The first measurements of CP violation in the B system will likely probe sin 2α, sin 2β and cos 2γ. Assuming that the CP angles α, β and γ are the interior angles of the unitarity triangle, we show that these measurements determine the angle set (α, β, γ) except for a twofold discrete ambiguity. If one allows for the possibility of new physics, the presence of this discrete ambiguity can make i...

The primary goal of the BaBar and Belle experiments is to overconstrain the CKM Unitarity Triangle. Measurements of the angles of this triangle, known as β, α, and γ (or φ1, φ2, and φ3) give insight into the Standard Model description of CP violation in the quark sector. BaBar and Belle have recorded almost 1 ab−1 combined, and have measured β to high precision. Measurements of α and γ are less...

A counterexample to Bell’s theorem is presented which uses a pair of photons instead of spin-1/2 particles used in our previous counterexamples. A locally causal protocol is provided for Alice and Bob, which allows them to simulate observing photon polarizations at various angles, and record their results as A = ± 1 ∈ S and B = ± 1 ∈ S, respectively. When these results are compared, the correla...

For a triangle in the hyperbolic plane, let α, β, γ denote the angles opposite the sides a, b, c, respectively. Also, let h be the height of the altitude to side c. Under the assumption that α, β, γ can be chosen uniformly in the interval (0, π) and it is given that α + β + γ < π, we show that the strong triangle inequality a + b > c + h holds approximately 79% of the time. To accomplish this, ...

An (α, β)-covered object is a simply connected planar region c with the property that for each point p ∈ ∂c there exists a triangle contained in c and having p as a vertex, such that all its angles are at least α and all its edges are at least β · diam(c)long. This notion extends that of fat convex objects. We show that the combinatorial complexity of the union of n (α, β)-covered objects of ‘c...

Many commonly used force fields for protein systems such as AMBER, CHARMM, GROMACS, OPLS, and ECEPP have amino-acid-independent force-field parameters for main-chain torsion-energy terms. Here, we propose a new type of amino-acid-dependent torsion-energy terms in the force fields. As an example, we applied this approach to AMBER ff03 force field and determined new amino-acid-dependent parameter...