Ví dụ về việc sử dụng Class numbers trong Tiếng anh và bản dịch của chúng sang Tiếng việt
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Gauss had to compute class numbers by hand.
Pressure-temperature ratings of valves are designated by class numbers.
The study of class numbers goes at least as far back as Carl Friedrich Gauss in the early 19th century.
That's interesting because it tells you this way in which class numbers are behaving unexpectedly.
Class numbers are limited, and students may need to pay a small charge for some activities.
Today mathematicians are actively engaged in the study of“class numbers” of number systems.
The fact that class numbers are not distributed randomly suggests something interesting is going on beneath the surface.
Together they formulated the Cohen-Lenstra heuristics, which are a series ofpredictions about how frequently particular kinds of class numbers should appear.
It was suggested we write the class numbers on the bags, but for some reason there was a lot of opposition and it was denied…”.
By the time Cohen and Lenstra made their predictions,computers made it possible to rapidly calculate class numbers for billions of different number rings.
We had bigger class numbers than ever before, and our school culture and employee morale were at an all-time low.
If you start to examine the group structure and its symmetries,then“suddenly it gives you what the distribution of class numbers should be on the nose,” said Bhargava.
For example, the heuristics predict that 43 percent of class numbers are divisible by 3 in situations where you're adjoining square roots of negative numbers. .
The methods Bhargava and his collaborators used have proved useful for bounding thenumber of solutions to a specific class of polynomial equation called elliptic curves, which is consistent with the way that class numbers seem to be situated at the intersection of many different mathematical fields.
In order to understand why class numbers are distributed as they are, mathematicians need to study the structure of the class groups that give rise to the class numbers.
Among his contributions, Gauss conjectured that there are infinitely many positive square roots that can be adjoined to the whole numbers without losing unique factorization-a proof of which remains the most sought-after result in class numbers(and is rumored to have frustrated Kurt Gödel enough to make him give up number theory for logic).
On their face, you would expect class numbers to be randomly distributed- that class number 5 occurs with the same frequency as class number 6, or that half of all class numbers are even.
Today mathematicians are circling in on the structure that underlies class numbers and inching closer to establishing the truth about long-conjectured values.
Today, research on class numbers remains inspired by Gauss, but much of it takes place in a context established in the late 1970s by the mathematicians Henri Cohen, emeritus professor of mathematics at the University of Bordeaux, and Hendrik Lenstra, who recently retired from Leiden University in the Netherlands.
And, while there's a long way to go before this happens,progress on class numbers could end up redeeming the original purpose of the number rings they describe.
For D fundamental this is the class number h(D).
When mathematicians are confronted with a class number, they want to know the structure of the underlying group it represents.
Each table needs to have a primary key, or unique field identifier,like Student ID, or Class number.
It is known that within Eastsea Academy, the smaller the class number, the more prestigious class. .
The number of different classes of ideals you need to add to a number ring in order torestore unique factorization is the ring's“class number.”.
These papers introduce Dirichlet series and determine, among other things,the formula for the class number for quadratic forms.
The senior class numbered 63, with 249 cadets listed in the yearbook, plus 29 in the college.
The high school senior class numbered 51, with 277 cadets listed in the yearbook, plus 34 in the college program.
The senior class numbered 26, with 192 cadets listed in the yearbook, including 13 coeds and 12 male cadet day students.
The senior class numbered 20, with 153 cadets listed in the yearbook, including 18 coeds, plus 46 students in grades 1-6 in a non-military elementary school.