Related papers: A Step towards an Easy Interconversion of Various …
A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are…
Many papers have presented multi-valued circuits in various technologies as a solution to reduce or solve interconnection issues in binary circuits. This assumption is discussed. While 4-valued signaling could divide by two the number of…
A real number is a rule that, when provided with a rational interval, answers Yes or No depending on if the real number ought to be considered to be in the given interval. Since the goal is to define the real numbers, this can only motivate…
Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since they typically…
We use recurrence equations (alias difference equations) to enumerate the number of formula-representations of positive integers using only addition and multiplication, and using addition, multiplication, and exponentiation, where all the…
This paper introduces a new method to perform signal processing using cells or atoms to synthesize variation in digital data stored in optical format. Interfacing small-scale biological or chemical systems with information stored on CD, DVD…
In the paper, I consider appearance of unit's digits in minor totals of a few integer sequences. The sequences include the sequence of even integers, sequence of odd integers and Faulhaber polynomial at $p = 2$. Application of difference…
A large multitude of scientific computing tools is available today. This article gives an overview of available tools and explains the main application fields. In addition basic principles of number representations in computing and the…
One of the most important and practical researches which has been considered by researchers is creating secure environments for information exchanges. Due to their structures, chaos systems are efficient tools in the are of data…
Natural numbers which are nontrivial multiples of some permutation of their base-$b$ digit representations are called permutiples. Specific cases include numbers which are multiples of cyclic permutations (cyclic numbers) and reversals of…
One of the most fundamental questions in Biology or Artificial Intelligence is how the human brain performs mathematical functions. How does a neural architecture that may organise itself mostly through statistics, know what to do? One…
We propose to use Digital Memcomputing Machines (DMMs), implemented with self-organizing logic gates (SOLGs), to solve the problem of numerical inversion. Starting from fixed-point scalar inversion we describe the generalization to solving…
Different types of network parameters have been used in electronics since long ago. The most typical network parameters, but not the only ones, are $S$, $T$, $ABCD$, $Z$, $Y$ , and $h$ that relate input and output signals in different ways.…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
A nested coordinate system is a reassigning of independent variables to take advantage of geometric or symmetry properties of a particular application. Polar, cylindrical and spherical coordinate systems are primary examples of such a…
In the last decades, great achievements have been made in the development of computing machines. However, due to exponential growth of transistor density and in particular due to tremendously increasing power consumption, researchers expect…
The moving computation on the edge or near to data is the new trend that can break the bandwidth wall and to unleash the power of next generation NVM or SCM memory. File system is the important OS subsystem that plays the role of mediator…
Unary coding is useful but it is redundant in its standard form. Unary coding can also be seen as spatial coding where the value of the number is determined by its place in an array. Motivated by biological finding that several neurons in…
Wristwatches have been a common fashion accessory addition for several people. However, the concept of using a seven-segment digital display or sometimes, even an analog indicator hasn't changed for a number of years. This project aims to…
The concept of porous numbers is presented. A number $k$ which is not a multiple of 10 is called {\it porous} if every number $m$ with sum of digits = $k$ and $k$ a divisor of both $m$ and digit reversal of $m$ has a zero in its digits. It…