Um caso especial de integrais binômias

The present paper shows that the sum of two binomial integrals, such as A ∫ x p (a + bx q)r dx + B ∫ x p (a + bx q)r dx, where A and B are real constants and p, q, r are rational numbers, can, in special cases, lead to elementary integrals, even if each by itself is not elementary. An example of the case considered is given by the integral ∫ x _____-___ 3 dx = 1/2 ∫ x-½ (x - 1)-⅓ dx - 6 √ x ³√(x - 1)4 = 1/3 ∫ x-½ (x - 1)-¾ dx On the rigth hand side of the last equality both integral are not elementary. But the use of integration by parts of one of them leads to the solution: ∫ x _____-___ 3 dx = x½ (x - 1)-⅓ + C. 6 √ x ³√(x - 1)4

Avaliação da capacidade de fixação de fósforo pelo solo

Phosphate "fixation" is the convertion of soluble into insoluble phosphate in the soil. There are many factors conditioning phosphate fixation by soil such as reactions originating less soluble compounds (phosphates of iron, aluminum, calcium, magnesium, etc.), PO4-3 adsorption by the colloidal fraction of soils, PO4-3 absorption by the soil microflora, etc. Certain soils of the state of São Paulo (Brazil) are relatively rich in both iron and aluminum oxides. PO4-3 fixation, using P31 and P32 has been verified by researchers, specially with "Terra Roxa". The known methods for fixation evaluation are conventional as this depends on phosphate solution concentration, pH, time of contact between soil and solution, relation of sample weight to solution volume, shaking time, etc. In this experiment, the following conventional method was used: 4 g of soil were shaken for 15 minutes at 30-40 rpm, in 300 ml Erlenmeyer flask in a Wagner shaking machine, together with 100 ml of 0,03 normal phosphate solution (being 0,01 normal as PO4-3 contributed by H8PO4 and 0,02 normal as PO4-3 from KH2PO4). After shaking it was set aside for 24 hours and then filtered. Phosphate was determined in a suitable aliquot of both the original solution (blank) and the soil extract, by the vanadomolibidic-phosphoric acid method. From phosphate concentration in the blank minus phosphate concentration in the soil stract the rate of fixation by 100 g of soil was calculated. The data obtained show that "Terra Roxa" and "Terra Roxa Misturada" have a fairly high PO4-3 fixation capacity, varying from 10 to 24 milliequivalents of PO4-3 per 100 g of soil.

A disponibilidade do potássio da "leucita de Poços de Caldas", estudada por meio do arroz

In order to know potassium availability in "leucita de Poços de Caldas" from Poços de Caldas, Minas Gerais, a Mitscherlich pot experiment was set up. The pots were filled with 6 kilograms of sieved (4 mm) "Terra Roxa Misturada" soil. Rice (Oryza sativa, L.), Dourado Agulha variety was the testing plant. Doses of potassium referred to are 1,5 g (as K(2)0) from both KCl and "leucita de Poços de Caldas". There were 6 treatments, with 3 repetitions, as follows: 1) Control; 2) NP + 1 dose K (KCl); 3) NP + 2 doses K (KCl)); 4) NP + 3 doses K (KCl); 5) NP + 1 dose K (leucita); 6) NP + 2 doses K (leucita) and 7) NP + 3 doses K (leucita). Each pot received 50 seeds. Five days after germination the seedlings were thinned to 35. Harvesting took place 4 months after germination. Potassium (as KCl) promoted an increase in yield of both stalk and grain as compared with control. Potassium content in the leaves was also higher in all treatment in which KCl was supplied. Potassium, as "leucita de Poços de Caldas» did not show any favorable effect on both stalk and grain yield and on its content in the leaves.

Fórmulas diretas de Ansheles

As "fórmulas diretas" do Professor Ansheles, cristalografista russo, são publicadas, sem dedução, na Cristalografia de BOLDYREV (1934), tradução para o espanhol de Candel Vila. No presente trabalho o autor deduz tais fórmulas, utilizando a projeção estereográfica.

