## Probability Problems and Estimation Algorithms Associated with Symmetric Functions

In this chapter, we offer a simple yet powerful approach in which the independent variables 1,..., n in multiple symmetric functions and Vieta's formulae are...

## No Big Bang in the Non-Expanding Universe

Briefly stated and applied to cosmological models is a theory of gravity in flat space-time. These models begin with a gravitational field that is equally...

## Biquadratic Equation with Four Unknowns

Number theory is strongly reliant on diophantine equations, which can take many different forms. There are a variety of Diophantine equations that have no solution,...

## Determination of Free Energy as Described by the New Axioms and Laws

Expanded Field Theory is used in this research. It transforms Classic Field Theory into a considerably broader theory with two additional axioms and eight rules....

## Study about Transformations Formulae and Certain Transformations: A Mathematical Approach

In this part, we've tried to come up with several transformation equations involving various transforms. Using Bailey's lemma to abstract many transforms such as Mellin,...

## Improved Hoeffding’s Lemma and Hoeffding’s Tail Bounds: A Recent Study

This chapter aims to enhance Hoeffding's lemma and, as a result, Hoeffding's tail limits. To begin, we'll offer Hoeffding's lemma with a proof that differs...

## Analysis of Methods for Calculating the Value of the Thermal Conductivity Coefficient in Numerical Modeling

Using the method of computational experiments on a computer, the effect of the method for calculating the values of the thermal conductivity coefficient at the...

## Applying the GSVD to the Analysis of the Augmented Lagrangian Method for Symmetric Saddle Point Problem

When using the iterative technique, the solution of the SPP needs appropriate computation in the case of the direct method and proper approximations of the...

## On Erdos – Lax and Turan Type Inequalities of a Polynomial

The above inequalities are respectively the well-known Erdӧs – Lax inequality and the Turẚn’s inequality. A natural question that follows is to investigate the extension...

## An Efficient K-means Algorithm: Generating Clusters Dynamically in MapReduce Framework

Background: K-Means is a popular partition-based clustering technique that divides an input dataset into a collection of groups. K-Means is a popular technique because of...