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.

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.

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.

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

Application of the maximum entropy method to the (2 + 1)D four-fermion model

We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the π and permit an estimate of the meson binding energy. We have, however, seen no signal of σ→ππ decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.

Operators manual : crane, truck, mounted, 3/4 cubic yards, 20 ton, w/clamshell, dragline and backhoe attachments, G.E.D., (Harnischfeger Corp model M 320T2), FSN 3810-151-4431.

"May 1971."

Operators manual : crane, truck, mounted, 3/4 cubic yards, 20 ton, w/clamshell, dragline, and backhoe attachments, G.E.D. (Harnischfeger Corp model M 320T2), FSN 3810-151-4431.

"May 1971."

On the approximation by convolution operators in homogeneous Banach spaces on R^d

AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20