Símbolos projetivos de Fedorow

Na Cristalografia de BOLDYREV, (1934), é deduzida uma equação geral de projetividade [13], que se aplica aos diferentes sistemas cristalográficos. O presente trabalho cuida dos símbolos projetivos de Fedorow, em cada sistema, através da projeção estereográfica.

Sôbre a expressão hr1 + kr2 + Ir3 = 0

Por meio da projeção estereográfica e geometria analítica é apresentada uma nova dedução da expressão hr1 + kr2 + lr3 = 0.

Mudança de eixos e símbolos projetivos

O presente trabalho apresenta uma nova dedução das expressões que servem, em cristalografia, à mudança de eixos coordenados, valendo-se o autor da projeção estereográfica.

Sôbre a formula de Miller das faces tautozonas

Apresenta o autor uma dedução nova, através da projeção estereográfica, da fórmula de Miller em que são interessadas faces em zona.

Cinética da reação de redução de nitrato a nitrito por actinomicetos isolados de solo I - Influência da concentração hidrogênio-iônica

Among some strains of Actinomycetes isolated from Latosol red-yelow soil during the four seasons of the year only few strains had the capacity to reduce nitrate to nitrite. The stronger activity was shown by t !he strains isolated in springtime and at a pH of 5,5.

Cinética da reação de redução de nitrato por actinomicetos isolados do solo II - Influência dos elementos minerais

Some strains of Actinomycetes showed variation in its activity to reduce nitrate to nitrite when the nutrient solution was modified in relation to the major elements. One of these strains incapable of !this reaction showed a strong activity in nutrient solution without K and little activity without P. Otherwise strains capable of reducing nitrate to nitrite had this capacity decreased in absence of each one of the following elements: K, P, Mg, e S. K showed to be the most important of them, followed by P, Mg e S. Without any of these elements the pH of the nutrient solution has to be increased from 5,5 to 6,5 for the strains capable to reduce nitrate to nitrite preserve its capacity. The time for the reaction is increased from 5 to 8 days and the amount of nitrite obtained is small.

Ocorrência de Actinomicetos com atividade proteolitica, em um solo cultivado

Among 327 strains of Actinomycetes isolated in 1958 during the four seasons, 97,85 per cent had proteolytic activity. Most of the strains wete isolated in spring time. About the organic matter no conclusions were reached, because it was mantained constant with a average value of 4.099. So the different number of the strains was a consequence of the season. We can conclude that the Latosol red-yellow soil, from where these microorganisms were isolated, has a strong proteolytic capacity, since this reaction is very strong in a maximum limit of sixteen days during the spring season. Consequently, this soil has one of the most importante caracteristics of fertility. The role of the Actinomycetes in the soil is so important of the soil microflora.

Atividade proteolítica e amonificante de vários tipos de solo do estado de São Paulo. I. - Solo latosol vermelho amarelo, com e sem cobertura morta

Os autores estudam, no presente trabalho, um solo tipo Latosol Vermelho Amarelo, com e sem cobertura morta, em 2 profundidades diferentes. Concluiram sôbre as vantagens de se manter um solo com cobertura morta que permite um aumento da microflora total e dos elementos nutritivos, confirmado pelo pronunciado índice de atividade protelítica e amonificante do solo.

Origem e formação das domácias em Coffea L.

No presente trabalho focalizamos o discutido problema da origem ou formação das domácias, escolhendo, inicialmente, as principais variedades de Coffea arabica L.. Na revisão da literatura, procuramos nos cingir unicamente à bibliografia que trata do assunto em aprêço. Apreciando convenientemente o problema da origem, duas hipóteses foram aventadas pelos autores para explicar a formação das domácias: l.ª) causada por insetos ou por ácaros (LUNDSTRÖEM e outros). 2.ª) caráter hereditário (CHEVALIER). Ambas as hipóteses foram consideradas com o objetivo de aclararmos o problema e concluimos, com CHEVALIER, que se trata de um caráter hereditário. O material constou de sementes, e de ramos com fôlhas de várias idades de cafeeiros que vieram das coleções vivas do Instituto Agronômico de Campinas. As observações morfológicas preliminares foram feitas com o auxílio do microscópio estereoscópico. As estruturas anatômicas foram apreciadas em córtes transversais longitudinais, coloridos com violeta-cristal e eritrosina, com espessura de 18 micra.

