Denote by {Fn} and {Ln} the Fibonacci numbers and Lucas numbers, respectively. Let Fn = Fn × Ln and Ln = Fn + Ln. Denote by {Pn} and {Qn} the Pell numbers and Pell-Lucas numbers, respectively. Let Pn = Pn × Qn and Qn = Pn + Qn. In this paper, we give some determinants and permanent representations of Pn, Qn, Fn and Ln. Also, complex factorization formulas for those numbers are presented. Key–Wo...

Baumslag conjectured in the 1970s that the automorphism tower of a finitely generated free group (free nilpotent group) must be very short. Dyer and Formanek [9] justified the conjecture concerning finitely generated free groups in the “sharpest sense” by proving that the automorphism group Aut(Fn) of a non-abelian free group Fn of finite rank n is complete. Recall that a group G is said to be ...

Fibronectin (FN) is a multifunctional glycoprotein involved in cell-matrix interactions. It exhibits a complex pattern of forms differing in respect to aminoacid and oligosaccharide composition. In this study we examined glycobiochemical and functional properties of the FN in benign prostatic hyperplasia (BPH) and prostatic cancer (PCa), attempting to resolve disease-related differences. Two BP...

Keratinocytes freshly isolated from unwounded skin could not attach and spread on fibronectin (FN)-coated culture dishes and could not bind and phagocytose FN-coated beads. These adhesive functions were activated, however, in keratinocytes that were isolated from healing wounds. Moreover, adhesiveness of basal keratinocytes to FN substrata was activated during epidermal cell or explant culture....

This paper studies the homotopy type of the configuration spaces Fn(X) by introducing the idea of configuration spaces of maps. For every map f : X → Y , the configuration space Fn(f) is the space of configurations in X that have distinct images in Y . We show that the natural maps Fn(X) ← Fn(f) → Fn(Y ) are homotopy equivalences when f is a proper cell-like map between d-manifolds. We also sho...

Proof. I It is straightforward to prove that D is both a normed vector space and an algebra over C. In order to prove that D is a Banach algebra, we check the followings: • The norm ‖ · ‖d onD is complete. Indeed, let { fn }∞ n=1 ⊂ D be a sequence such that ∑ n ‖ fn ‖d < ∞. Then both ∑ n fn and ∑ f ′ n converges uniformly in C([0, 1]) and hence f (x) = ∞ ∑ n=1 fn (x) = ∞ ∑ n=1 ( fn (0) + ∫ x 0 ...

Fibronectin (FN) and serum amyloid P component (SAP) markedly enhance phagocytosis mediated by the C3b and C3bi receptors of cultured human monocytes but not of granulocytes. (The C3b and C3bi receptors of granulocytes can be activated by treatment of these phagocytes with PMA.) Activation of monocyte C3 receptors by FN is developmentally regulated: Freshly explanted monocytes respond to FN wit...

Adhesion and residence-time-dependent desorption of two Staphylococcus aureus strains with and without fibronectin (Fn) binding proteins (FnBPs) on Fn-coated glass were compared under flow conditions. To obtain a better understanding of the role of Fn-FnBP binding, the adsorption enthalpies of Fn with staphylococcal cell surfaces were determined using isothermal titration calorimetry (ITC). Int...