Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

The Role of Immunity and Seasonality in Cholera Epidemics

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An algebraic q-deformed form for shape-invariant systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show that these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserves the shape-invariance property presented by the primary system. q-deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

DETECTION OF CELLULAR-IMMUNITY WITH THE SOLUBLE-ANTIGEN OF THE FUNGUS SPOROTHRIX-SCHENCKII IN THE SYSTEMIC FORM OF THE DISEASE

Sporothrix schenckii is the etiologic agent of sporotrichosis, a mycosis of world-wide distribution more commonly occurring in tropical regions. The immunological mechanisms involved in the prevention and control of sporotrichosis are not fully understood but apparently include both the humoral and cellular responses. In the present investigation, cellular immunity was evaluated by in vivo and in vitro tests in mice infected with yeast-like forms of S. schenckii. The disease developed systemically and cellular immunity was evaluated for a period of 10 weeks. The soluble antigen utilized in the tests was prepared from yeast form of the fungus through the sonication (20 min: 10 sonications at 50 W at 2-min intervals). Delayed hypersensitivity and lymphocyte transformation tests showed that the cellular immune response was depressed between the 4th and 6th week of infection when the animals were challenged with the soluble fungal antigen. This depression frequently indicates worsening of the disease, with greater involvement of the host. This is a promising field of research for a better understanding of the pathogeny of this mycosis.

Causal propagators for algebraic gauges

Applying the principle of analytic extension for generalized functions we derive causal propagators for algebraic non-covariant gauges. The so-generated manifestly causal gluon propagator in the light-cone gauge is used to evaluate two one-loop Feynman integrals which appear in the computation of the three-gluon vertex correction. The result is in agreement with that obtained through the usual prescriptions.

ANOTHER QUADRATURE RULE OF HIGHEST ALGEBRAIC DEGREE OF PRECISION

We consider certain quadrature rules of highest algebraic degree of precision that involve strong Stieltjes distributions (i.e., strong distributions on the positive real axis). The behavior of the parameters of these quadrature rules, when the distributions are strong c-inversive Stieltjes distributions, is given. A quadrature rule whose parameters have explicit expressions for their determination is presented. An application of this quadrature rule for the evaluation of a certain type of integrals is also given.

Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

Passive Immunity of Progeny from Broiler Breeders Vaccinated with Oil-Emulsion Bacterin Against Salmonella Enteritidis

Young poultry are very susceptible to Salmonella Enteritidis (SE) infections because of the absence of complete intestinal flora colonization and an immature immune system. This study evaluated the role of passive immunity on the resistance of young birds against early infections caused by SE. The progeny of broiler breeders vaccinated with an oil-emulsion bacterin was compared to the progeny of unvaccinated birds. Efficacy was determined by challenging birds at 1 and 14 days of age with SE Nal Spc strain, phage type 4. After challenge at 1 day of age, the progeny of vaccinated birds presented a significantly lower number (log(10)) of SE Nal Spc reisolation (P < 0.05) in liver (2.21), spleen (2.31), and cecal contents (2.85) compared with control groups (2.76, 3.02, and 6.03, respectively). The examination of the internal organs, 3 days after infection, revealed that 28% of the birds (7/25) from vaccinated breeders were positive, whereas 100% (25/25) of the chicks derived from unvaccinated birds were positive. Birds challenged at 14 days of age presented a lower number of positive samples compared with those challenged at 1 day of age, and the progeny of vaccinated birds presented statistically lower numbers (log(10)) of colony-forming units/ml of SE Nal Spc only in the cecal contents compared with nonvaccinated breeder progeny (2.11 vs. 2.94). Age seems to influence the susceptibility of birds to SE infections: in control groups, the number of positive birds at 14 days of age (9/25) was lower when compared with the group infected at 1 day of age (25/25). The number of positive fecal samples of the progeny of vaccinated birds was significantly lower (36) than those of the control group (108) after challenge at 1 day of age. Unchallenged progeny of vaccinated birds presented passive antibodies detectable by enzyme-linked immunosorbent assay (ELISA) up to 21 days of age. on the other hand, antibodies of the control group were detected by ELISA 14 days after challenge. These results show a significant contribution of breeder vaccination by increasing the resistance of the progeny against early SE infections. However, the bacteria were not completely eliminated, suggesting that additional procedures are needed to effectively control SE infections.

