We use Fourier-splitting method to establish the temporal decay estimates for weak solutions to the 3D generalized magneto-hydrodynamics equations firstly. We obtain not only the upper bounds estimates but also the lower bounds estimates of time decay for the solutions of these equations, moreover, the corresponding optimal algebraic time decay rates are found.
We consider the following near-Hamilton system
where a < 0, c > 0, 4bc > a2, 0 <|ε|<<1, f(x, y) and g(x, y) cubic polynomials of x and y. We obtain the upper bound of the number of isolated zeros of the Abelian integral.
We study modified maximal functions in a quasi-metric measure space (X, d, μ), where X is a set, μ stands for the Borel measure which is not doubling, d is a quasi-metric being quasi-symmetric. We establish the weak (1, 1) estimates and (Φ, Φ) type estimates for modified maximal functions, where Φ is more general than N-functions. As applications, we prove a generalized Lebesgue differential theorem in the quasi-metric measure space; the results of this paper can be applied to the Lie group G=(RN+1, o) associated with the Kolmogorov type operator with constant coefficients.
In this paper, the object of our discussion is a S3-geometry manifold S3/G, that is the obit space of S3 with free action of group G. The so called S3-geometry indicate that S3 is given the standard metric. The isometric transformation group is SO(4), and G is the discrete subgroup of SO(4). Our main result is that we use the projective resolution of Z over ZG-module and the relationship of the cohomology ring of K(G, 1) with the cohomology of G to obtain the Zm cohomology ring of the manifold M and the Bockstein homomorphism:Hn(M, Zm) → Hn+1(M, Zm). Using the above results, we have obtained the degrees of the map that from any S3-geometry manifold to the 3-Lens space.
In this paper the Casimir number of a special kind of Verlinde modular category l of rank n+1 is calculated to be 2n+4. As an application it follows from Higman's theorem that the Grothendieck algebra Gr(l) ⊗Z K over a field K is semisimple if and only if 2n+4 is a unit in K. This is equivalent to saying that the (n+1)-th Dickson polynomial En+1(X) of the second kind has no multiple factors in K[X]. If 2n+4 is zero in K, we use the factorizations of Dickson polynomials to describe the Jacobson radical of Gr(l) ⊗Z K explicitly.
The main purpose of this paper is using the trigonometric sums method and the properties of Gauss sums to study the computational problem of one kind hybrid power mean involving the cubic Gauss sums and Kloostermann sums, and give an interesting linear recurrence formula for it. As some applications of this recurrence formula, we obtained a series of asymptotic formulas for the high-th hybrid power mean involving the cubic Gauss sums and Kloostermann sums.
Let Aα2 be the weighted Bergman space on the unit polydisk, and l the space of all bounded composition operators between Bergman spaces endowed with operator norm, we characterize the topological connection of l using Hilbert-Schmidt differences of two composition operator in this paper.
We introduce a new concept of generalized distribution semi-groups induced by a bounded linear operator in Banach space and discuss the properties of this concept. In our approach, the generator of a generalized distribution semi-group may not be densely defined. Also introduced is the distributional solution of degenerate evolution equation in the sense of Laplace transformation. The constructive expression of the distributional solution for the degenerate evolution equation is given by the generalized distribution semi-group.
We consider the following oscillatory integral operator:
where the function f is assumed to be a Schwartz function on Rn and m, k > 0. In this paper, we characterize the sufficient and necessary conditions which ensure the boundedness for Tm,k,n from Lp(Rn) (1 ≤ p < ∞) to Lq(Rn). In addition, the operator Tm,k,n also maps L1(Rn) into l0(Rn).
There is a close connection between Hochschild homology groups of a k-algebra and cycles of the Gabriel quiver associated to the k-algebra. In this paper,based on the minimal projective bimodule resolution of a self-injective Koszul four-point algebra constructed by Furuya, we calculate the dimensions of Hochschild homology spaces of the algebra by using combinatorial methods, and give a k-basis of every Hochschild homology space in terms of cycles. Moreover, we obtain the dimensions of cyclic homology groups of the algebra when the base field k is of zero characteristic.
