When we know the subjective probabilities (degrees of belief) p1 and p2 of two statements S1 and S2 , and we have no information about the relationship between these statements, then the probability of S1 & S2 can take any value from the interval max(p1 + p2 ? 1; 0); min(p1; p2)]. If we must select a single number from this interval, the natural idea is to take its midpoint. The corresponding \...

A property of graphs is any class of graphs closed under isomorphism. Let P1,P2, . . . ,Pn be properties of graphs. A graph G is (P1,P2, . . . ,Pn)-partitionable if the vertex set V (G) can be partitioned into n sets, {V1, V2, . . . , Vn}, such that for each i = 1, 2, . . . , n, the graph G[Vi] ∈ Pi. We write P1◦P2◦ · · · ◦Pn for the property of all graphs which have a (P1,P2, . . . ,Pn)-partit...

with constants C ;p1;p2 depending only on ; p1; p2 and p := p1p2 p1+p2 hold. The rst 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 =1 is solved to the a rmative. This was originally considered to be the most natural case and is known as Calderon's conjecture [3]. ...

Fifteen ketone-containing peptides were designed, synthesized, and used to probe the effect of substitution at the P1' position on caspase-3 and -7 inhibition. Even with the large bias of Ac-Asp-Glu-Val-Asp at the P4-P1 positions, certain peptides with cyclic functionality in the P1' position show a dramatically reduced ability to inhibit these caspases. Additionally, trends toward isozyme sele...

Bethe-Salpeter equation in the non-commutative space for a scalarscalar bound state in the ladder approximation with instantaneous interaction is considered. We show that spatial non-commutativity leads to the normal Zeeman effects on the spectra of two body bound state. e-mail: [email protected] e-mail: [email protected] Non-commutativity of space-time has been recently a subject of ...

Two small satellites of Pluto, S/2005 P1 (hereafter P1) and S/2005 P2 (hereafter P2), have recently been discovered outside the orbit of Charon, and their orbits are nearly circular and nearly coplanar with that of Charon. Because the mass ratio of Charon-Pluto is ∼ 0.1, the orbits of P2 and P1 are significantly non-Keplerian even if P2 and P1 have negligible masses. We present an analytic theo...