Results 21 to 30 of about 71,240 (263)
Non-Homogeneous Cubic Equations [PDF]
Journal of the London Mathematical Society, 1964 Let \( \varphi(x) \) be a cubic polynomial in \(n\) variables with integral coefficients, and let \(C\) be the part of \(\varphi\) that is homogeneous of degree 3. Define the invariant \(h(C)\) as the codimension of the greatest rational linear space contained in the hypersurface \(C=0\); so that, for instance, \(h(C)=n\) if \(C=0\) has no rational ...
Davenport, H., Lewis, D. J.
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On the insolubility of one drawing problem II
Lietuvos Matematikos Rinkinys, 2016 It is shown in the article that, in general, it is not possible to draw a triangle using a compass and a straightedge given an angle and a bisector and a median drawn from the vertices of another different angles.
Jevgenijus Kirjackis +2 more
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On the stability of the Pexiderized cubic functional equation in multi-normed spaces [PDF]
Sahand Communications in Mathematical Analysis, 2018 In this paper, we investigate the Hyers-Ulam stability of the orthogonally cubic equation and Pexiderized cubic equation [f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),]in multi-normed spaces by the direct method and the fixed point method ...
Mahdi Nazarianpoor, Ghadir Sadeghi
doaj
Elementary theory of cubics and quartics
Lietuvos Matematikos Rinkinys, 2017 It is proved that cubic and quartic equations in real numbers can be solved elementarily, avoiding complex numbers and derivatives. Corresponding algorithms are presented.
Juozas Juvencijus Mačys
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, 2009 We consider the following Hamiltonian equation on the $L^2$ Hardy space on the circle, $$i\partial_tu=Π(|u|^2u) ,$$ where $Π$ is the Szegö projector. This equation can be seen as a toy model for totally non dispersive evolution equations. We display a Lax pair structure for this equation.
Gérard, Patrick, Grellier, Sandrine
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Publicationes Mathematicae Debrecen, 2009 To appear in the Publicationes Mathematicae ...
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Approximation of Mixed Euler-Lagrange σ-Cubic-Quartic Functional Equation in Felbin’s Type f-NLS
Journal of Function Spaces, 2021 In this research paper, the authors present a new mixed Euler-Lagrange σ-cubic-quartic functional equation. For this introduced mixed type functional equation, the authors obtain general solution and investigate the various stabilities related to the ...
John Michael Rassias +3 more
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A New Solution to a Cubic Diophantine Equation
Axioms, 2022 A positive integer, which can be written as the sum of two positive cubes in two different ways, is known as a “Ramanujan number”. The most famous example is 1729=103+93=123+13, which was identified by Ramanujan as the lowest such number.
John C. Butcher
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The cubic Pell equation $L$-function
Acta Arithmetica, 2023 For $d > 1$ a cubefree rational integer, we define an $L$-function (denoted $L_d(s)$) whose coefficients are derived from the cubic theta function for $\mathbb Q\left(\sqrt{-3}\right)$. The Dirichlet series defining $L_d(s)$ converges for $\text{Re}(s) > 1$, and its coefficients vanish except at values corresponding to integral solutions of $mx^3
Goldfeld, Dorian, Hinkle, Gerhardt
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Molecular characterization of covRS mutations in M1UK Streptococcus pyogenes
FEBS Open Bio, EarlyView.Group A Streptococcus (GAS) acquires covRS mutations driving a hypervirulent bacterial state, frequently associated with invasive disease‐like necrotizing fasciitis. We demonstrate that the newly emerged M1UK GAS lineage can also acquire these mutations.
Jarrad Pritchard +12 more
wiley +1 more source