in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

We investigate the general strategy of measuring cosmologically induced polarization by analyzing the polarization signature in the small scale limit. Polarization induced by cosmological scalar perturbations leads to a typical anisotropy pattern in the power spectrum, which can best be analyzed in Fourier domain. This allows one to unambiguously distinguish cosmological signal of polarization ...

The current understanding of chirality suggests the existence a connection between structure and angular momentum, including spin. This is particularly emphasized in chiral induced spin selectivity effect, where structures act as filters. However, recent discovery phonons have demonstrated that too may carry momentum which also can be regarded magnetic moments adding to total moment. Here, it s...

It has been realized that thermal shear plays a similar role as vorticity in polarizing spin of particles heavy ion collisions. We point out fundamental difference it leads to particle redistribution the medium. The gives rise an additional contribution polarization through self-energy, which is parametrically same order one considered so far literature. self-energy general gauge dependent. int...

We estimate the dust polarized emission in our galaxy at high galactic latitudes, which is the dominant foreground for measuring CMB polarization using the high frequency instrument (HFI) aboard Planck surveyor. We compare it with the level of CMB polarization and conclude that, for angular scales ≤ 1 • , the scalar-induced CMB polarization and temperature-polarization cross-correlation are muc...

The anisotropy and polarization of the cosmic microwave background radiation (CMBR) induced by the scalar and tensor metric perturbations are computed in the long-wavelength limit. It is found that the large-scale polarization of CMBR induced by the decaying tensor mode can reach a few percents. This is different from the scalar or inflation-induced tensor mode, whereas the polarization is at l...

Abnormal lipid-mediated hepatic inflammatory-immune dysfunction and chronic low grade inflammation play an important role in the pathogenesis of non-alcoholic fatty liver disease (NAFLD). Macrophage polarization is an important mechanism for the regulation of inflammatory response. Since PPAR-γ has emerged as a master regulator of macrophage polarization, we aimed to investigate the lipid-induc...

using hartree-fock su-sheriffer-heeger (hf-ssh) model, we have studied the dependence of the energies of the ground (magnetic triplet state) and the first exited (nonmagnetic singlet state) states of the size-2 trigonal zigzag graphene nanoflake (size-2 nf) on the intensity of an external in plane static electric field at zero temperature. we identify a transition from the magnetic triplet stat...