The effectiveness and quality of agricultural spraying largely depends on the technical efficiency of the nozzles installed in agricultural sprayers. The uniform spraying of plants results in a decrease in the amount of pesticides used in agricultural production and affects environmental safety. Both newly developed sprayers and those currently in use need quality control as well as an assessment of the performance of the spraying process, especially its uniformity. However, the models applied presently do not ensure accurate estimates or predictions of the spray liquid coverage uniformity of the treated surface. Generally, the distribution of the atomized liquid quantity is symmetrical and leptokurtic, which means that it does not fit well to the commonly used standard distribution. Therefore, there is a need to develop and design new tools for the evaluation, modeling, and prediction of such a process. The research problem studied in the present work was to find a new model for the distribution of atomized liquid quantity that could provide capabilities better than have been available so far to assess and predict the spraying process results. The research problem was solved through the formulation of a new function for the probability density distribution of sprayed liquid accumulation on the surface of the preset dimension size. The development of the new model was based on the results from a series of water atomization tests with an appropriate measurement device design based on the widely applied flat fan nozzles (AZ-MM type).
In the era of sustainable agriculture, the issue of proper and precise implementation of agrotechnical operations, without harmful effects on the natural environment, begins to play an important role. Statistical tools also become important, for example, when assessing the malfunction of plant cultivation equipment. The study presents a comparison of six nonparametric bootstrap methods used for construction of confidence intervals for the expected value of an average diameter of droplet stains following the spraying process. The simulation tests were carried out based on experiment with nozzle sprayer Lechler 110-03 using two spray nozzles: a new one and an old one. It was assumed that the distribution of the droplet stain size was consistent with the lognormal distribution. The paper considers the influence of the sample size, mean value and standard deviation of the droplet stain diameter on the interval range as well as on the estimated coverage probabilities of the confidence intervals. It was shown that in general these methods can be applied for this purpose. For the double bootstrap method and the studentized method, the empirical confidence levels of the constructed intervals turned out to be less distinct than the assumed level but the lengths of these intervals were greater than the lengths of intervals obtained using the other four methods.
In this paper, operator inequalities are provided for operator entropies transformed by a strictly positive linear map. Some results by Furuichi et al. [S. Furuichi, K. Yanagi, and K. Kuriyama. A note on operator inequalities of Tsallis relative operator entropy. Linear Algebra Appl., 407:19â31, 2005.], Furuta [T. Furuta. Two reverse inequalities associated with Tsallis relative operator entropy via generalized Kantorovich constant and their applications. Linear Algebra Appl., 412:526â537, 2006.], and Zou [L. Zou. Operator inequalities associated with Tsallis relative operator entropy. Math. Inequal. Appl., 18:401â406, 2015.] are extended. In particular, the obtained inequalities are specified for relative operator entropy and Tsallis relative operator entropy. In addition, some bounds for generalized relative operator entropy are established.
Abstract. In this paper, Csiszár and Tsallis f -divergences are studied for superquadratic and convex functions. Some comparison theorems for two divergences are provided. The obtained results, when used for nonnegative superquadratic functions, give some refinements of the original inequalities corresponding to nonnegative convex functions. Some majorization assumptions for the involved matrix are simplified from column stochasticity to entrywise-nonnegativity.Mathematics subject classification (2010): 26D15, 15B51, 94A17.
In this paper, we introduce new divergences called Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal in relation to convex functions. Some theorems, which give the lower and upper bounds for two new introduced divergences, are provided. The obtained results imply some new inequalities corresponding to known divergences. Some examples, which show that these are the generalizations of Rényi, Tsallis, and Kullback–Leibler types of divergences, are provided in order to show a few applications of new divergences.
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