a complete characterization for the essential normality of Nψ,ϕ. In particular, if ψ(z)= z, we simply write Mψ,ϕ and Nψ,ϕ as Mϕ and Nϕ respectively. This paper also studies compactness of evaluation operators L(0)∣nϕ and R(0)ϕnϕ, essential spectrum of compression operator Sz on Nϕ, essential normality of compression operators Sz and Sw on Nϕ.

This paper contains two parts toward studying abelian varieties from the classification point of view. In a series of papers, the current authors and T.-C. Yang obtain explicit formulas for the numbers of superspecial abelian surfaces over finite fields. In this paper, we give an explicit formula for the size of the isogeny class of simple abelian surfaces with real Weil number $\sqrt{q}$. This establishes a key step that one may extend our previous explicit calculations of superspecial abelian surfaces to those of supersingular abelian surfaces.The second part is to introduce the notion of genera and ideal complexes of abelian varieties with additional structures in a general setting. The purpose is to generalize the results of Yu on abelian varieties with additional structures to similitude classes, which establishes more results on the connection between geometrically defined and arithmetically defined masses for further investigation., Comment: 23 pages. Section 5.4 corrected

Zhao and Ho asked in a recent paper that for each T0 space X, whether KB(X) (the set of all irreducible closed sets of X whose suprema exist) is the canonical k-bounded sobrification of X in the sense of Keimel and Lawson. In this paper, we construct a counterexample to give a negative answer. We also consider the subcategory Topκ of the category Top0 of T0 spaces, and prove that the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category Topκ.

In 2002, in the paper entitled “A subspace theorem approach to integral points on curves”, Corvaja and Zannier started the program of studying integral points on algebraic varieties by using Schmidt’s subspace theorem in Diophantine approximation. Since then, the program has led a great progress in the study of Diophantine approximation. It is known that the counterpart of Schmidt’s subspace in Nevanlinna theory is H. Cartan’s Second Main Theorem. In recent years, the method of Corvaja and Zannier has been adapted by a number of authors and a big progress has been made in extending the Second Main Theorem to holomorphic mappings from C into arbitrary projective variety intersecting general divisors by using H. Cartan’s original theorem. We call such method “a Cartan’s Second Main Theorem approach”. In this survey paper, we give a systematic study of such approach, as well as survey some recent important results in this direction including the recent work of the author with Paul Voja.

This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli–Chern class on compact complex manifolds, and proved that the (1, 1) curvature form of the Levi–Civita connection represents the first Aeppli–Chern class which is a natural link between Riemannian geometry and complex geometry. In this paper, we study the geometry of compact complex manifolds with Levi–Civita Ricci-flat metrics and classify minimal complex surfaces with Levi–Civita Ricci-flat metrics. More precisely, we show that minimal complex surfaces admitting Levi–Civita Ricci-flat metrics are Kahler Calabi–Yau surfaces and Hopf surfaces.

In my former paper “A pre-order principle and set-valued Ekeland variational principle” (see [J. Math. Anal. Appl., 419, 904–937 (2014)]), we established a general pre-order principle. From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles (denoted by EVPs) in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy’s EVP in [On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381–396 (2011)], where the perturbation contains a weak τ-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle, but also can be applied to obtain the above Khanh and Quy’s EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances.

The well-known Hartman-Grobman Theorem says that a C1 hyperbolic diffeomorphism F can be locally linearized by a homeomorphism Φ. For parameterized systems Fθ, known results show that the corresponding homeomorphisms Φθ exist uniquely in a functional space equipped with the supremum norm and depend continuously on the parameter θ. In this paper, we further extend the results to Holder dependence of Φθ on θ by Pugh’s strategy, but introducing a kind of special Holder norm instead of the usual supremum norm in the proof to control the linear parts of Fθ. This requires a new Holder linearization result for every Fθ.

Recently, Geher and Semrl have characterized the general form of surjective isometries of the set of all projections on an infinite-dimensional separable Hilbert space using unitaries and antiunitaries. In this paper, we study the surjective L2-isometries of the projection lattice of an infinite dimensional Hilbert space and show that every such isometry can also be described by unitaries and antiunitaries.

This paper is mainly about holomorphic mappings associated with conic regions which are closely connected with k − ST(α). We introduce new subclasses of starlike (spirallike) functions, namely, S (k,α)(S (k,α,β)), and discuss their coefficient estimates and the Fekete-Szego-Goluzin’s problem. Then we generalize S (k,α,β) on the unit ball Bn in ℂn, that is, k-conic spirallike mappings of type β and order α. We obtain the growth, covering and distortion theorems of the generalized mappings. Besides that, we construct k-conic spirallike mappings of type β and order α on Bn through Sc(k,α,β) by the generalized Roper-Suffridge extension operators.

