Afrika Matematika最新文献

The main crux of this manuscript is to study the existence of weak solutions for nonlinear elliptic Dirichlet boundary value problems with the fractional (p(z))-Laplacian operator. Applying Galerkin method and Young measures with variable exponent fractional Sobolev spaces, the existence of weak solutions of the proposed problem is established. Our results improve and extend upon a variety of current studies that have been carried out within the same area of academic research.

The article investigates the nonlinear Schrödinger’s equation using nonlinear chromatic dispersion and a generalised temporal evolution. Lie symmetry retrieves quiescent optical solitons from the model. The solutions are implicit, with quadratures and expressed in terms of elliptic and periodic functions. The six self-phase modulation structures examined in this study were first introduced by Kudryashov.

Quantum calculus, which can be considered a generalization of classical calculus, is essential for many areas of mathematics. Recently, the work on quantum calculus and its applications to mathematics has increased significantly. This article investigates the connection between higher-dimensional algebraic structures and quantum calculus by considering q-biperiodic Fibonacci and q-biperiodic Lucas sequences in Cayley–Dickson algebras. In this article, we examine new relations between Cayley–Dickson algebras, which generalize complex numbers to higher dimensions by systematic doubling, and q-biperiodic Fibonacci and q-biperiodic Lucas sequences, using some useful notations from quantum calculus. We also present algebraic properties of q-biperiodic Fibonacci and q-biperiodic Lucas (2^k)-ons, binomial sums, generating functions and Binet formulas. Our approach not only extends current research on Cayley–Dickson structures but also provides q-analogues that can effectively address some mathematical problems.

In this paper, we first obtained some initial logarithmic coefficient bounds on a subclass of bounded turning functions associated with Bell numbers. For functions in this class, we determined the sharp bounds for the second Hankel determinant of logarithmic coefficients (H_{2,1}(F_{f}/2)) of bounded turning functions associated with Bell numbers. Furthermore, we calculated the bounds of third Hankel determinant of logarithmic coefficients (H_{3,1}(F_{f}/2)) of bounded turning functions subordinate to the function whose coefficients are Bell numbers. Finally, we calculated the third Hankel determinant of logarithmic coefficients of inverse functions.

This paper investigates the geometric implications of locally conformal almost cosymplectic structures on ((k, mu )')-spaces. We prove that there exist integrable distributions (mathcal {D}_{3}) and (mathcal {D}_{3}^{perp }) such that locally conformal almost cosymplectic ((k, mu )')-manifolds decompose locally as the Riemannian product of a totally geodesic manifold and a 2-dimensional totally geodesic surface with Gaussian curvature (-k).

In the proposed work, we introduce a new subclass of univalent analytic functions denoted by (mathcal {S}^{*}_{ChE}) defined in the open unit disk (mathbb { D}) with the help of subordination involving the quotient of the analytic representation of the cosine hyperbolic and exponential functions. For this function class, we determine sharp upper bounds of some of the initial coefficients, Fekete–Szegö functional and some sharp estimates of the Hankel determinant of different orders. Further, some sharp bounds of inverse and logarithmic coefficients, Zalcman and Krushkal inequalities are obtained for such a family. Our approach is based on the fact that the coefficients of functions in such a family and coefficients of corresponding Schwarz functions are interrelated. If we adopt this approach, exact estimate of the functional may easily be obtained. Furthermore, bounds for two-fold and three-fold symmetric functions belonging to said class are obtained.

Let (overline{G}=p^{1+2n}{:}G) be a finite split extension of an extra-special p-group (P=p^{1+2n}) by a group G. Since the center Z(P) is characteristic in P and hence normal in (overline{G}), we can construct the factor group (overline{F}=frac{overline{G}}{Z(P)}cong p^{2n}{:}G), where (P_1=p^{2n}) is an elementary abelian p-group. In this paper, the Fischer–Clifford matrices M(g) of (overline{G}) are constructed from the corresponding Fischer–Clifford matrices (widehat{M(g)}) of (overline{F}) by a method we called the lifting of Fischer–Clifford matrices. As an example, the ordinary character table of a 7-local maximal subgroup (7_{+}^{1+4}{:}(3times 2 S_7)) of the Monster (mathbb {M}) is re-constructed using the lifting method.

Let (kge 2) be an integer. The k-generalized Pell sequence ((P_{n}^{(k)})_{nge 2-k}) is defined by the initial values (0,0,ldots ,0,1)(k terms) and the recurrence (P_{n}^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+ldots +P_{n-k}^{(k)}) for all (nge 2). In this study, we deal with the Diophantine equation

in positive integers n, m, k, b, d, l with (kge 3,lge 2,~2le mle n,) (2le ble 10,) and (1le dle b-1,) and we show that all solutions of this equation are given by

and

Let G be a nontrivial connected graph with an edge coloring, and let (u,v in V(G)). A (u-v) path in G is said to be a rainbow path if no color is repeated on the edges of the path. Similarly, we define a rainbow geodesic. A rainbow connected graph G is a graph with an edge coloring such that every two vertices in G are connected by a rainbow path. Further, a strong rainbow connected graph G is a graph with an edge coloring such that every two vertices in G is connected by a rainbow geodesic. The minimum number of colors needed to make a graph rainbow connected is called the rainbow connection number, denoted ({{,textrm{rc},}}(G)), and the minimum number of colors needed to make a graph strong rainbow connected is called the strong rainbow connection number, denoted ({{,textrm{src},}}(G)). In this paper we determine ({{,textrm{rc},}}(G)) and ({{,textrm{src},}}(G)) when G is a n-dimensional rectangular grid graph, triangular grid graph, hexagonal grid graph, and a (weak) Bruhat graph, respectively. We show for all these families that ({{,textrm{src},}}(G)={{,textrm{diam},}}(G)).

The energy En(G) of a graph G is defined as the sum of the absolute values of its eigenvalues. The Hosoya index Z(G) of a graph G is the number of independent edge subsets of G, including the empty set. For any given degree sequence D, we characterize the caterpillar (mathcal {S}(D)) that has the minimum Z and En. We also show that (Z(mathcal {S}(D))<Z(mathcal {S}(Y))) and (En(mathcal {S}(D))<En(mathcal {S}(Y))) for any degree sequences (Y=(y_1,dots ,y_n)) and (D=(d_1,dots ,d_n)) with