Symmetry algebra of a generalized anisotropic harmonic oscillator

It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra

Jets, knots and tails in planetary nebulae: NGC 3918, K 1-2 and Wray 17-1

We analyze optical images and high-resolution, long-slit spectra of three planetary nebulae which possess collimated, low-ionization features. NGC 3918 is composed of an inner, spindle-shaped shell mildly inclined with respect to the plane of the sky. Departing from the polar regions of this shell, we find a two-sided jet expanding with velocities which increase linearly with distance from 50 to 100 km/s. The jet is probably coeval with the inner shell (with the age of approximately 1000 D yr, where D is the distance in kpc), suggesting that its formation should be ascribed to the same dynamical processes which also shaped the main nebula, and not to a more recent mass loss episode. We discuss the formation of the aspherical shell and jet in the light of current hydrodynamical and magnetohydrodynamical theories. K 1-2 is a planetary nebula with a close binary nucleus which shows a collimated string of knots embedded in a diffuse, elliptical shell. The knots expand with a velocity similar to that of the elliptical nebula (25 km/s), except for an extended tail located out of the main nebula, which linearly accelerates up to 45 km/s. We estimate an inclination on the line of the sight of 40 degres for the string of knots; once the orientation of the orbit is also determined, this information will allow us to test the prediction of current theories of the occurrence of polar jets from close binary systems. Wray 17-1 has a complex morphology, showing two pairs of low-ionization structures located in almost perpendicular directions from the central star, and embedded in a large, diffuse nebula. The two pairs show notable similarities and differences, and their origin is very puzzling.Comment: 20 pages plus 10 figures. ApJ recently published (ApJ 523, 721 (1999)

On the analytic-numeric treatment of weakly singular integrals on arbitrary polygonal domains

An alternative analytical approach to calculate the weakly singular free-space static potential integral associated to uniform sources is presented. Arbitrary oriented flat polygons are considered as integration domains. The technique stands out by its mathematical simplicity and it is based on a novel integral transformation. The presented formula is equivalent to others existing in literature, being also concise and suitable within a singularity subtraction framework. Generalized Cartesian product rules built on the double exponential formula are utilized to integrate numerically the resulting analytical 2D potential integral. As a consequence, drawbacks associated to endpoint singularities in the derivative of the potential are tempered. Numerical examples within a surface integral equation-Method of Moments framework are finally provided

Noether's Theorem and time-dependent quantum invariants

The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case of the generalized two-dimensional harmonic oscillator, the time-independent integrals of motion are shown to correspond to special Bragg-type symmetry properties. A detailed study for the non-stationary case of this quantum system is presented. The linear integrals of motion are constructed explicitly for the case of varying mass and coupling strength. They are obtained also from Noether's theorem. The general treatment for a multi-dimensional quadratic system is indicated, and it is shown that the time-dependent variations that give rise to the linear invariants, as conserved quantities, satisfy the corresponding classical homogeneous equations of motion for the coordinates.Comment: Plain TeX, 23 pages, preprint of Instituto de Ciencias Nucleares, UNAM Departamento de F\ii sica and Matem\'aticas Aplicadas, No. 01 (1994

On the Mechanism of the Copper-Catalyzed Enantioselective 1,4-Addition of Grignard Reagents to α,β-Unsaturated Carbonyl Compounds

The mechanism of the enantioselective 1,4-addition of Grignard reagents to α,β-unsaturated carbonyl compounds promoted by copper complexes of chiral ferrocenyl diphosphines is explored through kinetic, spectroscopic, and electrochemical analysis. On the basis of these studies, a structure of the active catalyst is proposed. The roles of the solvent, copper halide, and the Grignard reagent have been examined. Kinetic studies support a reductive elimination as the rate-limiting step in which the chiral catalyst, the substrate, and the Grignard reagent are involved. The thermodynamic activation parameters were determined from the temperature dependence of the reaction rate. The putative active species and the catalytic cycle of the reaction are discussed.

