Ideals, Valuations, and Divisors in Algebraic Extensions of Infinite Degree over ℚ

Author(s):  
Paulo Ribenboim
Keyword(s):  
2020 ◽  
Vol 10 (2) ◽  
pp. 85-90
Author(s):  
Al-Zgoul Mohammad ◽  
Attila Szilágyi

This paper shows the most common rotor systems which can be used to analyse a CNC turning center. Starting with the simplest rotor system representation (single-degree-offreedom) up to analysing multi-degree-of-freedom and infinite-degree-of-freedom rotor systems using the TMM (Transfer Matrix Method) when it comes to cases like multi desk rotors and Jeffcott-rotors.


1941 ◽  
Vol 14 (3) ◽  
pp. 628-640 ◽  
Author(s):  
E. H. Farmer

Abstract One of the consequences of the high-molecular character of rubber is the smallness of the effect on ultimate quantitative analysis of the presence of one or even several heteroatoms or groups in the long hydrocarbon chains. With rubber molecules possessing an average chain-length of about 4,500 isoprene units, the association of, say, ten nitrogen atoms wtih each chain would provide a nitrogen content of only about 0.0007 per cent, and the incorporation of about 0.005 per cent of ethereal oxygen in pure rubber hydrocarbon would be theoretically capable of providing sufficient linking material for an infinite degree of hetero-polymerization, or, if the oxygen were applied instead to produce the maximum possible degree of degradation, it would be capable of severing from one-quarter to one-third of the rubber chains. In view of these dimensions, and the fact that natural rubber normally contains difficultly removable hetero components, and is ready to take up additional amounts of oxygen, little progress can be made in the fundamental investigation of the complex molecules without a suitably accurate technique of chemical analysis, and this applies particularly to the determination of total oxygen and total nitrogen, and also to the determination of the six types of combined oxygen likely to be present in rubber, viz., hydroxylic, oxido-, ethereal, peroxidic, carbonyl and carboxylic. Unfortunately, great precision in estimation cannot be achieved without increasing greatly the rigour of the analytical technique, and perhaps it is not surprising that Midgley, Henne and Renoll's well-known high-precision method for determining carbon, hydrogen and, by difference, oxygen, still remains after five years the sole such chemical analytical method reported in the literature.


Studia Logica ◽  
1976 ◽  
Vol 35 (4) ◽  
pp. 447-451 ◽  
Author(s):  
Marek Tokarz
Keyword(s):  

Romansy 14 ◽  
2002 ◽  
pp. 507-515 ◽  
Author(s):  
Klaus Zimmermann ◽  
Igor Zeidis ◽  
Joachim Steigenberger

1963 ◽  
Vol 22 ◽  
pp. 33-56 ◽  
Author(s):  
Robert Steinberg

Our purpose here is to study the irreducible representations of semisimple algebraic groups of characteristic p 0, in particular the rational representations, and to determine all of the representations of corresponding finite simple groups. (Each algebraic group is assumed to be defined over a universal field which is algebraically closed and of infinite degree of transcendence over the prime field, and all of its representations are assumed to take place on vector spaces over this field.)


2002 ◽  
Vol 67 (2) ◽  
pp. 697-720 ◽  
Author(s):  
Denis R. Hirschfeldt

AbstractWe give some new examples of possible degree spectra of invariant relations on Δ20-categorical computable structures, which demonstrate that such spectra can be fairly complicated. On the other hand, we show that there are nontrivial restrictions on the sets of degrees that can be realized as degree spectra of such relations. In particular, we give a sufficient condition for a relation to have infinite degree spectrum that implies that every invariant computable relation on a Δ20-categorical computable structure is either intrinsically computable or has infinite degree spectrum. This condition also allows us to use the proof of a result of Moses [23] to establish the same result for computable relations on computable linear orderings.We also place our results in the context of the study of what types of degree-theoretic constructions can be carried out within the degree spectrum of a relation on a computable structure, given some restrictions on the relation or the structure. From this point of view we consider the cases of Δ20-categorical structures, linear orderings, and 1-decidable structures, in the last case using the proof of a result of Ash and Nerode [3] to extend results of Harizanov [14].


2005 ◽  
Vol 16 (06) ◽  
pp. 567-593
Author(s):  
T. M. GENDRON ◽  
A. VERJOVSKY

This paper concerns the description of holomorphic extensions of algebraic number fields. After expanding the notion of adele class group to number fields of infinite degree over ℚ, a hyperbolized adele class group [Formula: see text] is assigned to every number field K/ℚ. The projectivization of the Hardy space ℙ𝖧•[K] of graded-holomorphic functions on [Formula: see text] possesses two operations ⊕ and ⊗ giving it the structure of a nonlinear field extension of K. We show that the Galois theory of these nonlinear number fields coincides with their discrete counterparts in that 𝖦𝖺𝗅(ℙ𝖧•[K]/K) = 1 and 𝖦𝖺𝗅(ℙ𝖧•[L]/ℙ𝖧•[K]) ≅ 𝖦𝖺𝗅(L/K) if L/K is Galois. If K ab denotes the maximal abelian extension of K and 𝖢K is the idele class group, it is shown that there are embeddings of 𝖢K into 𝖦𝖺𝗅⊕(ℙ𝖧•[K ab ]/K) and 𝖦𝖺𝗅⊗(ℙ𝖧•[K ab ]/K), the "Galois groups" of automorphisms preserving ⊕ (respectively, ⊗) only.


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