sigma B (sigma 37) is a secondary species of RNA polymerase sigma factor found in the gram-positive bacterium Bacillus subtilis. To study the function of sigma B genetically, we sought mutations that block the expression of a gene (ctc) known to be transcribed by sigma B-containing RNA polymerase in vitro. One such mutation, called crl, was found to map in or near the structural gene (sigB) for...

The modern soliton theories [DJKM, SN, SS], which were developed in ending of last century, are known as the infinite dimensional analysis and gave us fruitful and beautiful results, e.g., relations of soliton equations to universal Grassmannian manifold, Plücker embedding, infinite dimensional Lie algebra, loop algebra, representation theories, Schur functions, Young diagram, and so on. They s...

The decay of the variance of a diffusive scalar in chaotic advection flow (or equivalently Batchelor-regime turbulence) is analyzed using a model in which the advection is represented by an inhomogeneous baker's map on the unit square. The variance decays exponentially at large times, with a rate that has a finite limit as the diffusivity kappa tends to zero and is determined by the action of t...

One of the best known discrete integrable systems is the billiard inside an n-dimensional ellipsoid. Veselov showed that generic complex invariant manifolds of the algebraic billiard map are open subsets of (coverings of) hyperelliptic Jacobians and that the restriction of the map to such manifolds is described by the shift by a constant vector (an algebraic addition law). Later, Dragovic and R...

We study the lifting of Schubert stratification homogeneous space complete real flags $R^{n+1}$ to its universal covering group $Spin_{n+1}$. call lifted strata Bruhat cells $Spin_{n+1}$, in keeping with homonymous classical decomposition reductive algebraic groups. present explicit parameterizations for these terms minimal-length expressions $\sigma=a_{i_1}... a_{i_k}$ permutations $\sigma\in ...

We show how to express a conformal map Φ of a general two connected domain in the plane such that neither boundary component is a point to a representative domain of the form Ar = {z : |z + 1/z| < 2r}, where r > 1 is a constant. The domain Ar has the virtue of having an explicit algebraic Bergman kernel function, and we shall explain why it is the best analogue of the unit disc in the two conne...