## Abel’s and Galois’s Proofs on Quintic Equations having no Radical Solutions are Invalid

In this work, the arguments of Abel and Galois that the quintic equations have no radical solutions are proven to be false. According to the...

## Consistency and Numerical Stability of the Euler Approximation for the Solution of Delay SDE’s with Possibly Discontinuous Initial Data

This study follows on from [1]'s work on Precise Estimates and [2]'s work on Approximation Theorems. We have shown that the S.F.D.E. Euler approximation considered...

## Assessment of Densities of Distributions of Solutions to Delay Stochastic Differential Equations with Discontinuous Initial Data (Part I)

The goal of this research is to show that the Integration by Parts formula we developed in this paper can be used to expand all...

## The Regularly Solvable Operators with Their Products and Spectra in Direct Sum Spaces

The generic quasi-differential expressions _1,_2,..., n of order n with complex coefficients and their formal adjoints on the interval are studied in this study (a,b)....

## Determination of Derivative – and Regularized Derivative Interpolation for Band-limited Functions

This chapter looks at the ill-posedness of derivative interpolation as well as a regularised derivative interpolation for band-limited signals. To check for ill-posedness, the Shannon...

## Minimum Cable Tensions for a Cable-based Parallel Robot with Application to Stability Analysis: A Descriptive Study

Parallel robots with cables instead of rigid linkages are known as cable-based parallel robots. The robots outperform their rigid-link counterparts in a number of ways....

## A Strict Proof That the Riemann Zeta Function Equation Has No Non-trivial Zeros

On the full complex plain, a standard approach is presented to verify that the Riemann Zeta function equation contains no non-trivial zeros. The Riemann Zeta...

## Five Mistakes in Riemann’s Original Paper in 1859 Made Riemann Hypothesis Meaningless

The original paper proposed by Riemann in 1859 has five main errors. The Riemann hypothesis is rendered useless. 1. When the left-hand side of an...

## Assessment of Distance Related Spectrum of the Zero-divisor Graph

For various values of n, the goal of this work is to discover the distance, distance Laplacian, and distance signless Laplacian of Denote the set...

## Study about Statistical Normalization and Back Propagation

Artificial Neural Networks (ANNs) are a prominent machine learning technique that has lately been used in a variety of medical and medically related industries. Diabetes...