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An Analytical Study of Diophantine Equations of Pythagorean Form: Causal Inferences on Hypothesized Relations between Quadratic and Non-quadratic Triples [PDF]
Athens Journal of EducationIn XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus’ “Arithmetica”, Pierre de Fermat stated that Diophantine equations of the Pythagorean form, x^n+y^n=z^n, have no integer solutions for n>2, and (x,y,z)>0.
Carmelo R. Cartiere
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Fast Stabiliser Simulation with Quadratic Form Expansions [PDF]
Quantum, 2022 This paper builds on the idea of simulating stabiliser circuits through transformations of {quadratic form expansions}. This is a representation of a quantum state which specifies a formula for the expansion in the standard basis, describing real and ...
Niel de Beaudrap, Steven Herbert
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The birational composition of arbitrary quadratic form with binary quadratic form
Журнал Белорусского государственного университета: Математика, информатика, 2022 Let f(X) and g(Y) be nondegenerate quadratic forms of dimensions m and n respectively over a field K, charK ≠ 2. Herein, the problem of the birational composition of f(X) and g(Y) is considered, namely, the condition is established when the product f(X)g(
Alexandr A. Bondarenko
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Mathematics, 2021 In this paper, we study estimates for quadratic forms of the type xTA−mx, m∈N, for symmetric matrices. We derive a general approach for estimating this type of quadratic form and we present some upper bounds for the corresponding absolute error ...
Marilena Mitrouli +3 more
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Real Quadratic-Form-Based Graph Pooling for Graph Neural Networks
Machine Learning and Knowledge Extraction, 2022 Graph neural networks (GNNs) have developed rapidly in recent years because they can work over non-Euclidean data and possess promising prediction power in many real-word applications.
Youfa Liu, Guo Chen
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Transactions of the American Mathematical Society, 1995 The results of Boyce for random Sturm-Liouville problems are generalized to random quadratic forms. Order relationships are proved between the means of eigenvalues of a random quadratic form and the eigenvalues of an associated mean quadratic form. Finite-dimensional and infinite-dimensional examples that show these are the best possible results are ...
Gregory, John, Hughes, H. R.
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On the stability of the difference analogue of the boundary value problem for a mixed type equation
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 This paper considers a difference problem for a mixed-type equation, to which a problem of integral geometry for a family of curves satisfying certain regularity conditions is reduced.
G.B. Bakanov, S.K. Meldebekova
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Supertropical quadratic forms I [PDF]
Journal of Pure and Applied Algebra, 2016 31 ...
Izhakian, Zur +2 more
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Stats, 2020 For a symmetric matrix B, we determine the class of Q such that Q t BQ is non-negative definite and apply it to panel data estimation and forecasting: the Hausman test for testing the endogeneity of the random effects in panel data models.
Bhimasankaram Pochiraju +3 more
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Wargaming with Quadratic Forms and Brauer Configuration Algebras
Mathematics, 2022 Recently, Postnikov introduced Bert Kostant’s game to build the maximal positive root associated with the quadratic form of a simple graph. This result, and some other games based on Cartan matrices, give a new version of Gabriel’s theorem regarding ...
Agustín Moreno Cañadas +2 more
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