We conjecture that splines of degree n can interpolate points on a smooth curve in R m with order of contact k ? 1 = n ? 1 + b(n ? 1)=(m ? 1)c at every n-th knot. Moreover, this Geometric Hermite Interpolant (GHI) has the optimal approximation order k + 1. We give a proof of this conjecture for planar quadratic spline curves and describe a simple construction of curvature continuous quadratic s...

Let $K$ be a field of prime characteristic $p$, $n>4 $ an integer, $f(x)$ irreducible polynomial over degree $n$, whose Galois group is either the full symmetric $S_n$ or alternating $A_n$. $l$ odd different from $Z[\zeta_l]$ ring integers in $l$th cyclotomic field, $C_{f,l}:y^l=f(x)$ corresponding superelliptic curve and $J(C_{f,l})$ its jacobian. We prove that all endomorphisms coincides with...

The Lie module of the group algebra FSn of the symmetric group is known to be not projective if and only if the characteristic p of F divides n. We show that in this case its nonprojective summands belong to the principal block of FSn. Let V be a vector space of dimension m over F , and let L(V ) be the n-th homogeneous part of the free Lie algebra on V ; this is a polynomial representation of ...

We study mappings obtained as s-periodic reductions of the lattice Korteweg-De Vries equation. For small s ∈ N we establish upper bounds on the growth of the degree of the numerator of their iterates. These upper bounds appear to be exact. Moreover, we conjecture that for s1, s2 co-prime the growth is ∼ (2s1s2)−1n2, except when s1 + s2 = 4 where the growth is linear ∼ n. Also, we conjecture the...

Let R = ⊕ n≥0 Rn be a Noetherian homogeneous ring with onedimensional local base ring (R0,m0). Let q0 ⊆ R0 be an m0-primary ideal, let M be a finitely generated graded R-module and let i ∈ N0. Let Hi R+ (M) denote the i-th local cohomology module of M with respect to the irrelevant ideal R+ := ⊕ n>0 Rn of R. We show that the first Hilbert-Samuel coefficient e1 ( q0, Hi R+ (M)n ) of the n-th gra...

“!Iyper-reduiidaiiI” robots have a very large or anfinile degree of k inemat ic redundancy. Thas paper zntrodaces a n e w generalized resolved rate technique for soli) I 11 g h ype rredun da n t m a n apulat or inverse kzne m a t i c ~ i i s i i r y a ‘backbone curve. ’ Thas method as applicahlr e v e n zn cases w h e n explzczt representataon of the hrickbone curve intransac geometry cannot be...

In the p resen t p a p e r we d e m o n s tra te th a t the c o n fo rm a tio n a l s ta te o f th e b ifu n c tio n a l enzym e r ib u lo se -1,5 -b isp h o sp h ate carb o x y lase /o x y g en ase is d iffe ren t in th e to b ac co m u ta n t S u /su w hen co m p ared to the w ild type to b acco o r sp inach . T he c o n fo rm a tio n a l s ta te o f th e to b acco m u ­ ta n t enzym e is ch ...

Cryptographic Boolean functions must be complex to satisfy Shannon’s principle of confusion. But the cryptographic viewpoint on complexity is not the same as in circuit complexity. The two main criteria evaluating the cryptographic complexity of Boolean functions on F n 2 are the nonlinearity (and more generally the r-th order nonlinearity, for every positive r < n) and the algebraic degree. Tw...

This letter deals with the relationship between the total number of k-walks in a graph, and the sum of the k-th powers of its vertex degrees. In particular, it is shown that the sum of all k-walks is upper bounded by the sum of the k-th powers of the degrees. Let G = (V,E) be a connected graph on n vertices, V = {1, 2, . . . , n}, with adjacency matrix A. For any integer k ≥ 1, let a ij denote ...