Unilag Journal of Mathematics and Applications

BRIEF STUDY ON SOME PROPERTIES OF SYMMETRIC CARDIO-BAZILEVIC FUNCTIONS

Jamiu Olusegun HAMZAT — 2025-06-24

Bazilevic functions consist of functions de ned by certain integral which are entirely univalent in the unit disk. They contain some other class of functions as special cases. In the recent time, the study of Bazilevic functions became so popular that researchers (especially in Geometric Function Theory, GFT) have had to study di erent subclasses of Bazilevic functions as related to various domains. However, their study seem to lack full vigour addressing relevant connections of Bazilevic functions to certain interesting domain called the symmetric cardioid domain. In characterization of these Bazilevic functions, the geometry of the image domains is very critical. Consequently, in this article, with the aid of Salagean derivative operator, the author derived a new Bazilevic class B^α_n (A;B;α), type α , associated with symmetric cardioid domain. This was achieved via the Hadamard product of certain fractional analytic function g(z) ^α and the normalized univalent function f(z) using subordination principle. In the sequel, a new geometrical formation regarding the said class of Bazilevic functions was obtained. Additionally, sharp bounds on the fi rst three Taylor-Maclaurin coefficients for functions belonging to the aforementioned class were obtained while the relationship of these bounds to the classical Fekete-Szego inequality was established using a very lucid Mathematical approach.

VOLATILITY AND RISK ANALYSIS OF SELECTED COMPANIES IN NIGERIAN STOCK EXCHANGE

JOSEPHINE NNEAMAKA ONYEKA-UBAKA — 2025-06-24

The study introduces GARCH family models in modelling stock returns volatility on investor’s decision-making and risk management in the Nigerian Stock Exchange market. Data (Dangote Cement PLC, Nigerian Flourmill, Guinness PLC, Nestle PLC and Unilever PLC) are sourced from ng.invest.com. The parameters of ARCH and GARCH models are estimated by maximum likelihood estimation method while the Lagrange Multiplier (LM) test is proposed testing heteroskedasticity. The results show that the data obtained within the sample period exhibit non-normality and no presence of autocorrelation in the squared standardized residuals. The FIGARCH model estimates the daily return series of Dangote Cement PLC, Nigerian Flourmill, Nestle PLC and Unilever PLC while the TGARCH model is more suitable for the Guinness PLC within the sampled period based on our diagnostic checks (Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)). These findings are significant as they provide stakeholders with a deeper understanding of the patterns in the series, the leverage effect and make informed decisions on how to manage the associated risks. It is also important to note that the government's intervention in supporting struggling companies through policy creation is crucial, especially during periods of reduced returns and high inflation.

A SEMI-ANALYTICAL METHOD FOR SOLVING FRACTIONAL ORDER GENERALIZED BURGERS- HUXLEY EQUATION WITH A REFINED INITIAL GUESS

RAZAQ ADEKOLA ODERINU — 2025-06-24

In this paper, a refined initial guess was incorporated into the Adomian Decomposition Method (ADM) in order to obtain an approximate solution to the classical order and fractional order Generalized Burgers-Huxley equations (GBHE). The first iteration was obtained using the refined initial guess and all other iterations are obtained using the ADM. The solutions obtained were computed as an infinite series with a fast convergence to the exact solution at classical order. The dependability and efficacy of the procedure are demonstrated by the supplied graph and the results.

MOLECULAR SIMULATION AND STOCHASTIC DOMINANCE ANALYSIS OF LIGANDS IN DRUGS FOR TREATMENT OF TB/HIV USING THE WEIGHTED GAMMA-RAYLEIGH DISTRIBUTION

