We first establish an equivalence theorem of Minkowski spaces by using results in centro-affine differential geometry. As applications in Finsler geometry, we prove that a Finsler manifold is a Berwald space if it is a Landsberg space and satisfies one of the following conditions: closed Cartan-type form, vanishing S curvature or vanishing mean Berwald curvature.
An extension of algebras is a homomorphism of algebras preserving identities. The relative global dimension of an extension f:B→A is defined to be the supremum of relative projective dimensions of all A-modules. We give a necessary and sufficient condition for an extension of algebras to have finite relative global dimension. As an application, we give a new short proof for a result in Hochschild [Relative homological algebra,Trans. Am. Math. Soc., 1956, 82: 246–269].
We are concerned with the existence of the periodic solutions for a class of weakly coupled systems. Under some sub-linear conditions about time-mapping, we prove the existence of at least one harnomic solution by applying the Poincaré–Bohl theorem and infinite periodic solutions with period 2mπ to equations by applying the higher dimensional version of the Poincaré–Birkhoff theorem, where m ∈ Z and m>1.
A finite group G is called a CN-group if every subgroup H of G is C-normal in G. In this paper, we will give first a complete classification of the 2-generator CN-p-groups. Then by applying the structure of the 2-generator CN-p-groups, we obtain the following results: If p is a odd prime, then G is a CN-p-group if and only if Φ(G)≤ Z(G). If p = 2, then G is a CN-p-group if and only if for any given a ∈ G and for any g ∈ Φ(G), we have ga=g or ga=g-1. We also get some criteria of CN-p-groups in terms of direct product of CN-p-groups.
We use the analysis method, the arithmetical properties of Dedekind sums and first kind Chebyshev polynomials to study the asymptotic estimation problem of one kind hybrid mean value involving the Dedekind sums and the first kind Chebyshev polynomials. At last, we obtain a sharp asymptotic formula for it.
The main purpose of this paper is using the analytic method and the properties of classical Gauss sums and trigonometric sums to study the computational problem of one kind hybrid power mean of two different Gauss sums, and give an exact computational formula for it.
Recently Ding has constructed certain cyclic codes by using new cyclotomy (V0,V1) and studied the properties. In this paper we construct new binary sequences of order two and length pq by using the cyclotomy (V0,V1), and calculate the autocorrelation values, linear complexity and minimal polynomials.
Let φ(n),S(n) be the Euler function and the Smarandache function of the positive integer n, respectively. Based on elementary methods and techniques, according to the algorithm formula of the Smarandache function, all solutions of the equation φ(pαm)=S(pαk) are given, where p is a prime, α and m are both positive integers, and gcd(m,p)=1. And then we get the solutions of the equation φ(n)=S(nk). Furthermore, all positive integers n satisfying the condition S(n)|σ(n) are determined. At last, basing on the Mobius transformation inversion theorem, we prove that the equation φ(n)=Σd|n S(d) has only two solutions, namely, n=25 and n=3×25.
The main purpose of this paper is using the analytic method and the properties of trigonometric sums to study the computational problem of one kind hybrid power mean of two different Gauss sums, and give an exact computational formula for it. As an application of our result, we give an exact formula for the number of solutions of one kind diagonal congruence equation mod p, where p is an odd prime.
The main purpose of this paper is using the elementary methods and the properties of the trigonometric sums to study the computational problem of one kind fourth power mean of the two-term exponential sums, and give a precise computational formula for it.
This paper establishes the boundedness of the commutator Mb generated by the Marcinkiewicz integral M and the regularized bounded mean oscillation space with the discrete coefficient RBMO(μ) over non-homogeneous metric measure space. Under the assumption that the dominating function λ satisfies the ∈-weak reverse doubling condition, when p ∈ (1,∞), the authors prove that the Mb is bounded on the Lebesgue space Lp(μ). Furthermore, the boundedness of the Mb on the Morrey space is also obtained.
In this work we extend the quantitative and sharp weighted bounds for the Ap theorem to the q-variation of ω-Calderón–Zygmund operators. These results make use of the new sparse dominating techniques given recently by Lerner to control the q-variation. Compared with the work of Hytönen etc., which also involved the sharp weighted estimates of q-variations,ω in our case only satisfies the Dini condition, and related cut-off is sharp.
We investigate the ergodic property of Markov chains in general state space, an exponentially ergodic conclusion Markov chains, adding conditions π(fp)<∞,p＞1. By using the coupling method, there exists the full absorption set, such that the Markov chain is f-exponentially ergodic on it.
In this article, some properties of measurable operators associated with a von Neumann algebra are considered. The concept of step operator is defined and it is proved that any positive measurable operator can be strongly approximated by some step operators on its domain, which means that any positive measurable operator can be strongly approximated by some projections on its domain. In addition, the measurability of composition operator of measurable operator and bounded operator is discussed.
Isometry is a significant subject in the study of the structure of space. In this paper, we will introduce a special F-space,b(2) space, and give the representation theorem for the onto isometric mapping on the unit spheres of the b(2) spaces, then we solved the Tingley's problem on b(2) space.
Let K/Fq be a global function field over the finite field Fq,and l be a prime number different from the characteristic of K. Denote by ζl a primitive l-th root of unity in a fixed algebraic closure of K. For two given elements a,b ∈ K*-(K*)l, we study in this paper the properties of radical extensions K(l√a) and K(l√a,l√b) of K. By the Kummer theory, we give a necessary and sufficient condition for K(l√a)/K and K(l√a,l√b)/K being not geometric extensions. Suppose that a,b ∈ K* - (K*)l are l-independent. For a prime divisor P of K and the corresponding discrete valuation ring OP, a necessary and sufficient condition for a,b,generating cyclic group (OP/P)* is presented by the properties of the above two function fields extensions. With the help of results obtained, the Dirichlet density of Ma,b, which is the set of prime divisors of K such that cyclic group (OP/P)* can be generated by a,b, is given explicitly in this paper.
We prove that the global Ding projective dimension and global Ding injective dimension coincide for any ring. We investigate the relationship between singularity categories and stable categories with respect to Ding modules, and characterize Gorenstein (regular) rings and the finiteness of left global dimension of rings in terms of singularity categories and Ding modules.
We discuss some algebraic properties of Toeplitz operators with a class of radial and quasi-homogeneous symbols on the Fock space of the complex plane. We give necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator, and study the zero-product problem of several such Toeplitz operators. Furthermore, the corresponding commuting problem of Toeplitz operators with quasi-homogeneous symbols is studied.
