An Explicit Form of Signum Function
In this paper, the author derives an analytical exact form of signum function, which evidently constitutes a fundamental concept of Communication Systems and Control Theory along with digital control systems and is also involved in many other fields of applied mathematics and engineering practices....
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/20/3246 |
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| author | John Venetis |
| author_facet | John Venetis |
| author_sort | John Venetis |
| collection | DOAJ |
| description | In this paper, the author derives an analytical exact form of signum function, which evidently constitutes a fundamental concept of Communication Systems and Control Theory along with digital control systems and is also involved in many other fields of applied mathematics and engineering practices. In particular, this significant function is performed in a simple manner as a finite combination of purely algebraic representations. The novelty of this work when compared to other analytical expressions of this nonlinear function is that the proposed explicit representation is not performed in terms of miscellaneous special functions, such as Bessel functions, error function, and beta function, and also is neither the limit of a function nor the limit of a sequence of functions with a point-wise or uniform convergence. |
| format | Article |
| id | doaj-art-efe59cd74a60422aa52617886d307c14 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-efe59cd74a60422aa52617886d307c142025-08-20T02:10:56ZengMDPI AGMathematics2227-73902024-10-011220324610.3390/math12203246An Explicit Form of Signum FunctionJohn Venetis0Section of Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 15773 Athens, GreeceIn this paper, the author derives an analytical exact form of signum function, which evidently constitutes a fundamental concept of Communication Systems and Control Theory along with digital control systems and is also involved in many other fields of applied mathematics and engineering practices. In particular, this significant function is performed in a simple manner as a finite combination of purely algebraic representations. The novelty of this work when compared to other analytical expressions of this nonlinear function is that the proposed explicit representation is not performed in terms of miscellaneous special functions, such as Bessel functions, error function, and beta function, and also is neither the limit of a function nor the limit of a sequence of functions with a point-wise or uniform convergence.https://www.mdpi.com/2227-7390/12/20/3246signum functionanalytical expressiontangent functionirrational quantityinteger part of real variable |
| spellingShingle | John Venetis An Explicit Form of Signum Function Mathematics signum function analytical expression tangent function irrational quantity integer part of real variable |
| title | An Explicit Form of Signum Function |
| title_full | An Explicit Form of Signum Function |
| title_fullStr | An Explicit Form of Signum Function |
| title_full_unstemmed | An Explicit Form of Signum Function |
| title_short | An Explicit Form of Signum Function |
| title_sort | explicit form of signum function |
| topic | signum function analytical expression tangent function irrational quantity integer part of real variable |
| url | https://www.mdpi.com/2227-7390/12/20/3246 |
| work_keys_str_mv | AT johnvenetis anexplicitformofsignumfunction AT johnvenetis explicitformofsignumfunction |