The Vertices of a Graph and Its Dimension

We show that a graph’s dimension is smaller than or equal to the cardinality of its vertices. Author(S) Details Volker W. Thürey Independent Researcher, Bremen, Germany. View Book:- https://stm.bookpi.org/RAMRCS-V4/article/view/4879

Reliability Analysis of a Multi-State Delivery Network through the Symbolic Derivation of a Probability-Ready Expression

The dependability of a multi-state delivery network (MSDN) with different suppliers, transfer stations, and marketplaces (depicted as vertices) connected by branches of multi-state capabilities, delivering a specific commodity or service between their end…

Determining the Sufficiency in Optimal Control without the Strengthened Condition of Legendre

In this paper, we develop a sufficiency theorem for an unconstrained Lagrange fixed-endpoint problem that provides sufficient conditions for processes that do not satisfy the traditional nonsingularity assumption, i.e., the strengthened Legendre condition…

A Counterexample of the Statement P = NP: Scientific Explanation

By generating a very simple example of unsolvability in polynomial time in a well-known NP-complete problem, it is proven that the classes P and NP do not coincide in this work. A random…

Channel Capacity Enhancement on Maximization of Modified Verma and Bose-Einstein Entropies by Gaussian Distribution

This chapter examined how to improve channel capacity by using a Gaussian distribution [5] and Kullback-[3] Leibler’s information measure of directed divergence to maximise modified Verma and Bose-Einstein entropies. Author(S) Details Rohit Kumar…

Study on Dual Bi-Directional Heuristic Development Framework

A multi-start heuristic framework is developed in this study. Heuristic convergence to high-quality optimum solutions is accelerated using the heuristic development approach. The Dual Bi-Directional (DBD) heuristic is a multi-start heuristic that uses…

A Phenomenological Relation for Decay Times: A Quantum Mechanical Approach

Georges Lemaitre was invited to a British Association symposium on the link between physicality and spirituality in London in 1931. In a report published in Nature titled ‘The Beginning of the World from…

Study on Fixed Effect versus Random Effects Modeling in a Panel Data Analysis; a Consideration of Economic and Political Indicators in Six African Countries

Individual heterogeneity in panel data analysis can be addressed to avoid bias in the final estimations. The data in a panel might be balanced or imbalanced, and the panel can be short or…

Study on Generalized Exponential Type Estimators for Ratio of Two Population Means Using Auxiliary Attribute in the Presence of Non-response

In this research, we offer generalised exponential type estimators for the ratio of two population means in the case of non-response utilising an auxiliary feature. Up to the first order of approximation, formulas…

Derivation of Second Order Partial Differential Equation Indicating Wave and Heat Equation through the Use of the Navier Stokes Equation for Unsteady and Incompressible Flow: Scientific Explanation

In this study, we used the Navier Stoke’s equation for unsteady and incompressible flow to approach the ideas of two-dimensional wave equation and one-dimensional heat equation. Our efforts have been backed up by…

Addressing Reserves and Pension Funds through Gambler’s Ruin and Generalized Brownian Motion Process

The random walk was used to model the reserve problem. Random walks are a classic example of a stochastic process that can be used to examine a variety of phenomena, including, as in…

Model Calibration at Different Stages in Cluster Sampling; Use of Penalized Splines in Semiparametric Estimation

Several writers have studied internal calibration and model help on semiparametric models based on kernel methods for estimating finite population totals. We extend this in this book chapter to investigate model calibration using…

Diagnostic Statistics and Predictive Statistics as a Re-Definition to Inferential Statistics

In any statistical book, the typical method for statistics is to begin with descriptive statistics, then probability, and finally inferential statistics. The relationship between descriptive and inferential statistics is considered probability. Inferential statistics…

Map Visualization of Boolean Manipulations in Qualitative Comparative Analysis

As advanced studies on the communicariont facility from the standpoints of their beneficiaries and social infrastructure, some fundamental concepts and technology relating well-being systems are examined. In an ageing society, we primarily mention…

Daily Life Support for and Widely Applicable Living Arrangement System under the Internet Environment: An Advanced Study

As advanced studies on the communicariont facility from the standpoints of their beneficiaries and social infrastructure, some fundamental concepts and technology relating well-being systems are examined. In an ageing society, we primarily mention…

A Study on Continuous Poisson-Rayleigh Distribution: Its Properties and Applications

The Poisson-Rayleigh distribution is a Poisson-based continuous probability distribution proposed in this article. The properties of the new distribution, such as quantile and reliability functions, and other important metrics, as well as its…