Dois teoremas sôbre a função gama

This paper proves the following theorems on the gamma function: Theorem I The integral ∫O∞ t u e-t dt = Γ ( u + 1 ) , where u, real or complex, is such that R (u) > -1, will not change its value if we substitute z = Q (cos φ + i sen φ) for the real variable t, being jconstant and such that - Π/2 < φ < Π/2 , Theorem II The integral ∫-∞∞ w2u + 1 e -w² dw = Γ ( u + 1 ) , where 2u + 1 is supposed to be a non negative even integer, will not change its value if we substitute z = w + fi, f being a real constant, for the real variable w. The proof of both theorems is obtained by means of the well known Cauchy theorem on contour integrals on the complex plane, as suggested by CRAMÉR (1, p. 126) and LEVY (3, p. 178).

Advances in pharmacological studies of silymarin

Silymarin is the flavonoids extracted from the seeds of Silybum marianum (L) Gearth as a mixture of three structural isomers: silybin, silydianin and silychristin, the former being the most active component. Silymarin protects liver cell membrane against hepatotoxic agents and improves liver function in experimental animals and humans. It is generally accepted that silymarin exerts a membrane-stabilizing action preventing or inhibiting membrane peroxidation. The experiments with soybean lipoxygenase showed that the three components of silymarin brought about a concentration-dependent non-competitive inhibition of the lipoxygenase. The experiments also showed an analogous interaction with animal lipoxygenase, thus showing that an inhibition of the peroxidation of the fatty acid in vivo was self-evident. Silybin almost completely suppressed the formation of PG at the highest concentration (0.3 mM) and proved to be an inhibitor of PG synthesis in vitro. In our experiments, silybin at lower dose (65 mg/Kg) decreased liver lipoperoxide content and microsomal lipoperoxidation to 84.5% and 68.55% of those of the scalded control rats respectively, and prevented the decrease of liver microsomal cytochrome p-450 content and p-nitroanisole-0-demethylase activity 24 h post-scalding. Effects of silymarin on cardiovascular systen have been studied in this university since 1980. O. O silymarin 800 mg/Kg/d or silybin 600 mg/Kg/d reduced plasma total cholesterol, LDL-C and VLDL-C. They however, enhanced HDL-C in hyperlipenic rats. Further studies showed that silymarin enhanced HDL-C in hyperlipemic rats. Further studies showed that silymarin enhanced HDL-C but didn't affect HDL-C, a property of this component which is beneficial to treatment of atherosclerosis. The results showed silymarin 80 mg or silybin 60 mg decreased in vitro platelet aggregation (porcentagem) in rats. The maximal platelet aggregation induced by ADP declined significantly, and time to reach maximal platelet aggregation and five-minute disaggregation didn't change. In our experiments, iv silybin 22,4 mg/kg lowered the amplitude and duration of diastolic blood pressure (DBP) more than those of systolic (SBP), but the descending aortic blood flow, cardiac contractility and ECG did not change significantly in anesthetized open-chest cats. The results indicated a reduction of peripheral resistance and dilatatory action on the resistant blood vessels. These effects are beneficial to coronary heart disease. We also observed the effects of silybin on morphological change, the release of glutamic oxaloacetate aminotrasferase (GOT) and lactate dehydrogenase (LDH) as well as the radioactivity of 3H-TdR incorporated into DNA in normal cardiac cells and cells infected by coxsackie B5, virus os newborn rats. The results showed that silynin did not affect the morphology of normal cell, and that the pathological change of cells infected by virus was delayed and reduced as compared to control. We have investigated the effect of silybin on synthesis and release of LTs in the cultured porcine cerebral basilar arteries (PCBA). Silybin 100 and 500 µmol/L declined the amounts of LTs released from the PCBA incubsated in the presence of A 23187, AA and indomenthacin. The result suggests that silybin can inhibit the activity of 5-lipoxygenase of cerebral blood vessel and may protect the brain from ischemia.

Aggregate stability by the "high energy moisture characteristic" method in an oxisol under differentiated management

Studies testing the High Energy Moisture Characteristic (HEMC) technique in tropical soils are still incipient. By this method, the effects of different management systems can be evaluated. This study investigated the aggregation state of an Oxisol under coffee with Brachiaria between crop rows and surface-applied gypsum rates using HEMC. Soil in an experimental area in the Upper São Francisco region, Minas Gerais, was studied at depths of 0.05 and 0.20 m in coffee rows. The treatments consisted of 0, 7, and 28 Mg ha-1 of agricultural gypsum rates distributed on the soil surface of the coffee rows, between which Brachiaria was grown and periodically cut, and compared with a treatment without Brachiaria between coffee rows and no gypsum application. To determine the aggregation state using the HEMC method, soil aggregates were placed in a Büchner funnel (500 mL) and wetted using a peristaltic pump with a volumetric syringe. The wetting was applied increasingly at two pre-set speeds: slow (2 mm h-1) and fast (100 mm h-1). Once saturated, the aggregates were exposed to a gradually increasing tension by the displacement of a water column (varying from 0 to 30 cm) to obtain the moisture retention curve [M = f (Ψ) ], underlying the calculation of the stability parameters: modal suction, volume of drainable pores (VDP), stability index (slow and fast), VDP ratio, and stability ratio. The HEMC method conferred sensitivity in quantifying the aggregate stability parameters, and independent of whether gypsum was used, the soil managed with Brachiaria between the coffee rows, with regular cuts discharged in the crop row direction, exhibited a decreased susceptibility to disaggregation.

