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.

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.

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Gravitational quasinormal modes of AdS black branes in d spacetime dimensions

The AdS/CFT duality has established a mapping between quantities in the bulk AdS black-hole physics and observables in a boundary finite-temperature field theory. Such a relationship appears to be valid for an arbitrary number of spacetime dimensions, extrapolating the original formulations of Maldacena`s correspondence. In the same sense properties like the hydrodynamic behavior of AdS black-hole fluctuations have been proved to be universal. We investigate in this work the complete quasinormal spectra of gravitational perturbations of d-dimensional plane-symmetric AdS black holes (black branes). Holographically the frequencies of the quasinormal modes correspond to the poles of two-point correlation functions of the field-theory stress-energy tensor. The important issue of the correct boundary condition to be imposed on the gauge-invariant perturbation fields at the AdS boundary is studied and elucidated in a fully d-dimensional context. We obtain the dispersion relations of the first few modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave (shear-mode) behavior of scalar (vector)-type low- frequency quasinormal mode is analytically and numerically confirmed. These results are found employing both a power series method and a direct numerical integration scheme.

Cyclic Maximal Ideals of Rings of Differential Operators over Power Series Rings

In [3], Bratti and Takagi conjectured that a first order differential operator S=11 +...+ nn+ with 1,..., n, {x1,..., xn} does not generate a cyclic maximal left (or right) ideal of the ring of differential operators. This is contrary to the case of the Weyl algebra, i.e., the ring of differential operators over the polynomial ring [x1,..., xn]. In this case, we know that such cyclic maximal ideals do exist. In this article, we prove several special cases of the conjecture of Bratti and Takagi.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

Spin Hall Effect in Symmetric Wells with Two Subbands

We investigate the spin Hall conductivity sigma (xy) (z) of a clean 2D electron gas formed in a two-subband well. We determine sigma (xy) (z) as arising from the inter-subband induced spin-orbit (SO) coupling eta (Calsaverini et al., Phys. Rev. B 78:155313, 2008) via a linear-response approach due to Rashba. By self-consistently calculating eta for realistic wells, we find that sigma (xy) (z) presents a non-monotonic (and non-universal) behavior and a sign change as the Fermi energy varies between the subband edges. Although our sigma (xy) (z) is very small (i.e., a parts per thousand(a)`` e/4 pi aEuro(3)), it is non-zero as opposed to linear-in-k SO models.

Vitaminas D e C para poedeiras na fase inicial de produção de ovos

Um experimento foi conduzido com o objetivo de avaliar os efeitos de duas fontes de vitamina D e três níveis de vitamina C sobre as características de desempenho, a qualidade interna e externa dos ovos, os níveis de cálcio total e iônico séricos e a resistência óssea de poedeiras. Foram utilizadas 288 galinhas da linhagem ISA Babcock B300® com 23 semanas de idade, durante um período experimental de 12 semanas. Utilizou-se o delineamento inteiramente ao acaso em arranjo fatorial 2 × 3, com os fatores: fontes de vitamina D (colecalciferol e 25-hidroxicolecalciferol - 25(OH)D3) e de vitamina C (0, 100 e 200 ppm), totalizando seis tratamentos com oito repetições de seis aves. O nível basal de colecalciferol foi de 2.756 UI/kg, correspondendo a 5,51 g do produto comercial Hy.D®/t de ração, como fonte de 25(OH)D3. Os fatores estudados não influenciaram o consumo de ração, a produção, o peso e a massa de ovos. Observou-se efeito da interação de fontes de vitamina sobre a conversão alimentar, que foi melhor quando utilizado metabólito 25(OH)D3 na ausência de vitamina C. Interações foram observadas para porcentagem de albúmen e porcentagem de gema, que aumentaram na presença de 200 ppm de vitamina C. O peso específico dos ovos, as concentrações de cálcio sérico, cinzas ósseas e a resistência à quebra não foram influenciadas pelas fontes de vitamina D e C. Houve interação para porcentagem e espessura de casca, cujos maiores valores foram obtidos com a suplementação de vitamina C na presença de 25(OH)D3. Em poedeiras na fase inicial de produção, a conversão alimentar é melhor com a utilização do 25(OH)D3 e a espessura e porcentagem de casca também melhoram com a utilização de 25(OH)D3 e a suplementação de vitamina C nas dietas (100 ou 200 ppm, respectivamente).

Synthesis of novel O-acylated-D-ribono-1,5-lactones and structural assignment supported by conventional NOESY-NMR and x-ray analysis

A practical method for the structural assignment of 3,4-O-benzylidene-D-ribono-1,5-lactones and analogues using conventional NMR techniques and NOESY measurements in solution is described. 2-O-Acyl-3,4-O-benzylidene-D-ribono-1,5-lactones were prepared in good yields by acylation of Zinner’s lactone with acyl chlorides under mildly basic conditions. Structural determination of 2-O-(4-nitrobenzoyl)-3,4-O-benzylidene-D-ribono-1,5-lactone was achieved by single crystal x-ray diffraction, which supports the results based on spectroscopic data.

