Afrika Matematika最新文献

This research presents an endogenous growth model driven by natural resource capital, where natural resource capital can be allocated across two sectors, considering the impact of resource usage on the production process for economic growth: the production of final consumption goods and the creation of technological capital. In our model, the endogenous variable is technological progress, which results from the transfer of natural resource capital to the technology sector of the economy. This study demonstrates that the optimal path of natural resource use, which maximizes benefits and minimizes costs, is crucial. Suppose an economy has abundant natural resources and focuses on resource-based production, in that case, production factors tend to shift toward natural resource sectors, potentially reducing economic growth. However, investing in the wealth of natural resources into technological development and innovation can foster economic growth. We also show that the growth of an economy is driven by the accumulation of natural resources over time. The results indicate that a higher ratio of natural capital to technological capital has a positive influence on technological production. Natural capital supports technological development and innovation, while technological capital enhances the development of natural resources. Additionally, the expropriation of natural resources in output production is unaffected by the ratio of per capita consumption to physical capital, indicating that natural resource expropriation does not effect economic growth.

We determine the rational homotopy type of the total space of the projectivization of the complex tangent bundle (tau : mathbb {C}^n longrightarrow E longrightarrow mathbb {C}P^n). We show that the total space P(E) of the projectivization bundle (P(tau ): mathbb {C}P^{n-1} longrightarrow P(E) longrightarrow mathbb {C}P^n) has the rational homotopy type of (U(n+1)/U(1) times U(1) times U(n-1)), where U(k) is the unitary group.

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