Innate Immunity in Wooless Lamb to Larvae of Amblyomma cajennense Tick (Fabricius, 1787) (Acari: Ixodidae)

P>The Cayenne tick Amblyomma cajennense infests preferably horses in its adult form but other mammal species in its immature stages and is the main vector of Rickettsia rickettsii, the Brazilian spotted fever pathogen. As wooless lambs are often raised on pasture together with horses, an experiment was performed to investigate their possible acquisition of resistance to A. cajennense after experimental infestations. Seven naive wooless lambs were infested thrice at 60 days interval with immature and adult instars of A. cajennense from a laboratory colony, the tick biotic potential being determined and biopsies of tick bite lesions taken to investigate the inflammatory cell component. Nearly 100% of larvae died in all infestations, while nymphs and adults fed normally throughout re-infestations. Microscopic features of adult tick bite lesions revealed predominance of neutrophils (38%) and eosinophils (36.8%), respectively, in the first and second infestations. In the third infestation, 43.6% of MN cells were found and about 31% of eosinophils. on the other hand, nymph bite lesions revealed in all infestations a predominance of eosinophils, increasing from 36% in the first infestation to 50.5% in the third one. It is concluded that wooless lambs present remarkable innate resistance against larvae of A. cajennense, but marked susceptibility to the other tick instars despite the migration of great number of eosinophils to the tick lesion.

Humoral and cell-mediated immunity in large non-toxic multinodular goitre

Humoral and cell-mediated immunity was investigated in fourteen patients with non-toxic multinodular goitre and ten healthy controls by in vitro methods. These included determination of sheep erythrocyte and complement rosette-forming cells in the peripheral blood, immunoglobulin levels, titres of thyroglobulin and microsomal antibodies and migration inhibition test using thyroid extract and phytohemagglutinin. When compared with controls the patients showed high IgA levels and positive response to thyroid antigen in the leucocyte migration inhibition test. There was no correlation between the leucocyte migration results and the presence of auto-antibodies. These findings indicate a possible role of cell-mediated immunity in non-toxic multinodular goitre.

Cell-mediated and humoral immunity in West syndrome

The immunological status of five children with West syndrome consequent to previous cerebral lesions was investigated. Three children had West syndrome and two were in transition from West to Lennox-Gastaut syndrome. All of them showed cellular immunological deficiencies in the following tests: sensitization to DNCB, intracutaneous reaction to PHA, inhibition of leukocyte migration, blastic transformation of lymphocytes, T and B lymphocytes in peripheral blood and levels of serum immunoglobulins. These immunological deficiencies, of different degrees of severity, were associated with frequent infections in these children. A possible association between the immunological deficiencies and autoimmunity is discussed.

Correlation between cell-mediated immunity and clinical forms of paracoccidioidomycosis

Cellular immune response to specific and non-specific stimulants was investigated, both in vivo and in vitro, in 29 healthy controls and in 53 previously untreated patients with the chronic isolated organic form (CIOF), the chronic mixed form (CMF) and the acute progressive form (APF) of paracoccidioidomycosis. The study included skin tests to Paracoccidioides brasiliensis antigen (PbAg) and phytohaemagglutinin (PHA), DNCB sensitization, determination of T lymphocytes and complement rosette-forming cells, lymphocyte transformation and leucocyte migration inhibition tests using PbAg and PHA. Patients displayed staggered cutaneous response to PHA and to PbAg, with marked decrease in intensity in the APF group. DNCB sensitization test and proliferative response of lymphocytes to PHA and PbAg were severely depressed in most of the patients. Leucocyte migration inhibition indices to PbAg were highly positive, while response to PHA was slightly decreased regardless of the clinical form. The number of T lymphocytes was reduced in most of patients and in them the number of complement-rosette forming cells was normal. The distribution of patients according to a suppression index, based in the results of the tests employed, revealed a tendency towards an increased degree of cellular immunosuppression from the least severe (CIOF) to the most severe (APF) clinical form of the disease. On the whole, the present study demonstrated a gamut of immunological reactivity in paracoccidioidomycosis. © 1985.

Quantum algebraic description of the Moszkowski model

In this paper we investigate the behaviour of the Moukowski model within the mnten of quantum algebras. The Moszkwski Hamiltonian is diagonalized aractly for different numbers of panicles and for various values of the deformalion parameter of the quanlum algebra involved. We also include ranking in our system and observe its variation as a function of the deformation parameters. © 1992 IOP Publishing Ltd.

Affine Lie algebraic origin of constrained KP hierarchies

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.