The topological trace formula is a computation of the Lefschetz number of a Hecke correspondence C acting on the weighted cohomology groups, defined in [GHM], of a locally symmetric space X . It expresses this Lefschetz number as a sum of contributions from fixed point components of C on the reductive Borel Serre compactification of X . The proof uses the Lefschetz fixed point formula of [GM2]....

Interaction of Pb(II) ion with modified banana shell (MBS) and banana shell (BS) during adsorption fromaqueous solution were investigated. Batch experiments were carried out to investigate the effect of contact time,pH, and IDMID ion concentration on adsorption efficiency. The favorable pll for maxim= Pb(II) adsorptionwas at 5.0. For the investigated IMOI) concentrations (10-80 mph), maximum ad...

We derive for the Navier-Stokes equation an exact equation satisfied by the dissipation rate correlation function, 〈ǫ(~x+~r, t+ τ)ǫ(~x, t)〉. In the equal time limit, for the homogeneous, isotropic state of fullydeveloped turbulence, we show that the correlation function behaves as Ar1 +Br2 with μ1 = 2−ζ6 and μ2 = z ′′ 4−ζ4 for r in the inertial range; the ζ’s are exponents of velocity structure...

Introduction: Multidimensional magnetic resonance spectroscopy (MRS) can provide additional information at the expense of longer acquisition time than 1D MRS. Assuming 2D MRS is sparse in wavelet domain, Iddo[1] first introduced compressed sensing (CS) [2,3] to reconstruct multidimensional MRS from partial and random free induction decay (FID) data. However, the darkness in 1D MRS derives from ...

(1) Let X be a real linear space and R1, R2 be finite sequences of elements of X. If lenR1 = lenR2, then ∑ (R1 +R2) = ∑ R1 + ∑ R2. (2) Let X be a real linear space and R1, R2, R3 be finite sequences of elements of X. If lenR1 = lenR2 and R3 = R1−R2, then ∑ R3 = ∑ R1− ∑ R2. (3) Let X be a real linear space, R1, R2 be finite sequences of elements of X, and a be an element of R. If R2 = aR1, then ...