A polynomial ideal I ⊆ R[x] is THk-exact if every linear polynomial that is non-negative over VR(I), the real variety of I , is a sum of squares of polynomials of degree at most k modulo I . Lovász recognized that a graph is perfect if and only if the vanishing ideal of the characteristic vectors of its stable sets is TH1-exact, and asked for a characterization of ideals which are TH1-exact. We...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

We theoretically examine equilibrium properties of the harmonically trapped ideal Bose and Fermi gases in quantum degeneracy regime. analyze thermodynamic characteristics with a finite number atoms by means known semiclassical approach perform comparison exact numerical results. For gas, we demonstrate deviations energy values originating from discrete level structure show that these are observ...

Lattice defects generated by radiation damage can diffuse to grain boundaries (GBs) and be annihilated at GBs. However, the precise role of GBs in annihilating the segregated defects remains unclear. Here, we employed multi-scale models to determine how interstitials are annihilated at small-angle tilt GBs (STGBs) in SiC. First of all, we found the pipe diffusion of interstitials in STGBs is sl...

This is a short survey of the main known results concerning annihilating polynomials for the Witt ring of quadratic forms over a field. 1991 A.M.S. Subject Classification : 11E81, 12F10, 19A22

Recently, so called annihilating filer-based low rank Hankel matrix (ALOHA) approach was proposed as a powerful image inpainting method. Based on the observation that smoothness or textures within an image patch corresponds to sparse spectral components in the frequency domain, ALOHA exploits the existence of annihilating filters and the associated rank-deficient Hankel matrices in the image do...

We recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. In all the examples emerging from physics, the minimal linear differential operators annihilating these diagonals of rational functions have been shown to actually possess orthogonal or symplectic differential Galois groups. In order to understand the emergence of such ...

Positron annihilation on a wide variety of atoms and molecules is studied. Room-temperature positrons confined in a Penning trap are allowed to interact with molecules in the form of low-pressure gases so that the interaction is restricted to binary encounters between a positron and a molecule. Data are presented for the g-ray spectra resulting from positrons annihilating in such interactions. ...