In this paper, the concepts of weak medial idempotent and quasi-medial idempotent of regular semigroups are introduced. The aim of this paper is to explore the properties of the two types of idempotents. Several regular semigroups having weak(quasi-) medial idempotents are constructed to indicate the relationship between weak medial idempotents and quasi-medial idempotents, various ways are given to confirm that an idempotent is a weak medial idempotent or a quasi-medial idempotent, and some descriptions of orthodox semigroups in terms of quasi-media idempotents are hold. At last, the structure theorem of every regular semigroup with a quasi-medial idempotent is obtained. As an application of the results, such kind of construction method help us to get a way to determine whether a regular semigroup contains a multiplicative inverse transversal or not.
In the Formal Deductive System L* of Fuzzy Propositional Calculus, the notion of closed theory is introduced and its properties are investigated. Furthermore, the completeness of Formal Deductive System L* is proved through closed theory based on formula set F(S). At first, in the formal deductive system L*, a concept of closed theory is introduced, and a method for extending theories to closed theories is given; at second, in the formal deductive system L*, a concept of total closed theory is introduced, and the existence of a total closed theory satisfying relevant conditions is proved; at third, in the formal deductive system L*, the properties of congruence relations determined by closed theories are investigated, a concept of strong congruence relations is introduced to formulas set F(S), and methods of changing each other between strong congruence relations and closed theories are revealed; at fourth, in the formal deductive system L*, it is proved that closed theory style L*-Lindenbaum algebras determined by closed theories are R0-algebras, and a closed theory-L*-Lindenbaum algebra is linear if and only if a closed theory is total; at last, the completeness of the formal deductive system L* is accomplished by making use of total closed theory style L*-Lindenbaum algebras, and the results obtained before have been improved.
The inclusion ideal graph of a ring R, written as ΓI(R), is a directed graph which has all nontrivial left rings of R as vertex set and there is a directed edge from a vertex I1 to a distinct vertex I2 if and only if I1 is properly contained in I2. In addition, the ideal-relation graph of a ring R, written as Γi(R), is also a directed graph which has R as vertex set and there is a directed edge from a vertex A to a distinct vertex B if and only if the left ideal of R generated by A is properly contained in the left ideal generated by B. Let Fq be a finite field, the set of n×n matrices over Fq be denoted by Mn(Fq). In this paper, both the automorphisms of ΓI(Mn(Fq)) and the automorphisms of Γi(Mn(Fq)) are characterized.
This article researches the batch Markov arrival process (BMAP) by using path-analysis method which is different from using conventional matrix analysis method. We are capable of calculating its jumping probability through the representation (Dk, k=0, 1, 2,...) of BMAP, demonstrating the fact that BMAP's phase process is time-homogeneous Markov chain, figuring out the transition probabilities and density matrix of the phase process. Moreover, if we give a Q process J with a finite state space and define the counting process of its jumping points as N, we can demonstrate that adjoint process X*=(N, J) of Q process J is a MAP. The MAP's transition probabilities and representation (D0, D1) are exactly worked out, which are expressed by density matrix Q.
The extinction and the stationary distribution to a stochastic SEIR epidemic model with nonlinear incidence rate in a population of varying size are discussed. Under moderate conditions, the existence-and-uniqueness of the global solution, exponential stability and the stationary distribution with ergodicity are obtained. By means of linearization and Fourier transform, we prove that the solution obeys a fourdimensional normal distribution, and the mean and the variance matrix are followed. Then numerical simulations are carried out to illustrate our results.
We consider a branching process indexed by a general renewal process. Assume that the renewal distribution satisfies the Cramér condition and the branching process belongs to the Böttcher case, i.e., if always at least two offspring are born, we obtain the large deviations of such process.