High resolution study of 104Pd(d,t)103Pd

Information collected in the present high resolution study of 104Pd(d,t)103Pd is interpreted within the systematics of the A ~ 100 region. The paper complements data previously presented by the S.Paulo Group, which were taken with the Pelletron-Enge-Spectrograph facility. A one-to-one correspondence to gamma ray results for 103Pd, collected by the Nuclear Data Sheets (NDS), was achieved and at least four open questions were settled. More reliable spectroscopic strengths were extracted in the present study.

Redescription of Hiatella meridionalis d'Orbigny, 1846 (Mollusca, Bivalvia, Hiatellidae) from Argentina

The redescription of Hiatella meridionalis (d’Orbigny, 1846) is provided as first attempt to improve the systematics of the genus in the regions of Atlantic and western Pacific. This reanalysis is based on specimens collected in the vicinity of the type localities and is based on detailed morphology of samples that some researches consider a single, wide ranging species. From the morphological characters, the more interesting are: a high quantity of papillae at incurrent siphon; the retractor muscles of siphon divided in two bundles; the small size of the palps; the muscular ring in the stomach; and the zigzag fashion of the short intestinal loops. These characters distinguish the species from the other hiatellids so far examined. Type material of the species was examined, by first time illustrated, and the lectotype is designated.

A new species of Dicrepidius Eschscholtz from Brazil and new records for D. ramicornis (Palisot de Beauvois) (Coleoptera, Elateridae, Elaterinae)

Dicrepidius brasilianus sp. nov., from Pará and Mato Grosso is described and illustrated. This is the second species of this genus recorded from Brazil. D. ramicornis (Palisot de Beauvois, 1805) is widely distributed from south of United States to south of Brazil. From Brazil, it was recorded from Minas Gerais, Rio de Janeiro, São Paulo and Santa Catarina states, but now other records are included. A comparison between the two Brazilian species and a discussion, including intraspecific variations, are presented.

The effects of the experimental infection from a focus of transmission of Schistosoma mansoni in a population of Biomphalaria tenagophila (D'Orbigny, 1835) in the region of "Vale do Ribeira de Iguape", Brazil

To observe the effects of the parasitic infection on the biology of B. tenagophila, field and laboratory populations of this mollusk from Itariri, in Vale do Ribeira, Brazil, were experimentally infected. Each mollusk received 10 miracidia of Schistosoma mansoni (SJ lineage) and was observed throughout the parasite's development. The biological variables were compared according to the criteria "group" and "infectious phase". The main damage caused by the parasitic infection manifested itself in reproduction, longevity and lesions on the shell of the mollusks in the patent phase. An infection rate of 58.8% was observed. Microanatomical study of the mollusk's digestive gland and ovotestis revealed the presence of evolving larval forms and cercariae. It was concluded that the effects of the parasitic infection on both populations were moderate, despite the low survival rate of the infected mollusks, the damage did not prevent either reproduction or the elimination of cercariae, which continued for a long time.

Vitamina D e doenças endocrinometabólicas

Atualmente, a insuficiência/deficiência de vitamina D tem sido considerada um problema de saúde pública no mundo todo, em razão de suas implicações no desenvolvimento de diversas doenças, entre elas, o diabetes melito tipo 2 (DMT2), a obesidade e a hipertensão arterial. A deficiência de vitamina D pode predispor à intolerância à glicose, a alterações na secreção de insulina e, assim, ao desenvolvimento do DMT2. Esse possível mecanismo ocorre em razão da presença do receptor de vitamina D em diversas células e tecidos, incluindo células-β do pâncreas, no adipócito e no tecido muscular. Em indivíduos obesos, as alterações do sistema endócrino da vitamina D, caracterizada por elevados níveis de PTH e da 1,25(OH)2D3 são responsáveis pelo feedback negativo da síntese hepática de 25-OHD3 e também pelo maior influxo de cálcio para o meio intracelular, que pode prejudicar a secreção e a sensibilidade à insulina. Na hipertensão, a vitamina D pode atuar via sistema renina-angiotensina e também na função vascular. Há evidências de que a 1,25(OH)2D3 inibe a expressão da renina e bloqueia a proliferação da célula vascular muscular lisa. Entretanto, estudos prospectivos e de intervenção em humanos que comprovem a efetividade da adequação do status da vitamina D sob o aspecto "prevenção e tratamento de doenças endocrinometabólicas" são ainda escassos. Mais pesquisas são necessárias para se garantir o benefício máximo da vitamina D nessas situações.