and Applied Analysis 3 Lemma 2.5 see 6 . Let y ∈ C 0, 1 and 1 < α 2, the unique solution of D 0 u t y t 0, 0 < t < 1, u 0 0, u 1 au ξ , 2.5

Full-overlap U+U collisions provide significantly larger initial energy densities at comparable spatial deformation, and significantly larger deformation and volume at comparable energy density, than semi-central Au+Au collisions. We show quantitatively that this provides a long lever arm for studying the hydrodynamic behavior of elliptic flow in much larger and denser collision systems and the...

Supertree methods construct trees on a set of taxa (species) combining many smaller trees on the overlapping subsets of the entire set of taxa. A 'quartet' is an unrooted tree over 4 taxa, hence the quartet-based supertree methods combine many 4-taxon unrooted trees into a single and coherent tree over the complete set of taxa. Quartet-based phylogeny reconstruction methods have been receiving ...

A signi cant problem in phylogeny is to reconstruct a semilabelled binary tree from few valid quartet splits of it. It is well-known that every semilabelled binary tree is determined by its set of all valid quartet splits. Here we strengthen this result by showing that its local (i.e. small diameter) quartet splits infer by a dyadic inference rule all valid quartet splits, and hence determine t...

Let Ay = f , A is a linear operator in a Hilbert space H, y ⊥ N(A) := {u : Au = 0}, R(A) := {h : h = Au, u ∈ D(A)} is not closed, ‖fδ − f‖ ≤ δ. Given fδ, one wants to construct uδ such that limδ→0 ‖uδ − y‖ = 0. Two versions of discrepancy principles for the DSM (dynamical systems method) for finding the stopping time and calculating the stable solution uδ to the original equation Ay = f are for...

1 Dot product of R The inner product or dot product of R is a function 〈 , 〉 defined by 〈u,v〉 = a1b1 + a2b2 + · · ·+ anbn for u = [a1, a2, . . . , an] , v = [b1, b2, . . . , bn] ∈ R. The inner product 〈 , 〉 satisfies the following properties: (1) Linearity: 〈au + bv,w〉 = a〈u,w〉+ b〈v,w〉. (2) Symmetric Property: 〈u,v〉 = 〈v,u〉. (3) Positive Definite Property: For any u ∈ V , 〈u,u〉 ≥ 0; and 〈u,u〉 =...

The spectrum of a square matrix A, denoted by σ(A) is the set of all eigenvalues of A. The spectral radius of A, denoted by ρ(A) is defined as: ρ(A) = max{|λ| : λ ∈ σ(A)} An eigenvalue of A that is larger in absolute value than any other eigenvalue is called the dominant eigenvalue; a corresponding eigenvector is called a dominant eigenvector. The most commonly encountered vector norm (often si...

Template-assembled synthetic G-quartet (TASQ) has been reported recently as a G-quadruplex ligand interacting with DNA according to an unprecedented, nature-inspired 'like likes like' approach, based on the association between two G-quartets, one being native (quadruplex) and the other one artificial (ligand). Herein, a novel TASQ-based ligand is designed, synthesized and its quadruplex-recogni...