The Fibonacci cube of dimension n, denoted as Γn, is the subgraph of n-cube Qn induced by vertices with no consecutive 1’s. We study the maximum number of disjoint subgraphs in Γn isomorphic to Qk, and denote this number by qk(n). We prove several recursive results for qk(n), in particular we prove that qk(n) = qk−1(n − 2) + qk(n − 3). We also prove a closed formula in which qk(n) is given in t...

Consider Dirichlet's problem in a plane domain SI with smooth boundary dSl. For the purpose of its approximate solution, an approximating domain 0 < It S 1, with polygonal boundary dilk is introduced where the segments of dük have length at most /;. A projection method introduced by Nitsche [6] is then applied on Qk to give an approximate solution in a finite-dimensional subspace of functions S...

We prove that if a subset of a d-dimensional vector space over a finite field with q elements has more than qd−1 elements, then it determines all the possible directions. We obtain a complete characterization if the size of the set is ≥ qd−1. If a set has more than qk elements, it determines a k-dimensional set of directions. We prove stronger results for sets that are sufficiently random. This...

Definition 2.1. Suppose p1, . . . , pk are polynomials in F[x] which are not all 0. Set I = 〈p1, . . . , pk〉. Let d denote the monic generator of I. We call d the greatest common divisor of the pi and write d = gcd(p1, . . . , pk). If d = 1, we say that the polynomials p1, . . . , pk is relatively prime. Note that, by definition, there exists polynomials q1, . . . , qk ∈ F[x] such that d = p1q1...

In mice, Quaking (Qk) is required for myelin formation; in humans, it has been associated with psychiatric disease. QK regulates the stability, subcellular localization, and alternative splicing of several myelin-related transcripts, yet little is known about how QK governs these activities. Here, we show that QK enhances Hnrnpa1 mRNA stability by binding a conserved 3' UTR sequence with high a...

Given a knot K in the 3-sphere, let QK be its fundamental quandle as introduced by D. Joyce. Its first homology group is easily seen to be H1(QK) ∼= Z. We prove that H2(QK) = 0 if and only if K is trivial, and H2(QK) ∼= Z whenever K is non-trivial. An analogous result holds for links, thus characterizing trivial components. More detailed information can be derived from the conjugation quandle: ...

Let φ be an analytic self-map of D and g∈H(D) . The boundedness and compactness of generalized composition operators

In this paper, by using the notions of ”not belonging” (∈) and ”non quasi-k-coincidence” (qk) of a fuzzy point with a fuzzy set, we define the notion of (∈,∈ ∨ qk)-fuzzy subgroups of a group which is a generalization of fuzzy subgroups and (∈,∈ ∨ q)-fuzzy subgroups. Aslo, we generalized the concept of ∈-level set, (∈ ∨ q)-level set and (∈,∈ ∨ q)level set by using ”not belonging” (∈) and ”non qu...

This paper characterizes the boundedness and compactness of the generalized composition operator (C φf)(z) = ∫ z 0 f ′(φ(ξ))g(ξ)dξ from Bloch type spaces to QK type spaces.

In this paper, we give some characterizations of intraregular semigroups by the properties of their (∈,∈ ∨qk)-fuzzy right ideals, (∈,∈ ∨qk)-fuzzy left ideals, (∈,∈ ∨qk)-fuzzy interior ideals, (∈,∈ ∨qk)fuzzy bi-ideals and (∈,∈ ∨qk)-fuzzy generalized bi-ideals. 2010 AMS Classification: 03E72, 20M12