Help


[permalink] [id link]
+
Page "Dedekind domain" ¶ 17
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

other and class
The other children in the class use this same coloring book and do a fairly good job with things their proper color.
The same restrictions apply after local sunset in the case of class 3, stations operating on regional channels, which after that time are required to operate under nighttime restrictions in order to protect each other.
With respect to other frequencies, these are designated as regional or local, and assigned for use by class 3, and class 4, stations, respectively, stations operating generally with lower power.
Therefore, under our longstanding allocation rules, on some of these channels no station other than the dominant ( class 1 ) -- A ) station is permitted to operate at night, so that the 1, -- A station can render service, interference free, wherever it can be received.
Additional class 2, assignments for daytime operation can be made without causing destructive interference to the class 1, stations or to each other, and by their operation provide additional service on these channels and additional local outlets for a large number of communities.
It might be pointed out that the integrating function of religion, for good or ill, has often supported or been identified with other groupings -- political, nationality, language, class, racial, sociability, even economic.
Also, although only a few of the students were intimately acquainted with each other in the beginning, most reported that when the semester ended their dearest and closest campus friendships were with members of that class.
On the other hand, the women class members appeared to reach a far greater understanding than have women members in other sections that it is more natural for males as a group to view sex as sex rather than always associating it with love as most women seem to do.
There have been very few cases of explicit conflict of interest between the middle class and any other class in the field of educational policy.
Like the other policy-making groups, these are middle class in their educational attitudes, and they attempt to act in the general public interest, as they see it.
`` This very seldom happens in this class or in other cases, and of course all of these matters led to a volume and an expense of the record beyond what ordinarily would occur ''.
And while no one expects total democracy on the academic scene, the scholar will be particularly sensitive to a line between first and second class citizenship drawn on any basis other than that of academic rank or professional achievement.
Attending the life class was my idea -- or rather, Askington's idea, but I was ripe for it, and the other two wouldn't have gone if I hadn't talked them into it.
A common criticism has been that many social science scholars ( such as economists, sociologists, and psychologists ) in Western countries focus disproportionately on Western subjects, while anthropology focuses disproportionately on the " other "; this has changed over the last part of the twentieth century as anthropologists increasingly, also study Western subjects, particularly variation across class, region, or ethnicity within Western societies, and other social scientists increasingly take a global view of their fields.
Statements in this class include the statement that P = NP, the Riemann hypothesis, and many other unsolved mathematical problems.
On the other hand, other foundational descriptions of category theory are considerably stronger, and an identical category-theoretic statement of choice may be stronger than the standard formulation, à la class theory, mentioned above.
The school has been highly influential in setting the agenda for historiography in France and numerous other countries, especially regarding the use of social scientific methods by historians, emphasizing social rather than political or diplomatic themes, and for being generally hostile to the class analysis of Marxist historiography.
It contains 10, 000 words, and is arranged, like other works of its class, in metre, to aid the memory.
He argues that Kant's " aesthetic " merely represents an experience that is the product of an elevated class habitus and scholarly leisure as opposed to other possible and equally valid " aesthetic " experiences which lay outside Kant's narrow definition.

other and Dedekind
In his professorial doctoral dissertation, On the Concept of Number ( 1886 ) and in his Philosophy of Arithmetic ( 1891 ), Husserl sought, by employing Brentano's descriptive psychology, to define the natural numbers in a way that advanced the methods and techniques of Karl Weierstrass, Richard Dedekind, Georg Cantor, Gottlob Frege, and other contemporary mathematicians.
In other words, the number line where every real number is defined as a Dedekind cut of rationals is a complete continuum without any further gaps.
Dedekind's construction of the number line ensures that two crossing lines always have one point in common because each of them defines a Dedekind cut on the other.
It is more symmetrical to use the ( A, B ) notation for Dedekind cuts, but each of A and B does determine the other.
There are at least three other characterizations of Dedekind domains which are sometimes taken as the definition: see below.
On the other hand, the ring of integers in a number field is always a Dedekind domain.
The other part of the answer is provided by the multiplicative group of units of the Dedekind domain, since passage from principal ideals
The first three, due to Georg Cantor / Charles Méray, Richard Dedekind and Karl Weierstrass / Otto Stolz all occurred within a few years of each other.
Ricci-Curbastro also published important works in other fields, including a book on higher algebra and infinitesimal analysis, and papers on the theory of real numbers, an area in which he extended the research begun by Dedekind.
The Disquisitiones was the starting point for the work of other nineteenth century European mathematicians including Ernst Kummer, J. P. G. Lejeune Dirichlet and Richard Dedekind.
For instance, in the construction of the real numbers from Dedekind cuts of rational numbers, the rational number is identified with the set of all rational numbers less than, even though the two are obviously not the same thing ( as one is a rational number and the other is a set of rational numbers ).

