GROUND-STATE-ENERGY OF SINGULAR POTENTIALS

It is shown that for singular potentials of the form lambda/r(alpha),the asymptotic form of the wave function both at r --> infinity and r --> 0 plays an important role. Using a wave function having the correct asymptotic behavior for the potential lambda/r(4), it is, shown that it gives the exact ground-state energy for this potential when lambda --> 0, as given earlier by Harrell [Ann. Phys. (NY) 105, 379 (1977)]. For other values of the coupling parameter X, a trial basis;set of wave functions which also satisfy the correct boundary conditions at r --> infinity and r --> 0 are used to find the ground-state energy of the singular potential lambda/r(4) It is shown that the obtained eigenvalues are in excellent agreement with their exact ones for a very large range of lambda values.

O oscilador harmônico singular revisitado

The one-dimensional Schrödinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive singular oscillator exhibits an infinite number of acceptable solutions provided the parameter responsible for the singularity is greater than a certain critical value, in disagreement with the literature. The problem for the whole line exhibits a two-fold degeneracy in the case of the singular oscillator, and the intrusion of additional solutions in the case of a nonsingular oscillator. Additionally, it is shown that the solution of the singular oscillator can not be obtained from the nonsingular oscillator via perturbation theory.

Renormalization group invariance of quantum mechanics

We propose a framework to renormalize the nonrelativistic quantum mechanics with arbitrary singular interactions. The scattering equation is written to have one or more subtraction in the kernel at a given energy scale. The scattering amplitude is the solution of a nth order derivative equation in respect to the renormalization scale, which is the nonrelativistic counterpart of the Callan-Symanzik formalism, Scaled running potentials for the subtracted equations keep the physics invariant fur a sliding subtraction point. An example of a singular potential, that requires more than one subtraction to renormalize the theory is shown. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Uma breve discussão sobre os possíveis estados ligados para uma classe de potenciais singulares

Investiga-se a equação de Schrödinger unidimensional com uma classe de potenciais V(|x|) que se anulam no infinito e apresentam singularidade dominante na origem na forma α/|x|β(0 < β < 2). A hermiticidade dos operadores associados com quantidades físicas observáveis é usada para determinar as condições de contorno apropriadas. Dupla degenerescência e exclusão de soluções simétricas, consoante o valor de β, são discutidas. Soluções explícitas para o átomo de hidrogênio e o potencial de Kratzer são apresentadas.

Properties of singular vectors using convective available potential energy as final time norm

We study the feasibility of using the singular vector technique to create initial condition perturbations for short-range ensemble prediction systems (SREPS) focussing on predictability of severe local storms and in particular deep convection. For this a new final time semi-norm based on the convective available potential energy (CAPE) is introduced. We compare singular vectors using the CAPE-norm with SVs using the more common total energy (TE) norm for a 2-week summer period in 2007, which includes a case of mesoscale extreme rainfall in the south west of Finland. The CAPE singular vectors perturb the CAPE field by increasing the specific humidity and temperature of the parcel and increase the lapse rate above the parcel in the lower troposphere consistent with physical considerations. The CAPE-SVs are situated in the lower troposphere. This in contrast to TE-SVs with short optimization times which predominantly remain in the high troposphere. By examining the time evolution of the CAPE singular values we observe that the convective event in the south west of Finland is clearly associated with high CAPE singular values.

Best approach regions for potential spaces

We characterize the approach regions so that the non-tangential maximal function is of weak-type on potential spaces, for which we use a simple argument involving Carleson measure estimates.

The influence of physical processes on extratropical singular vectors

An investigation is made of the impact of a full linearized physical (moist) parameterization package on extratropical singular vectors (SVs) using the ECMWF integrated forecasting system (IFS). Comparison is made for one particular period with a dry physical package including only vertical diffusion and surface drag. The crucial extra ingredient in the full package is found to be the large-scale latent heat release. Consistent with basic theory, its inclusion results in a shift to smaller horizontal scales and enhanced growth for the SVs. Whereas, for the dry SVs, T42 resolution is sufficient, the moist SVs require T63 to resolve their structure and growth. A 24-h optimization time appears to be appropriate for the moist SVs because of the larger growth of moist SVs compared with dry SVs. Like dry SVs, moist SVs tend to occur in regions of high baroclinicity, but their location is also influenced by the availability of moisture. The most rapidly growing SVs appear to enhance or reduce large-scale rain in regions ahead of major cold fronts. The enhancement occurs in and ahead of a cyclonic perturbation and the reduction in and ahead of an anticyclonic perturbation. Most of the moist SVs for this situation are slightly modified versions of the dry SVs. However, some occur in new locations and have particularly confined structures. The most rapidly growing SV is shown to exhibit quite linear behavior in the nonlinear model as it grows from 0.5 to 12 hPa in 1 day. For 5 times this amplitude the structure is similar but the growth is about half as the perturbation damps a potential vorticity (PV) trough or produces a cutoff, depending on its sign.

Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barabasi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks. Copyright (C) EPLA, 2009

Relativistic confinement of neutral fermions with a trigonometric tangent potential

The problem of neutral fermions subject to a pseudoscalar potential is investigated. Apart from the solutions for E = +/- mc(2), the problem is mapped into the Sturm-Liouville equation. The case of a singular trigonometric tangent potential (similar to tan gamma x) is exactly solved and the complete set of solutions is discussed in some detail. It is revealed that this intrinsically relativistic and true confining potential is able to localize fermions into a region of space arbitrarily small without the menace of particle-antiparticle production.

