We prove a relation between several easy-to-define numerical invariants of generic knots in H × S, and discuss its implication to contact geometry. 1. Definitions of Invariants The 2-dimensional hyperbolic space H2 is defined to be the upper half plane {(x, y) ∈ R2| y > 0} equipped with the metric ds2 = dx +dy y2 . STH2 is the unit tangent bundle of H2, i.e., the S1-bundle over H2 formed by tan...

Myosin is thought to generate movement of actin filaments via a conformational change between its light-chain domain and its catalytic domain that is driven by the binding of nucleotides and actin. To monitor this change, we have measured distances between a gizzard regulatory light chain (Cys 108) and the active site (near or at Trp 130) of skeletal myosin subfragment 1 (S1) by using luminesce...

We (numerically) construct new static, asymptotically AdS solutions where the conformal infinity is the product of time and S2 × S1. There always exist a family of solutions in which the S1 is not contractible and, for small S1, there are two additional families of solutions in which the S1 smoothly pinches off. This shows that (when fermions are antiperiodic around the S1) there is a quantum p...

The interaction between myosin subfragment 1 (S1) and actin filaments after the photolysis of P3-1-(2-nitrophenyl)ethyl ester of ATP (caged ATP) was analyzed with a newly developed freezing system using liquid helium. Actin and S1 (100 microM each) formed a ropelike double-helix characteristic of rigor in the presence of 5 mM caged ATP at room temperature. At 15 ms after photolysis, the ropelik...

We (numerically) construct new static, asymptotically AdS solutions where the conformal infinity is the product of time and S2 × S1. There always exist a family of solutions in which the S1 is not contractible and, for small S1, there are two additional families of solutions in which the S1 smoothly pinches off. This shows that (when fermions are antiperiodic around the S1) there is a quantum p...

From now on X denotes a set and S denotes a family of subsets of X. Now we state the propositions: (1) Let us consider sets X1, X2, a family S1 of subsets of X1, and a family S2 of subsets of X2. Then {a×b, where a is an element of S1, b is an element of S2 : a ∈ S1 and b ∈ S2} = {s, where s is a subset of X1 ×X2 : there exist sets a, b such that a ∈ S1 and b ∈ S2 and s = a × b}. Proof: {a × b,...