3,927 research outputs found
The Octonions
The octonions are the largest of the four normed division algebras. While
somewhat neglected due to their nonassociativity, they stand at the crossroads
of many interesting fields of mathematics. Here we describe them and their
relation to Clifford algebras and spinors, Bott periodicity, projective and
Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also
touch upon their applications in quantum logic, special relativity and
supersymmetry.Comment: 56 pages LaTeX, 11 Postscript Figures, some small correction
Value Discount of Business Groups Surrounding the Asia Financial Crisis: Evidence from Korean Chaebols
Asian Financial Crisis, Business Group, Chaebol, Diversification, Firm Value
Dipole-Allowed Direct Band Gap Silicon Superlattices
Silicon is the most popular material used in electronic devices. However, its
poor optical properties owing to its indirect band gap nature limit its usage
in optoelectronic devices. Here we present the discovery of super-stable
pure-silicon superlattice structures that can serve as promising materials for
solar cell applications and can lead to the realization of pure Si-based
optoelectronic devices. The structures are almost identical to that of bulk Si
except that defective layers are intercalated in the diamond lattice. The
superlattices exhibit dipole-allowed direct band gaps as well as indirect band
gaps, providing ideal conditions for the investigation of a direct-to-indirect
band gap transition. The transition can be understood in terms of a novel
conduction band originating from defective layers, an overlap between the
valence- and conduction-band edge states at the interface layers, and zone
folding with quantum confinement effects on the conduction band of
non-defective bulk-like Si. The fact that almost all structural portions of the
superlattices originate from bulk Si warrants their stability and good lattice
matching with bulk Si. Through first-principles molecular dynamics simulations,
we confirmed their thermal stability and propose a possible method to
synthesize the defective layer through wafer bonding
P-union and P-intersection of neutrosophic cubic sets
Conditions for the P-intersection and P-intersection of falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic sets to be an falsity-external (resp. indeterminacy-external and truthexternal) neutrosophic cubic set are provided. Conditions for the Punion and the P-intersection of two truth-external (resp. indeterminacyexternal and falsity-external) neutrosophic cubic sets to be a truthinternal (resp. indeterminacy-internal and falsity-internal) neutrosophic cubic set are discussed
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