Afrika Matematika最新文献

Given a semigroup S equipped with an involutive automorphism (sigma ), we determine the complex-valued solutions f, g, h of the functional equation

in terms of multiplicative functions and solutions of the special cases of sine and cosine–sine functional equations

and

where (chi :Srightarrow mathbb {C}) is a multiplicative function.

In this paper, we present the concept of continuous biframes in a Hilbert space. We examine the essential properties of biframes with an emphasis on the biframe operator. Moreover, we introduce a new type of Riesz bases, referred to as continuous biframe-Riesz bases.

In this investigation, we derive Fekete–Szegè inequalities and upper bounds for the second Hankel determinant for a new subclass of analytic functions in the open unit disk formed by the close-to-convex functions and the Salagean derivative operator. Additionally, there is discussion of a number of intriguing applications of the findings given here.

With the deepening of rigorous analysis in mathematics since the modern era, irregular pathological mathematical objects such as the Weierstrass function, Cantor set, and Koch curve, have been produced one after another, which result in some phenomena and problems that are difficult to explain by traditional mathematical theory. The measurement problem of the Cantor set is typical in these problems. According to the conventional mathematical theory, the measure of the Cantor set is zero. However, the zero-measure set constitutes infinite points which brings people confusion intuitively. Inspired by Fréchet’s fractional dimension, Hausdorff found the internal relationship between the fractional dimension and irregular pathological set based on Carathéodory measure and further created the Hausdorff measure, the predecessor of fractal measure, which not only solved the measurement problem of Cantor set but also paved the way of fractal theory. As the metric of nature, the fractal measure has unique and profound implications in ontology, epistemology, and methodology, in addition to accurately characterizing the magnitude of irregular objective things.

Let (mathscr {P}) be a commutative ring with unity, and let (A(mathscr {P})) denote the set of ideals of (mathscr {P}) having a nonzero annihilator. The annihilating-ideal graph of (mathscr {P}), denoted by (AG(mathscr {P})), is an undirected graph whose vertex set (A(mathscr {P})^*) consists of all nonzero ideals in (A(mathscr {P})), where two distinct vertices I and J are adjacent if and only if (IJ=(0)). In this paper, we investigate the structure of (AG(mathscr {P})) for Artinian non-local commutative rings. Our main results provide a complete characterization of all such rings for which the annihilating-ideal graph is a line graph, as well as those for which it is the complement of a line graph. In particular, we show that these graphs arise precisely for rings that decompose into specific finite direct products of fields and local rings with a unique nontrivial ideal.

In this paper, we provide some new integral representations for the generalized hypergeometric function. These results represent a generalization of formula [15.3.1, p.558] in [Handbook of mathematical functions with formulas, graphs, and mathematical tables. National Bureau of Standards, Applied Mathematics Series 55, 10th printing, Washington] by Abramowitz and Stegun, extending it beyond the Gauss hypergeometric function to include the generalized hypergeometric function. As applications of these results, we present several new integral representations for Catalan number and its different generalizations are established. In the end we also provide a derivative for the generalized hypergeometric function. This provides a broader framework for applying integral representations in various mathematical contexts, particularly in applied mathematics, functional analysis, and the theory of special functions.

The eccentricity matrix (epsilon (G),) of a connected graph G is obtained by retaining the maximum distance from each row and column of the distance matrix of G, and the other entries are assigned with 0. In this paper, we discuss the eccentricity spectrum of the subdivision vertex (edge) join of regular graphs. Also, we obtain new families of graphs having irreducible or reducible eccentricity matrix. Furthermore, we use these results to construct infinitely many (epsilon )-cospectral graph pairs as well as infinitely many pairs and triplets of non (epsilon )-cospectral (epsilon )-equienergetic graphs. Moreover, we present some new family of (epsilon )-integral graphs.

The aim of this work is to study frame theory in quaternionic Hilbert spaces. We provide a characterization of frames in these spaces through the associated operators. Additionally, we examine frames of the form ({L(u_i)}_{i in I}), where L is a bounded right (mathbb {H})-linear operator and ({u_i}_{i in I}) is a frame. We also show that every bounded, positive, invertible right (mathbb {H})-linear operator arises as a frame operator.

In this work, we use a novel identity to show a number of new Maclaurin-type inequalities for functions whose first derivatives are s-convex. We also deal with cases where the first derivatives are bounded and Lipschitzian. Applications in numerical integration and inequalities utilizing special means are provided out this research.

Let Z(R) be the center of a ring R and (g(x)) be a fixed polynomial in Z(R)[x]. In this paper, we continue the study of weakly (g(x))-invo clean rings. A ring R is called weakly (g(x))-invo clean if each element of R is a sum or difference of an involution and a root of $g(x)$. We determine the necessary and sufficient conditions for the skew Hurwitz series ring ((HR,alpha )) to be weakly (g(x))-invo clean, where (alpha) is an endomorphism of R. We also prove that the ring of the skew Hurwitz series ((HR,alpha )) is weakly invo-clean if and only if R is weakly invo-clean.