Exemplar Different-Level Quadratic Minimization, Division-by-Zero Issue, and Comparative Solutions

Zhang, Yunong; Ling, Yihong; Yang, Min; Li, Jian; Mao, Mingzhi

doi:10.1109/icsai.2018.8599431

Cited by 3 publications

(3 citation statements)

References 17 publications

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“…[21] Paper considers computing probabilities from zero divided by itself [22,23] Considers how division by zero is taught on an elementary level [24] Develops a method to avoid division by zero in Newton's Method [25] This work attempts to solve division by zero using a new form of optimization called Different-level quadratic minimization (DLQM) Equation = cosh − sinh can also be multiplied by p to give:…”

Section: Discussionmentioning

confidence: 99%

Applications of Semi-Structured Complex Numbers in Science and Engineering

Paul¹,

Wahid²

2023

Preprint

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Recently, a paper was written to reformulate and strengthen the theory of semi-structured complex numbers H (a new number set invented to enable division by zero). Whilst the paper had profound results, the application of this number set in many areas of engineering and science has not been fully explored. Consequently, the aim of this paper was to establish the number set H as a useful mathematical tool by providing an amalgam of results arising from its application in several areas of engineering and science. In the process, this paper makes four major contributions: these are (1) determining the product of the gradients of a horizontal and vertical line; (2) developing new Euler formulas relating exponential, trigonometric and hyperbolic functions in the 3D semi-structured complex number Euclidean space; (3) establishing semi-structured complex numbers as a better extension of the complex number set than quaternions; (4) resolving singularities that may arise in engineering and science equations (because of division by zero) to develop reasonable conclusions in the absence of experimental data. These results and their applications provide a firm foundation to advance the number set H as a useful mathematical tool.

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Section: Discussionmentioning

confidence: 99%

Applications of Semi-Structured Complex Numbers in Science and Engineering

Paul¹,

Wahid²

2023

Preprint

View full text Add to dashboard Cite

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“…[19] Paper considers computing probabilities from zero divided by itself [20,21] Considers how division by zero is taught on an elementary level [22] Develops a method to avoid division by zero in Newton's Method [23] This work attempts to solve division by zero using a new form of optimization called Different-level quadratic minimization (DLQM)…”

Section: Discussionmentioning

confidence: 99%

<strong>Utilizing Semi-structured Complex Numbers to Develop the First Division by Zero Calculator</strong>

Paul¹,

Wahid²

2023

Preprint

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Semi-structured complex numbers H was a number set developed to enable division by zero in ordinary algebraic equations. Its utility has been shown in mathematics and engineering. However, very little has been done to show its usefulness in computer science. Consequently, the aim of this paper was to show the utility of semi-structured complex numbers in computer science by developing a division by zero calculator. First two computer programs were written, one for a standard (STD) calculator and the other for a division by zero (DBZ) calculator. The programs were fed 20000 randomly generated arithmetic equations of varying lengths and the space and time complexity associated with processing these equations were measured and compared to determine the efficiency of each calculator. In the process, three major contributions were made: (1) A representation for semi-structured complex numbers that enables it to be easily used by a computer was developed; (2) It was demonstrated that the DBZ calculator outperforms the STD calculator in terms of efficiency; and, (3) It was shown that the number set H reduced the amount of error handling required to run a computer program. These results provide a firm foundation to advance the number set as a useful tool in computer science.

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“…[13] Paper considers computing probabilities from zero divided by itself [14,15] Considers how division by zero is taught on an elementary level [16] Develops a method to avoid division by zero in Newton's Method [17] This work attempts to solve division by zero using a new form of optimization called Different-level quadratic minimization (DLQM)…”

Section: Researchmentioning

confidence: 99%

Semi-Structured Complex Numbers:Extending the Cauchy–Riemann Equations and developing Semi-Structured Complex Analytic Functions

Jean Paul,

Wahid

2023

Preprint

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Real and complex analytic functions are largely studied in the field of complex analysis and are seen as very useful tools in solving problems in mathematics, physics and engineering. Real and complex numbers are a subset of semi-structured complex numbers (a new number set created to algebraically solve division by zero). Nevertheless, the properties of analytic functions made up of semi-structured complex variables (called semi-structured complex analytic functions) is yet to be explored. This limits the range of possible problems that can be resolved using analytic functions). In this regard, the aim of this paper was to expound upon the properties of semi-structured complex analytic functions and show their application in solving engineering problems. The results of this paper included (1) developing a full set of Cauchy–Riemann Equations for the semi-structured complex -space; (2) define sufficient and necessary conditions for a semi-structured complex function to be analytic; (3) determine the relationship between semi-structured complex analytic functions, Laplace’s Equations and Poisson’s Equations; and (5) provide an example of the use of these functions.

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Exemplar Different-Level Quadratic Minimization, Division-by-Zero Issue, and Comparative Solutions

Cited by 3 publications

References 17 publications

Applications of Semi-Structured Complex Numbers in Science and Engineering

Applications of Semi-Structured Complex Numbers in Science and Engineering

<strong>Utilizing Semi-structured Complex Numbers to Develop the First Division by Zero Calculator</strong>

Semi-Structured Complex Numbers:Extending the Cauchy–Riemann Equations and developing Semi-Structured Complex Analytic Functions

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