Cubic forms in 10 variables

1984 ◽  
pp. 104-108
Author(s):  
D. R. Heath-Brown
Keyword(s):  
Cubic Forms

scholarly journals Hydride-based antiperovskites with soft anionic sublattices as fast alkali ionic conductors

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Shenghan Gao ◽  
Thibault Broux ◽  
Susumu Fujii ◽  
Cédric Tassel ◽  
Kentaro Yamamoto ◽  
...  
Keyword(s):  
Experimental Studies ◽  
Ionic Conductivities ◽  
Cubic Phase ◽  
Ionic Conductors ◽  
Large Size ◽  
Migration Barriers ◽  
Soft Phonon Mode ◽  
Aliovalent Substitution ◽  
Cubic Forms ◽  
The Ideal

AbstractMost solid-state materials are composed of p-block anions, only in recent years the introduction of hydride anions (1s2) in oxides (e.g., SrVO2H, BaTi(O,H)3) has allowed the discovery of various interesting properties. Here we exploit the large polarizability of hydride anions (H–) together with chalcogenide (Ch2–) anions to construct a family of antiperovskites with soft anionic sublattices. The M3HCh antiperovskites (M = Li, Na) adopt the ideal cubic structure except orthorhombic Na3HS, despite the large variation in sizes of M and Ch. This unconventional robustness of cubic phase mainly originates from the large size-flexibility of the H– anion. Theoretical and experimental studies reveal low migration barriers for Li+/Na+ transport and high ionic conductivity, possibly promoted by a soft phonon mode associated with the rotational motion of HM6 octahedra in their cubic forms. Aliovalent substitution to create vacancies has further enhanced ionic conductivities of this series of antiperovskites, resulting in Na2.9H(Se0.9I0.1) achieving a high conductivity of ~1 × 10–4 S/cm (100 °C).

scholarly journals Simultaneous Additive Equations: Repeated and Differing Degrees

2017 ◽  
Vol 69 (02) ◽  
pp. 258-283 ◽  
Author(s):  
Julia Brandes ◽  
Scott T. Parsell
Keyword(s):  
Hybrid Systems ◽  
Existence Of Solutions ◽  
Square Root ◽  
Multiple Forms ◽  
Quadratic Equations ◽  
Asymptotic Formulae ◽  
Cubic Forms

Abstract We obtain bounds for the number of variables required to establish Hasse principles, both for the existence of solutions and for asymptotic formulæ, for systems of additive equations containing forms of differing degree but also multiple forms of like degree. Apart from the very general estimates of Schmidt and Browning–Heath–Brown, which give weak results when specialized to the diagonal situation, this is the first result on such “hybrid” systems. We also obtain specialized results for systems of quadratic and cubic forms, where we are able to take advantage of some of the stronger methods available in that setting. In particular, we achieve essentially square root cancellation for systems consisting of one cubic and r quadratic equations.

Copositive Symmetric Cubic Forms

2005 ◽  
Vol 112 (5) ◽  
pp. 462-466 ◽  
Author(s):  
Mowaffaq Hajja
Keyword(s):  
Cubic Forms

scholarly journals Cubic forms on Riemannian surfaces

1978 ◽  
Vol 103 (2) ◽  
pp. 181-185
Author(s):  
Alois Švec
Keyword(s):  
Riemannian Surfaces ◽  
Cubic Forms

scholarly journals On cubic forms permitting composition

1959 ◽  
Vol 10 (6) ◽  
pp. 917-917 ◽  
Author(s):  
R. D. Schafer
Keyword(s):  
Cubic Forms

Ternary cubic forms and Etale algebras

2009 ◽  
Vol 55 (1) ◽  
pp. 139-156 ◽  
Author(s):  
Melanie Raczek ◽  
Jean-Pierre Tignol
Keyword(s):  
Cubic Forms

scholarly journals Orbital L-functions for the Space of Binary Cubic Forms

2013 ◽  
Vol 65 (6) ◽  
pp. 1320-1383 ◽  
Author(s):  
Takashi Taniguchi ◽  
Frank Thorne
Keyword(s):  
Functional Equations ◽  
Companion Paper ◽  
Intrinsic Interest ◽  
Counting Functions ◽  
Cubic Fields ◽  
Cubic Forms

AbstractWe introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from their intrinsic interest, the results from this paper are used to prove the existence of secondary terms in counting functions for cubic fields. This is worked out in a companion paper.

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