Spectral Shift Function for the Perturbations of Schrödinger Operators at High Energy

2000 Mathematics Subject Classification: 35P20, 35J10, 35Q40.

Generalized D-Symmetric Operators I

2000 Mathematics Subject Classification: Primary: 47B47, 47B10; secondary 47A30.

Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.

Weighted Approximation by a Class of Bernstein-Type Operators

AMS classification: 41A36, 41A10, 41A25, 41Al7.

On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity

2000 Mathematics Subject Classification: Primary: 34L25; secondary: 47A40, 81Q10.

Stability of Ampelometric Characteristics of Vitis vinifera L. cv. 'Syrah' and 'Sauvignon blanc' Leaves: Impact of Within-vineyard Variability and Pruning Method/Bud Load

Historically, grapevine (Vitis vinifera L.) leaf characterisation has been a driving force in the identification of cultivars. In this study, ampelometric (foliometric) analysis was done on leaf samples collected from hand-pruned, mechanically pruned and minimally pruned ‘Sauvignon blanc’ and ‘Syrah’ vines to estimate the impact of within-vineyard variability and a change in bud load on the stability of leaf properties. The results showed that within-vineyard variability of ampelometric characteristics was high within a cultivar, irrespective of bud load. In terms of the O.I.V. coding system, zero to four class differences were observed between minimum and maximum values of each characteristic. The value of variability of each characteristic was different between the three levels of bud load and the two cultivars. With respect to bud load, the number of shoots per vine had a significant effect on the characteristics of the leaf laminae. Single leaf area and lengths of veins changed significantly for both cultivars, irrespective of treatment, while angle between veins proved to be a stable characteristic. A large number of biometric data can be recorded on a single leaf; the data measured on several leaves, however, are not necessarily unique for a specific cultivar. The leaf characteristics analysed in this study can be divided into two groups according to the response to a change in bud load, i.e. stable (angles between the veins, depths of sinuses) and variable (length of the veins, length of the petiole, single leaf area). The variable characteristics are not recommended to be used in cultivar identification, unless the pruning method/bud load is known.

Electronic Channels of Distributions: Challenges and Solutions for Hotel Operators

This paper addresses the issues of hotel operators identifying effective means of allocating rooms through various electronic channels of distribution. Relying upon the theory of coercive isomorphism, a think tank was constructed to identify and define electronic channels of distribution currently being utilized in the hotel industry. Through two full-day focus groups consisting of key hotel electives and industry practitioners, distribution channels wen identified as were challenges and solutions associated with each

Genetically Altered Foods: A Policy Issue for Multi-unit Food Service Operators

Although it is a substantial issue, the technology behind genetically altered foods and the concerns being raised about them are not well understood by most people. The authors discuss how genetically altered foods might fit into the business strategies of multi-unit food service operators as well as current policies and predispositions of multi-unit food service companies toward the use of genetically altered foods. They also outline the issues surrounding genetically altered food as they relate to the food service industry and provide a picture of where multi-unit food service operators currently stand on the technology

Electronic Channels of Distribution: Challenges and Solutions for Hotel Operators

This paper addresses the issues of hotel operators identifying effective means of allocating rooms through various electronic channels of distribution. Relying upon the theory of coercive isomorphism, a think tank was constructed to identify and define electronic channels of distribution currently being utilized in the hotel industry. Through two full-day focus groups consisting of key hotel executives and industry practitioners, distribution channels were identified as were challenges and solutions associated with each.

The spectra of linear fractional composition operators on weighted Dirichlet spaces

We completely determine the spectra of composition operators induced by linear fractional self-maps of the unit disc acting on weighted Dirichlet spaces; extending earlier results by Higdon [8] and answering the open questions in this context.

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Geometry of Dirac Operators

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M \hat{\mathcal{A}}(TM)\wedge \text{ch}(\mathcal{V}) \] where $\mathcal{V} =\text{Hom}_{\mathbb{C}l(TM)}(\slashed{\mathsf{S}},S)$. We prove the above statement with the means of the heat kernel of the heat semigroup $e^{-tD^2}$. The first outstanding result is the McKean-Singer theorem that describes the index in terms of the supertrace of the heat kernel. The trace of heat kernel is obtained from local geometric information. Moreover, if we use the asymptotic expansion of the kernel we will see that in the computation of the index only one term matters. The Berezin formula tells us that the supertrace is nothing but the coefficient of the Clifford top part, and at the end, Getzler calculus enables us to find the integral of these top parts in terms of characteristic classes.

Spectrally isometric elementary operators

We present criteria for unital elementary operators (of small length) on unital semisimple Banach algebras to be spectral isometries. The surjective ones among them turn out to be algebra automorphisms.

More elementary operators that are spectrally bounded

We discuss some necessary and some sufficient conditions for an elementary operator x↦∑ⁿ_i=1a_ixb_i on a Banach algebra A to be spectrally bounded. In the case of length three, we obtain a complete characterisation when A acts irreducibly on a Banach space of dimension greater than three.