The Spectrum of Weighted Mean Operators

1987 ◽  
Vol 30 (4) ◽  
pp. 446-449 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Large Class ◽  
Weighted Mean ◽  
Weighted Mean Operators ◽  
Cesàro Matrix ◽  
Special Case ◽  
Convergent Sequences

AbstractRecently J. B. Reade determined the spectrum of C, the Cesaro matrix of order 1, considered as an operator on c0, the space of null sequences. Previously F. P. A. Cass and the author had determined the spectra for a large class of weighted mean operators on c, the space of convergent sequences. Subsequently the author determined the fine spectra of these operators over c. This paper examines the spectra and fine spectra of weighted mean operators on c0, obtaining the result of Reade as a special case.

scholarly journals Betti numbers and pseudoeffective cones in 2-Fano varieties

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giosuè Emanuele Muratore
Keyword(s):  
Large Class ◽  
Betti Numbers ◽  
Fano Varieties ◽  
Higher Dimensional ◽  
Special Case ◽  
Answering Questions

Abstract The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher-dimensional analogous properties of Fano varieties. We consider (weak) k-Fano varieties and conjecture the polyhedrality of the cone of pseudoeffective k-cycles for those varieties, in analogy with the case k = 1. Then we calculate some Betti numbers of a large class of k-Fano varieties to prove some special case of the conjecture. In particular, the conjecture is true for all 2-Fano varieties of index at least n − 2, and we complete the classification of weak 2-Fano varieties answering Questions 39 and 41 in [2].

Weighted Mean Operators on lp

2000 ◽  
Vol 43 (4) ◽  
pp. 406-412 ◽  
Author(s):  
David Borwein
Keyword(s):  
Triangular Matrix ◽  
Weighted Mean ◽  
Weighted Mean Operators

AbstractAbstract. The weightedmean matrix Ma is the triangular matrix {ak/An}, where an > 0 and An := a1 + a2 + … + an. It is proved that, subject to ncan being eventually monotonic for each constant c and to the existence of for 1 < p < ∞ if and only if α < p.

Oxidoreductases: Significance for Humans and Microorganism

2020 ◽  
Author(s):  
Hussein Mahdi Kareem
Keyword(s):  
Large Class ◽  
Electron Donor ◽  
Electron Acceptor ◽  
Diagnostic Tests ◽  
Organic Substrates ◽  
Biochemical Reactions ◽  
Biomass Processing ◽  
Oxidation Reduction ◽  
Special Case ◽  
Made In

Oxidoreductases consist of a large class of enzymes catalyzing the transfer of electrons from an electron donor (reductant) to an electron acceptor (oxidant) molecule. Since so many chemical and biochemical transformations comprise oxidation/reduction processes, it has long been an important goal in biotechnology to develop practical biocatalytic applications of oxidoreductases. During the past few years, significant breakthrough has been made in the development of oxidoreductase-based diagnostic tests and improved biosensors, and the design of innovative systems for the regeneration of essential coenzymes. Research on the construction of bioreactors for pollutants biodegradation and biomass processing, and the development of oxidoreductase-based approaches for synthesis of polymers and functionalized organic substrates have made great progress. Proper names of oxidoreductases are in a form of “donor:acceptor oxidoreductase”; while in most cases “donor dehydrogenase” is much more common. Common names also sometimes appeared as “acceptor reductase”, such as NAD+ reductase. “Donor oxidase” is a special case when O2 serves as the acceptor. In biochemical reactions, the redox reactions are sometimes more difficult to observe, such as this reaction from glycolysis: Pi + glyceraldehyde-3-phosphate + NAD+ → NADH + H+ + 1,3-bisphosphoglycerate, where NAD+ is the oxidant (electron acceptor), and glyceraldehyde-3-phosphate functions as reductant (electron donor).

VARIATIONAL PROBLEMS ON UNBOUNDED TWO-DIMENSIONAL DOMAINS

1992 ◽  
Vol 02 (02) ◽  
pp. 183-201
Author(s):  
ARIE LEIZAROWITZ
Keyword(s):  
Control Theory ◽  
Large Class ◽  
Optimality Criterion ◽  
Variational Problems ◽  
Two Dimensional ◽  
Minimal Energy ◽  
Chemical Systems ◽  
Overtaking Optimality ◽  
Special Case ◽  
Class Of Functions

