## 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,...

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...

## 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....

## 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...