JOURNAL OF NATIONAL ACADEMY OF MATHEMATICS INDIA

Mucus and Serous Flow in Constricted Airways under the Influence of Time Varying Pressure Gradient

2024-11-28T11:00:14+00:00

In this paper, a two layer quasi steady cylindrical model of mucus transport in a constricted airway under a time
varying pressure gradient due to cough is studied. Mucus is treated as an incompressible Newtonian fluid in this model. The impact of slip condition due to immotile cilia, which forms a porous matrix, is also incorporated into the model. The study notes that as the constriction thickness and serous viscosity increase, the mucus and serous flow rate decrease. Additionally, it is observed that the flow rate of mucus and serous increases as the slip parameter and pressure drop increase. It is also found that the mucus flow rate increases as the mucus thickness increase. The study also reveals that the mucus flow rates decrease as the mucus viscosity increases.

Convergence of Picard Iteration to a Fixed Point in Soft Metric Space

2024-11-26T12:22:09+00:00

The aim of this paper is to introduce Picard Iteration in soft metric space when the set of parameters is a fi-nite set. We define the Picard operator and show its strong and weak convergence in soft metric space. This paper includes soft metric extensions of several important theorems of Picard iteration for metric space. Throughout the paper a comprehensive set of examples illustrating the discussed topics are presented.

Optimization and Constraint Satisfaction of Production Function in Industrial Organisation

2024-11-26T12:22:24+00:00

Recently businessmen, as well as industrialists, have been very much concerned about the theory of firm in order to make correct decisions regarding what item, how much and how, the quality of material and technological improvement also. The production function is formulated as a non-linear problem in the study whereby optimality is determined using KKT conditions and this approach has been demonstrated through theoretical analysis. These findings emphasize the significance of non-linearity in production models and thus contribute to better strategies of production management. The aim of this paper is to de-velop and use deterministic simulation models to analyze, improve, and optimize manufacturing process-es in industrial organization. The purpose of this study is to enhance our understanding of production dy-namics, as well as create deterministic simulation models for analyzing and optimizing production func-tions across industrial environments with an eye on fulfilling the constraint's satisfaction.

Parameter Estimation of Exponentiated Length Biased Exponential Distribution via Bayesian Approach

2024-11-28T11:00:57+00:00

In this paper, the exponentiated length-biased exponential distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.

Curvature Tensors On Lorentzian β-Kenmotsu Manifold

2024-11-30T06:05:36+00:00

The object of the present paper is to study some properties of Lorentgian β-Kenmotsu manifold. An irrotational pseudo projective curvature tensor in Lorentgian β-Kenmotsu manifold are studied. Finally we investigate pseudo W8 flat Lorentgian β-Kenmotsu manifold satisfying the relation R(X, Y ).S = 0, where S is the Ricci tensor.

Roles of Airflow Velocity and Porosity Parameter on Mucus Transport in the Human Lung Airways under the Influence of Time Varying Pressure Gradient

2024-11-26T12:24:16+00:00

This paper presents a two-layer circular unsteady state mathematical model and its analysis on mucus transport in the human lung airways. The model incorporates the roles of airflow velocity and porosity parameter on mucus transport under the influence of time varying pressure gradient generated due to coughing. The porosity parameter is incorporated because of immotile cilia forming a porous matrix bed in the serous sub-layer in contact with the epithelium in unhealthy state of human lung airways. The mod-el also incorporates the effect of airflow velocity caused by high shear stress that shears secretions and unwanted foreign particles off the bronchial wall and propels them towards the larger airways and trachea under a normal cough mechanism. In the model, the mucus layer is taken as a visco-elastic fluid and the serous layer as an incompressible Newtonian fluid. The analysis of the model reveals that mucus transport rate increases with increase in airflow velocity, porosity parameter, acceleration due to gravity, mucus layer thickness and pressure gradient. It is also noted that the mucus transport rate decreases with the in-crease in coughing duration, mucus viscosity and its elastic modulus and viscosity of serous layer fluid.