Let φ : Cn×Cn → C, φ((x1, ..., xn), (y1, ..., yn)) = (x1−y1)+ ...+ (xn − yn). We say that f : Rn → Cn preserves distance d ≥ 0 if for each x, y ∈ Rn φ(x, y) = d implies φ(f(x), f(y)) = d. We prove that if x, y ∈ Rn (n ≥ 3) and |x − y| = ( √ 2 + 2/n)k · (2/n)l (k, l are nonnegative integers) then there exists a finite set {x, y} ⊆ Sxy ⊆ Rn such that each unit-distance preserving mapping from Sxy...

Reaction of Mo(2)Cl(4)(dppm)(2) (dppm = bis(diphenylphosphino)methane) with 6 equiv of [n-Bu(4)N][CN] or [Et(4)N][CN] in dichloromethane yields [n-Bu(4)N](2)[Mo(2)(CN)(6)(dppm)(2)] (1) and [Et(4)N](2)[Mo(2)(CN)(6)(dppm)(2)] (2), respectively. The corresponding one- and two-electron oxidation products [n-Bu(4)N][Mo(2)(CN)(6)(dppm)(2)] (3) and Mo(2)(CN)(6)(dppm)(2) (4)were prepared by reactions o...

I mean... You know... We study certain analytic properties of the ordered and unordered configuration spaces Cn o (X) = {(q1, ..., qn) ∈ X | qi 6= qj ∀ i 6= j} and Cn(X) = {Q ⊂ X | #Q = n} of simply connected algebraic curves X = C and X = CP. For n ≥ 3 the braid group Bn(X) = π1(C(X)) of the curve X is non-abelian. A map F : Cn(X) → Ck(X) is called cyclic if the subgroup F∗(π1(C(X))) ⊂ π1(C(X)...

The rotational spectrum of the molecular negative ion CN(-) has been detected in the laboratory at high resolution. The four lowest transitions were observed in a low pressure glow discharge through C(2)N(2) and N(2). Conclusive evidence for the identification was provided by well-resolved nitrogen quadrupole hyperfine structure in the lowest rotational transition, and a measurable Doppler shif...

Let G = (V, E) be a graph. A subset D of V is called common neighbourhood dominating set (CN-dominating set) if for every v ∈ V −D there exists a vertex u ∈ D such that uv ∈ E(G) and |Γ(u, v)| > 1, where |Γ(u, v)| is the number of common neighbourhood between the vertices u and v. The minimum cardinality of such CN-dominating set denoted by γcn(G) and is called common neighbourhood domination n...

This paper describes strategies for automatic recognition of unknown variants of known words in a natural language processing system. The types of lexical variants which are detectable include in-flexional aberrations, ad hoc abbreviations and spelling/typographical errors. This technique is independent of any particular grammar or parsing formalism, and can be implemented as a lexical lookup r...

The necessary condition for eigenvalue values of a circulant matrix is studied It is then proved that the necessary condition also su ces the existence of a circulant matrix with the prescribed eigenvalue values Introduction An n n matrix C of the form C c c cn cn c c cn cn cn c cn c c cn c is called a circulant matrix As each row of a circulant matrix is just the previous row cycled forward on...