Biometric analysis of cotyledon leaves in castorbean sprouts

The growth of seedlings in the initial stages depends largely on the development and functioning of cotyledon leaves. They absorb carbon dioxide and carry photosynthesis until the first true leaf appears. This indicates the importance of this body in the life of plants and the need for its study. As for ricinus, in existing literature, symptoms of cotyledon leaves are often not mentioned at all. This work is intended to improve the morphological description of castor oil by studying the features of cotyledon leaves in seedlings. Measles of cotyledon leaves in the samples under study were carried out 8-10 days after the emergence of stairs. Given the length of the cotyledon leaves, the width and distance from the base to the widest place. For characterization of the form, the ratio of leaf width and distance to the widest part was calculated to its length. The performed studies showed that the available samples differ both in size and in the form of cotyledon leaves. Their length varied from 32.7 to 64.8 mm, width - 21.7 - 50.3 mm, the distance from the base to the widest space - 11.0 - 32.4 mm. It is established that with an increase in the overall dimensions there is a decrease in the relative width and displacement of the widest space from the base of the leaf to its middle. It is also established that the length of cotyledon leaves of the seedlings positively correlates with the length of the seeds. The correlation coefficient is 0.70. With an increase in the length of the cotyledon leaves increases their linear width, but decreases relative, that is, in the form they appear to be narrower. The correlation coefficient for these features is 0.79. Other regularities are observed from the distance to the widest place - there is an increase not only in absolute sizes (the correlation coefficient is 0.82), but also relative, though not so noticeable (the correlation coefficient is 0.18). In general, for oviposition is characteristic ovoid form of cotyledon leaves, the widest point of which is located a little closer to the base, at a distance of about 40-45% of their length. The given data show that among the rooms of our collection, which belong to the Persian and weed-field subspecies, plants with small cotyledon leaves are dominant. For the most part, these are forms in which its length is 35 - 45 mm. In common, Indian and Chinese subspecies more often found cotyledon leaves - 45 - 50 mm in length. In general, for samples of the usual subspecies it is possible to consider the typical length of cotyledon leaves from 45 to 60 mm. The largest size of this organ belongs to plants belonging to Zanzibar subspecies, although, given the small number of specimens in the collection, it can not be argued whether this is typical for a subspecies at all. In general, according to the species, the largest number of samples has mid-sized mid-sized cotton sheets. Among the 224 collection samples, 25.9% of the total number reached 45-50 mm, 21.0% - 40-45 mm and 19.2% - 50-55 mm. The remaining dimensional quantities were represented by fewer samples. The obtained data are in good agreement with the average seed sizes obtained for samples of our collection. The largest seeds are typical of specimens belonging to the common subspecies (13.4 mm), weed-field and Persian are small seeds (11.2 mm and 11.5 mm, respectively), and the other subspecies occupy an intermediate position for this indicator: in Zanzibar - 12.0 mm, in Chinese - 12.6 mm, in the Indian - 12.8 mm. Sometimes between the seeds and cotyledonous leaves can be noted similarity not only in changing the size, but even the shape. For example, the sample K-1047 has not only the narrowest cotyledons, but also the smallest seeds, the width of which is usually only 47.5% of the length. The obtained data show that morphological characteristics (size and shape) of cotyledon leaves of castor oil can serve as systematic features. It is shown that with an increase in the length of cotyledon leaves increases their linear width, while the relative, on the contrary, decreases. Also, there is an increase in the distance to their widest space. The change in the length of cotyledon leaves is proportional to the change in the length of the seeds. There is a direct correlation between their length and the size of the seeds of the corresponding specimens.

Novel Empirical Relations for Accurately Estimating the Eigenfrequencies of Cantilever Beams With Linear Width Variation

Dynamic analysis of variable cross-section beams has been the focus of numerous investigations because of its relevance to aeronautical, civil, and mechanical engineering. In this article, we analyze the case of isotropic Euler-Bernoulli cantilever beams having linearly varying width, constant thickness, and classical boundary conditions. The linear width variation is characterized by a taper parameter, which can be varied between zero and unity. The free transverse vibration problem is cast as a fourth order Sturm-Liouville eigenvalue problem, and numerically solved by using the differential transform technique. A five-parameter exponential fitting model is used to develop novel empirical relations to estimate the first five eigenfrequencies as functions of the taper parameter. The proposed empirical relations are able to predict the eigenfrequencies with an error of less than 0.1% with respect to the simulated values, which make them useful for practical design applications. Using the proposed empirical relations, we then examine the sensitivity of each eigenfrequency to the variation in taper parameter near zero and near unity.