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An Explicit Form of Ramp Function

AppliedMath, 2023
In this paper, an analytical exact form of the ramp function is presented. This seminal function constitutes a fundamental concept of the digital signal processing theory and is also involved in many other areas of applied sciences and engineering.
John Constantine Venetis
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Exploring the impact of explicit and implicit urban form on carbon emissions: Evidence from Beijing, China

Ecological Indicators, 2023
Urban form (UF) is an important factor influencing carbon emissions (CE), and it is necessary to fully understand the complex relationship between different UF and CE.
Yang Zheng, Linlin Cheng, Yifang Wang, Junqi Wang   +3 more
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Development of Mathematical Models in Explicit Form for Design and Analysis of Axial Flux Permanent Magnet Synchronous Machines

Applied Sciences, 2020
This article proposes a methodology for the design of double-sided coreless axial flux permanent magnet synchronous machines, which is based on a developed model for calculating the axial component of the magnetic flux density in the middle of the ...
Franjo Pranjić, Peter Virtič
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An Explicit Form of Signum Function

Mathematics
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 ...
John Venetis
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Integer composition, connection Appell constants and Bell polynomials

Journal of Numerical Analysis and Approximation Theory, 2021
We introduce an explicit form of the connection coefficients for Appell polynomial sequences via Toeplitz-Hessenberg matrix determinants. Generalizing, we give an explicit form of the connection coefficients for arbitrary   polynomial sequences and ...
Nataliia Luno
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Properties of Multivariable Hermite Polynomials in Correlation with Frobenius–Genocchi Polynomials

Mathematics, 2023
The evolution of a physical system occurs through a set of variables, and the problems can be treated based on an approach employing multivariable Hermite polynomials.
Shahid Ahmad Wani, Georgia Irina Oros, Ali M. Mahnashi, Waleed Hamali   +3 more
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Certain Properties and Applications of Δ_h Hybrid Special Polynomials Associated with Appell Sequences

Fractal and Fractional, 2023
The development of certain aspects of special polynomials in line with the monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable. The study presented in this paper follows this line of research.
Rabab Alyusof, Shahid Ahmmad Wani
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Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials

Mathematics, 2023
A comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions.
Mohra Zayed, Shahid Ahmad Wani, Yamilet Quintana   +2 more
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An explicit form for Kerov’s character polynomials [PDF]

Transactions of the American Mathematical Society, 2007
Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that this polynomial has integer coefficients, and made various conjectures. Recently, Śniady has proved Biane’s conjectured explicit form for the first family of nontrivial terms in
Goulden, I. P., Rattan, A.
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Explicit Plancherel Formula for the Space of Symplectic Forms [PDF]

International Mathematics Research Notices, 2021
Abstract We provide a Plancherel decomposition for the space of symplectic bilinear forms of rank $2n$ over a local non-Archimedean field $F$ in terms of that of $\operatorname{GL}_n(F)$.
Lapid, Erez, Offen, Omer
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