Results 221 to 230 of about 599,891 (278)

The detection of algebraic auditory structures emerges with self-supervised learning. [PDF]

PLoS Comput Biol
Orhan P, Boubenec Y, King JR.
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Logarithmic kinetics and bundling in random packings of elongated 3D physical links. [PDF]

Proc Natl Acad Sci U S A
Bonamassa I, Ráth B, Pósfai M, Abért M, Keliger D, Szegedy B, Kertész J, Lovász L, Barabási AL.   +8 more
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Pixel-Level and DNA-Level Image Encryption Method Based on Five-Dimensional Hyperchaotic System. [PDF]

Entropy (Basel)
Zhou M, Li X, Du W, Li J, Wei Z.
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Applications of newly defined diamond Pythagorean fuzzy CODAS method via multi-criteria decision-making problems. [PDF]

PLoS One
Khan MB, Cortez MV, Bin-Mohsin B, Ciurdariu L, Zamri N.   +4 more
europepmc   +1 more source

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ON ALGEBRAIC INDEPENDENCE OF ALGEBRAIC POWERS OF ALGEBRAIC NUMBERS

Mathematics of the USSR-Sbornik, 1985
This paper contains a complete proof of the following theorem. Let \(\alpha\neq 0,1\) be algebraic, let \(\beta\) be algebraic of degree \(d\geq 2\), and let t be the transcendence degree over \({\mathbb{Q}}\) of the field generated by the numbers (*) \(\alpha^{\beta},...,\alpha^{\beta^{d- 1}}\).
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Algebra and Algebraic Number Theory

1992
The 19th century was an age of deep qualitative transformations and, at the same time, of great discoveries in all areas of mathematics, including algebra. The transformation of algebra was fundamental in nature. Between the beginning and the end of the last century, or rather between the beginning of the last century and the twenties of this century ...
I. G. Bashmakova, A. N. Rudakov
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Algebraic numbers

1998
Abstract Many important numbers, such as ../2 and i, are solutions of polynomial equations. Such numbers are said to be algebraic, and we shall study their basic theory in this chapter. Algebraic numbers also occur frequently in the following context: We start with a polynomial f(X) over Q and we wish to study the solutions of the ...
A W Chatters, C R Hajarnavis
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Random Algebraic Numbers

Journal of Mathematical Sciences
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Realizing Algebraic Number Fields

1983
In the paper [13], the authors studied the problem of realizing rational division algebras in a special way. Let D be a division algebra that is finite dimensional over the rational field Q. If p is a prime, we say that D is p-realizable when there is a p-local torsion free abelian group A whose rank is the dimension of D over Q, such that D is ...
R. S. Pierce, C. I. Vinsonhaler
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