In this paper we introduce the notions of (Banach) density-equicontinuity and density-sensitivity. On the equicontinuity side, it is shown that a topological dynamical system is density-equicontinuous if and only if it is Banach density-equicontinuous. On the sensitivity side, we introduce the notion of density-sensitive tuple to characterize the multi-variant version of density-sensitivity. We further look into the relation of sequence entropy tuple and density-sensitive tuple both in measure-theoretical and topological setting, and it turns out that every sequence entropy tuple for some ergodic measure on an invertible dynamical system is density-sensitive for this measure; and every topological sequence entropy tuple in a dynamical system having an ergodic measure with full support is density-sensitive for this measure.

This paper is mainly devoted to proving the four equivalent defining properties of a CBA(κ) space. The proof is based on an interesting tool we established which describes the cyclical five-step deformation procedure for quadrangles in the model 2-plane $$S_\kappa^2$$ , including the limit shape of each step. As a byproduct we give a complete list of cyclical deformation procedures for all kinds of quadrangles on $$S_1^2$$ . At last we make a contrast of geometric properties of CBA with CBB spaces, including a comparison between their defining properties and a discussion about Alexandrov’s Lemma.

In this paper, we show that every super weakly compact convex subset of a Banach space is an absolute uniform retract, and that it also admits the uniform compact approximation property. These can be regarded as extensions of Lindenstrauss and Kalton’s corresponding results.

In this paper we prove an anticyclotomic Iwasawa main conjecture proposed by Perrin-Riou for Heegner points when the global sign is -1, using a recent work of the author on one divisibility of Iwasawa-Greenberg main conjecture for Rankin-Selberg p-adic L-functions. As a byproduct we also prove the equality for the above mentioned main conjecture under some local conditions., Comment: 13 Pages. Comments welcome

In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation $${{\cal S}^b}: = {\overline {\rm{\Delta }} ^{\alpha /2}} + b \cdot \nabla $$ where $${\overline {\rm{\Delta }} ^{\alpha /2}}$$ is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ K −1 . In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.

In this paper, let m ≥ 1 be an integer, M be an m-dimensional compact Riemannian manifold. Firstly the linearized Poincare map of the Lagrangian system at critical point x $${d \over {dt}}{L_q}\left( {t,x,\dot x} \right) - {L_p}\left( {t,x,\dot x} \right) = 0$$ is explicitly given, then we prove that Morse index and Maslov-type index of x are well defined whether the manifold M is orientable or not via the parallel transport method which makes no appeal to unitary trivialization and establish the relation of Morse index and Maslov-type index, finally derive a criterion for the instability of critical point and orientation of M and obtain the formula for two Maslov-type indices.

In this paper, using the method of blow-up analysis, we obtained a Trudinger—Moser inequality involving Lp-norm on a closed Riemann surface and proved the existence of an extremal function for the corresponding Trudinger—Moser functional.

In this paper we extend the Fibonacci-like maps to a wider class with the so-called “bounded combinatorics”. The Fibonacci-like renormalization operator $${\cal R}$$ is defined and we show that the orbit of each map from this class converges to a universal limit under iterates of $${\cal R}$$ .

Let f and g be functions in Fock—Sobolev space F2,m. In this paper, we completely characterize the boundedness and compactness of $${H_{\mathop f\limits^ - }}{T_{\mathop g\limits^ - }}$$ .

Let (M,g) be a compact Kahler manifold and (E,F) be a holomorphic Finsler vector bundle of rank r ≥ 2over M. In this paper, we prove that there exists a Kahler metric Φ defined on the projective bundle P(E)of E, which comes naturally from g and F. Moreover, a necessary and sufficient condition for Φ having positive scalar curvature is obtained, and a sufficient condition for Φ having positive Ricci curvature is established.

In this paper, assuming there is a fiberwise Morse function, we extend Bismut-Lott index theorem to the complex valued case.

In this paper, we study complex symmetric C0-semigroups on the Bergman space A2(ℂ+) of the right half-plane ℂ+. In contrast to the classical case, we prove that the only involutive composition operator on A2(ℂ+) is the identity operator, and the class of J-symmetric composition operators does not coincide with the class of normal composition operators. In addition, we divide semigroups {ϕt} of linear fractional self-maps of ℂ+ into two classes. We show that the associated composition operator semigroup {Tt} is strongly continuous and identify its infinitesimal generator. As an application, we characterize Jσ-symmetric C0-semigroups of composition operators on A2(ℂ+).

In this paper, we give the complete classifications of isoparametric hypersurfaces in Randers space forms. By studying the principal curvatures of anisotropic submanifolds in a Randers space (N, F) with the navigation data (h, W), we find that a Randers space form (N, F, dµBH) and the corresponding Riemannian space (N, h) have the same isoparametric hypersurfaces, but in general, their isoparametric functions are different. We give a necessary and sufficient condition for an isoparametric function of (N, h) to be isoparametric on (N, F, dµBH), from which we get some examples of isoparametric functions.

