2nd Degree Polynomial Research Articles

Fitting Mathematical Functions to Growth and Developmental Distance Curves of Physical Fitness

This study was designed to describe the growth and developmental distance curves of some physical fitness attributes chosen. The physical fitness attributes chosen were body linearity measured by stature, muscular strength by back strength, explosive strength and jumping ability by standing long jump, throwing ability by softball throw for distance, and running ability by 100m dash. These growth and developmental distance curves for 30 years could be described with considerably high precision by composite of three different functions; logistic function and 4th-degree polynomial for all attributes, and one of 2nd-degree polynomial, a type of truncated probability function and single vibration function. Then, each of these functions used was likely to reflect the nature of growth and developmental distance trend due to aging from childhood to maturity. The studies of this type have been reported only for physique attributes, so this was the first attempt regarding to physical fitness attributes.

Temperature Functions in Biology and Their Application to Algal Growth Constants

Various kinds of temperature rules have been proposed for biological use, but reasons for choosing one before another have seldom been given. Arguments for such choices should include both theoretical and mathematical-statistical aspects. In this paper the relationships of algal growth constants, such as ~t (maximum specific growth rate), q0 (minimum nutrient content of the algae), Y (yield coefficient) and Ks (halfsaturation constant for growth) with temperature (t) were investigated. The growth constants were estimated from growth experiments with the green alga Scenedesmus quadricauda performed in batch and P-limited chemostat cultures at t between 3 and 25°C. Additional growth data from different algal populations were estimated from 14C experiments in an incubator and in the field (0-20°C). The dependence of both (A and AZ (assimilation number) on t was generally described better by Belehradek's equation based on a view, i.e., the rate of biological processes is more likely controlled by physical processes such as diffusion and viscosity than by equations of Berthelot's or Van't Hoff-Arrhenius' types, which were derived from chemical processes. Within smaller t intervals, Burckhardt-Harvey's equation (linear) often gave an equally good fit. For Scenedesmus the parameter q0 can be described by a 2nd degree polynomial. The limit value of Y at ,t = 0 versus t can also be best described by Belehradek's equation. Both Ks and Y at ut = - seem to be independent of t. Many examples from zoology also show statistically the most accurate fit to Belehradek's equation. On the whole, biological processes seldom show exponential increases with t. For example, the RGT-rule (Q0l), which is so widely used even today, often gives artificial breaks in the temperature coefficients. An equation of Belehradek's type should therefore be more generally accepted, also because its parameters appear to have some ecological significance.

Seasonal Variation in Vegetative and Reproductive Development in Zinnia elegans Jacq.

Abstract Cultivars of Zinnia elegans Jacq. were grown under long day (LD) photoperiods in the greenhouse in spring (Sp), summer (Su), fall (F), and winter (W) over 2 years to determine days from seed sowing to flowering (DTF), flower diameter (FD), height (H), node number below first inflorescence (NN), and the role of irradiance and temperature on DTF. All cultivars flowered earliest in Su, and latest in W. Cactus-flowered (cactus) cultivars (‘Carved Ivory’, ‘Rosy Future’, ‘Torch’) flowered later and were greater in H, FD, and NN compared to pompon cultivars (‘Cherry Ruffles’, ‘Pink Ruffles’, ‘Scarlet Ruffles’, ‘Yellow Ruffles’). The principal factor affecting DTF and NN was the season, whereas H and FD variation were due mainly to cultivar differences. Year X season interactions were significant for DTF, H, FD, and NN, but seasonal trends each year were similar. Mean daily temperature (MDT) from transplanting until flowering (DTFT) was lowest in W, highest in Su, and showed a linear correlation with DTFT for cactus (r = −0.89) and pompon (r = −0.92) cultivars. Mean daily photosynthetic photon flux (PPF) for DTFT was highest in Sp, followed by Su, F, and W due to greenhouse shading during Su and part of F; the relation between PPF and DTFT was described by a 2nd degree polynomial for cactus (r = −0.96) and pompon (r = −0.98) cultivars. DTFT was more a function of MDT than PPF for Sp, Su, and F crops, whereas late flowering of the W crop was due to lower MDT and PPF. Results demonstrate that Z. elegans can be accurately scheduled as a greenhouse crop on a year-round basis.

