1000 resultados para Lei da conservação (Fisica)


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v. 13 [supplement]

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The author proves that equation, Σy n ΣZx | ΣxyZx ΣxZx ΣxZ2x | = 0, Σy ΣZx Σy2x | where Z = 10-cq and q is a numerical constant, used by Pimentel Gomes and Malavolta in several articles for the interpolation of Mitscherlih's equation y = A [ 1 - 10 - c (x + b) ] by the least squares method, always has a zero of order three for Z = 1. Therefore, equation A Zm + A1Zm -1 + ........... + Am = 0 obtained from that determinant can be divided by (Z-1)³. This property provides a good test for the correctness of the computations and facilitates the solution of the equation.

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Statistical analyses of an experiment on wheat were carried out with the aid of Mitscherlich's law. The experiment was made in Ponta Grossa, Paraná, by the Ministry of Agriculture of Brasil. Lime, in the form of Ca(OH)2, was applied at the levels of 0, 2, 4, 6 and 8 metric tons per hectare. A 5 x 5 Latin square was used. Lime was applied in 1940 and wheat was cultivated in the same plots for several years. The following fertilizers were annually used for all plots: NaNO3 100 kilograms per hectare, Superphosphate 350 kilograms per hectare, K2S04 80 kilograms per hectare. The statistical analysis of the data collected in 1941, 1942, 1943, 1947 and 1948, carried out in accordance with the methods previously introduced by Pimentel Gomes and Malavolta (1949 a, 1949 b) and Pimentel Gomes (1950), proved: I. That Mitscherlich's law could be correctly applied to the data. II. That there was a statistically significant effect of lime on wheat yield. III. That the optimum amount of lime to be applied to the soil lies between 5 and 15 hundred kilograms of Ca(OH)2 per hectare. IV. That there is a migration of calcium from some plots to others, in such a way that the data obtained in 1947 and 1948 are not representative of the amounts of lime applied in 1940. V. That the analysis of variance can be used, as the Bartlett test shows that the variances at the distinct levele of lime application are not statistically different. It must be noted that, with improved variety and fertilization, the yield was rised to about 2500 kilograms per hectare in 1947, and 1600 in 1948, being only of about 100 kilograms per hectare in 1940.

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This paper deals with the estimation of the residual effect of fertilizers through the use of Mitscherlich's law. The formulas and reasonings now presented are a further development of those introduced previously by PIMENTEL GOMES (2). The new formulas allow the estimation of the residual effect h in cases where the experiments are carried out in the same plots for two or three subsequent years (or crops). In an experiment analysed as an example, the residual effect of calcium hydroxide was estimated to be h = 0.423, that is, about 42%, so that one should advise the use of frequent application of small amounts of lime instead of heavy quantities used at long intervals.

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The author studies, with the aid of Mitscherlich's law, two experiments of sugar cane fertilization with vinasse. The first one, carried out in Piracicaba, State of S. Paulo, by ARRUDA, gave the following yields. No vinasse 47.0 tons/ha. 76.0 tons/ha. 250 c.m./ha. of vinasse 75.0 do. 112.0 do. 500 do. 90.0 do. 112.0 do. 1000 do. 98.0 do. 107.0 do. Data without NPK were appropriate for the fitting of the law, the equation of which was found to be: y = 100.8 [1 - 10 -0.00132 (x + 206) ], where y is measured in metric tons/hectare, and x in cubic meters/hectare. The optimum amount of vinasse to be used is given by the formula x* = 117.2 + 1 log w u , ______ ____ 0.00132 250 t being u the response to the standard dressing of 250 cubic meters/hectare of vinasse, w the price per ton of sugar cane, and t the price per cubic meter for the transportation of vinasse. In Pernambuco, a 3(4) NPK vinasse experiment gave the following mean yields: No vinasse 41.0 tons/hectare 250 cm./ha. of vinasse 108.3 do. 500 do. 134.3 do. The equation obtained was now y = 150.7 [1 - 10 -000165 (x + 84)], being the most profitable level of vinasse x* = 115.2 + 1 log w u , _______ ____ 0.00165 250 t One should notice the close agreement of the coefficients c (0.00132 in S. Paulo and 0.00165 in Pernambuco). Given the prices of Cr$ 20.00 per cubic meter for the transportation of vinasse (in trucks) and Cr$ 250.00 per ton of sugar cane (uncut, in the fields) the most profitable dressings are: 236 c.m./ha. of vinasse in S. Paulo, and 434 c.m./ha. in Pernambuco.