Seven views on approximate convexity and the geometry of K-spaces

As in Hokusai's series of paintings "Thirty six views of mount Fuji" in which mount Fuji's is sometimes scarcely visible, the central topic of this paper is the geometry of $K$-spaces although in some of the seven views presented $K$-spaces are not easily visible. We study the interplay between the behaviour of approximately convex (and approximately affine) functions on the unit ball of a Banach space and the geometry of Banach K-spaces.Comment: 2 figure

Sacrectomía en bloque para tumores gigantes del sacro preservando las raíces de S1. Reporte de nueva técnica quirúrgica y resultado funcional

Los tumores primarios de sacro son lesiones raras que se caracterizan por ser localmente agresivos, de naturaleza osteolítica y con gran potencial para recurrir a corto plazo. Se han descrito mútiples opciones de manejo y tratamiento de los mismos, incluyendo quimioterapia y radioterapia además de resección quirúrgica con el fin de proveer control a largo plazo sobre el crecimiento tumoral y/o cura definitiva. (5, 6, 7) Dada la naturaleza histológica de dichas lesiones, la sacrectomía en bloque es la técnica quirúrgica que menos recurrencia local implica (8) sin embargo, dado el compromiso extenso que presentan los tumores sacros en el momento del diagnóstico, usualmente la resección quirurgica implica el sacrificio de raíces nerviosas, impactando directamente en morbilidad a largo plazo. Las complicaciones mayores secundarias que más frecuentemente se observan incluyen alteración para la deambulación, función genitourinaria y gastrointestinal, y finalmente, función sexual. (4). El objetivo del presente articulo es describir tres casos en donde se realizan sacrectomía en bloque de tumores primarios de sacro con preservación de raices nerviosas y sus desenlaces a 36 meses de seguimiento postquirúrgico.Sacral primary tumors are rare lesiones that are characterized to be locally expansive and agressive, often present with osteolysis and with great chances to recurr at short-run term after a first surgical reseccion. There are multiple described options for management and treatment, including radiotherapy and chemotherapy for the relief of pain and surgical reseccion in order to provide long-term control over tumor growth or definitive cure. Given the nature of such lesions, en bloc sacrectomy is the surgical technique that involves less local recurrence, however, given the extensión of sacral tumors at diagnosis, usually surgical resection means sacrificing nerve roots, directly impacting over long-term morbidity. Secondary major complicactions most frequently observed include impaired ambulation, genitourinary, gastrointestinal and sexual function. The aim of this article is to describe three cases where en bloc sacrectomy were performed for management of primary sacral tumors (two gigant cell tumors and one hemangioma) with preservation of nerve roots and their outcome up tu 36 months of postoperative follow-up

Heavy metal content of vegetables irrigated with mixtures of wastewater and sewage sludge in Zimbabwe: Implications for human health

There is growing public concern in Zimbabwe over the illegal cultivation of vegetables on soils amended with sewage sludge or irrigated with admixtures of sewage and sewage sludge. Excessive accumulation of heavy metals in agricultural soils may not only result in environmental contamination, but lead to elevated heavy metal uptake by crops, which may affect food quality and safety. The work reported here studied heavy metal concentrations in crops irrigated with sewage sludge and sewage/sewage sludge admixtures at Firle Municipal Farm in Harare. The crops analysed in this study are heavily contaminated with the four regulated elements Cd, Cu, Pb and Zn. This contamination is at its highest in two of the staple dietary crops maize and tsunga. Tsunga leaves contained 3.68 mg kg-1 Cd, over 18 times the permissible level by the EU standards (0.2 mg kg-1); Cu concentrations were 111 mg kg-1, 5 times the EU Standard (20 mg kg-1); concentrations of Pb were 6.77 mg kg-1, over 22 times the permissible levels allowed by both EU standards and UK guidelines (0.3 mg kg-1); Zn concentrations were 221 mg kg-1, over 4 times the guideline value (50 mg kg-1). The other plants (beans, maize, peppers and sugarcane) also contained concentrations of heavy metals above the permissible levels. Furthermore the concentrations observed in this study were higher than those reported by other workers who have examined vegetation from other contaminated sites. This study highlights the potential risks involved in the cultivation and consumption of vegetables on plots irrigated with sewage sludge, a practice which may place at risk the health of the urban population who consume these vegetables