Experimentos com os nematieidas D. D, E.D.B., C.B.P. e Vapam no combate aos nematódeos que parasitam a batatinha em São Paulo

The writers report results on the application of four fumigants (D. D., E. D. B.-40, C. B. P. and Vapam) for control of root-knot and meadow nematodes attacking potato in beds filled with soil artificially inoculated. The data obtained were as follows: a) as reported by previous authors, potato is sensitive to C.B.P., the toxical effects of which disapearing only about 6 and half months after application. On the other hand, C.B.P. proved to have a significative residual nematicidal value, protecting the seeds from root-knot nematodes for a period of two years; b) D. D., E. D. B., and Vapam were effective for controling root-knot but with no residual value, having to be used prior to each planting; c) at the rates used, no nematicide was effective to control meadow nematodes; d) in the conditions of the experiments, all nematicides incited attacks bv Streptomyces scabies. Actually, in some cases scab did not affect any tuber from the check while the entire production from the treated beds was heavily desfigured. The writers assume that as the nematicides killed protozoa and too many bacteria-eating nematodes, they destroyed the biological equilibrium existing in the soil, thus allowing the S. scabies population to reach a high level.

O problema técnico-econômico da adubação

The authors discuss from the economic point of view the use of a few functions intended to represent the yield y corresponding to a level xof the nutrient. They point out that under conditions of scarce capital what is actually most important is not to obtain the highest profit per hectare but the highest return per cruzeiro spent, so that we should maximize the function z = _R - C_ = _R_ - 1 , C C where R is the gross income and C the cost of production (fixed plus variable, both per hectare). Being C = M + rx, with r the unit price of the nutrient and Af the fixed cost of the crop, wo are led to the equation (M + rx)R' - rR = 0. With R = k + sx + tx², this gives a solution Xo = - Mt - √ M²t² - r t(Ms - Kr)- _____________________ rt on the other hand, with R = PyA [1 - 10-c(x + b)], x0 will be the root of equation (M + rx)cL 10 + r 10c(x + b) = 0 (12). Another solution, pointed out by PESEK and HEADY, is to maximize the function z = sx + tx² _________ m + rx where the numerator is the additional income due to the nutrient, and m is the fixed cost of fertilization. This leads to a solution x+ = - mt - √m²t² - mrst (13) _________________ rt However, we must have x+< _r_-_s_ I if we want to satisfy t _dy_ > r. dx This condition is satisfied only if we have m < _(s__-__r)² (14), - 4 t a restriction apparently not perceived by PESEK and HEADY. A similar reasoning using Mitscherlich's law leads to equation (mcL 10 + r) + cr(L 10)x - r 10cx = 0 (15), with a similar restriction. As an example, data of VIEGAS referring to fertilization of corn (maize) gave the equation y - 1534 + 22.99 x - 0. 1069 x², with x in kg/ha of the cereal. With the prices of Cr$ 5.00 per kilo of maize, Cr$ 26.00 per kilo of P2O3,. and M = Cr$ 5,000.00, we obtain x0 = 61 kg/ha of P(2)0(5). A similar reasoning using Mitscherlich's law leads to x0 = 53 kg/ha. Now, if we take in account only the fixed cost of fertilization m = Cr$ 600.00 per hectare, we obtain from (13) x+ = 51 kg/ha of P2O5, while (14) gives x+ - 41 kg/ha. Note that if m = Cr$ 5,000.00, we obtain by formula (13) x+ = 88 kg/ha of P2O5, a solution which is not valid, since condition (14) is not satisfied.