Geometric approach to Fletcher's ideal penalty function

Original article can be found at: www.springerlink.com Copyright Springer. [Originally produced as UH Technical Report 280, 1993]In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.Peer reviewe

Antiferromagnetic ordering and dipolar interactions of YbAlO3_3

In this paper we report low-temperature magnetic properties of the rare-earth perovskite material YbAlO$_3$. Results of elastic and inelastic neutron scattering experiment, magnetization measurements along with the crystalline electrical field (CEF) calculations suggest that the ground state of Yb moments is a strongly anisotropic Kramers doublet, and the moments are confined in the $ab$-plane, pointing at an angle of $\varphi = \pm 23.5^{\circ}$ to the $a$-axis. With temperature decreasing below $T_{\rm N}=0.88$ K, Yb moments order into the coplanar, but non-collinear antiferromagnetic (AFM) structure $AxGy$, where the moments are pointed along their easy-axes. In addition, we highlight the importance of the dipole-dipole interaction, which selects the type of magnetic ordering and may be crucial for understanding magnetic properties of other rare-earth orthorhombic perovskites. Further analysis of the broad diffuse neutron scattering shows that one-dimensional interaction along the $c$-axis is dominant, and suggests YbAlO$_3$ as a new member of one dimensional quantum magnets.Comment: 8 pages, 6 figure

Near Sharp Strichartz estimates with loss in the presence of degenerate hyperbolic trapping

We consider an $n$-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schr\"odiner equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension $n$ and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary $\beta>0$ loss. This is in contrast to \cite{ChWu-lsm}, where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension

Conflicting discourses of church youths on masculinity and sexuality in the context of HIV in Kinshasa, Democratic Republic of Congo

Masculinity studies are fairly new and young churchgoers are an under-researched group in the current Congolese church context. In response to this knowledge gap, this paper attempts to explore discourses of young  churchgoers from deprived areas of Kinshasa regarding masculinity and sexuality in the era of HIV. A series of 16 semi-structured interviews were conducted with unmarried young churchgoers from the Salvation Army, Protestant and Revival churches. The interviews were tape-recorded, transcribed verbatim and analysed using discourse analysis. Five main discourses emerged: ‘we are aware of the church message on sex’, ‘young men need sex’, ‘young women need money’, ‘to use or not to use condoms’ and ‘we trust in the church message’. Although all informants knew and heard church messages against premarital sex, many of them were sexually active. The perception was that young men were engaged in sexual activities with multiple partners as a result of sexual motivations surrounding masculinity and sexual potency, while young women sought multiple partners through transactional and intergenerational sex for economic reasons. These sexual practices of young people conflicted with church messages on sexual abstinence and faithfulness. However, a small number of participants challenged current gender norms and suggested alternative ways of being a man or a woman. To elucidate these  alternatives, we suggest that church youths and church leaders might take concrete actions to deconstruct misconceptions about being men. In this way, they can possibly enhance a frank and fruitful dialogue on sex, sexuality and gender to promote positive masculinities and constructive partnerships to prevent HIV.Keywords: masculinity, sexuality, young churchgoers, HIV prevention, gender equality, DR CongoDans le contexte actuel des e´glises Congolaises, les e´tudes relatives a` la masculinite´ sont presque re´centes et les jeunes chre´tiens constituent un groupe d’individus qui ne font pas l’objet des recherches scientifiques  approfondies. En re´ponse a` cette insuffisance de connaissances dans le contexte a` VIH, le pre´sent article tente d’explorer les discours relatifs a` la masculinite´ et a` la sexualite´ des jeunes chre´tiens issus des  quartiers de´favorise´s de Kinshasa. Une se´rie de 16 interviews semi-structure´es ont e´te´ mene´s aupre`s des jeunes chre´tiens ce´libataires appartenant a` l’Arme´e du Salut, aux e´glises Protestantes et a` celles du Re´veil du Congo. Les interviews ont e´te´ enregistre´es et analyse´es en utilisant la me´thode du discours. Cinq discours ont e´merge´ notamment: « Nous connaissons le message des e´glises au sujet du sexe », « les garc¸ons ont besoin des rapports sexuels », « les filles ont besoin d’argent », « faudrait-il utiliser ou ne pas utiliser les condoms » et « nous croyons dans le message des e´glises ». Alors que tous les participants  connaissaient le message des e´glises qui interdisent les rapports sexuels pre´maritaux, beaucoup d’entre eux e´taient de´ja` sexuellement actifs. Les garc¸ons ont e´te´ perc¸us comme des personnes qui ont des rapports sexuels avec plusieurs partenaires concomitants pour prouver leur masculinite´ et leur puissance sexuelle. Les filles chercheraient a` avoir des rapports sexuels mercantiles et interge´ne´rationnels avec des partenaires  multiples a` des fins e´conomiques. Ces pratiques sexuelles des jeunes s’opposent aux discours des e´glises  qui promeuvent l’abstinence sexuelle et la fide´lite´. Cependant, quelques participants ont remis en cause les normes courantes du genre et ont sugge´re´ des alternatives en ce qui concerne l’identite´ des hommes et des femmes. Pour les e´lucider, nous proposons que les jeunes chre´tiens et les leaders des e´glises puissent mener des actions concre`tes dans le but de de´construire les conceptions errone´es de ce que veut dire eˆtre homme. Ce faisant, ils peuvent probablement maximiser les chances d’un dialogue franc et productif en ce qui concerne le sexe, la sexualite´ et le genre afin de promouvoir la masculinite´ positive et le partenariat  constructif, susceptibles de pre´venir l’infection a` VIH.Mots cle´s: masculinite´, sexualite´, jeunes chre´tiens, pre´vention du VIH, e´galite´ du genre, RD Cong

Quantum ergodicity for restrictions to hypersurfaces

Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple dynamical condition, the restrictions of eigenstates to N are also quantum ergodic.Comment: 22 pages, 1 figure; revised according to referee's comments. To appear in Nonlinearit

Ytterbium divalency and lattice disorder in near-zero thermal expansion YbGaGe

While near-zero thermal expansion (NZTE) in YbGaGe is sensitive to stoichiometry and defect concentration, the NZTE mechanism remains elusive. We present x-ray absorption spectra that show unequivocally that Yb is nearly divalent in YbGaGe and the valence does not change with temperature or with nominally 1% B or 5% C impurities, ruling out a valence-fluctuation mechanism. Moreover, substantial changes occur in the local structure around Yb with B and C inclusion. Together with inelastic neutron scattering measurements, these data indicate a strong tendency for the lattice to disorder, providing a possible explanation for NZTE in YbGaGe.Comment: 4 pages, 4 figure, supplementary inf