Acidobasic properties of molten potassium tetrahalogenogallates (X=Cl,I)

Molten potassium tetrachlorogallate and potassium tetraiodogallate were studied in terms of halogenoacidity, based on X^? ion-exchange. Titration of KX solution with GaX₃ were achieved and characterized by the shift of cathodic voltammetric curves. Autodissociation constants K_i,X/mol² kg^?1 were determined: ?log K_i,Cl=4.25±0.05 and ?log K_i,I=2.6±0.05, as well as the solubility values of KX: 0.41±0.02 and 0.80±0.02 mol kg^?1 for KCl and KI respectively.     

Some relations between additive functions,II

Aequationes mathematicae -     

Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

Erasure Decoding for Gabidulin Codes

We present a new approach of the decoding algorithm for Gabidulin Codes. In the same way as efficient erasure decoding for Generalized Reed Solomon codes by using the structure of the inverse of the VanderMonde matrices, we show that, the erasure(t erasures mean that t components of a code vector are erased) decoding Gabidulin code can be seen as a computation of three matrice and an affine permutation, instead of computing an inverse from the generator or parity check matrix. This significantly reduces the decoding complexity compared to others algorithms. For t erasures with t ≤ r, where r = n − k, the erasure algorithm decoding for Gab _{n, k} (g) Gabidulin code compute the t symbols by simple multiplication of three matrices. That requires rt + r(k − 1) Galois field multiplications, t(r − 1) + (t + r)k field additions, r ² + r(k + 1) field negations and t(k + 1) field inversions.