An effective singular oscillator for Duffin-Kemmer-Petiau particles with a nonminimal vector coupling: a two-fold degeneracy

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Renormalization of singular potentials and power counting

We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r(2) potential perturbed by a 1/r(4) correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range counterterms that renormalize the scattering amplitude. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis. (C) 2008 Elsevier B.V. All rights reserved.

Estratégias de cuidado de enfermagem singular e multidimensional à criança e a família no processo de hospitalização

No período de 2008 a 2010, o número de internações pediátricas, no Brasil, foi de 2.985.527. As causas desencadeadoras da hospitalização infantil podem ser biológicas, hereditárias, sociais, econômicas e ambientais. É comum o adoecimento ocorrer pela associação de causas, havendo crianças com predisposição para apresentarem múltiplos fatores de risco. Seja qual for a etiologia, a hospitalização frequentemente gera desconforto à criança e à sua família, por vivenciarem um ambiente impessoal e contraditório às condições do cotidiano. Cabe à equipe de enfermagem prestar um cuidado humanizado, singular e ampliado. Os objetivos do estudo são: compreender o significado do cuidado de enfermagem à criança hospitalizada e identificar estratégias de cuidado de enfermagem singular e multidimensional que atendam às necessidades da criança e da família no processo de hospitalização. Trata-se de uma pesquisa qualitativa, do tipo exploratório-descritivo. Os dados foram coletados por meio da técnica de Grupo Focal com a equipe de enfermagem que atuava em unidades pediátricas de duas instituições hospitalares do Rio Grande do Sul. Para tanto, foram realizados cinco encontros, no mês de setembro de 2013. Os dados foram analisados com base na Análise Focal Estratégica, a qual contemplou tanto as potencialidades e oportunidades, quanto as fragilidades e desafios no cuidado à criança hospitalizada, ampliando, assim, novas discussões para a busca de estratégias de cuidado de enfermagem singular e multidimensional. Os resultados foram sustentados por meio de duas produções científicas, quais sejam: “O cuidado à criança/família no processo de hospitalização na perspectiva de equipes de enfermagem”; “Ampliando estratégias de cuidado de enfermagem singular e multidimensional à criança/família em processo de hospitalização”. A primeira apresentou cinco categorias: Significando o cuidado de enfermagem à criança hospitalizada; Reconhecendo que o cuidado vai além do hospital; Relevância das figuras materna e paterna; Lidando com várias coisas; e Importância do cuidado multidimensional. A segunda produção resultou em três categorias: Encontrando estratégias criativas de cuidado de enfermagem à criança hospitalizada; Reconhecendo estratégias de cuidado à família no processo de hospitalização da criança; e Distinguindo estratégias de cuidado relacionadas à equipe de enfermagem no processo de hospitalização infantil. Foram garantidos todos os critérios que fundamentam a Resolução 466/12, que trata das pesquisas envolvendo seres humanos. Conclui-se que a equipe de enfermagem busca alternativas para minimizar os traumas relacionados à hospitalização, por meio do diálogo com a criança e sua família, a brinquedoteca e ludicidade para melhorar a aceitação da hospitalização, dentre outras.

Defective Apoptosis In Intestinal And Mesenteric Adipose Tissue Of Crohn's Disease Patients.

Crohn's disease (CD) is associated with complex pathogenic pathways involving defects in apoptosis mechanisms. Recently, mesenteric adipose tissue (MAT) has been associated with CD ethiopathology, since adipose thickening is detected close to the affected intestinal area. However, the potential role of altered apoptosis in MAT of CD has not been addressed. To evaluate apoptosis in the intestinal mucosa and MAT of patients with CD. Samples of intestinal mucosa and MAT from patients with ileocecal CD and from non-inflammatory bowel diseases patients (controls) were studied. Apoptosis was assessed by TUNEL assay and correlated with the adipocytes histological morphometric analysis. The transcriptional and protein analysis of selected genes and proteins related to apoptosis were determined. TUNEL assay showed fewer apoptotic cells in CD, when compared to the control groups, both in the intestinal mucosa and in MAT. In addition, the number of apoptotic cells (TUNEL) correlated significantly with the area and perimeter of the adipose cells in MAT. Transcriptomic and proteomic analysis reveal a significantly lower transcript and protein levels of Bax in the intestinal mucosa of CD, compared to the controls; low protein levels of Bax were found localized in the lamina propria and not in the epithelium of this tissue. Furthermore, higher level of Bcl-2 and low level of Caspase 3 were seen in the MAT of CD patients. The defective apoptosis in MAT may explain the singular morphological characteristics of this tissue in CD, which may be implicated in the pathophysiology of the disease.

Design, Synthesis And Biological Evaluation Of Hybrid Bioisoster Derivatives Of N-acylhydrazone And Furoxan Groups With Potential And Selective Anti-trypanosoma Cruzi Activity.

Hybrid bioisoster derivatives from N-acylhydrazones and furoxan groups were designed with the objective of obtaining at least a dual mechanism of action: cruzain inhibition and nitric oxide (NO) releasing activity. Fifteen designed compounds were synthesized varying the substitution in N-acylhydrazone and in furoxan group as well. They had its anti-Trypanosoma cruzi activity in amastigotes forms, NO releasing potential and inhibitory cruzain activity evaluated. The two most active compounds (6, 14) both in the parasite amastigotes and in the enzyme contain the nitro group in para position of the aromatic ring. The permeability screening in Caco-2 cell and cytotoxicity assay in human cells were performed for those most active compounds and both showed to be less cytotoxic than the reference drug, benznidazole. Compound 6 was the most promising, since besides activity it showed good permeability and selectivity index, higher than the reference drug. Thereby the compound 6 was considered as a possible candidate for additional studies.