RESEARCH & REVIEWS: DISCRETE MATHEMATICAL STRUCTURES

Detecting Electronic Circuitboard Thermal Abnormalities with Dynamic Hypernumbers

M. Burgin — 2024-04-15

This paper introduces the algebra of data acquisition using dynamic hypernumbers used in predicting thermal abnormalities with a rapid forecasting algorithm. Algebraic rules are defined for monitoring data from multiple sources. Each data source is considered a dynamic receptive synchronized hypernumber for building the resulting dynamic hypernumber. The algebraic dynamic hypernumber
definition is used to present a low-complexity algorithm for identifying the thermal state of an electronic circuit board. The algorithm is implemented by translating the pixel colors from an infrared camera into a dynamic hypernumber temperature index. The dynamic hypernumber algorithm output is used to dynamically predict the thermal process. This prediction allows the detection of thermal abnormalities. It is shown that the method of building a dynamic hypernumber from the set of the circuit board temperatures has less electronic and computational complexity in comparison with looking for elevated temperature areas. Considering dynamic hypernumbers are acquired from the stochastic process, regression polynomials are used with best criteria fit theory to find the continuous mathematical expression of such numbers. The solution of non-linear operator equations for computing the coefficients of the polynomial is obtained using the constructive hypernumber.

Creating a New Coding and Decoding Algorithm Based on Violin Notes

Bahar KULOĞLU — 2024-03-14

Throughout history, people have sent their messages using encryption so that only the person they want can read them. Today, thanks to the internet and other communication networks, data can be transmitted and accessed worldwide. For this reason, it is of great importance that digital data is transmitted correctly to the other party and in a stronger, higher quality and more secure way during transmission. In this context, developing different decoding algorithms by constantly approaching coding and decoding studies from different perspectives is of great importance in the world of encryption. Based on this purpose, in this study, we presented a different, not obvious approach to the world of encryption and discussed the coding and decoding study on the violin, one of the musical instruments. In this study, a different perspective was brought to the previous coding and decoding studies and coding and decoding algorithms were created with the help of frets and notes on the violin strings, which are musical instruments. In the coding processes here, the American Standard Code for Information Interchange system was used to find the numerical code values of the letters. In this way, not only the reliability of the coding and decoding process was increased, but also the verification of information was tried to be kept at a high rate.

Riemannian Metric based Smart Senor for Testing Corona Virus

Sandeep Dubey — 2024-03-30

This paper proposes an electronic device based on Riemannian metric for testing corona virus. Hamilton’s evolution equation based sensor presents the nodes of corona virus through the Riemannian metric. The initial position and terminal position of corona virus based interval is defined with respect to the time. This is measured by Riemannian metric. There exists the functional F, which is the probable structure of corona virus and its variant over the manifold M (included variants also), f is the functional change of the structure of the corona virus, fe is the variants in the structure of the corona virus. The classified testing range of corona virus is installed in the sensor system but its dynamic tracing is performed by the Riemannian metric. There is applied the tensor and curvature concept so that the deviation in the result to be minimized.

On Pell Functions and Pell Numbers

mine uysal — 2024-03-06

Number sequences have been studied by many scientists for many years because they find applications in nature and many branches of science. The most well-known number sequence among these integer sequences is the Fibonacci sequence. Later, these integer sequences were generalized and many number sequences were defined and their properties were examined. One of these is Pell number sequences. Pell numbers can be calculated in a way similar to the recurrence relation of Fibonacci numbers. The Pell numbers Pn are defined by

The first few terms of Pell numbers are 1,2,5,12,29,... . In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. In addition to being used to approximate the square root of two, Pell numbers can also be used to find square triangle numbers, create integer approximations to the right isosceles triangle, and solve certain combinatorial numbering problems. In this study, we define Pell functions on real numbers R. We give the relations between Pell functions and Pell numbers. We examine Pell functions using the concept of the p − odd and p − even functions. Additionally, if p is a Pell function, then

Graph Theory: Its Importance and Application in Recent development of Science and Engineering

Niky Baruah — 2024-03-30

Graph Theory is widely used in all the basic sciences including social science, due to its intrinsic simplicity it has got a lot of application in computer science, computer networks, engineering, genetics, data structure etc. Graphs are nothing but mathematical structure that helps in representing our everyday problem in a precise graphical manner. Graph Theory is the area of applied mathematics that deals with the study of objects and the relationship about them. The issue of finding the shortest path is extensively researched within network flow optimization problems. It holds significant relevance in multiple scientific and engineering domains, particularly in areas like transportation and traffic control, where solving various types of shortest path problems becomes essential.The transportation scientist requires a very flexible and efficient shortest path methods and applications, to solve the real world problem both from the time point of view, and also for the memory requirements applied for the same. Also, graph theoretical reasoning can cast light on such problems, providing tools which help in making decisions and help in finding answers to a variety of specific problems or questions which arises in the attempt to tackle the broader issues. Every real world problem can be converted into a mathematical problem and can be solved with the help of graph theory. Due to its intrinsic nature, graph theory is one of the important tool to study various mathematical structures and to analysis its insights.