Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions by Motlatsi Molati, Chaudry Masood Khalique

“…We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.…”
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Invariants de Witt des involutions de bas degré en caractéristique 2 by Tignol, Jean-Pierre

“…The same construction on central simple algebras of degree $4$ associates to every unitary involution a $2$-fold and a $4$-fold Pfister quadratic forms, and to every orthogonal involution a $1$-fold and a $3$-fold quasi-Pfister forms. …”
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Quadratic Killing tensors on symmetric spaces which are not generated by Killing vector fields by Matveev, Vladimir S., Nikolayevsky, Yuri

“…We answer this question in the negative by constructing explicit examples of quadratic Killing tensor fields which are not quadratic forms in the Killing vector fields on the quaternionic projective spaces $\mathbb{H} P^n, \, n \ge 3$, and on the Cayley projective plane $\mathbb{O} P^2$.…”
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The Baker–Schmidt problem for dual approximation and some classes of manifolds by Hussain, Mumtaz, Schleischitz, Johannes

“…Concretely, for codimension two or three, we provide examples of manifolds where the dependent variables can be chosen as quadratic forms. Our method requires the manifold to have even dimension at least the minimum of four and half the dimension of the ambient space. …”
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Bregman divergences for physically informed discrepancy measures for learning and computation in thermomechanics by Andrieux, Stéphane

“…This study is motivated by the need of “discrepancy measures” between physically constrained fields that are used both in traditional algorithms, analysis methods and data driven modelling or applications as well.We give also a characterization of symmetrical Bregman divergences through their generating functions which can only be quadratic forms. Some properties of the Bregman divergence and the introduced concept of Bregman Gap between couples of dual quantities are given, and some existing errors in thermomechanics are recovered. …”
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RETRACTED: On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem by Andrea Ossicini

“…In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fermat’s extraordinary equation. …”
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SYNTHESIS OF DESIGN PARAMETERS OF MULTI-PURPOSE DYNAMIC SYSTEMS by Oleksandr Kutsenko, Mykhailo Alforov, Andrii Alforov

“…The solution is based on the method of simultaneously reducing two positive-definite quadratic forms to diagonal form. Analytical results have been obtained that make it possible to calculate the mathematical expectation of the criterion under the normal multidimensional distribution law of the vector of random initial perturbations. …”
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