Strict solutions u of genuinely nonlinear homogeneous hyperbolic equations in two independent variables with initial data f(x) of compact support become singular after a time interval of order parallelf parallel(-1). In higher dimensions solutions initially of compact support are likely to have life expectancies of orders parallelf parallel(-2+epsilon) at least. This is proved for the special c...

We show that for a generic conformal metric perturbation of compact hyperbolic 3-manifold $\Sigma$ with Betti number $b_1$, the order vanishing Ruelle zeta function at zero equals $4-b_1$, while in case it is equal to $4-2b_1$. This contrast 2-dimensional where topological invariant. The proof uses microlocal approach dynamical functions, giving geometric description generalized Pollicott-Ruell...

The general non-split scalar coset of supergravity theories is discussed.The symmetric space sigma model is studied in two equivalent formulations and for different coset parametrizations.The dualisation and the local first order formulation is performed for the non-split scalar coset G/K when the rigid symmetry group G is a real form of a non-compact semisimple Lie group (not necessarily split...

We consider the inhomogeneous biharmonic nonlinear Schr dinger (IBNLS) equation in $${\mathbb {R}}^N$$ , $$\begin{aligned} i \partial _t u +\Delta ^2 -|x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$ where $$\sigma > 0$$ and $$b . first study local well-posedness $${\dot{H}}^{s_c}\cap \dot{H}^2 $$ for $$N\ge 5$$ $$0<s_c<2$$ $$s_c=\frac{N}{2}-\frac{4-b}{2\sigma }$$ Next, we established a Gagliardo-...

We characterize the tempered part of automorphic Langlands category D-mod(Bun_G) using geometry big cell in affine Grassmannian. deduce that, for $G$ non-abelian, D-modules have no de Rham cohomology with compact supports. The latter fact boils down to a concrete statement, which we prove Ran space and some explicit t-structure estimates: non-abelian $\Sigma$ smooth curve, Borel-Moore homology ...

Abstract We consider metrizable ergodic topological dynamical systems over locally compact, $\sigma $ -compact abelian groups. study pure point spectrum via suitable notions of almost periodicity for the points system. More specifically, we characterize mean generic points. then go on and show how Besicovitch periodic determine both eigenfunctions measure in this case. After this, those arising...

We use a three-dimensional lattice model of proteins to investigate systematically the global properties of the polypeptide chains that determine the folding to the native conformation starting from an ensemble of denatured conformations. In the coarse-grained description, the polypeptide chain is modeled as a heteropolymer consisting of N beads confined to the vertices of a simple cubic lattic...