Let B_2,p:={z∈C²:|z₁|²+|z₂|p<1} (0 < p < 1). Then, B_2,p (0 < p < 1) is a non-convex complex ellipsoid in C² without smooth boundary. In this article, we establish a boundary Schwarz lemma at z₀ ∈ ∂B_2,p for holomorphic self-mappings of the non-convex complex ellipsoid B_2,p, where z₀ is any smooth boundary point of B_2,p.

In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.

Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang[20, 21], Gardner, Hug, and Weil[5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.

In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the density.

The multi-dimensional system of nonlinear partial differential equations is considered. In two-dimensional case, this system describes process of vein formation in higher plants. Variable directions finite difference scheme is constructed. The stability and convergence of that scheme are studied. Numerical experiments are carried out. The appropriate graphical illustrations and tables are given.

In this article, we consider the drift parameter estimation problem for the nonergodic Ornstein-Uhlenbeck process defined as dX_t=θX_tdt + dG_t, t ≥ 0 with an unknown parameter θ > 0, where G is a Gaussian process. We assume that the process {X_t, t ≥ 0} is observed at discrete time instants t₁=△_n,…, t_n=n△_n, and we construct two least squares type estimators and for θ on the basis of the discrete observations {X_ti, i=1,…, n} as n → ∞. Then, we provide sufficient conditions, based on properties of G, which ensure that and  are strongly consistent and the sequences √n△_n(-θ) and √n△_n(-θ) are tight. Our approach offers an elementary proof of[11], which studied the case when G is a fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). As such, our results extend the recent findings by[11] to the case of general Hurst parameter H ∈ (0, 1). We also apply our approach to study subfractional Ornstein-Uhlenbeck and bifractional Ornstein-Uhlenbeck processes.

This article is devoted to characterizing the boundedness and compactness of multiplication operators from Hardy spaces to weighted Bergman spaces in the unit ball of Cⁿ.

In this article, we prove hyperstability results of the generalized Cauchy-Jensen functional equation
αf(x+y/α+ z)=f(x) + f(y) + αf(z)
for any fixed positive integer α ≥ 2 in ultrametric Banach spaces by using fixed point method.

The purpose of this article is to investigate (s,t)-weak tractability of multivariate linear problems in the average case setting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s,t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.

In this article, we prove a Picard-type Theorem and a uniqueness theorem for non-Archimedean analytic curves in the projective space Pⁿ(F), where the characteristic of F is 0 or positive. In the main results of this article, we ignore the zeros with large multiplicities.

Associated with an immersion φ:S³ → CP³, we can define a canonical bundle endomorphism F:TS³→TS³ by the pull back of the Kähler form of CP³. In this article, related to F we study equivariant minimal immersions from S³ into CP³ under the additional condition (▽_XF)X=0 for all X ∈ ker (F). As main result, we give a complete classification of such kinds of immersions. Moreover, we also construct a typical example of equivariant non-minimal immersion φ:S³ → CP³ satisfying (▽_XF)X=0 for all X ∈ ker (F), which is neither Lagrangian nor of CR type.

Let M be a (2k+2l+2)-dimensional smooth manifold. For such M, Bande and Hadjar introduce a new geometric structure called contact pair which roughly is a couple of 1-forms of constant classes with complementary kernels and foliations. We show the relationship between a pair of vector fields for a contact pair and a quadruple of functions on M. This is a generalization of the classical result for contact manifolds.

In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space. The disjoint supercyclic properties of weighted translations on locally compact discrete groups, the direct sums of finite classical weighted backward shifts, and the bilateral backward operator weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space l²(Z) never satisfy the d-Supercyclicity Criterion by a simple proof.

We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bⁿ. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_Ω^*(β, A, B), strong and almost spirallike mappings of type β and order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.

Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel, the specific constructions of Strebel differentials are difficult. Two special kinds of special Strebel differentials are constructed in [5, 6]. The Strebel rays [3] and the eventually distance minimizing rays [9] are important in Teichmüller spaces and moduli spaces, respectively. Motivated by the study of [3, 9], two special kinds of Strebel rays in the real hyper-elliptic subspace of Teichmüller space and two special kinds of EDM rays in the real hyper-elliptic subspace of moduli space are studied in this article.

In this article, we focus on the Cauchy problem for the generalized IMBq system in n-dimensional space, which arises from DNA. We show the global existence and decay estimates of solution for a class of initial velocity, provided that the initial value is suitably small.

In this article, the authors consider the weighted bounds for the singular integral operator defined by

where Ω is homogeneous of degree zero and has vanishing moment of order one, and A is a function on Rⁿ such that ▽A ∈ BMO(Rⁿ). By sparse domination, the authors obtain some quantitative weighted bounds for T_A when Ω satisfies regularity condition of L^r-Dini type for some r ∈ (1, ∞).

A pair of Banach spaces (X, Y) is said to be stable if for every ε-isometry f:X → Y, there exist γ > 0 and a bounded linear operator T:L(f) → X with ||T|| ≤ α such that ||Tf(x)-x|| ≤ γε for all x ∈ X, where L(f) is the closed linear span of f(X). In this article, we study the stability of a pair of Banach spaces (X, Y) when X is a C(K) space. This gives a new positive answer to Qian's problem. Finally, we also obtain a nonlinear version for Qian's problem.

In this article, we consider the non-linear difference equation
(f(z + 1)f(z)-1)(f(z)f(z-1)-1)=P(z, f(z))/Q(z, f(z)),
where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z) are estimated. Furthermore, we study the forms of rational solutions of the above equation.

In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu[21] and Qian[23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.

This article is concerned with the impermeable wall problem for an ideal polytropic model of non-viscous and heat-conductive gas in one-dimensional half space. It is shown that the 3-rarefaction wave is stable under some smallness conditions. The proof is given by an elementary energy method and the key point is to do the higher order derivative estimates with respect to t because of the less dissipativity of the system and the higher order derivative boundary terms.