In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

In this paper a version of LFG will be developed, which has only one level of representation and is equivalent to the modified version of [2], presented in [3]. The structures of this monostratal version are f-structures, augmented by additional information about the derived symbols and their linear order. For these structures it is possible to define an adequate concept of direct derivability ...

We point out errors in the derivation of the periodicity of the interference structure of the Mie extinction curve, recently published in ABSORPTION AND SCATTERING OFLIGHTBY SMALL PARTICLES, by C. F. Bohren and D. R. Huffman (Wiley, New York, 1983).

We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case. PACS: 03.30.+p; 01.40.-d; 01.55.+b

-Several new results on binary ( d , k ) codes are given. First, a new derivation for the capacity of these codes based upon information theoretic principles is given. Based upon this result the spectrum of a ( d , k ) code is computed. Finally, the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the ( d , k ) constraint is ...

The purpose of this paper is to introduce the notion a generalized derivation which derivates prescribed family smooth vector-valued functions several variables. basic calculus rules are established and then result derived shows that if function $f$ satisfies an addition theorem whose determining operation derivable with respect additive $d$, itself $d$. As application approach, new proof gener...

1. The Michaelis constants for both isoenzymes for both substrates depend strongly on ionic concentration, being approximately proportional to phosphate concentration over considerable ranges. This is probably an effect of anions only. 2. In the absence of added salt, Km (2-oxoglutarate) (anionic isoenzyme) -is so small as to be .i.ndeterminate. 3. Km (L-aspartate) (anionic isoenzyme) passes th...

Let D be a division ring, T be a variable over D, σ be an endomorphism of D, δ be a σ-derivation on D and R = D[T ;σ, δ] the left skew polynomial ring over D. We show that the set (V alν(R), ) of σ-compatible real valuations which extend to R a fixed proper real valuation ν on D has a natural structure of parameterized complete non-metric tree, where is the partial order given by μ μ̃ if and onl...

Over a field IF of any characteristic, for a commutative associative algebra A with an identity element and for the polynomial algebra IF [D] of a commutative derivation subalgebra D of A, the associative and the Lie algebras of Weyl type on the same vector space A[D] = A ⊗ IF [D] are defined. It is proved that A[D], as a Lie algebra (modular its center) or as an associative algebra, is simple ...