In this paper, first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism. Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order 4. Moreover, we propose a hyperfield of order 4 which is not as a quotient hyperfield $${F \over G}$$ . Finally, some programs written in MATLAB which are based on obtained results compute the number of polygroups, weak polygroups and Krasner hyperfields of order 4 up to isomorphism.

This paper is concerned with general n × n upper-triangular operator matrices with given diagonal entries. The characterizations of perturbations of their left (resp. right) Weyl spectrum and Weyl spectrum are given, based on the space decomposition technique. Moreover, some sufficient and necessary conditions are given under which the left (resp. right) Weyl spectrum and the Weyl spectrum of such operator matrix, respectively, coincide with the union of the left (resp. right) Weyl spectrum and the Weyl spectrum of its diagonal entries.

In this paper, we study and characterize locally projectively flat singular square metrics with constant flag curvature. First, we obtain the sufficient and necessary conditions that singular square metrics are locally projectively flat. Furthermore, we classify locally projectively flat singular square metrics with constant flag curvature completely.

In this paper, on homogeneous groups, we study the Littlewood-Paley operators in variable exponent spaces. First, we prove that the weighted Littlewood-Paley operators are controlled by the weighted Hardy-Littlewood maximal function, and obtain the vector-valued inequalities of the Littlewood-Paley operators, including the Lusin function, Littlewood-Paley g function and $$g_\lambda ^*$$ function. Second, we prove the boundedness of multilinear Littlewood-Paley $$g_{\psi, \lambda}^*$$ function.

In this paper we study the complete space-like λ-surfaces in the three dimensional Minkowski space $$ℝ_1^3$$. As the result, we obtain a complete classification theorem for all the complete space-like λ-surfaces $$x:{M^2} \to ℝ_1^3$$ with the second fundamental form of constant length. This is a natural extension to the λ-surfaces in $$ℝ_1^3$$ of a recent interesting classification theorem by Cheng and Wei for λ-surfaces in the Euclidean space ℝ3.

Let Gi be closed Lie groups of U(n), Ωi be bounded Gi-invariant domains in ℂn which contains 0, and O(ℂn)Gi = ℂ, for i = 1, 2. It is known that if f: Ω1 →} Ω2 is a proper holomorphic mapping, and f−1{0} = {0}, then f is a polynomial mapping. In this paper, we provide an upper bound for the degree of such a polynomial mapping using the multiplicity of f.

As known to all, it is quite difficult to compute the fundamental group of a surface of general type. In this paper, applying Moishezon-Teicher’s algorithm, we investigate the fundamental group of a special surface of general type with zero topological index, namely, the Galois cover of the (2,3)-embedding of ℂℙ1 × T. Because the full presentation of the group is very complicated, we compute its special quotient and get an interesting result about its structure.

The main purpose of this paper is using the analytic method and the properties of the character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and the two-term exponential sums, and give several interesting identities and asymptotic formulae for them.

In this paper, we construct random two-faced families of matrices with non-Gaussian entries to approximate a bi-free central limit distribution with a positive definite covariance matrix. We prove that, under modest conditions weaker than independence, a family of random two-faced families of matrices with non-Gaussian entries is asymptotically bi-free from a two-faced family of constant diagonal matrices.

In this paper, we prove quasi-modularity property for the twisted Gromov-Witten theory of $$\mathcal{O}(3)$$ over ℙ2. Meanwhile, we derive its holomorphic anomaly equation.

In this paper we give a classification of special endomorphisms of nil-manifolds: Let $f:N/\Gamma \rightarrow N/\Gamma$ be a covering map of a nil-manifold and denote by $A:N/\Gamma \rightarrow N/\Gamma$ the nil-endomorphism which is homotopic to $f$. If $f$ is a special $TA$-map, then $A$ is a hyperbolic nil-endomorphism and $f$ is topologically conjugate to $A$., Comment: 23 pages. arXiv admin note: text overlap with arXiv:1008.4500 by other authors

In this paper, we generalize the concept of asymptotic Hankel operators on $$H^2(\mathbb{D})$$ to the Hardy space $$H^2(\mathbb{D}^n)$$ (over polydisk) in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence. Meanwhile, we introduce ith-partial Hankel operators on $$H^2(\mathbb{D}^n)$$ and obtain a characterization of its compactness for n > 1. Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on $$H^2(\mathbb{D}^n)$$ . It is also shown that a Toeplitz operator with symbol ϕ is asymptotic Hankel if and only if ϕ is holomorphic function in $$L^\infty(\mathbb{T}^n)$$ .

In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular, for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.

This paper studies the ℳ0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the ℳ0-shadowing property is described by the set of all Anosov diffeomorphisms. The C1-stably ℳ0-shadowing property on a non-trivial transitive set implies the diffeomorphism has a dominated splitting.

