Geometria de superficies: una aproximació a la figura de Gausss

Gauss va publicar l’any 1827 Disquisitiones generales circa superficies curvas, obra que ha resultat fonamental en el desenvolupament de la geometria diferencial a partir del segle XIX. La documentació de la qual es disposa sobre la gènesi i el desenvolupament de les idees d’aquesta obra, ens permet, a més de presentar els principals resultats que hi apareixen, fer una aproximació a la figura de Gauss, al seu estil matemàtic

1.° Anonymi tractatus de compositione astrolabii. — 2.° Theorica planetarum : authore Gerardo Carmonensi. — 3.° Joannis de Sacrobosco tractatus de sphaera : multa sub finem desiderantur. — 4.° Practica ad componendum cylindrum. — 5.° Compositio astrolabii nova. — 6.° Canones quadrantis novi. — 7.° Canones cylindri. — 8.° Canones astrolabii. — 9.° Anonymi tractatus de compositione sphaerae solidae cum armillis. — 10.° Anonymi practica de modo mensurandi in geometria. — 11.° Algorismus specialis et astronomicus. — 12.° La maniére de connoistre les heures de nuit. — 13.° Anonymi tractatus de compositione quadrantis. — 14.° Canones, sive utilitates quadrantis.

Colbertinus

De les dades composicionals a una geometria euclidiana sobre el símplex

La reflexió sobre la naturalesa de les dades composicionals i sobre la metodologia estadística específica per a la seva anàlisi condueix a la construcció de l'espai de les composicions i a la seva estructuració com un espai vectorial euclidià, del qual el símplex n'és l'espai suport. S'il·lustren sobre el diagrama ternari alguns dels elements més característics d'aquesta geometria

Geometria y depositos de las cubetas glaciolacustres del Pirineo

Mediante la combinación de métodos geomorfológicos y sondeos eléctricos, se han estudiado 6 cubetas lacustres cuaternarias de origen glacial en el Pirineo. Esterri d'Aneu, Benasque y Bono son unos claros ejemplos de cubetas de sobreexcavación glacial. El Seminari de Vilaller constituye un ambiente lacustre proglacial debido a un cierre morrénico. El lago de Taüll como ejemplo de un ambiente lacustre yuxtaglacial debido también a una obturación morrénica y la laguna de Les Basses d'Ules, en el valle de Arán, formada a partir de procesos de fracturación del substrato rocoso después de la retirada del glaciar del Garona. Debido al elevado contraste entre la resistividad de los diferentes materiales cuaternarios de recubrimiento y el substrato rocoso, se ha podido determinar mediante sondeos eléctricos el espesor del cuaternario y diferenciar las diversas formaciones que lo constituyen. En general, aparecen 3 formaciones cuaternarias sobre el substrato rocoso paleowico: una unidad glaciolacustre que es relativamente conductora, una unidad fluviodeltaica de resistividad variable pero con valores más elevados que la anterior, y una unidad superior de resistividades muy variables según la cubeta y que, en general, es más resistente. La potencia del relleno cuaternario es muy variable según la cubeta. Así encontramos espesores de más de 300 metros de media en la cubeta de Esterri d'Aneu y de tan solo unos pocos metros en Les Basses d'Ules.

Proteinuria Increases Plasma Phosphate by Altering Its Tubular Handling.

Proteinuria and hyperphosphatemia are cardiovascular risk factors independent of GFR. We hypothesized that proteinuria induces relative phosphate retention via increased proximal tubule phosphate reabsorption. To test the clinical relevance of this hypothesis, we studied phosphate handling in nephrotic children and patients with CKD. Plasma fibroblast growth factor 23 (FGF-23) concentration, plasma phosphate concentration, and tubular reabsorption of phosphate increased during the proteinuric phase compared with the remission phase in nephrotic children. Cross-sectional analysis of a cohort of 1738 patients with CKD showed that albuminuria≥300 mg/24 hours is predictive of higher phosphate levels, independent of GFR and other confounding factors. Albuminuric patients also displayed higher plasma FGF-23 and parathyroid hormone levels. To understand the molecular mechanisms underlying these observations, we induced glomerular proteinuria in two animal models. Rats with puromycin-aminonucleoside-induced nephrotic proteinuria displayed higher renal protein expression of the sodium-phosphate co-transporter NaPi-IIa, lower renal Klotho protein expression, and decreased phosphorylation of FGF receptor substrate 2α, a major FGF-23 receptor substrate. These findings were confirmed in transgenic mice that develop nephrotic-range proteinuria resulting from podocyte depletion. In vitro, albumin did not directly alter phosphate uptake in cultured proximal tubule OK cells. In conclusion, we show that proteinuria increases plasma phosphate concentration independent of GFR. This effect relies on increased proximal tubule NaPi-IIa expression secondary to decreased FGF-23 biologic activity. Proteinuria induces elevation of both plasma phosphate and FGF-23 concentrations, potentially contributing to cardiovascular disease.

Associations of Urinary Uromodulin with Clinical Characteristics and Markers of Tubular Function in the General Population.

