In this paper, we analyze the recurrence relations generalized from the Tower of Hanoi problem of the form T (n, α, β) = min1≤t≤n{αT (n− t, α, β)+β S(t, 3)}, where S(t, 3) = 2−1 is the optimal solution for the 3-peg Tower of Hanoi problem. It is shown that when α and β are natural numbers and α ≥ 2, the sequence of differences of T (n, α, β)’s, i.e., T (n, α, β) − T (n − 1, α, β), consists of n...

Abstract β-catenin-signaling promotes proliferation and survival in epithelial, neuronal, mesenchymal lineages, but is dispensable for B- T-cell development. β-catenin activation a common oncogenic driver throughout all types of cancer with the exception T-lymphoid malignancies. Unlike epithelial tissues, we found that T-cells consistently lack expression. Instead, both were highly sensitive to...

The current cascade form adaptive notch filters have two different ways to adjust its parameters. First, each section is adapted individually (AI). Second, all sections are adapted simultaneously (AS). As to the complexity of tmckingp sinusoids, the AI structure is linear with p but the AS structure is proportional to p 2. However, the AS structure has smaller bias in frequency estimates than t...

A bipartite graph G is called (α, β)-biregular if all vertices in one part of G have the degree α and all vertices in the other part have the degree β. An edge coloring of a graph G with colors 1, 2, 3, . . . , t is called an interval t-coloring if the colors received by the edges incident with each vertex of G are distinct and form an interval of integers and at least one edge of G is colored ...

Let T > 0, Ω ⊂ Rn (n ∈ N) be a given bounded domain, ∂Ω = Γ0 ∪ Γ1 (Γ1 = ∅) (where Γ0 is the interior boundary and Γ1 the outer boundary), Γ0 ∩ Γ1 =∅. For simplicity, we assume that Γ0,Γ1 ∈ C∞ and ω = ∅ is a given subdomain of Ω. Denote the characteristic function of ω by χω, and the unit outward normal vector of Ω by (n1, . . . ,nn). Put Q = Ω× (0,T), Qω = ω× (0,T), and Σ= ∂Ω× (0,T). Let ai j(x...

Abstract Introduction Metacognition, also-known-as subjective cognitive functioning, is an important predictor of decline and previous work has identified age, education, mental health symptoms as predictors. Sleep essential for optimal neurocognitive functioning; such, sleep may also play role in determining estimates metacognition. However, it currently unknown if associated with metacognitio...

Let T be a quadratic operator on a complex Hilbert space H. We show that T can be written as a product of two positive contractions if and only if T is of the form aI ⊕ bI ⊕ ( aI P 0 bI ) on H1 ⊕H2 ⊕ (H3 ⊕H3) for some a, b ∈ [0, 1] and strictly positive operator P with ‖P‖ ≤ | √ a− √ b| √ (1− a)(1− b). Also, we give a necessary condition for a bounded linear operator T with operator matrix ( T1...