We present new proofs of two results on the billiard ball problem by Rychlik R] and Bialy B]. x0. INTRODUCTION. We will give new proofs of two results on the billiard ball problem by Rychlik R] and Bialy B]. The original proofs were based on variational considerations. In our approach the variational context is absent, the dynamical system takes the center stage. We hope the simpliications prov...

Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the variables involved that is manifestly inconsistent. On the other hand, a phase space path integral based on coherent states entails variables that exhibit a self...

Let n≥2 and 1≤q2, then |∂Ω|=0. In 1≤q0.

Measurements of attenuation for the Earth's longest period modes can be significantly biased by the effects of frequency splitting. Using our previously developed methods of time domain synthesis of split normal modes, we measure Q without such a bias. We also conduct numerical experiments to confirm the errors in Q measurements which result from neglecting the effects of splitting. In contrast...

A t-intersecting constant dimension subspace code C is a set of k-dimensional subspaces in projective space \(\mathrm {PG}(n,q)\), where distinct intersect exactly t-dimensional subspace. classical example such the sunflower, all pass through same t-space. The sunflower bound states that if \(|C| > \left( \frac{q^{k + 1} - q^{t 1}}{q \right) ^2 1\). In this article we will look at case \(t=0\) ...