Unilag Journal of Mathematics and Applications

HYERS-ULAM-RASSIAS STABILITY OF CERTAIN PERTURBED NONLINEAR LIENARD TYPE OF SECOND DIFFERENTIAL EQUATIONS

2024-07-30T07:45:01+00:00

In this paper the Hyers-Ulam-Rassias stability of certain perturbed nonlinear second order differential equations of Lienard type was studied, using some new modifications of Grownwall-Bellman-Bihari Integral inequality. Some examples are given to illustrate our results.

ON ZAGREB COINDEX POLYNOMIALS FOR SOME SPECIAL GRAPHS

2024-07-30T07:45:01+00:00

Zagreb polynomial is a polynomial in which the power of the indeterminate is a Zagreb index, Zagreb index is a graph invariant as it remains fixed under graph homomorphism. The complement of a graph is needed to compute the Zagreb coindex as well as the polynomial. In this paper we looked at the size of the complement graphs under consideration and the formulae for their Zagreb coindex polynomials.The graphs are cycle C_n, wheel W_n, path P_n, complete graph K_n and the complete bipartite graph K_m;n.

ERGODIC THEOREM FOR QUANTUM DYNAMICAL SEMIGROUP ON DECOHERENCE-FREE SUBALGEBRA OF A QUANTUM MARKOV SEMIGROUP

2024-07-30T07:45:01+00:00

In this work, we study ergodic theorem for quantum dynamical semigroup on decoherence-free subalgebra of quantum Markov semigroup. A quantum dynamical semigroup of non-expansive maps which has at least one stationary point was established on decoherence-free subalgebra.The measurability of the semigroup was then used to ensure the weak convergence of the Cesaro means to a stationary point.

MARKOV SWITCHING DYNAMIC REGRESSION MODEL: APPLICATION TO FINANCIAL DATA

2024-07-30T07:45:01+00:00

Hidden Markov Models are used to study occurrences where a portion of the phenomenon is observable while the rest is unobservable. The model consists of two sets of random variables, namely, unobservable and observable random variables. Markov models are usually used to model the unobservable variable part of the hidden Markov model; a time-series regression model is used to model the observable part of the model. Then, the two random variables produce a regime-switching model known as the Markov-switching dynamic regression model with a distinct probability distribution. The parameters of this resulting model can be estimated using the maximum likelihood estimation method, and the characteristics of the regression model vary with the presiding regime of the model. The regression objective of this work is to explain the variability in the Nigerian monthly inflation rates using the variability in the average monthly United States dollar exchange rates. The correlation between the two datasets is determined using the least squares regression model and the Markov switching dynamic regression model. The Markov switching regression (Regime 2) model represents the high-variance regime. It explains the regression objectives more than the OLS regression model, as shown in the results. Consequently, it shows that when the Markov state model is in the high variance regime, Nigeria's economy shows a recession. The results depict that the regime-switching model outperformed the single regime model in capturing the properties of the data from the comparative analysis.

A COMPARATIVE ANALYSIS OF SOME SELECTED MACHINE LEARNING ALGORITHMS FOR CLASSIFICATION AND PREDICTION OF DIABETES TYPES

2024-07-30T07:45:01+00:00

Diabetes mellitus is one of the most common human diseases worldwide and may cause several health-related complications. It is responsible for considerable morbidity, mortality and economic loss. A timely diagnosis and prediction of this disease could provide patients with an opportunity to take the appropriate preventive and treatment strategy. To gain an understanding of risk factors, the study explores the comparison of six classification algorithms along with the artificial neural network algorithm in the prediction of diabetes types. The analysis of data from patient records shows four main predictors of type 1 & type 2 diabetes: Age, Ulcer Duration, White Blood Cell (WBC) and Erythrocyte Sedimentation Rate (ESR). All the classification algorithms based on accuracy, precision, recall, and F-measure show good results for the parameters with accuracy greater than 95%. However, random forest and k-nearest neighbor algorithms provided 99% accuracy for the train/test split. Thus, these models can be applied to make a reasonable classification of type 1 and type 2 diabetes. Hence, the study ensures a timely diagnosis and prediction of this disease for appropriate preventive and treatment strategy.

IMPULSIVE SALE-PROFIT MODEL

2024-07-30T07:45:01+00:00

This paper considers optimization problems that arise from mathematical economics involving the impulsive sale-profit model of a company producing some items in a mechanically independent non-competitive market situation. The sale and profit profiles of the company are analyzed using a variable allocation of funds for sales promotions, minimizing the cost functional subject to impulsive control and Lyapunov Functional. We formulate the sales projection of the company using the `parasitic control measure' and the impulsive-averaging technique. The result shows that the sale is bounded in a redundant market situation if some sale parameters are finite. The approximate solution and the error of approximation of the model exist.

THREE-STEP SECOND DERIVATIVE HYBRID BLOCK BACKWARD DIFFERENTIATION FORMULAE FOR SOLVING SYSTEM OF DIFFERENTIAL ALGEBRAIC EQUATIONS (DAES)

2024-07-30T07:45:01+00:00

This paper presents a new Second Derivative Hybrid Block Backward Di fferentiation Formulae (SDHBBDF) for solving series of engineering problems that are represented by some sets of Di erential-Algebraic Equations (DAEs). The main and complimentary methods, were developed by collocation and interpolation techniques that are combined as a set of block equations. The analysis of the method showed that it is consistent, convergent, and satis fied the L-stability condition. The SDHBBDF was implemented on some physical problems of DAEs with broad intervals and the numerical results demonstrated that the method is accurate, efficient and suitable for solving DAEs. Moreso, the method compared favorably well with some excellent methods in the literature.

ESTIMATES OF SECOND AND THIRD HANKEL DETERMINANTS FOR BAZILEVIC FUNCTION OF ORDER GAMMA

2024-07-30T07:45:01+00:00

In the recent time, the study of Bazilevic functions became so popular that researchers, especially in Geometric Function Theory, have had to study different subclasses of Bazilevic functions in different directions. How- ever, their study seem to lack full stamina addressing relevant connections of Bazilevic functions to some properties such as coefficient bounds, sharp bounds of the Fekete-Szego functional as well as the Hankel determinants for functions belonging to some specific subclasses of Bazilevic functions. Consequently, in this article, with the aid of Salagean derivative operator, the author derived the Bazilevic class T_n^α(γ), of order γ, type α, via the convolution of the fractional analytic function g(z)^α and the normalized univalent function f (z) in the open unit disk. In the sequel, sharp bounds on the Taylor-Maclaurin coeffi- cients a_k(α) for functions belonging to the aforementioned class were obtained while the relationship of these bounds to the classical Fekete-Szego inequality H₂(1) and Hankel determinants H₂(2) and H₃(1) were established using a clear Mathematical approach. Some of the consequences of the results so obtained were discussed as corollaries.