Effects of Reduction and Reoxidation of Structural Iron on the Surface Charge and Dissolution of Dioctahedral Smectites

AbstractThe effect of Fe oxidation state on the surface charge (CEC) and solubility of smectites were studied using the <2-μm, Na+-saturated fraction of an Upton, Wyoming; a Czechoslovakian; and a New Zealand montmorillonite; and a Garfield, Washington, nontronite. The reduction of structural Fe3+ in the octahedral sheet of each clay produced a net increase in the negative surface charge of the clay. The observed cation-exchange capacities deviated from the linear relationship predicted by charge-deficit calculations, assuming changes only in the Fe2+/Fe3+ ratio, and reversibly followed Fe reduction according to a 2nd-degree polynomial function. The deviations suggest reversible changes in mineral structure and composition during Fe reduction.These clays were susceptible to partial dissolution in citrate bicarbonate (CB) and citrate-bicarbonate-dithionite (CBD) solutions. Small amounts of Fe and Si dissolved as a result of Fe reduction in CBD, but affected <1% of the total clay mass except for the Czechoslovakian clay in which 2% of the clay dissolved. Although slightly more Fe dissolved than Si, no change in surface charge was noted. Almost no dissolution of these elements was detected in CB solution. In contrast, significant Al was detected in the CB solution, suggesting a heterogeneous dissolution mechanism. The CEC, however, was unchanged by the CB treatment. These results may be explained by the adsorption of hydrogen ions into the vacated Al3+ sites in the mineral structure. Dissolution seems to have been independent of the effects of Fe oxidation state on surface charge.

Eating as a function of body weight and of hours deprivation

Five pigeons were allowed one hour of access to food after variable intervals of deprivation averaging 23 hours. Five other pigeons were allowed one hour of food after fixed 23 hour intervals. It was found that the amount eaten by birds in an environment continually alternating between deprivation and one-hour ad lib feeding could be better predicted as a linear function of their body weights than as a 2nd degree polynomial function of the number of hours they were deprived.

Power studies of tests for uniformity, II

Results from a study of six statistics for testing that a sample is from a uniform distribution on the unit interval (0,1) are reported. The test statistics are all well-known and each of them was originally proposed because they should have high against some alternative distributions. The tests considered are the Pearson probability product test, the Neyman smooth test, the Sukhatme test, the Durbin-Kolmogorov test, the Kuiper test, and the Sherman test. Results are given for each of these tests against each of four classes of alternatives. Also, the most powerful test against each member of the first three alternatives is obtained, and the powers of these tests are given for the same sample sizes as for the six general omnibus test statistics. These values constitute a power envelope against which all tests can be compared. The Neyman smooth tests with 2nd and 4th degree polynomials are found to have good and are recommended as general tests for uniformity.

Effects of Rearing Temperature and Larval Density on Longevity, Size, and Fecundity in the Biting Gnat Culicoides variipennis1, 2

The effects of rearing temperature and larval density on longevity (mean survival time, 50% survival time, and mean maximal survival time), size (dry weight and wing length), and fecundity (number of eggs oviposited) were studied in female Culicoides variipennis (Coquillett). Dry weight and wing length were inversely proportional to both larval density (number of larvae per ml of rearing medium) and to rearing temperature. These relationships were described by a 1st and 2nd degree polynomial regression equation ( P <0.01) respectively. Dry weight and wing length were directly proportional to each other as described by a 2nd degree polynomial regression equation ( P <0.01). Confidence intervals at the 95% level were calculated for predicting dry weight from wing length. Studies of the longevity and fecundity of female flies of different sizes showed that larger flies were advantageous for research and for colony production because they lived longer and produced more eggs than did smaller flies.

Evaluation of Sopelem Presa 226RC Plotter for Independent Model Triangulation

The Presa 226RC is a first-order stereorestitution instrument accepting wide angle and super wide angle aerial photography. It is relatively unknown to photogrammetrists in North America. It was tested for the stability of its perspective centers, accuracy of plate measurements, and its suitability for independent model triangulation. Departure of perspective center coordinates from instrument zero position when moved through maximum rotational range amounts to 0.04 mm in x, 0.04 mm in y, and 0.02 mm in z. Base component displacements by" and bz’ needed in relative orientation cause an apparent shift of about 0.03 mm in all three directions. Standard deviations of plate coordinates of 20 grid intersections used in perspective center stability tests are: σx′ = ±0.007 mm, σy′ = ±0.007 mm, σx″ = ±0.006 mm, and σy″ = ±0.004 mm. Independent model triangulation of four separate short strips of a heavily controlled area was adjusted by Schut’s 2nd degree polynomial adjustment. Standard deviations at plate scale are σx = ± 0.012 mm; σy = ± 0.012 mm. The relative accuracy of vertical control points is about 1/8,000 of the flying height.