other and rings
Another set of methods is the aromatization of cyclohexanes and other aliphatic rings: reagents are catalysts used in hydrogenation such as platinum, palladium and nickel ( reverse hydrogenation ), quinones and the elements sulfur and selenium.
Minsk has a digital metropolitan network ; waiting lists for telephones are long ; fixed line penetration is improving although rural areas continue to be undeserved ; intercity-Belarus has developed fibre-optic backbone system presently serving at least 13 major cities ( 1998 ); Belarus's fibre optics form synchronous digital hierarchy rings through other countries ' systems ; an inadequate analogue system remains operational.
The most common options are either a rear hub or multiple chain rings combined with multiple sprockets ( other combinations of options are possible but less common ).
Diamond films are being grown on valve rings, cutting tools, and other objects that benefit from diamond's hardness and exceedingly low wear rate.
On icy as opposed to rocky bodies, other morphological forms appear which may have central pits rather than central peaks, and at the largest sizes may contain very many concentric rings – Valhalla on Callisto is the type example of the latter.
Examples include cardboard cutouts, which can be used to make tassels, fringe, and many other items ; a pom-pom circle, used to make pom-poms ; a tape measure and a gauge measure, both used for measuring crocheted work and counting stitches ; a row counter ; and occasionally plastic rings, which are used for special projects.
The pyrrolidine rings keep out of each other ’ s way when the polypeptide chain assumes this extended helical form, which is much more open than the tightly coiled form of the alpha helix.
" Shime-daiko " ( 締め太鼓, tightened drum ), have heads sewn onto iron rings, which are then laced to each other around the drum body.
Examples are the product of sets ( see Cartesian product ), groups ( described below ), the product of rings and of other algebraic structures.
" In the early 20th century, the term " French fried " was being used in the sense of " deep-fried ", for other foods such as onion rings or chicken.
As with more conventional marriage ceremonies, couples often exchange rings during a handfasting, symbolizing their commitment to each other.
The collar is tightened against the end of the thread, while the rings are tightened against each other.
These pumps should be distinguished from other penis pumps ( supplied without compression rings ) which, rather than being used for temporary treatment of impotence, are claimed to increase penis length if used frequently, or vibrate as an aid to masturbation.
I mean by this that the other world is composed of a series of concentric rings, which as one penetrates deeper into the other world, grow larger.
Rings can fuse with other rings on an edge to give polycyclic compounds.
The most notable planetary rings known in the Solar System are those around Saturn, but the other three gas giants of the Solar System ( Jupiter, Uranus and Neptune ) also possess ring systems of their own.
A later study published in 2010 revealed that imaging of Rhea from the Cassini mission was inconsistent with the predicted properties of the rings, suggesting that some other mechanism is responsible for the magnetic effects that had led to the ring hypothesis.
However, in other rings, the ideals may be distinct from the ring elements, and certain properties of integers, when generalized to rings, attach more naturally to the ideals than to the elements of the ring.
Besides S < sub > 8 </ sub >, several other rings are known.
* At some weddings the couple may declare that each is sanctified to the other, and / or repeat other vows, and exchange rings.
Ashley notes that it was once common for sailors ' wedding rings, where gold wire was wrought to incorporate the " true lovers " knot such that resultant ring would comprise two tori: each flexible to move about the other ; yet nevertheless inseparable.
To achieve these goals, Boehm adapted a system of axle-mounted keys with a series of " open rings " ( called brille, German for " eyeglasses ", as they resembled the type of eyeglass frames common during the 19th century ) that were fitted around other tone holes, such that the closure of one tone hole by a finger would also close a key placed over a second hole.

0.262 seconds.