BACKGROUND AND OBJECTIVES: Allelic variants in UMOD, the gene coding for uromodulin, are associated with rare tubulointerstitial kidney disorders and risk of CKD and hypertension in the general population. The factors associated with uromodulin excretion in the normal population remain largely unknown, and were therefore explored in this study. DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS: Urinary uromodulin excretion was measured using a validated ELISA in two population-based cohorts that included more than 6500 individuals. The Swiss Kidney Project on Genes in Hypertension study (SKIPOGH) included 817 adults (mean age±SD, 45±17 years) who underwent renal ultrasonography and performed a 24-hour urine collection. The Cohorte Lausannoise study included 5706 adults (mean age, 53±11 years) with fresh spot morning urine samples. We calculated eGFRs using the CKD-Epidemiology Collaboration formula and by 24-hour creatinine clearance. RESULTS: In both studies, positive associations were found between uromodulin and urinary sodium, chloride, and potassium excretion and osmolality. In SKIPOGH, 24-hour uromodulin excretion (median, 41 [interquartile range, 29-57] mg/24 h) was positively associated with kidney length and volume and with creatinine excretion and urine volume. It was negatively associated with age and diabetes. Both spot uromodulin concentration and 24-hour uromodulin excretion were linearly and positively associated (multivariate analyses) with eGFR<90 ml/min per 1.73 m(2). CONCLUSION: Age, creatinine excretion, diabetes, and urinary volume are independent clinical correlates of urinary uromodulin excretion. The associations of uromodulin excretion with markers of tubular functions and kidney dimensions suggest that it may reflect tubule activity in the general population.

Construção e avaliação de um eletrodo tubular sensível ao íon hidrogênio como detector em sistemas de análise em fluxo

The construction of a tubular hydrogen ion-selective potentiometric electrode without inner reference solution, based on the tridodecylamine (TDDA) ionophore, and its evaluation in a flow system are described. TDDA was dissolved in 2-nitrophenyl octyl ether, dispersed in a PVC membrane and applied directly to a conducting support which consisted of an epoxy resin and graphite mixture. The electrode was designed with a tubular geometry to effort facilities to be coupled as part of a flow injection network. The main working characteristics such as response time, linear pH range, selectivity and life time were evaluated and compared with those obtained which a conventionally shaped electrode based on the same sensor. The electrode showed a slope of 51-52 mV dec-1 within a linear pH range from 4.0 up to 12.0.

Sistema automático para determinação seqüencial de cianeto livre e total empregando eletrodo tubular íon-seletivo de membrana homogênea

This study presents an automated system for potentiometric determination of free and total cyanide which employs a homogeneous membrane tubular ion-selective electrode. After the electrode is assembled, it is connected to a system composed of 3 three-way solenoid valves, sample line, carrier line, acid stream, and gas diffusion chamber. A Turbo Pascal® computer program, developed specifically for this task, automatically performs all the steps involved in data acquisition and processing. The proposed analytical procedure offers operational simplicity, since detection is performed by a tubular electrode, whose assembly is fast and easy. The system has shown reproducibility (r.s.d. < 0.5%, n=6) and high speed (30 readings/hour); it is efficient for determination of free and total cyanide in waste waters of starch processing plants. The detection limit was 1.2x10-5 and 1.5x10-5 mol L-1, for determination of free and total cyanide, respectively. The linear response range was between 1.2x10-5 and 1.0x10-2 mol L-1 for free cyanide and between 1.5x10-5 and 1.0x10-2 for total cyanide.

Estudo da geometria da uréia por métodos ab initio e simulação computacional de líquidos

A study was carried out on the urea geometries using ab initio calculation and Monte Carlo computational simulation of liquids. The ab initio calculated results showed that urea has a non-planar conformation in the gas phase in which the hydrogen atoms are out of the plane formed by the heavy atoms. Free energies associated to the rotation of the amino groups of urea in water were obtained using the Monte Carlo method in which the thermodynamic perturbation theory is implemented. The magnitude of the free energy obtained from this simulation did not permit us to conclude that urea is non-planar in water.

Influência da geometria da plataforma na determinação de chumbo em zidovudina (AZT) por ET AAS

The aim of this work was to compare the performances of the L'vov and integrated platforms in order to overcome the interferences found on lead determination in zidovudine by ET AAS. Pyrolysis and atomization temperatures found with integrated platform were 700 and 1400°C, respectively. The characteristic masses were 12.7 ± 1.2 pg with integrated platform and 11.1 ± 1.3 pg with grooved platform. The ratio between the slopes of zidovudine and aqueous curves shows a decrease in the interferences when the L'vov platform is used (bAZT/b aq = 0.97 ± 0.10) and the detection limit found was 0.03 µg.g-1. That ratio was 0.85 ± 0.07 with the integrated platform.

Espectros eletrônicos de alguns complexos de geometria octaédrica de Ni2+: uma introdução prática à teoria do campo cristalino no curso de graduação

The experiment introduces the undergraduate students to the crystal field theory. The electronic spectra of the octahedral complexes of [Ni(L)n]2+ (L = H2O, dmso, NH3 and en) obtained in the experiment are used to calculate 10Dq and B parameters. The experiment shows how the parameters can be calculated and correlated with the nature of the ligands and the field intensities produced.

Coordenadas cartesianas moleculares a partir da geometria dos modos normais de vibração

A simple method to obtain molecular Cartesian coordinates as a function of vibrational normal modes is presented in this work. The method does not require the definition of special matrices, like the F and G of Wilson, neither of group theory. The Eckart's conditions together with the diagonalization of kinetic and potential energy are the only required expressions. This makes the present approach appropriate to be used as a preliminary study for more advanced concepts concerning vibrational analysis. Examples are given for diatomic and triatomic molecules.

De geometria Dei

Invocatio: D.D.

"Quem não é geômetra não entre!" Geometria, Filosofia e Platonismo

O objetivo deste artigo é analisar, a partir dos textos de Platão e de comentadores, a apresentação de argumentos a favor da utilização da matemática e da geometria como propedêutica à aprendizagem da filosofia, bem como investigar as reverberações da ontologia e da epistemologia platônicas nesse programa pedagógico. Pretende-se, ainda, apontar comparativamente similaridades entre crises nos fundamentos da matemática e seu impacto na concepção de racionalidade, tanto no universo grego antigo como na contemporaneidade.