For simplicity, we use the following convention: Y is a non empty set, P1, P2 are partitions of Y , A, B are subsets of Y , i is a natural number, x, y, x1, x2, z0 are sets, and X, V , d, t, S1, S2 are sets. The following proposition is true (1) If X ∈ P1 and V ∈ P1 and X ⊆ V, then X = V. Let us consider S1, S2. We introduce S1 ⋐ S2 and S2 ⋑ S1 as synonyms of S1 is finer than S2. We now state s...

We consider the question whether two queries to SAT are as powerful as one query. We show that if PNP[1] = PNP[2] then Locally either NP = coNP or NP has polynomial-size circuits. PNP = PNP[1]. p2 p2=1. p2 = UPNP[1] \RPNP[1]. PH = BPPNP[1]. Moreover we extend work of Hemaspaandra, Hemaspaandra and Hempel to show that if P p2 [1] = P p2 [2] then p2 = p2 . We also give a relativized world where P...

(2) ‖Hα(f1, f2)‖p ≤ Cα,p1,p2‖f1‖p1‖f2‖p2 with constants Cα,p1,p2 depending only on α, p1, p2 and p := p1p2 p1+p2 hold. The first result of this type is proved in [4], and the purpose of the current paper is to extend the range of exponents p1 and p2 for which (2) is known. In particular, the case p1 = 2, p2 = ∞ is solved to the affirmative. This was originally considered to be the most natural ...

PURPOSE House-dust-mite (HDM) major allergen Der p2 shares homology and function with Toll-like receptor (TLR) signaling protein myeloid differentiation-2 (MD2) and may lead to airway inflammation. Should Der p2 be internalized by human airway epithelium, it has the theoretical propensity to potentiate epithelium activation. This study aimed to demonstrate the internalization of Der p2 by airwa...

(2) ‖Hα(f1, f2)‖p ≤ Cα,p1,p2‖f1‖p1‖f2‖p2 with constants Cα,p1,p2 depending only on α, p1, p2 and p := p1p2 p1+p2 hold. The first result of this type is proved in [4], and the purpose of the current paper is to extend the range of exponents p1 and p2 for which (2) is known. In particular, the case p1 = 2, p2 = ∞ is solved to the affirmative. This was originally considered to be the most natural ...

Purinergic signalling has been implicated in many biological processes, and ATP and other extracellular nucleotides might have therapeutic potential in the treatment of cancer by signalling through P2 receptors. Different P2 receptor subtypes have been identified in a variety of different cancer types, in both primary samples of human cancer tissue and cell lines. Recent evidence suggests that ...

The title compound, (sodium magnesium) [magnesium iron(III) silicon] disilicate, (Na0.97Mg0.03)(Mg0.43Fe0.17 Si0.40)Si2O6, is isotypic with ordered P2/n omphacite. Its structure is characterized by single chains of corner-sharing SiO4 tetrahedra, extending along the c axis, which are crosslinked by bands of edge-sharing octahedra (site symmetry 2), statistically occupied by (Mg + Fe + Si). Betw...

Let P1, P2 be graph properties. A vertex (P1,P2)-partition of a graph G is a partition {V1, V2} of V (G) such that for i = 1, 2 the induced subgraph G[Vi] has the property Pi. A property R = P1◦P2 is defined to be the set of all graphs having a vertex (P1,P2)-partition. A graph G ∈ P1◦P2 is said to be uniquely (P1,P2)-partitionable if G has exactly one vertex (P1,P2)-partition. In this note, we...

The current status of ligand gated ion channel P2X and G protein-coupled P2Y receptor subtypes is described. This is followed by a summary of what is known of the distribution and roles of these receptor subtypes. Potential therapeutic targets of purinoceptors are considered, including those involved in cardiovascular, nervous, respiratory, urinogenital, gastrointestinal, musculo-skeletal and s...