Results 11 to 20 of about 117,201 (178)

Composition of binary quadratic forms

Journal of Number Theory, 1982
AbstractComposition of binary quadratic forms over an arbitrary commutative base ring is shown to be closely related to homomorphisms (and in particular isomorphisms) of the corresponding even Clifford algebras.
openaire   +4 more sources

Petrographic structures and Hardy – Weinberg equilibrium

Записки Горного института, 2020
The article is devoted to the most narrative side of modern petrography – the definition, classification and nomenclature of petrographic structures. We suggest a mathematical formalism using the theory of quadratic forms (with a promising extension to ...
Yury L. VOYTEKHOVSKY, Alena A. ZAKHAROVA
doaj   +1 more source

On some extensions of Gauss’ work and applications

Open Mathematics, 2020
Let K be an imaginary quadratic field of discriminant dK{d}_{K} with ring of integers OK{{\mathcal{O}}}_{K}, and let τK{\tau }_{K} be an element of the complex upper half plane so that OK=[τK,1]{{\mathcal{O}}}_{K}={[}{\tau }_{K},1].
Jung Ho Yun, Koo Ja Kyung, Shin Dong Hwa
doaj   +1 more source

Drug repurposing based on a quantum-inspired method versus classical fingerprinting uncovers potential antivirals against SARS-CoV-2.

PLoS Computational Biology, 2022
The COVID-19 pandemic has accelerated the need to identify new antiviral therapeutics at pace, including through drug repurposing. We employed a Quadratic Unbounded Binary Optimization (QUBO) model, to search for compounds similar to Remdesivir, the ...
Jose M Jimenez-Guardeño, Ana Maria Ortega-Prieto, Borja Menendez Moreno, Thomas J A Maguire, Adam Richardson, Juan Ignacio Diaz-Hernandez, Javier Diez Perez, Mark Zuckerman, Albert Mercadal Playa, Carlos Cordero Deline, Michael H Malim, Rocio Teresa Martinez-Nunez   +11 more
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Binary quadratic forms with the same value set [PDF]

Indagationes Mathematicae
Étienne Fouvry, Peter Koymans
exaly   +5 more sources

Binary quadratic forms as dessins [PDF]

Journal de théorie des nombres de Bordeaux, 2017
We show that the class of every primitive indefinite binary quadratic form is naturally represented by an infinite graph (named çark) with a unique cycle embedded on a conformal annulus. This cycle is called the spine of the çark. Every choice of an edge of a fixed çark specifies an indefinite binary quadratic form in the class represented by the çark.
Uludag, A. Muhammed, Zeytin, Ayberk, Durmus, Merve   +2 more
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Rings and ideals parametrized by binary n-ic forms [PDF]

, 2010
The association of algebraic objects to forms has had many important applications in number theory. Gauss, over two centuries ago, studied quadratic rings and ideals associated to binary quadratic forms, and found that ideal classes of quadratic rings ...
Wood, Melanie Matchett
core   +1 more source

Completely p-primitive binary quadratic forms [PDF]

Journal of Number Theory, 2018
Let $f(x,y)=ax^2+bxy+cy^2$ be a binary quadratic form with integer coefficients. For a prime $p$ not dividing the discriminant of $f$, we say $f$ is completely $p$-primitive if for any non-zero integer $N$, the diophantine equation $f(x,y)=N$ has always an integer solution $(x,y)=(m,n)$ with $(m,n,p)=1$ whenever it has an integer solution.
Oh, Byeong-Kweon, Yu, Hoseog
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Arithmetic progressions in binary quadratic forms and norm forms [PDF]

, 2019
We prove an upper bound for the length of an arithmetic progression represented by an irreducible integral binary quadratic form or a norm form, which depends only on the form and the progression's common difference.
Elsholtz, Christian, Frei, Christopher
core   +2 more sources

Hilbert polynomials of the algebras of $SL_ 2$-invariants

Karpatsʹkì Matematičnì Publìkacìï, 2018
We consider one of the fundamental problems of classical invariant theory, the research of Hilbert polynomials for an algebra of invariants of Lie group $SL_2$.
N.B. Ilash
doaj   +1 more source