Norms of powers of the Volterra operator

The norms of them-th powers of the Volterra operatorV onL ²[0, 1] are computed form=1,...,10. These numbers suggest that the sequencem!V is bounded above and below, which is shown, and that this sequence converges to 1/2, which is conjectured.     

Synthesis and structural characterization of five new coordination polymer chain structures using a new,Z-shaped ligand, 2,2′-bis-(4-pyridylethynyl)tolane

Using the new ligand, 2,2-bis-(4-pyridylethynyl)tolane we have synthesized five new coordination polymers: HgBr₂[2,2-bis-(4-pyridylethynyl)tolane] (1), HgI₂[2,2-bis-(4-pyridylethynyl)tolane] (2), Ni(acetylacetonate)₂[2,2-bis-(4-pyridylethynyl)tolane] (3), Zn(acetylacetonate)₂[2,2-bis-(4-pyridylethynyl)tolane] (4), and Cu(hexafluoro acetylacetonate)₂[2,2-bis-(4-pyridylethynyl)tolane]CHCl₃ (5). 2,2-Bis-(4-pyridyl ethynyl)tolane is a rigid ligand with a Z-shape that promotes the formation of zig-zag chains. Compounds 1– 5 were characterized by single crystal X-ray diffraction; and compounds 1– 3 were additionally characterized by IR, elemental analysis, and thermogravimetric analysis. Compound 1 crystallizes in the monoclinic space group C2/c with a = 29.761(3) Å, b = 5.0531(5) Å, c = 16.7823(15) Å, = 104.090(2), V = 2447.9(4) ų, Z = 4. Each mercury is bound to two tolane ligands and two bromine anions, resulting in a tetrahedral coordination environment. Compound 2 crystallizes in the monoclinic space group P2/c, with a = 20.3061(17) Å, b = 5.6303(5) Å, c = 24.5459(19) Å, = 110.338(2), V = 2631.4(4) ų, Z = 4. Here also, each mercury is bound to two tolane ligands and two iodine anions in a tetrahedral coordination environment. The ligand orientation differs in compounds 1 and 2 being trans oriented in 1 and cis oriented in 2. Compound 3 crystallizes in the monoclinic space group P2₁/c with a = 14.5947(14) Å, b = 6.3082(6) Å, c = 18.3939(18) Å, = 112.112(2), V = 1568.9(3) ų, Z = 2. Each nickel is bound to two tolane ligands and two bidentate AcAc anions, resulting in an octahedral coordination environment. Compound 4, which is isostructural with 3, also crystallizes in the monoclinic space group P2₁/c with a = 14.6990(9) Å, b = 6.2724(4) Å, c = 18.6433(11) Å, = 112.8610(10), V = 1583.86(17) ų, Z = 2. Compound 5 crystallizes in the triclinic space group P-1 with a = 6.5487(4) Å, b = 11.6471(7) Å, c = 14.3225(9) Å, = 70.1360(10), = 89.3990(10), = 88.7680(10), V = 1027.18(11) ų, Z = 1. Each copper in 5 is bound to two tolane ligands and two bidentate hfAcAc anions, resulting in an octahedral coordination environment identical to that found in 3 and 4.     

Noncommutative maximal ergodic theorems for positive contractions

Let M be a von Neumann algebra equipped with a normal semifinite faithful trace τ. Let T be a positive linear contraction on M such that τ○T?τ and such that the numerical range of T as an operator on L₂(M) is contained in a Stoltz region with vertex 1. We show that Junge and Xu's noncommutative Stein maximal ergodic inequality holds for the powers of T on Lp(M), 1<p?∞. We apply this result to obtain the noncommutative analogue of a recent result of Cohen concerning the iterates of the product of a finite number of conditional expectations.     

A matrix problem over a central quadratic skew field extension

Let F⊂G=F(u) be a central quadratic skew field extension (such that the generator u is central in G) and a natural (G,G)-bimodule. We deal with the matrix problem on finding a canonical form for rectangular matrices over W with help of left elementary transformations of their rows and right elementary transformations of columns over G. We solve this problem reducing it in the separable (resp. inseparable) case to the semilinear (resp. pseudolinear) pencil problem.     

On the residue classes of integer sequences satisfying a linear three term recurrence formula

In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))_n?0 and (U(n))_n?0, which are ultimately periodic modulo m, e.g.

     

Best linear unbiased prediction for linear combinations in general mixed linear models

The general mixed linear model can be written as . In this paper, we mainly deal with two problems. Firstly, the problem of predicting a general linear combination of fixed effects and realized values of random effects in a general mixed linear model is considered and an explicit representation of the best linear unbiased predictor (BLUP) is derived. In addition, we apply the resulting conclusion to several special models and offer an alternative to characterization of BLUP. Secondly, we recall the notion of linear sufficiency and consider it as regards the BLUP problem and characterize it in several different ways. Further, we study the concepts of linear sufficiency, linear minimal sufficiency and linear completeness, and give relations among them. Finally, four concluding remarks are given.     

Mannheim partner curves in 3-space

In this paper, we study Mannheim partner curves in three dimensional space. We obtain the necessary and sufficient conditions for the Mannheim partner curves in Euclidean space and Minkowski space , respectively. Some examples are also given. Supported by NSFC, No.10371013; Joint Research of NSFC and KOSEF, NEU     

Systems of generalized nonlinear variational inequalities and its projection methods

Based on relaxed cocoercive monotonicity, a new generalized class of nonlinear variational inequality problems is presented. Our results improve and extend the recent ones announced by [H. Y. Huang, M. A. Noor, An explicit projection method for a system of nonlinear variational inequalities with different (γ,r)$(\gamma ,r)$-cocoercive mappings, Appl. Math. Comput. 190 (2007) 356–361; S. S. Chang, H. W. Joseph Lee, C. K. Chan, Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329–334; R. U. Verma, Generalized system for relaxed cocoercive variational inequalities and its projection methods, J. Optim. Theory Appl. 121 (2004) 203–210; M. A. Noor, General variational inequalities, Appl. Math. Lett. 1 (1988) 119–121] and many others.     

Generalized quasi-variational-like hemivariational inequalities

In this paper, we introduce and study a new class of generalized quasi-variational-like hemivariational inequalities with multi-valued η$\eta$-pseudomonotone operators in Banach spaces. Some new existence theorems of solutions for this class of generalized quasi-variational-like hemivariational inequalities are proved. The results presented in this paper generalize and extend some known results.