Zeros of Weakly Holomorphic Modular Forms of Levels 2 and 3

Let M-k(#)(N) be the space of weakly holomorphic modular forms for Gamma(0)(N) that are holomorphic at all cusps except possibly at infinity. We study a canonical basis for M-k(#)(2) and M-k(#)(3) and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

How gender fair are German schoolbooks in the twenty-first century? An analysis of language and illustrations in schoolbooks for mathematics and German

Schoolbooks convey not only school-relevant knowledge; they also influence the development of stereotypes about different social groups. Particularly during the 1970s and 1980s, many studies analysed schoolbooks and criticised the overall predominance of male persons and of traditional role allocations. Since that time, women’s and men’s occupations and social functions have changed considerably. The present research investigated gender portrayals in schoolbooks for German and mathematics that were recently published in Germany. We examined the proportions of female and male persons in pictures and texts and categorized their activities, occupational and parental roles. Going beyond previous studies, we added two criteria: the use of gender-fair language and the spatial arrangements of persons in pictures. Our results show that schoolbooks for German contained almost balanced depictions of girls and boys, whereas women were less frequently shown than men. In mathematics books, males outnumbered females in general. Across both types of books, female and male persons were engaged in many different activities, not only gendertyped ones; however, male persons were more often described via their profession than females. Use of gender-fair language has found its way into schoolbooks but is not used consistently. Books for German were more gender fair in terms of linguistic forms than books for mathematics. For spatial arrangements, we found no indication for gender biases. The results are discussed with a focus on how schoolbooks can be optimized to contribute to gender equality.

2011 Sonia Kovalevsky Math for Girls Day Evaluation Forms

Presenter, student and teacher evaluation forms for the 6th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 29, 2011.

2014 Sonia Kovalevsky Math for Girls Day Evaluation Forms

Presenter, student and teacher evaluation forms for the 9th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 25, 2014.

Partial regularity of minimizers of a functional involving forms and maps

We discuss the partial regularity of minimizers of energy functionals such as (1)/(p)integral(Omega)[sigma(u)dA(p) + (1)/(2)delu(2p)]dx, where u is a map from a domain Omega is an element of R-n into the m-dimensional unit sphere of Rm+1 and A is a differential one-form in Omega.

Assessment Criteria for Non-auditorial Educational Forms in Informatics

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Tamed and Compatible Symplectic Forms on Four-Dimensional Almost Complex Lie Algebras

We are able to give a complete description of four-dimensional Lie algebras g which satisfy the tame-compatible question of Donaldson for all almost complex structures J on g are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms.? Note that Donaldson asked his question for compact four-manifolds. In that context, the problem is still open, but it is believed that any tamed almost complex structure is in fact compatible with a symplectic form. In this presentation, I will define the basic objects involved and will give some insights on the proof. The key for the proof is translating the problem into a Linear Algebra setting. This is a joint work with Dr. Draghici.

Quadratic and symmetric bilinear forms on modules with unique base over a semiring

Peer reviewed

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.

Chronic Telogen Effluvium And Female Pattern Hair Loss Are Separate And Distinct Forms Of Alopecia: A Histomorphometric And Immunohistochemical Analysis.

Chronic telogen effluvium (CTE), a poorly understood condition, can be confused with or may be a prodrome to female pattern hair loss (FPHL). The pathogenesis of both is related to follicle cycle shortening and possibly to blood supply changes. To analyze a number of histomorphometric and immunohistochemical findings through vascular endothelial growth factor (VEGF), Ki-67, and CD31 immunostaining in scalp biopsies of 20 patients with CTE, 17 patients with mild FPHL and 9 controls. Ki-67 index and VEGF optical density were analyzed at the follicular outer sheath using ImageJ software. CD31 microvessel density was assessed by a Chalkley grid. Significant follicle miniaturization and higher density of nonanagen follicles were found in FPHL, compared with patients with CTE and controls. Ki-67+ index correlated positively with FPHL histological features. The FPHL group showed the highest VEGF optical density, followed by the CTE and control groups. No differences were found in CD31 microvessel density between the three groups. Histomorphometric results establish CTE as a distinct disorder, separate from FPHL from its outset. Its pathogenic mechanisms are also distinct. These findings support the proposed mechanism of 'immediate telogen release' for CTE, leading to cycle synchronization. For FPHL, accelerated anagen follicular mitotic rates and, thus, higher Ki-67 and VEGF values, would leave less time for differentiation, resulting in hair miniaturization.

Use Of Experimental Design To Optimize A Triple-potential Waveform To Develop A Method For The Determination Of Streptomycin And Dihydrostreptomycin In Pharmaceutical Veterinary Dosage Forms By Hplc-pad.

An HPLC-PAD method using a gold working electrode and a triple-potential waveform was developed for the simultaneous determination of streptomycin and dihydrostreptomycin in veterinary drugs. Glucose was used as the internal standard, and the triple-potential waveform was optimized using a factorial and a central composite design. The optimum potentials were as follows: amperometric detection, E1=-0.15V; cleaning potential, E2=+0.85V; and reactivation of the electrode surface, E3=-0.65V. For the separation of the aminoglycosides and the internal standard of glucose, a CarboPac™ PA1 anion exchange column was used together with a mobile phase consisting of a 0.070 mol L(-1) sodium hydroxide solution in the isocratic elution mode with a flow rate of 0.8 mL min(-1). The method was validated and applied to the determination of streptomycin and dihydrostreptomycin in veterinary formulations (injection, suspension and ointment) without any previous sample pretreatment, except for the ointments, for which a liquid-liquid extraction was required before HPLC-PAD analysis. The method showed adequate selectivity, with an accuracy of 98-107% and a precision of less than 3.9%.

Licenças medicas de professores de educação fisica : expressando especificidades em estudo na Rede Municipal de Ensino, Campinas - SP

Universidade Estadual de Campinas . Faculdade de Educação Física

Interleukin-22 forms dimers that are recognized by two interleukin-22R1 receptor chains

Interleukin-22 (IL-22) is a class 2 cytokine whose primary structure is similar to that of interleukin 10 (IL-10) and interferon-gamma (IFN-gamma). IL-22 induction during acute phase immune response indicates its involvement in mechanisms of inflammation. Structurally different from IL-10 and a number of other members of IL-10 family, which form intertwined inseparable V-shaped dimers of two identical polypeptide chains, a single polypeptide chain of IL-22 folds on itself in a relatively globular structure. Here we present evidence, based on native gel electrophoresis, glutaraldehyde cross-linking, dynamic light scattering, and small angle x-ray scattering experiments, that human IL-22 forms dimers and tetramers in solution under protein concentrations assessable by these experiments. Unexpectedly, low-resolution molecular shape of IL-22 dimers is strikingly similar to that of IL-10 and other intertwined cytokine dimeric forms. Furthermore, we determine an ab initio molecular shape of the IL-22/IL-22R1 complex which reveals the V-shaped IL-22 dimer interacting with two cognate IL-22R1 molecules. Based on this collective evidence, we argue that dimerization might be a common mechanism of all class 2 cytokines for the molecular recognition with their respective membrane receptor. We also speculate that the IL-22 tetramer formation could represent a way to store the cytokine in nonactive form at high concentrations that could be readily converted into functionally active monomers and dimers upon interaction with the cognate cellular receptors.

Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

We investigate synchronization in a Kuramoto-like model with nearest neighbor coupling. Upon analyzing the behavior of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.