The Number of Solutions of Cubic Equations over Q3

Saburov, Mansoor; Ahmad, Mohd Ali Khameini

doi:10.17576/jsm-2015-4405-18

Cited by 10 publications

(4 citation statements)

References 15 publications

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“…Furthermore, it is noteworthy that the solution to a depressed cubic formula is well known within diverse mathematical frameworks [38][39][40]:…”

Section: Mathematical Mass-spring Formulationmentioning

confidence: 99%

Polarization state conversion achieved by chiral mechanical metamaterial

Mangach,

Achaoui,

Kadic

et al. 2024

New J. Phys.

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Chiral metamaterials have paved the way for progress in wave propagation and polarization control. In particular, chiral elastic metamaterials attracted considerable scientific attention due to their distinctive properties such as acoustical activity and auxeticity. Such characteristics arise from additional degrees of freedom for tuning the embedded micro- and macro-rotations. Herein, we use 3D chiral mechanical metamaterials to realize the polarization state conversion functionnality. A structural design of a 3D chiral metamaterial capable to induce up to 90° rotation in the plane of polarization is presented. This feature enables a straightforward switch between the three polarization states existing within a solid material, namely, longitudinal state, shear horizontal state, and shear vertical state. Efficient conversion from longitudinal movement to transverse movement is demonstrated. A discrete mass-spring model is proposed for these 3D chiral structures that describes the conversion behaviors based on the corresponding elastic coefficients. The engineered chiral metamaterial polarization converter is a promising device for efficient momentum conservation conversions. This allows converting longitudinal waves into shear waves while preserving the initial stimulating wave characteristics.

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“…Furthermore, it is noteworthy that the solution to a depressed cubic formula is well known within diverse mathematical frameworks [38][39][40]:…”

Section: Mathematical Mass-spring Formulationmentioning

confidence: 99%

Polarization state conversion achieved by chiral mechanical metamaterial

Mangach,

Achaoui,

Kadic

et al. 2024

New J. Phys.

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“…In the paper (Saburov & Ahmad 2015 (in press) we study the number of solutions of the cubic equations over …”

Section: I4 (Ii) Letmentioning

confidence: 99%

Solvability of Cubic Equations over Q3

Saburov¹,

Ahmad²

2015

JSM

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“…The solvability criterion for quadratic equations over the p−adic field was provided in all classical p−adic analysis books. Recently, in the series of papers [14,15], [19]- [21], the solvability criterion and the number of roots of cubic equations over the p−adic field were studied. This paper is a continuation of previous studies and we are aiming to locally describe all roots of cubic equations over the p−adic field for p > 3.…”

Section: Introductionmentioning

confidence: 99%