Let μM,D be the self-affine measure uniquely determined by the iterated function system (IFS){φd(x)=M-1(x+d)}d∈D with equal weight, where M ∈ Mn(R) is an expanding matrix and D⊂Rn is a finite digit set. The spectrality or nonspectrality of μM,D is directly connected with the existence of orthogonal exponential basis (Fourier basis) in the Hilbert space L2(μM,D), and has been received much attention in recent years. In this paper, we provide several sufficient conditions for self-affine measures to be non-spectral. The results here extend the corresponding non-spectral criterions of Dutkay, Jorgensen and others in a simple manner.
Using the Littlewood-Paley decomposition technique, Fourier transform and inverse Fourier transform, we study the boundedness of bilinear Fourier multiplier operators on the scales of inhomogeneous Triebel-Lizorkin and Besov spaces with positive smoothness.
The relationship between James constant J(X) and the Jordan-von Neumann type constant C-∞(X) is given to show there exists a example such that C-∞(X)< CZ(X). Moreover, some sufficient conditions for normal structure in terms of the constant C-∞(X) and the Benavides constant R(a, X) are presented. These results improve some known results.
We studied the best restriction approximation problems using entire functions of exponential type as the approximation tools on some generalized Sobolev classes of smooth functions defined by the differential operator induced by an algebraic polynomial with only real zeros. By the methods of Fourier transform and periodization, etc, we obtained the exact constants of the average relative widths and the best restriction approximation on the generalized Sobolev classes in the L2(R) norm, and obtained the asymptotic results of the best restriction approximation on the generalized Sobolev classes in the L1(R) norm and the uniform norm for the case that the polynomial has a zero of multiplicity at most 2 at the point 0.
In a series of papers Mauduit and Sárközy introduced and studied the measures of finite sequences of k symbols. In this paper we construct large family of pseudorandom sequences of k symbols with length pq using the residue class ring modulo pq and the methods of discrete logarithm, and study the pseudorandom properties.
The existence of the iterative solution for the operator equation A(x, y) = Lx is studied by the techniques of partially order and the theorem of cone in Banach space, where neither A nor L need to be continues or compactness. Besides, we construct some new iterative sequences and study their approximation, then we get some new theorems. Finally, we apply the new results presented in this paper to study the solvability of a class of integral-differential equation.
The matrix representations of a class of fourth order boundary value problems with eigenparameter-dependent boundary conditions which have a finite spectrum are investigated. We first prove that for any positive integer m, the considered problem has at most 2m + 6 eigenvalues. Next, we show that this fourth order boundary value problem with eigenparameter-dependent boundary condition is equivalent to a class of matrix eigenvalue problem in the sense that they have exactly the same eigenvalues.
Full subsemigroups are defined as subsemigroups containing all idempotents. A semigroup is said to be a ▽fs-semigroup if its full subsemigroups form a chain under inclusion. The aim of this paper is to investigate abundant ▽fs-semigroups. Some characterizations of such semigroups are obtained. In particular, the structures of completely 0-simple ▽fs-semigroups and primitive abundant ▽fs-semigroups satisfying the regularity condition are established.
We investigate the asymptotic properties of the estimators of quantile difference based on left truncated and right censored data. The TJW product-limit estimator of the distribution function with the left truncated and right censored data is used to provide the empirical estimator of the quantile difference. Meanwhile, another smoothed kernel estimator for the quantile difference is established. Using the theory of empirical process, the expressions of the asymptotic bias and variance of the two estimators are derived. The large sample properties, such as consistency and asymptotic normality, for the estimators are obtained. A small simulation study shows that in the sense of mean squared loss, the smoothed estimator is more efficient than the non-smoothed estimator.
The structure of the finitely generated nilpotent groups with infinite cyclic Frattini subgroups are completely determined. More exactly, the following theorem is proved. Let G be a finitely generated nilpotent group. Then the Frattini subgroup of G is infinite cyclic if and only if G has a decomposition G = S×F×T, where F is a free abelian group of rank s, T = Zm1 ⊕ Zm2 ⊕ … ⊕ Zmu, m1, m2, …, mu are square free integers greater than 1, m1|m2|… |mu,
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where d1, d2, …, dr are integers and d1|d2|… |dr. Moreover, (d1, d2, …, dr; s; m1, m2, …, mu) is an isomorphic invariant of G. That is to say, if H is also a finitely generated nilpotent group with infinite cyclic Frattini subgroup, then G is isomorphic to H if and only if they have the same invariants.
It is proved in this paper that a connected cochain DG algebra A is a Koszul Calabi-Yau DG algebra if either its cohomology graded algebra H(A) or its underlying graded algebra A# is the algebra k<x,y>/(xy+yx) generated by degree 1 elements x,y.
A finite group G is called a PNN-group if every minimal subgroup X of G is either normal in G or self-normalizing. In this paper the authors investigate properties of a PNN-group in general and then classify the non-PNN-groups whose proper subgroups are all PNN-groups.
The set of pairs with disjoint neighborhoods of a graph G is defined as disj(G)={(u,v): NG(u)∩NG(v)=Ø. In the article in which Füredi made significant progress on the Murty-Simon Conjecture, Füredi proved an important lemma: |E(G)|+|disj(G)|≤?n2/2」 for any graph on n vertices. We make an intensive study of the sum |E(G)|+|disj(G)| and give a generalization of this lemma.
A version of weighted grand Lebesgue space with parameter is introduced. The boundedness of sublinear operators under certain size conditions on these spaces are discussed. Particularly, the corresponding results for the commutators formed by certain sublinear operators and BMO functions are also considered.
We discuss the recurrence of birth and death process in a class of random environments. Under some special conditions, a strong law of large number is proven, and then applied it to discuss its recurrence and transience.