ENO EMMANUELLA AKARAWAK — 2025-06-24

The recent treatment for Tuberculosis involves a prolonged study of a combination of antibiotics with toxic side-effects and is associated with poor patient compliance. This has resulted to the multi-drug resistant (MDR) and extensively-drug resistant (XDR) strains of M. tuberculosis. The number of anti-TB drugs currently in the pipeline is insufficient to address this major health challenge. Therefore, there is an urgent need to discover and develop new and efficient drugs against TB. Studying the interaction and functioning of drug components is the first step in the discovery process and Molecular docking is one of the methods that have been used to study drug interaction and functioning. In this study, a molecular dynamics simulation study of ligands (Ethambutol, Isoniazid, Rifampicin, Streptomycin, Pyrazinamides) that are responsible for the effectiveness of Anti-TB/HIV therapy was carried out. Additionally, the Weighted Gamma-Rayleigh distribution (WGRD) is introduced in this research work, and used in testing the stochastic dominance of the binding affinity of the ligands to the Anti-TB/HIV drugs. Results showed that Rifampicin has higher binding affinity as it has (first order stochastically) dominated Streptomycin and Pyrazinamide. Isoniazid has (first order stochastically) dominated Ethambutol. Also, Isoniazid has great power in reducing toxicity of Anti-TB/HIV drug. The results from this study provide an avenue for good health policy and prospective planning, especially in Anti-TB/HIV drug development.

NUMERICAL APPROXIMATION OF OPTIMAL CONTROL PROBLEMS CONSTRAINED BY DYNAMIC EQUATIONS VIA GALERKIN METHOD

Matthew Folorunsho Akinmuyise — 2025-06-24

The research investigates the application of the Galerkin method to optimal control problems constrained by coupled dynamic equations. These
constrained problems are reformulated into unconstrained ones using the Hamiltonian approach, which facilitates the determination of boundary conditions
for both the state and costate variables. By assuming a polynomial solution, the weighted and residual functions were derived. The Orthogonality of the
product of these functions leads to the formation of a system of linear equations. Solving these equations provides the solution for the boundary condi-
tions through direct substitution. This scheme was developed for the Lagrange form of optimal control problems to assess its accuracy in approximating exact
solutions. Several optimal control problems with known exact solutions were solved using the proposed scheme, and the results were compared to evaluate
its e ectiveness.

SOLUTION TO THE PROBLEM OF REGULAR MAPS ON BOUNDED LOJID ALGEBRAS

Emmanuel Ilojide — 2025-06-24

Lojid algebras are algebras of type (2,0). Regular maps play a vital role in the study of bounded lojid algebras. They are particularly useful in conceptualizing ideals and subalgebras of lojid algebras. It is therefore important to nd a set system through which they can be studied. This paper primarily concerns the development of a set system that accounts for the study of all regular maps on bounded lojid algebras and also to solve the open problem that arose in the study of the theory of lojid algebras.

THE NEUTROSOPHIC HOM - GROUPS AND NEUTROSOPHIC HOM - SUBGROUPS I

Sunday Adesina Adebisi — 2025-06-24

Hom-groups are the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map. The neu-
trosophic set is a powerful tool in dealing with incomplete, indeterminate and inconsistent data that exist in the real world. Neutrosophic set is characterized
by the truth membership function in the set (T), indeterminacy membership function in the set (I) and falsity membership function in the set (F) where
0 ≤ T + I + F ≤ 3+. In this work, e orts are intensi ed to clearly exemplify and create distinctions between certain structural ( classical ) groups , which
are neutrosophic Hom groups and those which are not. Some examples of the neutrosophic Hom groups are also carefully constructed with elementary fea-
tures and characterizations such as the subgroup series as well as their lattices. Finally , the certainty of the Lagranges theorem involving the subgroup of any
nite neutrosophic Hom - group G(I)

BI- UNIVALENT PROBLEM FOR CERTAIN GENERALIZED CLASS OF ANALYTIC FUNCTIONS INVOLVING Q-INTEGRAL OPERATOR ASSOCIATED WITH NEPHROID DOMAIN

Olalekan Fagbemiro — 2025-06-24

The authors in this article study a new subclass of bi-univalent functions involving q-integral operator associated with nephroid domain by using the concept of subordination and bi-linear fractional principles.We further employed our investigation to determine new coecient bounds and subsequently obtain the Fekete-Szego inequalities for functions belonging to the aforementioned subclass were obtained.