Pseudodifferential Operators and Weighted Normed Symbol Spaces

2000 Mathematics Subject Classification: 35S05.

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.

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

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

Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions

2010 Mathematics Subject Classification: 47B33, 47B38.

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.

Música e surdez: o ensino de música numa perspectiva bilíngue na escola regular

The present study focuses on the development of pedagogical activities in Music Teaching, aiming to enhance the accessibility of musical knowledge for both deaf and hearing students, using a bilingual approach in regular schools. Few studies address Music and Deafness, and those that do focus exclusively on the context of special education, and specifically the deaf student, which signals the urgent need for conducting research on this issue in the context of inclusion – empirically and carried out on school grounds. Therefore, we developed our study at a Natal City Public Elementary school, in a class of 6th graders, comprised of 37 students, 3 of whom were deaf. The objective of the study was to develop a proposal for a pedagogical intervention in Music Teaching, using a bilingual approach, with deaf and hearing students, in the context of regular school classes. The research is based on the theoretical framework presented in Penna (2010), Brito (2001) and Fonterrada (2008), with reference to music education, and Haguiara-Cervellini (2003), Finck (2009) and Louro (2006), with reference to inclusion in teaching music. To achieve this objective, we developed a proposal for intervention based on the methodological dictates of intervention research, presented in studies by Jobim and Souza (2011) in light of the theoretical concepts posited by Mikhail Bakhtin, which assert that knowledge is produced through interaction between subjects, dialogically and through alterity. This methodology was carried out in pedagogical workshops, conceived as spaces for the construction of knowledge, mobilizing participants to engage in ludic activities of musical experimentation. Content covered in these workshops focused on Pulse and Rhythm – basic elements in music education – demonstrating that awareness about and sensitivity to these elements is not limited to the auditory sensory perception of the student, once the entire body is used as an agent of acquisition and expression. Thus, we began the trajectory of our research from the starting point of the identification and perception of „Pulse‟, using one‟s own body and the body of classmates, representing it through physical expressions and movement. Subsequently, this Pulse was extended from the body to a percussion instrument, and was then represented graphically as lines of rhythm, constituting a process of reading and writing; ultimately the intervention culminated in the class presentation with the musical group De Pau e Lata (Stick and Can). In our analysis, faced with the challenges and possibilities presented in our study, findings showed satisfactory results with regard to the participation of all of the students: completing the activities proposed in the class, asking questions when they did not understand, positioning themselves when they thought it necessary, expressing opinions about the work completed, evaluating the workshops given, interacting, helping in the activities, constructing knowledge collaterally, experimenting and experiencing musical elements through the body in activities that applied to both groups (deaf and hearing) in the one class. These indications elucidate the viability of teaching music to deaf and hearing students, using a bilingual approach, and based on experiences with the body and communicative and cultural specificities involved, confirming, as well, the role of Sign Language as a mediator in the teaching/learning process.

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.