Afrika Matematika最新文献

The main results of this paper are to discuss the primary results of fuzzy differential equations with time-varying delay (FDDEs) via the generalized Caputo fractional derivative. We establish the existence of a unique solution for FDDEs using the method of steps and the generalized Gronwall inequality. Sufficient conditions are proposed to ensure the finite-time stability (FTS) of FDDEs. Finally, we explore specific examples to illustrate and reinforce the results obtained.

In this paper, we partition, enumerate and classify hyper nearrings up to isomorphism of order less than 4 and then determine their automorphism groups.

The purpose of this paper is to study the completeness properties of interval metric spaces. The idea of convergence and Cauchyness of sequences with respect to an interval metric are studied to introduce the notions of i-convergent and i-Cauchy sequences respectively. Several relevant results including relations between convergent and i-convergent sequences, Cauchy and i-Cauchy sequences are established. A characterization for completeness of an interval metric space is given in terms of completeness of metric spaces.

The random forest (RF) algorithm is considered as a powerful statistical classifier that is more popular in other fields but is relatively unknown in HEA(s)’s prediction phase. In this research, Random Forest (RF) technique is used to investigate phase selection principles effectively utilizing a large experimental case study on 401 distinct HEAs, comprising 174 (SS), 54 (IM), and 173 (SS+IM) phases. The accuracy of the proposed method is almost 10% higher than SVM and KNN for classifying HEA(s). Moreover, the precision of the proposed method is similar to ANN. Experimental results indicate the validity and reliability of the RF-based diagnosis method.

The symplectic group (Sp_{2n}(2)) has an affine maximal subgroup of structure (ASp_n=2^{2n-1}{:}Sp_{2n-2}(2)) which is a split extension of an elementary abelian 2-group (N=2^{2n-1}) by (G=Sp_{2n-2}(2)). The vector space (N=2^{2n-1}) and its dual (N^{*}) are not equivalent as (2n-1) dimensional G-modules over GF(2). Therefore, a split extension of the form (overline{G}_n=N^{*}{:}Sp_{2n-2}(2)ncong N{:}Sp_{2n-2}(2)) exists. In this paper, it will be shown that (overline{G}_ncong text {Aut}(2^{2n-2}{:}Sp_{2n-2}(2))= left( 2^{2n-2}{:}Sp_{2n-2}(2)right) {:} 2) for (nge 3). Moreover, the ordinary irreducible characters of (overline{G}_n) are studied through the lens of Fischer-Clifford theory. As an example, the Fischer-Clifford matrix technique is used to construct the set Irr((overline{G}_5)) of the group (overline{G}_5=2^9{:}Sp_{8}(2)) which is associated with the affine subgroup (ASp_5=2^9{:}Sp_{8}(2)) of (Sp_{10}(2)).

The Bessel function and its various generalizations have extensively been studied in various branches of applied mathematics and theoretical physics, including the Geometric Function Theory. In this paper, we study basic characteristics of Bessel functions of order (mu ) and degree (nu ). Among the results that we investigate are the results giving the characteristic properties of univalence, convexity and starlikeness. We further investigate the conditions under which the function (L_{mu ,nu }) are strongly convex and strongly starlike. Several corollaries are also mentioned depicting the usefulness of the main results, one of the Corollary providing improvement in a result for normalized Bessel function.

In this paper, we consider a finite delay integro-differential equation with a nonlinear kernel in a general Banach space. The nonlinear part is assumed to be continuous with respect to a fractional power of the linear part in the second variable. We prove, using the semigroup theory, the local existence, continuous dependence of the initial data, the phenomena of blowing up, regularity, and compactness properties of the so-called mild solution. An application is provided to illustrate our results.

The reconstruction of potential function using nodal parameters is an inverse problem that has been studied in this work. An efficient and highly helpful transformation allowed for the extraction of a reconstruction formula for the problem’s potential function by a narrow collection of nodal data only. Additionally, the method’s efficacy was shown by a few numerical illustrations.

In this work, we investigate the existence of mild solution for semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces. Using Mönch’s fixed point theorem, the theory of Grimmer’s resolvent operator and the idea of measures of non-compactness, we prove the existence results. At the end, an example is given to further illustrate the conclusions drawn from the theoretical study.

The degree of approximation (in Hölder metric) of a periodic function belonging to a specific Hölder class by its Abel–Poisson means of Fourier series and of the conjugate function by the conjugate Abel–Poisson means of the conjugate series of the Fourier series is obtained.