On the bilinear and cubic forms of some symplectic connected sums

2012 ◽  
Vol 28 (9) ◽  
pp. 1809-1822
Author(s):  
Wei Wang
Keyword(s):  
Connected Sums ◽  
Cubic Forms

Quasipositive Links and Connected Sums

2020 ◽  
Vol 54 (1) ◽  
pp. 64-67
Author(s):  
S. Yu. Orevkov
Keyword(s):  
Connected Sums

Constructing symplectic manifolds

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Final Section ◽  
Symplectic Manifolds ◽  
Homotopy Equivalence ◽  
Codimension Two ◽  
Open Manifolds ◽  
Connected Sums ◽  
Symplectic Forms ◽  
Ambient Manifold ◽  
Blowing Up ◽  
Four Manifolds

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

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.

scholarly journals The four-genus of connected sums of torus knots

2017 ◽  
Vol 164 (3) ◽  
pp. 531-550
Author(s):  
CHARLES LIVINGSTON ◽  
CORNELIA A. VAN COTT
Keyword(s):  
Linear Combinations ◽  
Torus Knots ◽  
Connected Sums ◽  
The Third

AbstractWe study the four-genus of linear combinations of torus knots:g4(aT(p, q) #-bT(p′, q′)). Fixing positivep, q, p′, andq′, our focus is on the behavior of the four-genus as a function of positiveaandb. Three types of examples are presented: in the first, for allaandbthe four-genus is completely determined by the Tristram–Levine signature function; for the second, the recently defined Upsilon function of Ozsváth–Stipsicz–Szabó determines the four-genus for allaandb; for the third, a surprising interplay between signatures and Upsilon appears.

Copositive Symmetric Cubic Forms

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

Export Citation Format

Share Document