Afrika Matematika最新文献

The group scheme of ternary automorphisms of a perfect finite dimensional evolution algebra (mathcal {A}) is computed. The main advantage of using group schemes is that it allows to apply the Lie functor to determine the Lie algebra of ternary derivations of (mathcal {A}). Using the generalised inverse of a matrix, we provide a precise classification of all ternary derivations of an arbitrary finite-dimensional evolution algebra (mathcal {A}). The ternary derivations of all 2-dimensional evolution algebras are also computed.

The aim of this paper is to introduce the concept of semi-Császár structures and investigate their relationship with the well-known notion of pre-nearness structures on frames. More explicitly, we define the category of semi-Császár frames and establish a connection with the category of covering pre-nearness frames. We provide conditions under which semi-Császár structures relate with pre-uniformities on frames. Finally, we present a frame counterpart to the relationship between symmetric syntopogenous structures and nearness spaces as established by Herrlich (Gen Topol Appl 4(3):191–212, 1974).

In both the management and modelling of epidemic outbreaks, the ability to determine the start of a wave of infections is of vital importance. Not only does this advantage the modelling of the outbreak, but, if done in real-time, can assist with a nation’s response to the disease. In this study, a bidirectional long-short-term-memory (Bi-LSTM) network is used to determine the start and end of the COVID-19 waves experienced in the district and metropolitan municipalities of Gauteng, South Africa, from 2020-2022 as well as the waves of the cholera outbreaks occurring in the Beira area of Mozambique between 1999 and 2005, in real-time. The problem of real-time scaling of the data prior to the first wave of an epidemic is addressed using globally available real-time information from first waves experienced in other countries and independent territories alongside the observed South African data. The use of the Bi-LSTM predicted starting dates is demonstrated for the second waves of COVID-19 infections experienced in Gauteng in 2020/21. Using the predicted starting dates, spatial-SEIR models are used to predict hospitalisations as a result of COVID-19 infections in each of the district and metropolitan municipalities of Gauteng. The fitted Bi-LSTM model demonstrates effectiveness in predicting the start and end dates of epidemic waves in real-time, allowing for pre-emptive disease modelling and predictions of spread. Moreover, it is shown that the use cases for the fitted model are not limited to COVID-19 studies, but can also be applied to other disease outbreaks that follow similar wave patterns.

The purpose of this paper is to utilize Abel-Gontscharoff and Hermite interpolation polynomials to prove new bounds for identities related to generalizations of Steffensen’s inequality. This will be achieved through the use of the weighted Hermite–Hadamard-type inequality utilizing ((n+2)-)convex functions.

Tuberculosis (TB) remains one of the leading causes of mortality among human immunodeficiency virus (HIV)—infected individuals. Existing models frequently fail to capture the complex dynamic relationship between TB and HIV, making it challenging to implement targeted public health policies and allocate resources efficiently. In this work, we explore the complex interactions between TB and HIV co-infection using topological data analysis (TDA). Using a dataset of 657 HIV-positive patients initiating TB treatment, the study employs TDA and machine learning models. The TDA Mapper graph constructed reveals distinct clusters of individuals that align closely with their antiretroviral therapy (ART) treatment status and history of TB infection. The Mapper graph information is used as additional feature for machine learning models. Logistic regression and linear support vector machine (SVM) models demonstrate the highest predictive accuracy. Findings underscore the necessity for early ART initiation to improve patient outcomes and offer valuable insights into improving treatment protocols or enhancing resource allocation for TB-HIV management, particularly in high-burden areas like South Africa.

This paper investigates Lagrangian-like submanifolds, the analogues of Lagrangian submanifolds in cosymplectic geometry and lays the underlying work by studying their linear algebraic properties, including an analysis of the Lagrangian-like Grassmannian (U(n)/O(n)). Moving into the manifold setting, we establish geometric results concerning the local structure of these submanifolds. In particular, we prove a relative Moser theorem that ensures the stability of cosymplectic structures under deformations and a cosymplectic Weinstein theorem that provides a canonical local model, ((T^*L times mathbb {R}, omega _{text {can}}, eta _{text {can}})), near any Lagrangian-like submanifold (L). Applications of these results include the construction of a Weinstein-like chart near the identity in the group of cosymplectomorphisms, thus bridging the geometry with topological and dynamical invariants via fixed points and a newly introduced co-flux homomorphism for cosymplectomorphisms.

Poliomyelitis is a deadly viral disease caused by various strains and highly contagious. The wild poliovirus (WPV) is the most harmful, attacking the host’s nervous system, leading to paralysis and death within hours. Vaccination remains the main effective prevention measure which protect the population at high risk composed mainly of children under 5 years of age. In Cameroon, a fourth-dose vaccination campaign was introduced to eradicate the disease, and the country was declared polio-free in 2020 by WHO. However, in 2021, two cases were detected again. This paper evaluates the effectiveness of the multi-dose vaccination strategy to eliminate Polio in Cameroon, using mathematical modelling. The study formulates and analyses a compartmental mathematical model with four vaccination classes, focusing on the administration of the oral polio vaccine (OPV) and the inactivated polio vaccine (IPV). Using combined data on reported cases and vaccine coverage, we calibrate and validate the model, estimate the basic reproduction number (mathcal {R}_0), and make predictions about the dynamics of the disease until 2035. The model exhibits a backward bifurcation phenomenon, which is a potential explanation why poliomyelitis is persistent in Cameroon with sporadic cases despite being declared polio-free. Sensitivity analysis reveals that asymptomatic carriers spread the disease more than symptomatic cases. our model suggests that, though the current vaccination scheme may eliminate Polio, a vaccine efficacy 85% administered to at least 85% newborns during the first-dose around is enough to accelerate its eradication by 2035.

The split variational inclusion problem has recently attracted great research attention due to its wide areas of applications. Several iterative methods have been proposed and studied by many researchers for approximating the solution of the problem. However, most of these methods require computation of the operator norm, which is often very difficult to compute or even estimate. In this paper, we introduce a new inertial iterative method (which does not require knowledge of the operator norm) for approximating the common solution of Split Variational Inclusion Problem (SVIP), Equilibrium Problem (EP) and Common Fixed Point Problem (CFPP) of multivalued demicontractive mappings in real Hilbert spaces. Our method employs self-adaptive step size and inertial technique to accelerate the rate of convergence. Under some mild assumptions, we establish the strong convergence of the sequence generated by the proposed algorithm. Finally, we present some applications and numerical examples to illustrate the applicability of our method as well as comparing it with some related methods in the literature. Our results extend and improve some of the existing results in the current literature.

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.