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A new mathematical equation is introduced in this paper: w = f - 1/(b/f +(1/(f-s)-b-f)exp(kt)) where W is the size at any convenient unit of time /, s is the initial size, f is the upper asympotic size, k is the growth coefficient (k > 0), and b is the constant. The new equation encompasses the logistic equation and therefore should be considered as a generalized version of the classical logistic equation. With its additional fourth para­meter 6, the new equation yields an unfixed value of inflexion point which enables it to possess good flexibility for depicting diverse growth patterns. In order to evaluate the fitness of the new growth equation, some commonly encountered models are compared to the new one using 12 sets of somatic growth data of mammalian species including hamster, rat, vole, pika, mouse, rabbit, cattle, and bear, The new equation possesses excellent fitness to each data set, suggesting that it is worth being considered by growth data analysts.
Background. Food spoilage is a process in which the quality parameters decrease and products are no longer edible. This is a cumulative effect of bacteria growth and their metabolite production, which is a factor limiting shelf life. Thus, the aim of the study was to evaluate whether microbiological growth models for total viable count (TVC) and Clostridium strain bacteria are reliable tools for prediction of microbiological changes in spreadable processed cheese. Material and methods. Investigations were conducted for two types of bacteria: TVC and Clostridium in following temperature: 8°C, 20°C and 30°C. A total number of aerobic bacteria was determined based on standard PN-EN ISO 4833:2004 and Clostridium was detected by using microbiological procedure for sulphite-reducing anaerobic spore-bacteria with a selective nourishment. During the analysis nonlinear regression and Baranyi and Roberts primary model were used. Results. For temperatures 20°C and 30°C, Baranyi and Roberts model, for total viable count showed determination coefficient of 70%. The models prepared for Clostridium, in these temperatures, showed much lower R2, respectively 25% and 30%. At the abovementioned temperatures also the expiration of product shelf life was much shorter and amounted 70 days at 20°C and 7 days at 30°C. For both types of bacteria incubated at 8°C the numbers of bacteria decrease until the expiration of product shelf life. Conclusions. Models used in the analyses, Baranyi and Roberts and nonlinear regression, poorly matched the experimental data, hence they are not reliable tools. Nevertheless, they gave information about dynamic of microbiological changes in spreadable processed cheese.
The growth of the scale radius was followed in seven fish species (roach, bream, rudd, humped rockcod, perch, halibut, and zander). The results obtained by analyzing a total of 11304 individuals were compared with corresponding data on the standard length growth of each species. The mathematical description of growth was done with the following six models: the von Bertalanffy equation, the Ford-Walford formula, the second order polynomial, the Gompertz model, the power function, and the modified power function. Data on length growth and length growth versus scale radius growth, which were used to determine the scale radius growth of each species, were taken from the literature. The growth of both the scale radius and body length of the species analyzed was fairly uniform: the increment ratios, averaged for the entire growth period, were close to 0.9. However, slightly higher values, hence more uniform growth, were recorded in radius growth (0.93) than in fish length growth (0.90). The fish length increments in the first two years of life were lower than the scale radius increments during the same time.
Przedstawiono wykorzystanie analizy regresji prostej do stworzenia modeli wzrostu rozsady kapusty chińskiej (Brassica rapa var. chinensis, pak choy) względem czasu, jak też do przewidywania rozwoju liści tych roślin na podstawie temperatur efektywnych (stopniodni). Opracowane modele czasowe charakteryzowały się wysokimi współczynnikami determinacji R2 wynoszącymi od 0,765 do 0,880 (dla wysokości rozsady) oraz od 0,964 do 0,970 (liczba liści). Dla temperatur efektywnych dopasowanie danych przewidywanych, dotyczących rozbudowy aparatu liściowego rozsady, do rzeczywistych wynosiło ponad 89%. Rozsadę produkowano w dwóch terminach, wysiewając nasiona na początku III dekady lipca (1. termin) i na początku sierpnia (2. termin). Rozsada przygotowywana w terminie późniejszym posiadała większą wysokość rozetek oraz powierzchnię i długość liści. Charakteryzowała się również większą świeżą masą części nadziemnej, jednocześnie niższą zawartością suchej masy, cukrów rozpuszczalnych i karotenoidów w porównaniu do 1. terminu. Stwierdzono istotne zróżnicowanie w analizowanych parametrach roślin ze względu na czynnik odmianowy. Cechy rozsady kapusty chińskiej były w dużej mierze skorelowane z cechami dojrzałych rozet oraz z plonem ogólnym tego warzywa.
The aim of the present paper was to analyse relative errors and variability coefficients for estimated values of maximum specific growth rate (µmax) and saturation constant (Ks) in the Monod's growth model in the case when these values are determined on the basis of data from steady states of two chemostatic continuous cultures, and also on the basis of the above to propose the procedure for the dilution rate selection so that the analysed quantities attained minimum values. The above-mentioned relative errors and variability coefficients were analysed at assumption that the relative errors of determined values used for estimation, i.e. the dilution rate and substrate concentration in fermenter, are constant. It was found that in the analysed estimation method both relative error so as variability coefficient for saturation constant are higher than for maximum specific growth rate and that the relative errors and variability coefficients values for both estimated parameters are then minimum when one culture is carried on at possible low dilution rate and the second at the dilution rate close to the washout rate. It was also established that carrying on one continuous culture at the fixed in advance dilution rate it cannot be possible to always select the dilution rate of the second culture, so that the simultaneous minimization of relative error for µmax and Ks was possible. It also relates to the minimization of variability coefficient.
The present study was conducted to determine the quantitative effects of light and temperature on growth and development of organic tomato (Solanum lycopersicum L.) seedlings in a glasshouse under ecological conditions of Samsun Province of Turkey. Seedlings were grown in four different periods (seeds sown on 29 September for 1st period; 2 December for 2nd period; 18 March for 3rd period and 6 July for 4th period). In order to create different light intensities, shading material having a shading capacity of 50% in 1, 2 and 3 layers was used in each period after seeding. The effects of light and temperature on plant growth and development (leaf area, stomatal conductivity, leaf chlorophyll content, plant height, stem diameter and total plant vegetative dry weight) and the number of days from sowing to plantation of seedlings, were investigated. Obtained results revealed decreasing number of days from sowing to seedling plantation with increasing light intensities. Finally, the number of days from sowing to seedling plantation to be used in organic tomato seedling production was modeled based on the variations in temperature and light intensity (r2 = 0.92).
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