Orientational order parameters of a de Vries–type ferroelectric liquid crystal obtained by polarized Raman spectroscopy and x-ray diffraction

The orientational order parameters 〈P2〉 and 〈P4〉 of the ferroelectric, de Vries–type liquid crystal 9HL have been determined in the SmA* and SmC* phases by means of polarized Raman spectroscopy, and in the SmA* phase using x-ray diffraction. Quantum density functional theory predicts Raman spectra for 9HL that are in good agreement with the observations and indicates that the strong Raman band probed in the experiment corresponds to the uniaxial, coupled vibration of the three phenyl rings along the molecular long axis. The magnitudes of the orientational order parameters obtained in the Raman and x-ray experiments differ dramatically from each other, a discrepancy that is resolved by considering that the two techniques probe the orientational distributions of different molecular axes. We have developed a systematic procedure in which we calculate the angle between these axes and rescale the orientational order parameters obtained from x-ray scattering with results that are then in good agreement with the Raman data. At least in the case of 9HL, the results obtained by both techniques support a “sugar loaf” orientational distribution in the SmA* phase with no qualitative difference to conventional smectics A. The role of individual molecular fragments in promoting de Vries–type behavior is considered

ZnO (Ag-N) Nanorods Films Optimized for Photocatalytic Water Purification

ZnO nanorods (NRs) films, nitrogen-doped (ZnO:N), and ZnO doped with nitrogen and decorated with silver nanostructures (ZnO:N-Ag) NRs films were vertically supported on undoped and N doped ZnO seed layers by a wet chemical method. The obtained films were characterized structurally by X-ray diffraction. Morphological and elemental analysis was performed by scanning electron microscopy, including an energy dispersive X-ray spectroscopy facility and their optical properties by Ultraviolet-Visible Spectroscopy. Analysis performed in the NRs films showed that the nitrogen content in the seed layer strongly affected their structure and morphology. The mean diameter of ZnO NRs ranged from 70 to 190 nm. As the nitrogen content in the seed layer increased, the mean diameter of ZnO:N NRs increased from 132 to 250 nm and the diameter dispersion decreased. This diameter increase occurs simultaneously with the incorporation of nitrogen into the ZnO crystal lattice and the increase in the volume of the unit cell, calculated using the X-ray diffraction patterns and confirmed by a slight shift in the XRD angle. The diffractograms indicated that the NRs have a hexagonal wurtzite structure, with preferential growth direction along the c axis. The SEM images confirmed the presence of metallic silver in the form of nanoparticles dispersed on the NRs films. Finally, the degradation of methyl orange (MO) in an aqueous solution was studied by UV-vis irradiation of NRs films contained in the bulk of aqueous MO solutions. We found a significant enhancement of the photocatalytic degradation efficiency, with ZnO:N-Ag NRs film being more efficient than ZnO:N NRs film, and the latter better than the ZnO NRs film. View Full-Text

A CMOS Morlet Wavelet Generator

The design and characterization of a CMOS circuit for Morlet wavelet generation is introduced. With the proposed Morlet wavelet circuit, it is possible to reach a~low power consumption, improve standard deviation (σ) control and also have a small form factor. A prototype in a double poly, three metal layers, 0.5 µm CMOS process from MOSIS foundry was carried out in order to verify the functionality of the proposal. However, the design methodology can be extended to different CMOS processes. According to the performance exhibited by the circuit, may be useful in many different signal processing tasks such as nonlinear time-variant systems