Estimation of Quantum Entropies
Global Stability of a Predator-Prey Fishery Model with Non-Selective Harvesting: A Study of Linear Optimal Control
Comparative Analysis of Finite Difference Method (FDM) and Physics-Informed Neural Networks (PINNs)
The Hull Domination Number of a Graph
K Out of N Integrated Reliability Model with Multiple Stage Optimization using Four Components of Heuristic Programming Approach
An Introduction to Various Types of Mathematics Teaching Aids
A Simple Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems
A New Approach to Variant Assignment Problem
A Homotopy Based Method for Nonlinear Fredholm Integral Equations
Proof of Beal's Conjecture and Fermat Last Theorem using Contra Positive Method
Trichotomy–Squared – A Novel Mixed Methods Test and Research Procedure Designed to Analyze, Transform, and Compare Qualitative and Quantitative Data for Education Scientists who are Administrators, Practitioners, Teachers, and Technologists
Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining the Application Process of the Tri–Squared Test
A New Hilbert-Type Inequality In Whole Plane With The Homogeneous Kernel Of Degree 0
Introducing Trinova: “Trichotomous Nomographical Variance” a Post Hoc Advanced Statistical Test of Between and Within Group Variances of Trichotomous Categorical and Outcome Variables of a Significant Tri–Squared Test
Surfaces in R3 with density
Motivated by the importance of entropy functions in quantum data compression, entanglement theory, and various quantum information-processing tasks, this study demonstrates how classical algorithms for entropy estimation can effectively contribute to the construction of quantum algorithms for universal quantum entropy estimation. Given two quantum i.i.d. sources with completely unknown density matrices, algorithms are developed for estimating quantum cross entropy and quantum relative entropy. These estimation techniques represent a quantum generalization of the classical algorithms by Lempel, Ziv, and Merhav.
A proposed two-dimensional modified Lotka-Volterra fishery model in terms of predator-prey aims to explore the effect of non-selective harvesting on the predator and prey populations. The study delves into various essential aspects of the dynamical system, including positivity, uniform boundedness, and persistence. Points of equilibrium are identified. The system's local and global stability are thoroughly examined and discussed. Moreover, the research explores the concept of bionomic equilibrium, a scenario where economic rent is entirely dissipated. Extending the bioeconomic model, the study investigates a linear optimal control problem to determine the most effective harvesting strategy. Utilising Pontryagin's maximum principle, the optimal control is characterised. The findings indicate that maximum allowable effort should be exerted whenever the net revenue per unit effort surpasses the total net marginal revenue of predator and prey stocks. Numerical simulations, using data on the marine artisanal fishery in Ghana, are conducted to validate the theoretical discoveries. The outcomes reveal that the fishery can support sustainable harvesting of both predator (tuna) and prey (sardinella) populations, as long as the optimal harvesting effort is set at 100,000 fishing trips annually.
In this analysis, the solutions of the Linear and Non-Linear models are explored and compared using two distinct methods: the Finite Difference Method (FDM) and the Physics-Informed Neural Networks (PINNs). Initially, the solution is derived employing the principles of FDM, followed by solving the same problem using the methodology of PINNs. Subsequently, a comparative examination of the solution graphs with the exact solution is conducted.
For a connected graph G = (V, E), the hull number h(G) of a graph G is the minimum cardinality of a set of vertices whose convex hull contains all vertices of G. A hull set S in a connected graph G is called a minimal hull set of G if no proper subset of S is a hull set of G.A subset D of vertices in G is called a dominating set if every vertex not in D has at least one neighbor in D. A Hull dominating set M is both a Hull and a dominating set. The hull (domination, hull domination) number h(G),(γ(G),γh (G)) of G is the minimum cardinality among all hull (dominating, hull dominating) sets in G. Hull domination number of certain classes of graphs are determined. Connected graph of order p with hull domination number p or p-1 are characterized. It is shown that for every two integers a,b≥2 with 2≤a≤b, there is a connected graph G such that γh (G)=a and γg (G)=b, where γg (G) is the geodetic domination number of a graph.
Integer variables are among the neo-logistic programming issues that most frequently pertain to system reliability improvement. If 'k' out of 'n' elements are present in each technology, then the configuration can be employed with 'k' out of 'n' systems. Only particular objective function structures and restrictions may be used in a heuristic technique to precisely address a dependability optimization problem. As more constraints are placed on it, the more useful it becomes; it is worthless for boosting dependability in a large system. This paper analyzes existing research on integrated reliability models with redundancy and explores system reliability optimization before proposing new recommendations.
