Fermat’s well-known factorization algorithm is based on finding a representation of natural numbers $N$ as the difference squares. In 1895, Lawrence generalized this idea and applied it to multiples $kN$ original number. A systematic approach choose suitable values for $k$ was introduced by Lehman in 1974, which resulted first deterministic considerably faster than trial division. paper, we c...

We consider the totally real cyclic quintic fields Kn = Q(θn), generated by a root θn of the polynomial fn(x) = x 5 + nx − (2n + 6n + 10n + 10)x + (n + 5n + 11n + 15n + 5)x + (n + 4n + 10n + 10)x + 1. Assuming that m = n4 + 5n3 + 15n2 + 25n + 25 is square free, we compute explicitly an integral basis and a set of fundamental units of Kn and prove that Kn has a power integral basis only for n = ...

The present study was undertaken to investigate the effects of specific inhibitors of calmodulin-dependent protein kinase II (CamKII) on macroscopic voltage-dependent K(+) current (K(V)) recorded from rabbit portal vein smooth muscle cells. Inhibition of L-type Ca(2+) current facilitation by 1 microM KN-62, a blocker of CamKII, was first demonstrated and provided evidence for functional CamKII ...

The photophysics and photochemistry of kynurenine (KN) covalently bound to the amino acids lysine, cysteine, and histidine, the antioxidant glutathione, and the protein lysozyme have been studied by optical spectroscopy with femto- and nanosecond time resolution. The fluorescence quantum yield of the adducts of KN to amino acids is approximately 2 times higher than that of the free KN in soluti...

An associahedral set is a combinatorial object generated by Stasheff associahedra {Kn} and equipped with appropriate face and degeneracy operators. Associahedral sets are similar in many ways to simplicial or cubical sets. In this paper we give a formal definition of an associahedral set, discuss some naturally occurring examples and construct an explicit geometric diagonal ∆ : C∗(Kn) −→ C∗(Kn)...

Lower extremity injuries are a frequent outcome of automotive accidents. While the lower extremity injury criterion is based on fracture of bone, most injuries are of less severity. Recent studies suggest microscopic, occult fractures that have been shown to be precursors of gross bone fractures, may occur in the kneecap (patella) for impacts with rigid and deformable interfaces due to excessiv...

We write K or Kd for the set of convex bodies in Rd, that is, compact convex sets with nonempty interior in Rd. Assume K ∈ K and x1, . . . , xn are random, independent points chosen according to the uniform distribution in K. The convex hull of these points, to be denoted by Kn, is called a random polytope inscribed in K. Thus Kn = [x1, . . . , xn] where [S] stands for the convex hull of the se...

Computational modeling via the finite element method is an important tool used in injury biomechanics, and validation is required to give confidence in a model’s results. In the validation of the Global Human Body Models Consortium (GHBMC) mid-sized male model (M50), frontal and lateral validation was performed. This study presents a subset of that work, focusing on lateral impacts in full body...

For each positive integer n ≥ 2, there is a well-known regular orientable Hamiltonian embedding of Kn,n, and this generates a regular face 2-colourable triangular embedding of Kn,n,n. In the case n ≡ 0 (mod 8), and only in this case, there is a second regular orientable Hamiltonian embedding of Kn,n. The current paper presents an analysis of the face 2-colourable triangular embedding of Kn,n,n ...