In this paper, by applying Nevanlinna theory, we will mainly investigate the existence and characteristic estimates of transcendental solutions of two types of difference-composite functional equations and a class of system of difference-composite functional equations, and obtain some results. Some examples show that the condition in Theorems are precise.
In this paper, we obtain two interesting results on homologically smooth connected cochain DG algebras. More precisely, we show that any Koszul DG A-module in Dfg(A) is compact, when A is a homologically smooth connected cochain DG algebra with a Noetherian cohomology graded algebra H(A). We prove that the homologically smoothness of A is equivalent to Dfg(A)=Dc(A), if A is a Koszul connected cochain DG algebra such that H(A) is a Noetherian graded algebra with a balanced dualizing complex.
Let K/F be a cyclic extension of prime degree l of global function fields, where F is finite separable extension of Fq(T). Using Conner and Hurrelbrink's exact hexagon for function fields and other exact hexagon from short exact sequences, we study in this paper the structure of Sylow l-subgroup of the ideal class group of K. To be clear, we consider separately the two possibilities, when l divides the ideal class number of F and when it does not. Meanwhile, we summarize in this paper several conditions that characterize when every unit of F is norm of an element of the field K.
We study the second order degenerate differential equations with finite delay:(Mu')'(t) + αu'(t)=Au(t) + Gu't + Fut + f(t) (t ∈[0,2π]) with periodic boundary conditions u(0)=u(2π), (Mu)'(0)=(Mu)'(2π) in periodic Triebel-Lizorkin spaces. Using operator-valued Fourier multipliers theorems in Triebel-Lizorkin spaces Fp,qs(T; X), we give necessary and sufficient conditions for the Fp,qs-well-posedness of above equations.
We give a new perturbation analysis method for Moore-Penrose bounded quasi-linear projection generalized inverse of closed linear operators in Banach spaces. The key tool used in this paper is the generalized Neumann lemma, which is very different from the generalized Banach lemma used in other results. We obtain another perturbation theorem for the Moore-Penrose bounded quasi-linear generalized inverse of closed linear operators and three inequalities for error estimation.
In this paper, the stability of heteroclinic loop connecting two hyperbolic saddles with one dimensional unstable manifold is considered in arbitrarily finite dimensional spaces. By taking a suitable linear transformation and coordinate change to straighten the local stable manifold and the local unstable manifold, we construct the Poincaré map by composing the singular flow map and the regular flow map. By estimating the modules of some vectors rather skillfully, we obtain the ratio of the distance between the first recurrent point and the heteroclinic point to the distance between the initial point and the heteroclinic point. As a direct consequence, we derive the concise stability criterion of the heteroclinic loop connecting two hyperbolic saddles with one-dimentional unstable manifold for the higher dimensional system.
Let b ≥ 2, D1, D2 ⊆ {0, 1,..., b -1}, S1, S2 ⊆ N and S1 ∩ S2=∅. Let E be a set defined by digit restrictions of (1.1). In this paper, we discuss the fractal dimensions of E, prove the upper and lower Assouad dimension formulas of E.
The main purpose of this paper is using the estimate for trigonometric sums and the properties of character sums to study the computational problem of one kind hybrid power mean involving the two-term exponential sums and polynomial character sums, and give two interesting computational formulae for it.
In this article, the authors investigate the regularity properties of the centered Kakeya (Nikodym) maximal operator KN(with N>2) and its fractional variant Kα,N (with 0 < α < d). More precisely, the authors prove that, the operator Kα,N is bounded and continuous from W1,p(Rd to W1,p(Rd for 1 < p < ∞ and q=dp/(d -αp) with 0 ≤ α < d/p, and the operator KN is bounded and continuous on the fractional Sobolev spaces Ws,p(Rd, inhomogeneous Triebel-Lizorkin spaces Fsp,q(Rd and inhomogeneous Besov spaces Bsp,q(Rd for all 0 < s < 1 and 1 < p, q < ∞. In addition, two pointwise estimates for the derivatives of the fractional Kakeya maximal functions and the regularity properties for the discrete versions of these operators are also presented.
For any k ≥ 1, k-Jordan product of two elements x,y in a ring R is defined by {x, y}k={{x, y}k-1, y}1, where {x, y}0=x and {x, y}1=xy + yx. Assume that R is a unital prime ring with a nontrivial idempotent. It is shown that a surjective map f:R → R satisfies {f(x), f(y)}2={x, y}2 for all x, y ∈ R if and only if there exists some λ ∈ C (the extended centroid of R) with λ3=1 such that one of the following statements holds:(1) if the characteristic of R is not 2, then f(x)=λx holds for all x ∈ R; (2) if the characteristic of R is 2, then f(x)=λx + μ(x) holds for all x ∈ R, where μ:R → C is a map. As an appication, such maps on factor von Neumann algebras are characterized.
The main result of this paper is to give the concrete form of the largest topological closure of the power-set Quantale over an ordered semigroup. Based on which, it is proved that the category Quant of Quantale is a fully reflective subcategory of the category OSGrp★ of ordered semigroups. Finally, we give an application for the Quantale completions of ordered semigroups.
This paper studies the asymptotic behavior of solutions for equations of the two-dimensional Ladyzhenskaya fluid with periodic boundary conditions. The authors first prove the existence of the pullback attractor for the associated process. Then they establish the existence and uniqueness of the invariant Borel probability measure contained in the pullback attractor.
This paper is concerned with curvatures of doubly warped product (DWP) of Hermitian manifolds. The necessary and sufficient conditions for a compact nontrivial DWP-Hermitian manifold to have constant holomorphic sectional curvature were obtained. This study provides us an effective way to construct new Hermitian manifolds which satisfy the first or the second Einstein condition.
In[Construction for de Bruijn sequences with large stage, Des. Codes Cryptogr, 2017, 85(2):343-358], the authors constructed many de Bruijn sequences with large stages, by using irreducible polynomials with degree n. From the adjacency matrix of the irreducible polynomial, one can calculate the number of de Bruijn sequences in theory that can be constructed by the methods in[6]. We calculate the adjacency matrix of a special class of irreducible polynomials, which has degree n and periods l=(2n -1)/3 and l=(2n -1)/5.
By calculating the integral of distance function on self-similar measure with the help of circle mapping, we provide the average distance of self-similar flower fractal in terms of self-similar measure and apply the result to evolving flower networks.
We use the mean residual lifetime function to analyze the length biased data with right censorship. When the truncated time satisfies the stationarity assumption, the left truncated and right censored data turns to be the length-biased data and has special property. In order to improve the efficiency of the estimators, we use the combining estimating equation method that incorporates the additional information about length-biased sampling scheme to do the inference. The simulation shows that the combining estimating equation method performs better than the naive method which regards length-biased data as the left truncated data.
