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).

The aim of this paper is to show that under some mild conditions a functional equation of multiplicative $(alpha,beta)$-derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner $(alpha,beta)$-derivation.

a unital $c^*$ -- algebra $mathcal a,$ endowed withthe lie product $[x,y]=xy- yx$ on $mathcal a,$ is called a lie$c^*$ -- algebra. let $mathcal a$ be a lie $c^*$ -- algebra and$g,h:mathcal a to mathcal a$ be $bbb c$ -- linear mappings. a$bbb c$ -- linear mapping $f:mathcal a to mathcal a$ is calleda lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

We investigate the problem of nding a computable witness for the exis-tential quantiier in a formula of the classical rst-order predicate logic. The A-resolution calculus based on the program derivation algorithm A of C-L. Chang, R. C-T. Lee and R.Waldinger is used for nding a deenite substitution t for an existentially bound variable y in some formula F , such that F ft=yg is provable. The ter...

Detailed derivation of the MF and BP algorithms We show here detailed derivation of the new MF and BP algorithms. In our main paper, we present simplified derivation which needs an assumption that the number S i of mixtures is the same for all sites, i.e., S i = S for any i. In what follows, we present complete derivation of the two algorithms which do not require this assumption; several equat...

Let F be the underlying base field of characteristic p > 3 and denote by W and S the even parts of the finite-dimensional generalized Witt Lie superalgebra W and the special Lie superalgebra S, respectively. We first give the generator sets of the Lie algebras W and S. Using certain properties of the canonical tori of W and S, we then determine the derivation algebra of W and the derivation spa...

in this paper, we introduce the notion of derivation on krasner hyperrings as follows: the function d : r  r isa derivation on a krasner hyperring r if for all , , ry x  ) ( ) ( = ) ( y d x d y x d   andd (x  y) d (x)  y  x  d ( y). then, we investigate some fundamental properties of derivation on krasnerhyperings and prime krasner hyperrings. also, we introduce differential krasner hy...

The following question is studied and answered: Is it possible to stably approximate f if one knows: 1) f δ ∈ L ∞ (R) such that f − f δ < δ, and 2) f ∈ C ∞ (R), f + f ≤ c? Here f := sup x∈R |f (x)| and c > 0 is a given constant. By a stable approximation one means L δ f δ − f ≤ η(δ) → 0 as δ → 0. By L δ f δ one denotes an estimate of f. The basic result of this paper is the inequality for L δ f...

The aim of this paper is to summarize some motivations and results concerning generators of rings of constants of derivations, especially in the positive characteristic case. 1. Preliminaries. Let k be a field of characteristic p > 0. Denote by k[X] the polynomial algebra k[x1, . . . , xn] and by k(X) the field of rational functions k(x1, . . . , xn). A k-linear mapping d : k[X] → k[X] is calle...