The paper presents the models for moisture evaluation using a set of the reflectometric sensors in some types of building materials. The readouts reveal the relationship between the building material moisture, being assessed gravimetrically and the apparent permittivity values obtained by the TDR...

We solve problems concerning the coefficients of functions in the class \(\mathcal {T}(\lambda )\) of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: \(|a_4-a_2 a_3|\) and \(|a_2 a_4 -a_3{}^2|\). The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in \(\mathcal {T}(\lambda )\). Furthermore, we find the upper and the lower bounds of functionals of Fekete–Szegö type. Finally, we present some conclusions for the classes \(\mathcal {T}\) and \(\mathcal {T}(1/2)\).

In this paper, we discuss two well-known coefficient functionals $a_2{a}_4-{a_3}^2$ and $a_4-a_2{a}_3$ . The first one is called the Hankel determinant of order 2. The second one is a special case of Zalcman functional. We consider them for functions in the class ${\mathcal{Q}}_{\mathbb{R}}\left(\frac{1}{2}\right)$ of analytic functions with real coefficients which satisfy the condition $\mathrm{Re}f\left(z\right)z>\frac{1}{2}$ for z in the unit disk $\mathsf{\Delta }$ . It is known that all coefficients of $f\in {\mathcal{Q}}_{\mathbb{R}}\left(\frac{1}{2}\right)$ are bounded by 1. We find the upper bound of $a_2{a}_4-{a_3}^2$ and the bound of $|a_4-a_2{a}_3|$ . We also consider a few subclasses of ${\mathcal{Q}}_{\mathbb{R}}\left(\frac{1}{2}\right)$ and we estimate the above mentioned functionals. In our research two different methods are applied. The first method connects the coefficients of a function in a given class with coefficients of a corresponding Schwarz function or a function with positive real part. The second method is based on the theorem of formulated by Szapiel. According to this theorem, we can point out the extremal functions in this problem, that is, functions for which equalities in the estimates hold. The obtained estimates significantly extend the results previously established for the discussed classes. They allow to compare the behavior of the coefficient functionals considered in the case of real coefficients and arbitrary coefficients.

In the paper there are presented models for moisture assessment applying the two reflectometric sensors in the cellular concrete samples. The readouts express the dependence between the cellular concrete moisture, measured in gravimetric way and the apparent permittivity values achieved by the...

In this paper we study coefficient problems in some subclasses of close-to-convex functions. More precisely, we determine the upper bounds of the third and the fourth logarithmic coefficients, $\gamma_3$ and $\gamma_4$, for functions in some subclasses of analytic and univalent functions in the unit disc $\mathbb{D}$. In our research we use not only classical results, but also recent results obtained by Efraimidis.

The application of methods using graphs to model a variety of engineering issues has been known for several decades, but the application of graph algorithms to model the urban water management issues is a completely new approach. The article reviews the scientific literature on integrated urban...