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词汇 example_english_number-theory
释义

Examples of number theory


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What are the implications of seasonality for index numbertheory?
Decimal reckoning would not only reconcile coinage to simple numbertheory, but also would make the exercise of accounting apparent to the plainest inhabitant.
Traditional bilateral index numbertheory implicitly assumes that variations in the price of a commodity within a period can be ignored.
It is related to numbertheory, algebra and category theory, and it has applications to information retrieval systems, automatic code generation, data transformations and coding.
Another interesting aspect of numbertheory was that it was absolutely useless-pure mathematics at its purest.
It admits many other simple descriptions and serves as a typical example for various objects, in combinatorics, numbertheory, symbolic dynamics and geometry.
The methods used in the proof are those of analytic numbertheory.
Typical examples of such systems come from numbertheory and admit non-hyperbolic periodic orbits.
We made the choice of set theory terminology since some parts of this paper could have some interest in group theory and numbertheory.
The distribution of quadratic residues and non-residues is an old problem in numbertheory.
These applications include results in additive numbertheory and in the study of graph colouring problems.
Let us recall some facts from algebraic numbertheory.
We then give applications to numbertheory and to the statistics of cuspidal windings.
And, like numbertheory, knot theory was totally, totally useless.
Our approach, originating in probabilistic numbertheory, requires information on the generating functions only in the convergence disc and rather weak smoothness on the circumference.
All of these examples relate to numbertheory.
The method of proof of both theorems follows the lines of the error term result for the prime number theorem in analytic numbertheory.
By using elementary methods from numbertheory, we can show the following.
Various index number formulas are justified from the viewpoint of the economic approach to index numbertheory by making separability assumptions on consumers' intertemporal preferences.
Index numbertheory is something that not many people today pay attention to.
But if hyperreals are introduced and, as a result, standard numbertheory and standard decision-theory no longer suffice, the practicality of the wager is compromised.
Quasicrystals, tilings and algebraic numbertheory: some preliminary connections.
With the invention of ideal algebraic numbers in algebraic numbertheory, points at infinity, and imaginary points and curves in projective geometry, this idea took on central importance.
A decoding problem in dynamics and in numbertheory.
Many such examples come from numbertheory.
This example is to illustrate the relationship between the notion of ramification on an algebraic stack to the classical notion of ramification in algebraic numbertheory.
What is fascinating about numbertheory is that it uses very deep methods to attack problems that are in some sense very "natural" and also simple to formulate.
Topological dynamics and combinatorial numbertheory.
Ultrafilters and combinatorial numbertheory.
He made fundamental contributions to combinatorics, numbertheory, numerical analysis and probability theory.
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Constants arise in many different areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, numbertheory and calculus.
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He is a specialist of model theory, numbertheory and algebraic geometry.
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Since this is, however, a numbertheory, such interpretations are useful, but not strict.
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Algebraic numbertheory studies various number rings that generalize the set of integers.
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His primary academic interests are combinatorics on words, formal languages, automata theory, and algorithmic numbertheory.
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He further advanced modular arithmetic, greatly simplifying manipulations in numbertheory.
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However, analytic numbertheory has had many conjectures supported by large amounts of numerical evidence that turn out to be false.
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His research interests include abstract algebra, numbertheory, group schemes, and the history of mathematics.
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There he was using computers to advance numbertheory.
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He also made major investigations in the areas of gamma functions, modular forms, divergent series, hypergeometric series and prime numbertheory.
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Peano arithmetic is adequate for a good deal of numbertheory, including the notion of prime number.
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Other discrete aspects of numbertheory include geometry of numbers.
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There is no rigorous and widely accepted definition of the notion of elementary proof in numbertheory.
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His other interests included algebraic numbertheory, mathematical economics and geometry of numbers.
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Algebraic numbertheory is also used in the study of arithmetic hyperbolic 3-manifolds.
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His main fields of study were algebra, numbertheory and combinatorics.
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Dirichlet series play a variety of important roles in analytic numbertheory.
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He also did work in numbertheory and found a method of constructing magic squares.
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After contributions from other fields such as numbertheory and geometry, the group notion was generalized and firmly established around 1870.
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It is specialized for numbertheory, primality testing, factoring, and large integers (up to 2600 digits).
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His work in pure mathematics included working with monodiffric functions, fractional order mappings, graph theory, analytic functions, and numbertheory.
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Class groups of algebraic number fields were among the earliest examples of factor groups, of much interest in numbertheory.
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Arithmetic is an elementary part of numbertheory.
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Using this notation, several results in transcendental numbertheory become much easier to state.
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His primary interests include numbertheory and arithmetic algebraic geometry, particularly zeta functions over finite fields.
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In the main, he worked on numbertheory and infinite series.
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Applications of "p" -adic analysis have mainly been in numbertheory, where it has a significant role in diophantine geometry and diophantine approximation.
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He wrote down nearly no proofs in numbertheory; he had no models in the area.
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The theory of modular forms (and, more generally, automorphic forms) also occupies an increasingly central place in the toolbox of analytic numbertheory.
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Algebraic differential equations are widely used in computer algebra and numbertheory.
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She has made contributions to dynamics and its connections to numbertheory.
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This unique factorization property is the basis on which much of numbertheory is built.
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The deeper properties of these numbers are studied in numbertheory.
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He also utilised his time in archaeological studies, and contributed in the field of statistics and numbertheory.
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His research focuses on algebraic graph theory, as well as analytic numbertheory.
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The requirement of computability reflects on and contrasts with the approach used in analytic numbertheory to prove the results.
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Numbertheory is branch of pure mathematics devoted primarily to the study of the integers.
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He created and developed the geometry of numbers and used geometrical methods to solve problems in numbertheory, mathematical physics, and the theory of relativity.
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The applications are mostly in numbertheory, particularly to adelic algebraic groups.
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He made notable contributions to numbertheory and algebraic geometry.
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Most of the functions normally studied in numbertheory are primitive recursive.
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Moreno has over sixty publications under his name, including two books, on topics dealing with algebra and numbertheory.
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The same objects can be studied using methods from algebraic geometry, module theory, analytic numbertheory, differential geometry, operator theory, algebraic combinatorics and topology.
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Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and numbertheory.
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Oscillatory integral operators often appear in many fields of mathematics (analysis, partial differential equations, integral geometry, numbertheory) and in physics.
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It spans a broad range of mathematical fields: numbertheory, geometry, analysis, combinatorics and graph theory.
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They play an important role in numbertheory and topology.
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His research interests include time series analysis, stochastic global optimisation, probabilistic methods in search and numbertheory.
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These names reflect a basic concept in numbertheory, the 2-order of an integer: how many times the integer can be divided by 2.
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So from the notation for the "divides" relation of numbertheory, one may denote the set of factors of an integer by.
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It has researchers working in many areas of mathematics, particularly in algebra and numbertheory.
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He made some famous contributions to modern analytic numbertheory.
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Complex analysis, in particular the theory of conformal mappings, has many physical applications and is also used throughout analytic numbertheory.
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Examples come from fractional ideals in algebraic numbertheory, so that the definition captures that theory.
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Additive numbertheory has close ties to combinatorial numbertheory and the geometry of numbers.
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They also play an important role in numbertheory, algebra, and representation theory.
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His works on model theory of various structures related to algebra, geometry and numbertheory have been widely influential.
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This has had applications to model theory of finite and asymptotic structures, simple theories and topics in analytic numbertheory.
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Abelian varieties defined over algebraic number fields are a special case, which is important also from the viewpoint of numbertheory.
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A proof or disproof of this would have far-reaching implications in numbertheory, especially for the distribution of prime numbers.
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These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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