Diclib.com
Λεξικό ChatGPT

Αναζήτηση λεξικού Προσαρμοσμένες λύσεις

Εισάγετε μια λέξη ή φράση σε οποιαδήποτε γλώσσα 👆

Γλώσσα:

Μετάφραση και ανάλυση λέξεων από την τεχνητή νοημοσύνη ChatGPT

Σε αυτήν τη σελίδα μπορείτε να λάβετε μια λεπτομερή ανάλυση μιας λέξης ή μιας φράσης, η οποία δημιουργήθηκε χρησιμοποιώντας το ChatGPT, την καλύτερη τεχνολογία τεχνητής νοημοσύνης μέχρι σήμερα:

πώς χρησιμοποιείται η λέξη
συχνότητα χρήσης
χρησιμοποιείται πιο συχνά στον προφορικό ή γραπτό λόγο
επιλογές μετάφρασης λέξεων
παραδείγματα χρήσης (πολλές φράσεις με μετάφραση)
ετυμολογία

Τι (ποιος) είναι Gauss sums - ορισμός

SUM

Gauss sums; Gaussian sum

Gauss sum

In algebraic number theory, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typically

https://en.wikipedia.org/wiki/Gauss_sum

Gauss notation

NOTATION FOR MATHEMATICAL KNOTS

Gauss code; Extended Gauss code; Extended Gauss notation; Gauss word; Gauss diagram

Gauss notation (also known as a Gauss code or Gauss word) is a notation for mathematical knots. It is created by enumerating and classifying the crossings of an embedding of the knot in a plane.

https://en.wikipedia.org/wiki/Gauss_notation

Carl Friedrich Gauss

GERMAN MATHEMATICIAN AND PHYSICIST (1777–1855)

Johann Carl Friedrich Gauss; Karl Gauss; Carl Frederich Gauss; Karl Friedrich Gauss; Carl Gauss; C. F. Gauss; Carl F. Gauss; Carl Friedrich Gauß; Johann Friedrich Karl Gauss; C.F. Gauss; Carl friedrich gauss; Carl Friederich Gauss; C. F. Gauß; Guass; CF Gauss; Karl Friedrich Gauß; Carl Freidrich Gauss; Johann Carl Friedrich Gauß; Carl Gauß; Friedrich gauss; Gauss; Johann Karl Friedrich Gauss; Carolus Fridericus Gauss; Princeps mathematicorum; Religious views of Carl Friedrich Gauss; Gauß, Johann Carl Friedrich; Carl Friedrich Gausz

<person> A German mathematician (1777 - 1855), one of all time greatest. Gauss discovered the method of least squares and Gaussian elimination. Gauss was something of a child prodigy; the most commonly told story relates that when he was 10 his teacher, wanting a rest, told his class to add up all the numbers from 1 to 100. Gauss did it in seconds, having noticed that 1+...+100 = 100+...+1 = (101+...+101)/2. He did important work in almost every area of mathematics. Such eclecticism is probably impossible today, since further progress in most areas of mathematics requires much hard background study. Some idea of the range of his work can be obtained by noting the many mathematical terms with "Gauss" in their names. E.g. Gaussian elimination (linear algebra); Gaussian primes (number theory); Gaussian distribution (statistics); Gauss [unit] (electromagnetism); Gaussian curvature (differential geometry); Gaussian quadrature (numerical analysis); Gauss-Bonnet formula (differential geometry); {Gauss's identity} (hypergeometric functions); Gauss sums ({number theory}). His favourite area of mathematics was number theory. He conjectured the Prime Number Theorem, pioneered the {theory of quadratic forms}, proved the {quadratic reciprocity theorem}, and much more. He was "the first mathematician to use complex numbers in a really confident and scientific way" (Hardy & Wright, chapter 12). He nearly went into architecture rather than mathematics; what decided him on mathematics was his proof, at age 18, of the startling theorem that a regular N-sided polygon can be constructed with ruler and compasses if and only if N is a power of 2 times a product of distinct Fermat primes. (1995-04-10)

Βικιπαίδεια

Gauss sum

In algebraic number theory, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typically

G(\chi ):=G(\chi ,\psi )=\sum \chi (r)\cdot \psi (r)

where the sum is over elements r of some finite commutative ring R, ψ is a group homomorphism of the additive group R⁺ into the unit circle, and χ is a group homomorphism of the unit group R^× into the unit circle, extended to non-unit r, where it takes the value 0. Gauss sums are the analogues for finite fields of the Gamma function.

Such sums are ubiquitous in number theory. They occur, for example, in the functional equations of Dirichlet L-functions, where for a Dirichlet character χ the equation relating L(s, χ) and L(1 − s, χ) (where χ is the complex conjugate of χ) involves a factor

{\frac {G(\chi )}{|G(\chi )|}}.

https://en.wikipedia.org/wiki/Gauss sum