Generalized D-Symmetric Operators I

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

CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the well-known methods and a newly proposed method for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions in terms of self-adjoint boundary conditions. The new method has the advantage that it does not require explicitly evaluating deficient subspaces and deficiency indices (these latter are determined in passing) and that boundary conditions are of explicit character irrespective of the singularity of a differential expression. General assertions and constructions are illustrated by examples of well-known quantum-mechanical operators like momentum and Hamiltonian.

Spectral analysis of finite section normal integral operators

Some continuity and differentiability properties of the eigenvalues and eigenfunctions of finite section normal integral operators are proved. These are the extension of corresponding results for symmetric operators ([4.], 554–566; K. B. Athreya and R. Vittal Rao, to appear; [10.], 463–471.

Disjoint mixing operators

Chan and Shapiro showed that each (non-trivial) translation operator acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing.

Schrodinger and Dirac operators with the Aharonov-Bohm and magnetic-solenoid fields

We construct all self-adjoint Schrodinger and Dirac operators (Hamiltonians) with both the pure Aharonov-Bohm (AB) field and the so-called magnetic-solenoid field (a collinear superposition of the AB field and a constant magnetic field). We perform a spectral analysis for these operators, which includes finding spectra and spectral decompositions, or inversion formulae. In constructing the Hamiltonians and performing their spectral analysis, we follow, respectively, the von Neumann theory of self-adjoint extensions of symmetric operators and the Krein method of guiding functionals.

Existence of disjoint weakly mixing operators that fail to satisfy the Disjoint Hypercyclicity Criterion

Recently, Bès, Martin, and Sanders [11] provided examples of disjoint hypercyclic operators which fail to satisfy the Disjoint Hypercyclicity Criterion. However, their operators also fail to be disjoint weakly mixing. We show that every separable, infinite dimensional Banach space admits operators T1,T2,…,TN with N⩾2 which are disjoint weakly mixing, and still fail to satisfy the Disjoint Hypercyclicity Criterion, answering a question posed in [11]. Moreover, we provide examples of disjoint hypercyclic operators T1, T2 whose corresponding set of disjoint hypercyclic vectors is nowhere dense, answering another question posed in [11]. In fact, we explicitly describe their set of disjoint hypercyclic vectors. Those same disjoint hypercyclic operators fail to be disjoint topologically transitive. Lastly, we create examples of two families of d-hypercyclic operators which fail to have any d-hypercyclic vectors in common.

A Raman spectroscopic comparison of calcite and dolomite

Raman spectroscopy was used to characterize and differentiate the two minerals calcite and dolomite and the bands related to the mineral structure. The (CO3)2− group is characterized by four prominent Raman vibrational modes: (a) the symmetric stretching, (b) the asymmetric deformation, (c) asymmetric stretching and (d) symmetric deformation. These vibrational modes of the calcite and dolomite were observed at 1440, 1088, 715 and 278 cm−1. The significant differences between the minerals calcite and dolomite are observed by Raman spectroscopy. Calcite shows the typical bands observed at 1361, 1047, 715 and 157 cm−1, and the special bands at 1393, 1098, 1069, 1019, 299, 258 and 176 cm−1 for dolomite are observed. The difference is explained on the basis of the structure variation of the two minerals. Calcite has a trigonal structure with two molecules per unit cell, and dolomite has a hexagonal structure. This is more likely to cause the splitting and distorting of the carbonate groups. Another cause for the difference is the cation substituting for Mg in the dolomite mineral.

Os paradoxos de Prior e o calculo proposicional deôntico relevante E¹.

Cruz, Ângela Maria Paiva. Os paradoxos de Prior e o cálculo proposicional deôntico relevante. Princípios, Natal, v. 4, p. 05-18, 1996.

An evaluation of the impact of Inner City Development's Cooperative Home School: An educational alternative program to increase the quality and level of education in San Antonio's West Side community

The research study was intended to evaluate the effectiveness of Inner City Development's (I.C.D.) Cooperative Home School, an educational alternative program to the Title I public schools of San Antonio's West Side community. The study investigated students', parents' and tutors' perception of parental involvement and educational resources. The study also investigated each student's academic achievement. ^ The study found that students progressed toward expected math proficiency at a faster rate than they did in reading proficiency. However, because the target population size was small and a comparison group was not used, the results of this study are only suggestive. This research also indicated that study subjects believed students' quality and level of education increased substantially since program exposure. Study subjects mainly attributed the students' strides in academic performance to the increased amount of individualized attention students received in the small twelve-student class size. Study subjects were more satisfied with the home school's educational resources than those of the Title I public schools. Study subjects also perceived that parental involvement both at home and at school increased since enrollment in the home school program because: (1) there were more opportunities for involvement in the home school; and (2) parents felt closer to the tutors than the teachers in public school. ^ This evaluation also suggested improvements to program operations. With the help of additional volunteers, I.C.D. program operators could improve collection and organization of academic records. Furthermore, as suggested by program participants, science could be added to the curriculum. Lastly, a formal tutor orientation could be implemented to familiarize and train tutors on classroom management procedures. ^

Os paradoxos de Prior e o calculo proposicional deôntico relevante E¹.

Cruz, Ângela Maria Paiva. Os paradoxos de Prior e o cálculo proposicional deôntico relevante. Princípios, Natal, v. 4, p. 05-18, 1996.

Os paradoxos de Prior e o calculo proposicional deôntico relevante E¹.

Cruz, Ângela Maria Paiva. Os paradoxos de Prior e o cálculo proposicional deôntico relevante. Princípios, Natal, v. 4, p. 05-18, 1996.

Kac-Akhiezer formula for normal integral operators

The Kac-Akhiezer formula for finite section normal Wiener-Hopf integral operators is proved. This is an extension of the corresponding result for symmetric operator [2, 3, 4, 5, 6, 7].

Coherence of the real symmetric Hardy algebra

Let D denote the open unit disk in C centered at 0. Let H-R(infinity) denote the set of all bounded and holomorphic functions defined in D that also satisfy f(z) = <(f <(z)over bar>)over bar> for all z is an element of D. It is shown that H-R(infinity) is a coherent ring.

Syntheses and Crystal Structures of Fused Thiophenes: [7]Helicene and Double Helicene, a D-2-Symmetric Dimer of 3,3 '-Bis(dithieno[2,3-b:3 ',2 '-d]thiophene)

The efficient synthesis of (TMS)(2)-[7]helicene (rac-3) and double helicene, a D-2-symmetric dimer of 3,3'-bis(dithieno-[2,3-b:3',2'-d]thiophene) (rac-4) was developed. The crystal structures of 3 and 4 show both strong intermolecular pi-pi interactions and S center dot center dot center dot S interactions. UV/vis spectra reveal that both 3 and 4 show significant pi-electron delocalization.