Ordens não inteiras em cinética química

Starting from zero-, first-, and second-order integrated laws for chemical kinetics, some cases are shown which produce fractional orders. Taking the Michaelis-Menten mechanism as a first example, it is shown that substrate order can go from 1 to zero, depending on relative concentration of enzyme and substrate. Using other examples which show fractional orders higher than one and even negative (inhibition), it is shown that the presence of an equilibrium before or parallel to the rate determining step can be the reason for fractional orders, which is an indication of a more complex mechanism.

Sintonização de estados quânticos: um estudo numérico do oscilador harmônico quântico

The quantum harmonic oscillator is described by the Hermite equation.¹ The asymptotic solution is predominantly used to obtain its analytical solutions. Wave functions (solutions) are quadratically integrable if taken as the product of the convergent asymptotic solution (Gaussian function) and Hermite polynomial,¹ whose degree provides the associated quantum number. Solving it numerically, quantization is observed when a control real variable is "tuned" to integer values. This can be interpreted by graphical reading of Y(x) and |Y(x)|², without other mathematical analysis, and prove useful for teaching fundamentals of quantum chemistry to undergraduates.

Analysis of the relationship intensity, duration, frequency of disaggregated daily rainfall in southern Rio Grande do Sul, Brazil

The intensity, duration, and frequency relationship (IDF) of rainfall occurrence may be done through continuous records of pluviographs or daily pluviometer values . The objective of this study was to estimate the intensity-duration-frequency relationships of precipitation, using the method of daily rainfall disaggregation, at weather stations located to the southern half of the state of Rio Grande do Sul; comparing them with those obtained by rain gauge records, in places considered homogeneous from the meteorological point of view. The IDF equation parameters were estimated from daily rainfall disaggregation data, using the method of nonlinear optimization. To validate the equations confidence indices and efficiency and the "t" Student test, among maximum intensity values obtained from the disaggregated daily rainfall durations of 10; 30; 60 min and 6; 12 and 24 h and those extracted from existing IDF equations. For all studied stations and return periods, the trust index values were regarded as "optimal", i.e., greater than 0.85. The maximal intensity of rainfall obtained by daily rainfall disaggregation have similarity with those obtained by relations IDF standards. Thus, the method constitutes a feasible alternative in obtaining the IDF relationships.

Method adjustment and equation set of maximum rainfall intensity, duration and frequency in the Mato Grosso do Sul State

Due to the lack of information concerning maximum rainfall equations for most locations in Mato Grosso do Sul State, the alternative for carrying out hydraulic work projects has been information from meteorological stations closest to the location in which the project is carried out. Alternative methods, such as 24 hours rain disaggregation method from rainfall data due to greater availability of stations and longer observations can work. Based on this approach, the objective of this study was to estimate maximum rainfall equations for Mato Grosso do Sul State by adjusting the 24 hours rain disaggregation method, depending on data obtained from rain gauge stations from Dourado and Campo Grande. For this purpose, data consisting of 105 rainfall stations were used, which are available in the ANA (Water Resources Management National Agency) database. Based on the results we concluded: the intense rainfall equations obtained by pluviogram analysis showed determination coefficient above 99%; and the performance of 24 hours rain disaggregation method was classified as excellent, based on relative average error WILMOTT concordance index (1982).

Bartlett-Lewis of rectangular pulse modified model: estimate of parameters for simulation of precipitation in sub-hourly duration

The Bartlett-Lewis Rectangular Pulse Modified (BLPRM) model simulates the precipitous slide in the hourly and sub-hourly and has six parameters for each of the twelve months of the year. This study aimed to evaluate the behavior of precipitation series in the duration of 15 min, obtained by simulation using the model BLPRM in situations: (a) where the parameters are estimated from a combination of statistics, creating five different sets; (b) suitability of the model to generate rain. To adjust the parameters were used rain gauge records of Pelotas/RS/Brazil, which statistics were estimated - mean, variance, covariance, autocorrelation coefficient of lag 1, the proportion of dry days in the period considered. The results showed that the parameters related to the time of onset of precipitation (λ) and intensities (μx) were the most stable and the most unstable were ν parameter, related to rain duration. The BLPRM model adequately represented the mean, variance, and proportion of the dry period of the series of precipitation lasting 15 min and, the time dependence of the heights of rain, represented autocorrelation coefficient of the first retardation was statistically less simulated series suitability for the duration of 15 min.