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...

Background Peripheral neuropathy (PN) is often associated with specific diseases; however, research suggests that idiopathic PN is prevalent in older adult populations [1]. Foot ulceration is the traditional medical concern with PN, but people with PN may also have disproportionately more falls [2]. Therefore, our objective was to evaluate associations between PN and prospectively-ascertained f...

The l-component (edge) connectivity of a graph G, denoted by cκl(G) (cλl(G)), is the minimum number vertices (edges) whose removal from G results in disconnected with at least l components. pancake Pn popular underlying topology for distributed systems. In paper, we determine cκl(Pn) and cλl(Pn) 3 ≤ 5.

A reduction relation m −→ is defined by the following reduction rules. This relation computes the simple substitution φ that can be applied to a pattern to match a particular value, or returns the undefined substitution ⊥ if no such simple substitution exists. {(p1, p2) 7→ (v1, v2)} m −→ {p1 7→ v1} ⊗ {p2 7→ v2} {K (p1, . . . , pn) 7→ K (v1, . . . , vn)} m −→ {p1 7→ v1} ⊗ . . .⊗ {pn 7→ vn} {K (p...

In this paper we give a recursive formula for the sequence of primes {pn} and apply it to find a necessary and sufficient condition in order that a prime number pn+1 is equal to pn+2. Applications of previous results are given to evaluate the probability that pn+1 is of the form pn + 2; moreover we prove that the limit of this probability is equal to zero as n goes to ∞. Finally, for every prim...

BACKGROUND To determine the association of insulin resistance, metabolic syndrome (MetS) with peripheral neuropathy (PN). METHODS This cross-sectional study consisted of 2035 subjects in Shanghai who were classified as with MetS and without MetS. The new International Diabetes Federation (IDF) criterion was used to define MetS. HOMA-IR was applied to evaluate insulin resistance. All subjects ...

Synthesis and characterisation of new permethylpentalene (Pn*) zirconium bis(amido) Pn*Zr cyclopentadienyl mono(amido) complexes their reactivity with carbon dioxide.

Given a monotone property P of graphs, write Pn for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in Pn and the functions |Pn|. We also examine the measure eP (n), the maximum number of edges in a graph of Pn.

Albumin, prealbumin, retinol-binding protein, and transferrin were all measured on the sera of 39 cancer patients before and during parenteral nutrition (PN). At the outset of PN, the concentrations of all of these proteins were low, as compared to reference values, and thus quantitatively reflected the degree of malnutrition. Prealbumin proved to be the most interesting parameter during PN: (1...