Two infrared absorption bands attributed to substitutional boron-phosphorus pairs in silicon are observed. The bands are close to the single, isolated boron band and all show approximately the same frequency shift with change in boron isotope. The pair bands occur near 599.7 and 629 cm−1 for 11B and 622.9 and ∼655 cm−1 for 10B. The results are compared with the theory of Elliott and Pfeuty. The number of pair bands, their isotope shift, and their proximity to the isolated B band are in agreement with theory. The Δν ∼ 30 cm−1 is an order of magnitude larger than predicted by the isotopic model indicating changes in force constants.
In this paper, we deal with magmas the simplest algebras with a single binary operation. The main result of our research is algorithms for generating chain of finite magmas based on the self-similarity principle of its Cayley tables. In this way the cardinality of a magmas domain is twice as large as the previous one for each magma in the chain, and its Cayley table has a block-like structure. As an example, we consider a cyclic semigroup of binary operations generated by a finite magmas operation with a low-cardinality domain, and a modify the Diffie-Hellman-Merkle key exchange protocol for this case.
Algebras of finitary relations naturally generalize the algebra of binary relations with the left composition. In this paper, we consider some properties of such algebras. It is well
known that we can study the hypergraphs as finitary relations. In this way the results can be applied to graph and hypergraph theory, automatons and artificial intelligence.
The theory of ordered structures like a (lattice) ordered semigroups is applied to graphs and automatons as well as to coding, programming and artificial intelligence. In this paper an algebraic structure on an underlying set of binary relations is considered. The structure includes the operations of Boolean algebra, inverse and composition. It is defined a dual semigroup to the binary relations ordered semigroup, and then the general properties of dual operations are studied.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.