We consider the functional IΩ(u) = ∫Ω [ψ (u(x,y)) + ½K (∇ u)]dxdy defined for real valued functions u on ℝ2 and study its minimization over a certain class of functions u(·, ·). We look for a minimizer u⋆ which is universal in the sense that IΩ(u⋆)≤IΩ(u) for every bounded domain (in a certain class) and for every u(·, ·) which satisfies u|∂Ω=u⋆|∂Ω. This optimality notion is an extension to a multivariable situation of the overtaking optimality criterion used in control theory, and the minimal-energy-configuration concept employed in the study of certain chemical systems. The existence of such universal minimizers is established for a large class of variational problems. In the special case were K(∇ u) = ½ |∇ u|2 these minimizers are characterized as the functions u⋆(x, y)=ϕ(ax+by+c) for some explicitly computable ϕ:ℝ1→ℝ1 and constants a, b and c.

scholarly journals CYCLIC COSET ORBIFOLDS

2000 ◽  
Vol 15 (24) ◽  
pp. 3829-3860 ◽  
Author(s):  
J. EVSLIN ◽  
M. B. HALPERN ◽  
J. E. WANG
Keyword(s):  
Large Class ◽  
Ground State ◽  
Duality Transformations ◽  
Stress Tensors ◽  
Special Case

We apply the new orbifold duality transformations to discuss the special case of cyclic coset orbifolds in further detail. We focus in particular on the case of the interacting cyclic coset orbifolds, whose untwisted sectors are ℤλ(permutation)-invariant g/h coset constructions which are not λ copies of coset constructions. Because λ copies are not involved, the action of ℤλ(permutation) in the interacting cyclic coset orbifolds can be quite intricate. The stress tensors and ground state conformal weights of all the sectors of a large class of these orbifolds are given explicitly and special emphasis is placed on the twisted h subalgebras which are generated by the twisted (0, 0) operators of these orbifolds. We also discuss the systematics of twisted (0, 0) operators in general coset orbifolds.

scholarly journals Matrix transformations from absolutely convergent series to convergent sequences as general weighted mean summability methods

2000 ◽  
Vol 24 (8) ◽  
pp. 533-538
Author(s):  
Jinlu Li
Keyword(s):  
Classical Result ◽  
Sufficient Conditions ◽  
Convergent Series ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Weighted Mean ◽  
Summability Methods ◽  
Necessary And Sufficient ◽  
Convergent Sequences

We prove the necessary and sufficient conditions for an infinity matrix to be a mapping, from absolutely convergent series to convergent sequences, which is treated as general weighted mean summability methods. The results include a classical result by Hardy and another by Moricz and Rhoades as particular cases.

scholarly journals Perfect Packings in Quasirandom Hypergraphs II

2015 ◽  
Vol 25 (4) ◽  
pp. 595-611
Author(s):  
JOHN LENZ ◽  
DHRUV MUBAYI
Keyword(s):  
Large Class ◽  
General Result ◽  
Triple System ◽  
Blow Up ◽  
List Type ◽  
Uniform Hypergraphs ◽  
Special Case

For each of the notions of hypergraph quasirandomness that have been studied, we identify a large class of hypergraphs F so that every quasirandom hypergraph H admits a perfect F-packing. An informal statement of a special case of our general result for 3-uniform hypergraphs is as follows. Fix an integer r ⩾ 4 and 0 < p < 1. Suppose that H is an n-vertex triple system with r|n and the following two properties: •for every graph G with V(G) = V(H), at least p proportion of the triangles in G are also edges of H,•for every vertex x of H, the link graph of x is a quasirandom graph with density at least p. Then H has a perfect Kr(3)-packing. Moreover, we show that neither of the hypotheses above can be weakened, so in this sense our result is tight. A similar conclusion for this special case can be proved by Keevash's Hypergraph Blow-up Lemma, with a slightly stronger hypothesis on H.

An inequality involving Radon-Nikodym derivatives

1967 ◽  
Vol 63 (1) ◽  
pp. 195-198 ◽  
Author(s):  
J. F. C. Kingman
Keyword(s):  
Large Class ◽  
Simple Proof ◽  
Negative Numbers ◽  
Slight Generalization ◽  
Image Position ◽  
Special Case

In (2) a simple proof was given of the following inequality of Atkinson, Watterson and Moran (l), a slight generalization of a result of Scheuer and Mandel ((4), see also (3)) which is of importance in genetics. If aij, pi, qj (i, j = 1, 2, 3,…) are non-negative numbers withand ifthenand if then This result is shown in (2) to be a special case of a large class of inequalities involving sets of non-negative numbers depending on several indices, and ‘partial averages’ over subsets of those indices.

Sign in / Sign up

Export Citation Format

Share Document