On Transcendental Numbers: New Results and a Little History

被引：8

作者：

Marcus, Solomon ^{[1
,2
]}

Nichita, Florin F. ^{[1
]}

机构：

[1] Romanian Acad, Inst Math, 21 Calea Grivitei St, Bucharest 010702, Romania

[2] Romanian Acad, 125 Calea Victoriei St, Bucharest 010071, Romania

来源：

AXIOMS | 2018年 / 7卷 / 01期

关键词：

Euler's identity; Euler's relation; transcendental numbers; transcendental operations/functions; transcendence; Yang-Baxter equation; hyperbolic functions; logical implication;

D O I：

10.3390/axioms7010015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Bringing toghether mathematical and philosophical ideas related to transcendental numbers, this paper begins with a survey on transcendence and transcendental numbers, it then presents several properties of the transcendental numbers e and pi, and then it gives the proof of a new inequality for transcendental numbers. Also, in relationship with these topics, we study solutions to the Yang-Baxter equation from hyperbolic functions and from logical implication.

引用

页数：7

共 16 条

[1]

BREGER H, 1986, STUD LEIBNITIANA, V18, P112

[2] On evaluating ∫+∞-∞eax(x-2b)dx by contour integration round a parallelogram [J].

Desbrow, D .

AMERICAN MATHEMATICAL MONTHLY, 1998, 105 (08) :726-731

[3]

Dyson F., 2009, NOTICES AM MATH SOC, V56, P212

[4] YANG-BAXTER EQUATION, MAJORANA FERMIONS AND THREE BODY ENTANGLING STATES [J].

Ge, Mo-Lin ;

Yu, Li-Wei ;

Xue, Kang ;

Zhao, Qing .

INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2014, 28 (09)

[5] Hopf Algebra Symmetries of an Integrable Hamiltonian for Anyonic Pairing [J].

Links, Jon .

AXIOMS, 2012, 1 (02) :226-237

[6]

Marcus S., 2014, INT J COMMUN RES, V4, P60

[7]

Marcus S., 2014, CONV LIT, P17

[8]

Nichita F.F., 2017, J COALGEBRAS UNIFICA

[9]

Nichita F.F., 2011, TRANSDISCIPL J ENG S, V2011, P42

[10] On Transcendental Numbers [J].

Nichita, Florin F. .

AXIOMS, 2014, 3 (01) :64-69

← 1 2 →