This paper is devoted to investigating the existence and uniqueness of mild solution to the 3D incompressible micropolar fluid system in the Fourier-Herz framework. By taking advantage of microlocal analysis and the mutual effect in the same frequency range of convection term, we give a special initial data (u0, ω0) whose norm of $$F\dot B_{1, q}^{- 1}\left({q > 2} \right)$$ is arbitrarily small, however, the couple (u0, ω0) produces a solution which is arbitrarily large in $$F\dot B_{1, q}^{- 1}$$ after an arbitrarily short time. This implies the system is ill-posed in the sense of “norm inflation” as q > 2.

In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet L-function at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.

This paper gives a generalization of the classical Borel’s Lemma. Then as an application of this generalized Borel’s Lemma, a uniqueness theorem for two linearly non-degenerate meromorphic maps of ℂm into ℙn(ℂ) (n ≥ 2) sharing 2n + 2 hyperplanes in general position is proved.

Let H2(γ) be the Hilbert space over the bidisk $$\mathbb{D}^2$$ generated by a positive sequence γ = {γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H2(γ) with γ = {γnm}n,m≥0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk $$\mathbb{D}^2$$ .

In this paper we study the derivatives of Frobenius and the derivatives of Hodge—Tate weights for families of Galois representations with triangulations. We generalize the Fontaine—Mazur $$\mathcal{L}$$ -invariant and use it to build a formula which is a generalization of the Colmez—Greenberg—Stevens formula. For the purpose of proving this formula we show two auxiliary results called projection vanishing property and “projection vanishing implying $$\mathcal{L}$$ -invariants” property.

Usually, the condition that T is bounded on L2(ℝn) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(f)= ∑i λiT(ai), provided that f = ∑i λiai in L2 (ℝn), where ai is an L2 atom of this Hardy space. So far, the L2 atomic decomposition of local Hardy spaces hp(ℝn), 0 > p ≤ 1, hasn’t been established. In this paper, we will solve this problem, and also show that hp(ℝn) can also be characterized by discrete Littlewood-Paley functions.

This paper is concerned with small quadratic perturbations to one parameter family of generic reversible quadratic vector fields with a simple center. The first objective is to show that this system exhibits two small amplitude limit cycles emerging from a Hopf bifurcation. The second one we prove that the system has no limit cycle around the weak focus of order two. The results may be viewed as a contribution to proving the conjecture on cyclicity proposed by Iliev (1998).

In this paper, we prove that the nonautonomous Schrodinger flow from a compact Riemannian manifold into a Kahler manifold admits a local solution. Under some certain conditions, the solution is unique and has higher regularity.

In the previous article "Hearts of twin cotorsion pairs on exact categories", we introduced the notion of the heart for any cotorsion pair on an exact category with enough projectives and injectives, and showed that it is an abelian category. In this paper, we construct a half exact functor from the exact category to the heart. This is analog of the construction of Abe and Nakaoka for triangulated categories. We will also use this half exact functor to find out a sufficient condition when two different hearts are equivalent., 26 pages

In this paper, we study the initial-boundary value problem for the semilinear pseudo-parabolic equations ut − ΔXut − ΔXu = |u|p−1u, where X = (X1,X2,…,Xm) is a system of real smooth vector fields which satisfy the Hormander’s condition, and ΔX = $${{\rm{\Delta}}_X} = \sum\nolimits_{j = 1}^m {X_j^2} $$ is a finitely degenerate elliptic operator. By using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy. The asymptotic behavior of the global solutions and a lower bound for blow-up time of local solution are also given.

In this paper, we investigate the positive solutions of $$\mathfrak{L}u=\frac{\partial u}{\partial t}$$ on self-shrinkers, then get some gradient estimates and Harnack inequalities for the positive solutions.

Let V be an asymptotically cylindrical Kahler manifold with asymptotic cross-section $$\mathfrak{D}$$ . Let ( $$E_{\mathfrak{D}},\phi_{\mathfrak{D}}$$ ) be a stable Higgs bundle over $$\mathfrak{D}$$ , and (E, e) a Higgs bundle over V which is asymptotic to ( $$E_{\mathfrak{D}},\phi_{\mathfrak{D}}$$ ). In this paper, using the continuity method of Uhlenbeck and Yau, we prove that there exists an asymptotically translation-invariant projectively Hermitian Yang-Mills metric on (E,e).

This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge-Ampere equation detD2u(x) = b(x)f (u(x)), u > 0, x ∈ Ω, where Ω is a strictly convex and bounded smooth domain in ℝN with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b ∈ C∞ (Ω) is positive in Ω, but may be appropriate singular on the boundary.

Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl’s theorem, where f ∊ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl’s theorem for f(T).