Transgenic citrus plants expressing the citrus tristeza virus p23 protein exhibit viral-like symptoms

The 23 kDa protein (p23) coded by the 3'-terminal gene of Citrus tristeza virus (CTV), a member of the genus Closterovirus with the largest genome among plant RNA viruses, is an RNA-binding protein that contains a motif rich in cysteine and histidine residues in the core of a putative zinc-finger domain. On this basis, a regulatory role for CTV replication or gene expression has been suggested for p23. To explore whether over-expression of this protein in transgenic plants could affect the normal CTV infection process, transgenic Mexican lime plants were generated carrying the p23 transgene, or a truncated version thereof, under the control of the cauliflower mosaic virus (CaMV) 35S promoter. Constitutive expression of p23 induced phenotypic aberrations that resembled symptoms incited by CTV in non-transgenic lime plants, whereas transgenic plants expressing the p23 truncated version were normal. The onset of CTV-like symptoms in p23 transgenic plants was associated with the expression of p23, and its accumulation level paralleled the intensity of the symptoms. This demonstrates that p23 is involved in symptom development and that it most likely plays a key role in CTV pathogenesis. This is the first case in which a protein encoded by a woody plant-infecting RNA virus has been identified as being directly involved in pathogenesis in its natural host. This finding also delimits a small region of the large CTV genome for the future mapping of specific pathogenic determinants

Paraneoplastic thrombocytosis in ovarian cancer

<p>Background: The mechanisms of paraneoplastic thrombocytosis in ovarian cancer and the role that platelets play in abetting cancer growth are unclear.</p> <p>Methods: We analyzed clinical data on 619 patients with epithelial ovarian cancer to test associations between platelet counts and disease outcome. Human samples and mouse models of epithelial ovarian cancer were used to explore the underlying mechanisms of paraneoplastic thrombocytosis. The effects of platelets on tumor growth and angiogenesis were ascertained.</p> <p>Results: Thrombocytosis was significantly associated with advanced disease and shortened survival. Plasma levels of thrombopoietin and interleukin-6 were significantly elevated in patients who had thrombocytosis as compared with those who did not. In mouse models, increased hepatic thrombopoietin synthesis in response to tumor-derived interleukin-6 was an underlying mechanism of paraneoplastic thrombocytosis. Tumorderived interleukin-6 and hepatic thrombopoietin were also linked to thrombocytosis in patients. Silencing thrombopoietin and interleukin-6 abrogated thrombocytosis in tumor-bearing mice. Anti–interleukin-6 antibody treatment significantly reduced platelet counts in tumor-bearing mice and in patients with epithelial ovarian cancer. In addition, neutralizing interleukin-6 significantly enhanced the therapeutic efficacy of paclitaxel in mouse models of epithelial ovarian cancer. The use of an antiplatelet antibody to halve platelet counts in tumor-bearing mice significantly reduced tumor growth and angiogenesis.</p> <p>Conclusions: These findings support the existence of a paracrine circuit wherein increased production of thrombopoietic cytokines in tumor and host tissue leads to paraneoplastic thrombocytosis, which fuels tumor growth. We speculate that countering paraneoplastic thrombocytosis either directly or indirectly by targeting these cytokines may have therapeutic potential. </p&gt

Clinical Risk Score to Predict Pathogenic Genotypes in Patients With Dilated Cardiomyopathy

Background: Although genotyping allows family screening and influences risk-stratification in patients with nonischemic dilated cardiomyopathy (DCM) or isolated left ventricular systolic dysfunction (LVSD), its result is negative in a significant number of patients, limiting its widespread adoption. Objectives: This study sought to develop and externally validate a score that predicts the probability for a positive genetic test result (G+) in DCM/LVSD. Methods: Clinical, electrocardiogram, and echocardiographic variables were collected in 1,015 genotyped patients from Spain with DCM/LVSD. Multivariable logistic regression analysis was used to identify variables independently predicting G+, which were summed to create the Madrid Genotype Score. The external validation sample comprised 1,097 genotyped patients from the Maastricht and Trieste registries. Results: A G+ result was found in 377 (37%) and 289 (26%) patients from the derivation and validation cohorts, respectively. Independent predictors of a G+ result in the derivation cohort were: family history of DCM (OR: 2.29; 95% CI: 1.73-3.04; P < 0.001), low electrocardiogram voltage in peripheral leads (OR: 3.61; 95% CI: 2.38-5.49; P < 0.001), skeletal myopathy (OR: 3.42; 95% CI: 1.60-7.31; P = 0.001), absence of hypertension (OR: 2.28; 95% CI: 1.67-3.13; P < 0.001), and absence of left bundle branch block (OR: 3.58; 95% CI: 2.57-5.01; P < 0.001). A score containing these factors predicted a G+ result, ranging from 3% when all predictors were absent to 79% when ≥4 predictors were present. Internal validation provided a C-statistic of 0.74 (95% CI: 0.71-0.77) and a calibration slope of 0.94 (95% CI: 0.80-1.10). The C-statistic in the external validation cohort was 0.74 (95% CI: 0.71-0.78). Conclusions: The Madrid Genotype Score is an accurate tool to predict a G+ result in DCM/LVSD