We introduce and study the relative left derived functor Torn(F,F') (-,-) in the module category, which unifies several related left derived functors. Then we give some criteria for computing the F-resolution dimensions of modules in terms of the properties of Torn(F,F') (-,-). We also construct a complete and hereditary cotorsion pair relative to balanced pairs. Some known results are obtained as corollaries.
This paper deals with the Lp-consistency of wavelet estimators for a density function based on size-biased random samples. More precisely, we firstly show the Lp-consistency of wavelet estimators for independent and identically distributed random vectors in Rd. Then a similar result is obtained for negatively associated samples under the additional assumptions d = 1 and the monotonicity of the weight function.
In this paper, we introduce the fractional wavelet transformations (FrWT) involving Hankel-Clifford integral transformation (HClIT) on the positive half line and studied some of its basic properties. Also we obtain Parseval's relation and an inversion formula. Examples of fractional powers of Hankel-Clifford integral transformation (FrHClIT) and FrWT are given. Then, we introduce the concept of fractional wavelet packet transformations FrBWPT and FrWPIT, and investigate their properties.
We obtain the weighted sum identities for
Let F = Q(√p), where p = 8t+1 is a prime. In this paper, we prove that a special case of Qin's conjecture on the possible structure of the 2-primary part of K2OF up to 8-rank is a consequence of a conjecture of Cohen and Lagarias on the existence of governing fields. We also characterize the 16-rank of K2OF , which is either 0 or 1, in terms of a certain equation between 2-adic Hilbert symbols being satisfied or not.
In this paper, we introduce the definition of generalized Day-James space on Rn (n ≥ 2) and give a characterization of it, which extend some known results. In addition, we provide a sufficient and necessary condition for Day-James space, which reappeared Day's construction for any two-dimensional normed space to make Birkhoff orthogonality symmetry.
Let A be a factor. For A,B ∈ A, define by [A,B]* = AB-BA* the skew Lie product of A and B. In this article, it is proved that a map Φ :A→A satisfies Φ([[A,B]*, C]*) = [[Φ(A),B]*,C]* + [[A, Φ(B)]*, C]* + [[A,B]*, Φ(C)]* for all A,B,C ∈ A if and only if Φ is an additive *-derivation.
It has been proved that the vanishing of Tate homology is a sufficient condition for the derived depth formula to hold in [J. Pure Appl. Algebra, 219, 464-481 (2015)]. In this paper, we investigate when Tate homology vanishes by studying the stable homology theory for complexes. Properties such as the balancedness and vanishing of stable homology for complexes are studied. Our results show that the vanishing of this homology can detect finiteness of homological dimensions of complexes and regularness of rings.
A graph is called claw-free if it contains no induced subgraph isomorphic to K1,3. Matthews and Sumner proved that a 2-connected claw-free graph G is Hamiltonian if every vertex of it has degree at least (|V(G)|-2)/3. At the workshop C&C (Novy Smokovec, 1993), Broersma conjectured the degree condition of this result can be restricted only to end-vertices of induced copies of N (the graph obtained from a triangle by adding three disjoint pendant edges). Fujisawa and Yamashita showed that the degree condition of Matthews and Sumner can be restricted only to end-vertices of induced copies of Z1 (the graph obtained from a triangle by adding one pendant edge). Our main result in this paper is a characterization of all graphs H such that a 2-connected claw-free graph G is Hamiltonian if each end-vertex of every induced copy of H in G has degree at least |V(G)|/3+1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.
Let M be a complete, simply connected Riemannian manifold with negative curvature. We obtain an interpolation of Hardy inequality and Moser-Trudinger inequality on M. Furthermore, the constant we obtain is sharp.