On the minimal number of critical points of functions on h-cobordisms

Let (W,M,M'), dim W > 5, be a non-trivial h-cobordism (i.e., the Whitehead torsion of (W,V) is non-zero). We prove that every smooth function f: W --> [0,1], f(M)=0, f(M')=1 has at least 2 critical points. This estimate is sharp: W possesses a function as above with precisely two critical points.Comment: 7 pages, Late

Elliptic operators in odd subspaces

An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with boundary, or as spectral subspaces for self-adjoint elliptic differential operators of odd order. Index formulas are obtained for operators in odd subspaces on closed manifolds and for general boundary value problems. We prove that the eta-invariant of operators of odd order on even-dimesional manifolds is a dyadic rational number.Comment: 27 page

Charge density wave transport in submicron antidot arrays in NbSe3

We demonstrate for the first time that a periodic array of submicrometer holes (antidots) can be patterned into thin single NbSe3 crystals. We report on the study of charge density wave (CDW) transport of the network of mesoscopic units between antidots. Size of the elementary unit can be as small as 0.5 micron along the chain axis and (0.2 micron) x (0.3 micron) in cross section. We observe size effects for Ohmic residual resistance and in CDW transport current-voltage characteristics in submicronic networks.Comment: 4 pages with 1 table and 10 figures. Submitted to European Physical Journa

Dynamics of meteor streams

The overwhelming majority of meteor streams are generally assumed to be formed due to the decay of comets. The most effective process of the release of solid particles from a cometary nucleus is their ejection by sublimating gases when the comet approaches the Sun. The results of investigation of the Geminids and Quadrantids meteor stream evolution show that under the influence of planetary perturbations, the stream may originally be flat but then thicken depending on the variation range of orbital inclinations. Eventually, due to planetary perturbations, a meteor stream may take such a shape as to cause the start of several active showers at different solar longitudes