The norm varieties and the varieties with special correspondences play a major role in the proof of the Bloch-Kato Conjecture by M. Rost and V. Voevodsky. In the present paper we show that a variety which possesses a special correspondence is a norm variety. As an unexpected application we give a positive answer to a problem of J.-P. Serre about groups of type E8 over Q. Apart from this we incl...

Let U be the unit polydisc of C n and φ = (φ1, . . . , φn) a holomorphic selfmap of U. By Bp(Un), B 0 (U) and B 0∗ (U) denote the p-Bloch space, Little p-Bloch space and Little star p-Bloch space in the unit polydisc U respectively, where p, q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between Bp(Un) (B 0(Un) or B 0∗ (U) ) and Bq(...

We consider the Josephson Effect between two spatially separated BoseEinstein condensates of atoms each of which can be in two hyperfine states. We derive simple equations of motion for this system closely analogous to the Bloch equations. We also map the dynamics of the system onto those of a classical particle in a well. We find novel density and spin modes of oscillation and new stable equil...

Bloch and Okounkov’s correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of ĝl ∞ modules of level one. Recent works have calculated these character functions for higher levels for ĝl ∞ and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type D of h...

We consider reaction-diffusion systems on the infinite line that exhibit a family of spectrally stable spatially periodic wave trains u0(kx− ωt; k) that are parameterized by the wave number k. We prove stable diffusive mixing of the asymptotic states u0(kx + φ±; k) as x → ±∞ with different phases φ− 6= φ+ at infinity for solutions that initially converge to these states as x → ±∞. The proof is ...

CONTENTS We use Zagier's method to compute the critical values of the 1. Introduction symmetric square L-functions of six cuspidal eigenforms of level 2. Calculating the Critical Values one with rational coefficients. According to the Bloch-Kato 3. Tables of Results conjecture, certain large primes dividing these critical values 4. An Observation must be the orders of elements in generalised Sh...

Spencer Bloch and the author formulated a general conjecture (Tamagawa number conjecture) on the relation between values of zeta functions of motives and arithmetic groups associated to motives. We discuss this conjecture, and describe some application of the philosophy of the conjecture to the study of elliptic curves. 2000 Mathematics Subject Classification: 11G40.

The problem of concentric pervious spheres carrying a fluid source at their centre and rotating slowly with different uniform angular velocities Ω1, Ω2 about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists, and the couple, rate of dissipated energy is found analytically in the present situation. The expression of couple on inner sphere rotating...

We define a volume function on configurations of four points in the sphere S which is invariant under the action of PU(2, 1), the automorphism group of the CR structure defined on S by its embedding in C. We show that the volume function, constructed using appropriate combinations of the dilogathm function of Bloch-Wigner, satisfies a five term relation in a more general context which includes ...