Let \(0<\rho<n\) and \(\mu_{\Omega}^{\rho}\) be the Parametrized Marcinkiewicz integrals operator. In this work, the bondedness of \(\mu_{\Omega}^{\rho}\) is discussed on Herz spaces \(\dot{K}_{p(\cdot)}^{\alpha,q(\cdot)}(\mathbb{R}^{n})\), where the two main indices are variable exponent. The boundedness of the commutators generated by BOM function, Lipschitz function and parametrized Marcinkiewicz integrals operator is also discussed.
In this article, we present new fractional Hadamard and Fejér-Hadamard inequalities for generalized fractional integral operators containing Mittag-Leffler function via a monotone function. To establish these inequalities we will use exponentially \(m\)-convex functions. The presented results in particular contain a number of fractional Hadamard and Fejér-Hadamard inequalities for functions deducible from exponentially \(m\)-convex functions.
The paper construct continuous and discrete distribution laws, used to assess risks in information systems. Generalized expressions for continuous distribution laws with maximum entropy are obtained. It is shown that, in the general case, the entropy also depends on the type of moments used to determine the numerical characteristics of the distribution law. Also, probabilistic model have been developed to analyze the sequence of independent trials with three outcomes. Expressions for their basic numerical characteristics are obtained, as well as for calculating the probabilities of occurrence of the corresponding events.
This research focuses on the effect salinity on the structural strengths of conventional concrete. The unreinforced beam, cylinder and cube specimens produced were cured up to 120 days in different curing medium and tested at varying predetermined curing age. The physio-chemical properties of Unilag tap and lagoon water, physical properties, workability, compressive, split tensile and flexural strengths were determined. Two curing media (salt water I & salt water II) having five times (5\(\times\)) and ten times (10\(\times\)) the chloride content of lagoon water were simulated. The results revealed that the structural strengths of concrete samples cured in lagoon water recorded lower strengths when compared to samples cured in salt water I but higher in strength development than samples cured in salt water II. The percentage decrease in structural strengths increased from lagoon water to salt water II which recorded the highest value of 29.35%, 17.67% and 33.65% at 28-day for compressive, tensile and flexural strengths respectively. The mathematical models developed using Modified Regression Approach to predict the structural strengths were in good agreement with the experimental data. This research reveals that the salt water solution simulation in the laboratory does not fully replicate the aggressiveness of actual marine water (environment).
Modern day technological advancement has resulted in manufacturing industries intensify the use and application of thin plates in their productions thereby, resulting in increased research awareness in the study of dynamic behavior of thin plates. This research analyzes the free vibration dynamic behavior of thin rectangular plates resting on elastic Winkler and Pasternak foundations using two-dimensional differential transformation method. The reliability of the obtained analytical solutions are validated with results presented in cited literature and confirmed very precise. However, the analytical solutions obtained are used to investigate the influence of elastic foundations, homogeneity and thickness variation on the dynamic behavior of the plates under clamped and condition. From the results obtained, it is realized that increase in non-homogenous material results in corresponding increase in natural frequency of the plates. Also, increase in Winkler, Pasternak and combine Winkler and Pasternak foundations stiffness leads to increase in natural frequency of the plates. Increase in thickness results to natural frequency increases. The findings will serve as benchmark for further study of plate vibration research.
