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Exempel på hur man kan använda MODULI i en mening

• For larger results, an old method, still in common use, consists of using several small moduli that are pairwise coprime, and applying the Chinese remainder theorem for recovering the result modulo the product of the moduli.
• The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of shtukas.
• Thus, the quotient of the upper half-plane by the action of the modular group is the so-called moduli space of elliptic curves: a space whose points describe isomorphism classes of elliptic curves.
• At Harvard, Zariski's students included Shreeram Abhyankar, Heisuke Hironaka, David Mumford, Michael Artin and Steven Kleiman—thus spanning the main areas of advance in singularity theory, moduli theory and cohomology in the next generation.
• In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects.
• One motivation was to construct moduli spaces in algebraic geometry as quotients of schemes parametrizing marked objects.
• Degenerate conics, as with degenerate algebraic varieties generally, arise as limits of non-degenerate conics, and are important in compactification of moduli spaces of curves.
• In joint work with George Lusztig, Deligne applied étale cohomology to construct representations of finite groups of Lie type; with Michael Rapoport, Deligne worked on the moduli spaces from the 'fine' arithmetic point of view, with application to modular forms.
• Density functional theory (DFT) provides reliable methods for determining several forms of elastic moduli that characterise distinct features of a material's reaction to mechanical stresses.
• In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles.
• Counting constants, with n = 2g + 2, the collection of n points subject to the action of the automorphisms of the projective line has (2g + 2) − 3 degrees of freedom, which is less than 3g − 3, the number of moduli of a curve of genus g, unless g is 2.
• The set of complex structures on a given orientable surface, modulo biholomorphic equivalence, itself forms a complex algebraic variety called a moduli space, the structure of which remains an area of active research.
• One expects, intuitively, that deformation theory of the first order should equate the Zariski tangent space with a moduli space.
• In general, these possess large moduli spaces of vacua which are not related by any symmetry, for example, the masses of the various excitations may differ at various points on the moduli space.
• Originally, they were introduced by Alexander Grothendieck to keep track of automorphisms on moduli spaces, a technique which allows for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth.
• These two moduli problems parametrize the same objects, but the stacky version remembers automorphisms of vector bundles.
• In this section we mainly deal with moduli of continuity that are concave, or subadditive, or uniformly continuous, or sublinear.
• A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli.
• In collaboration with his advisor Yuri Manin, he constructed the moduli space of Yang–Mills instantons, a result that was proved independently by Michael Atiyah and Nigel Hitchin.
• It is also known, by a result of Osgood, Phillips, and Sarnak that the moduli space of Riemann surfaces of a given genus does not admit a continuous isospectral flow through any point, and is compact in the Fréchet–Schwartz topology.

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