scholarly journals Parallel and on-line addition in negative base and some complex number systems

1996 ◽  
pp. 175-182 ◽  
Author(s):  
Christiane Frougny
Keyword(s):  
Complex Number ◽  
Number Systems ◽  
On Line ◽  
Negative Base

Negative Base Number Systems

1957 ◽  
Vol EC-6 (2) ◽  
pp. 123-123 ◽  
Author(s):  
Louis B. Wadel
Keyword(s):  
Base Number ◽  
Number Systems ◽  
Negative Base

scholarly journals A Note on Resultants of Equations in a Cyclic Number System

1932 ◽  
Vol 3 (1) ◽  
pp. 26-29
Author(s):  
R. Wilson
Keyword(s):  
Division Algebra ◽  
Complex Number ◽  
Number System ◽  
Number Systems ◽  
Image Position

§ 1. Introduction. Little is known concerning the theory of resultants of equations other than in the complex number system. The cyclic number systems provide a simple example which is not a division algebra. In such a system with n units er. any number y ≡ y0 + y1e1 + y2e2 + … + yn−1en−1 has coefficients yr drawn from a field, and the units satisfy the product law:

Preliminaries

2021 ◽  
pp. 1-24
Author(s):  
Adel N. Boules
Keyword(s):  
Complex Number ◽  
Continuous Functions ◽  
Uniform Continuity ◽  
Weierstrass Theorem ◽  
Mathematical Concepts ◽  
Number Systems ◽  
Set Operations ◽  
Basic Set ◽  
Bounded Sets ◽  
Complex Number Field

In addition to giving a very brief reminder of set notation and basic set operations, this chapter provides a brief refresher on basic mathematical concepts. The natural, rational and real number systems are taken for granted. However, it does develop at length the Cauchy criterion and its equivalence to the completeness of the real line, and the Bolzano-Weierstrass theorem, as well as the complex number field, including its completeness. Embryonic manifestations of completeness and compactness can be seen in this chapter. Examples include the nested interval theorem and the uniform continuity of continuous functions on compact intervals, and the proof of the Heine-Borel theorem in chapter 4 is squarely based on the Bolzano-Weierstrass property of bounded sets.

The binding of fork head proteins to DNA is partly determined by cooperation of bases

2006 ◽  
Vol 1 (4) ◽  
pp. 594-608
Author(s):  
Václav Mach
Keyword(s):  
Transcription Factors ◽  
Dna Binding ◽  
Binding Sites ◽  
In Silico ◽  
Dna Recognition ◽  
Simple Algorithm ◽  
Fork Head ◽  
Statistical Algorithm ◽  
On Line ◽  
Negative Base

AbstractOur previous study revealed that DNA recognition by the insect Fork head transcription factors depends on specific combinations of neighboring bases, a phenomenon called the base cooperation effect. This study presents a simple algorithm designed for in silico investigation of the base cooperation effect. The algorithm measures and evaluates observed and expected frequencies of various base combinations within a set of aligned binding sites. Consequently, statistically significant differences between the observed and expected frequencies are interpreted as evidence of either positive or negative base cooperation effect. Our current results suggest that the base cooperation affects DNA binding of the vertebrate members of the Fork head family, similarly to their insect homologies.The statistical algorithm used in this study is available on line (http://blast.entu.cas.cz/bias/index.htm).

scholarly journals Arithmetics in number systems with a negative base

2011 ◽  
Vol 412 (8-10) ◽  
pp. 835-845 ◽  
Author(s):  
Z. Masáková ◽  
E. Pelantová ◽  
T. Vávra
Keyword(s):  
Number Systems ◽  
Negative Base
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