(1) If $R$ is an affine algebra of dimension $d\geq 4$ over $\overline{\mathbb{F}}_{p}$ with $p>3$, then the group structure on ${\rm Um}_d(R)/{\rm E}_d(R)$ nice. (2) a commutative noetherian ring 2$ such that E}_{d+1}(R)$ acts transitively Um}_{d+1}(R),$ Um}_{d+1}(R[X])/{\rm E}_{d+1}(R[X])$

An antimagic labeling of a graph G is bijection f:E(G)?{1,…,|E(G)|} such that the weights w(x)=?y?xf(y) distinguish all vertices. A well-known conjecture Hartsfield and Ringel (1990) every connected other than K2 admits an labeling. For set distances D, D-antimagic f:V(G)?{1,…,|V(G)|} weight?(x)=?y?ND(x)f(y) distinct for each vertex x, where ND(x)={y?V(G)|d(x,y)?D} D-neigbourhood x. If ND(x)=r,...

CD spectra and difference-CD spectra of (a) two DNA X RNA hybrid duplexes (poly[r(A) X d(U)] and poly[r(A) X d(T)]) and (b) three hybrid triplexes (poly-[d(T) X r(A) X d(T)], poly[r(U) X d(A) X r(U)], and poly[r(T) X d(A) X r(T)]) were obtained and compared with CD spectra of six A X U- and A X T-containing duplex and triplex RNAs and DNAs. We found that the CD spectra of the homopolymer duplex...

Let Moldn,d be the moduli of rank d subalgebras Mn over Z. For x∈Moldn,d, let A(x)⊆Mn(k(x)) subalgebra corresponding to x, where k(x) is residue field x. In this article, we apply Hochschild cohomology Moldn,d. The dimension tangent space TMoldn,d/Z,x Z at x can calculated by H1(A(x),Mn(k(x))/A(x)). We show that H2(A(x),Mn(k(x))/A(x))=0 a sufficient condition for canonical morphism Moldn,d→Z be...

a l t h o u g h m o s t c o m p a n i e s s p e n d l e s s o n p r o d u c t d e s i g n, e x p e r i e n c e s h o w s t h a t, t h e s e c o m p a n i e s h a v e t o p a y h i g h e r c o s t s d u e t o p r o d u c t i o n p r o b l e m s o r l o s s o f m a r k e t. l i t e r a t u r e s t u d i e s s h o w t h a t t h e d e s i g n f o r s i x s i g m a i s a p o w e r f u l a p p r o a ...

s e l e c t i o n o f a p p r o p r i a t e g r o u n d m o t i o n i s a k e y e l e m e n t w i t h i n a n y s e i s m i c a s s e s s m e n t o f s t r u c t u r e s. m a n y m e t h o d o l o g i e s h a v e b e e n d e v e l o p e d i n o r d e r t o s e l e c t a n d s c a l e g r o u n d m o t i o n r e c o r d s f o r t h e p u r p o s e o f r e s p o n s e h i s t o r y a n a l y s i ...

Let R be an associative prime ring, U a Lie ideal such that u2 ∈ U for all u ∈ U . An additive function F : R→ R is called a generalized derivation if there exists a derivation d : R→ R such that F(xy)= F(x)y + xd(y) holds for all x, y ∈ R. In this paper, we prove that d = 0 or U ⊆ Z(R) if any one of the following conditions holds: (1) d(x) ◦F(y)= 0, (2) [d(x),F(y) = 0], (3) either d(x) ◦ F(y) ...