Some Dynamic Inequalities via Diamond Integrals for Function of Several Variables

In this paper, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals of time scale calculus. These extensions are used to generalize Hardy-type inequalities with general kernels via diamond integrals for the function of several variables. Some Hardy Hilbert and Polya Knop type inequalities are also discussed as special cases. Classical and new inequalities are deduced from the main results using special kernels and particular time scales.

On Multi-Index Mittag–Leffler Function of Several Variables and Fractional Differential Equations

In this paper, we have studied a unified multi-index Mittag–Leffler function of several variables. An integral operator involving this Mittag–Leffler function is defined, and then, certain properties of the operator are established. The fractional differential equations involving the multi-index Mittag–Leffler function of several variables are also solved. Our results are very general, and these unify many known results. Some of the results are concluded at the end of the paper as special cases of our primary results.

ON POINTWISE APPROXIMATION OF FUNCTIONS OF SEVERAL VARIABLES BY SINGULAR INTEGRALS

We prove a theorem on weighted pointwise convergence of \ multidimensional integral operators with radial kernels to generating function of several variables, which are in general non-integrable in $n$-dimensional Euclidean space $E_{n}$ in the sense of Lebesgue$.$ Main result holds at almost every point of $E_{n}.$

Synthetic Series of Electricity Generation through a Photovoltaic System by using Different Panel Temperature Models

The electric energy produced by photovoltaic systems is a function of several variables that present random behavior, such as solar irradiance, ambient temperature, wind speed, and relative humidity. Several models describe the energy produced by these systems, which reflect the various factors that influence the generation and how significant these influences are. In this way, the present work aims to compare some panel temperature models and the electrical energy produced from a photovoltaic system located in the Midwest of Brazil. The applied methodology aims to evaluate the expected averages and standard deviations of the monthly synthetic series of generated energy to identify the main random variables that influence the electric generation. The results indicate the model that best describes the physical system concerning the randomness of the variables involved, the photovoltaic technology, the location, and the measurement period.

Coefficients for Calculation of Deformation-Strength Characteristic of Concrete for Injection with Two-Stage Expansion

Strength of concrete is a function of several variables, such as: water / cement ratio, portland cement activity, filler quality, etc., adjusting which you can achieve the required strength. However, the introduction of the concrete admixtures, changing holding conditions of the samples, the volume restriction can affect the strength of the due to exposure impacts both the kinetics of hydration processes and on the structure formation of cement paste. The article presents the results of investigation the influence of the amount of gas-forming admixture, the presence, type and amount of superplasticizer, the ratio sand / cement, aggregate size and water-cement ratio on gassing and expansion of the mixture in the first stage and propose coefficient of effectiveness of gassing and of expansion. The authors proposed a formula to describe the dependence of the relative deformations of expansion of the concentration of aggregate. In order to assess the conditions in which there is a mixture, it is proposed to use the indicator - coefficient of congestion of expansion, to account for the influence of hardening conditions on the strength of the concrete - coefficient hardening conditions. The authors proposed to consider the impact of prescription and technological factors by introducing system of correction coefficients.

On an estimate of a distance function of several variables and related problems

We present new sharp estimates concerning distance function which leads to generalizations of some of our results on extremal problems in Bergman type classes.