We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras [1] with which one can replace the traditional multivector expansion of Cl(g) with an expansion in terms of simple (also: pure) spinors. We show that a Clifford algebra with 2m generators is the direct sum of 2m spinor subspaces S characterized as being left eigenvectors of Γ; furthermore we prove that the well ...

Finite Field Arithmetic plays an important role in coding theory, cryptography and their applications. Several hardware solutions using Finite Field Arithmetic have already been developed but none of them are user programmable. This is probably one reason why BCH codes are not commonly used in mobile communication applications even though these codes have very desirable properties regarding bur...

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yiel...

Previously, hepatic iron overload resembling that in hereditary hemachromatosis (HH) has been found in beta 2-microglobulin knockout (beta 2m-/-) mice. We have now characterized iron metabolism in beta 2m-/- mice. The mutant mice fail to limit the transfer of iron from mucosal cells into the plasma. Transferrin saturation is abnormally high. Pathologic iron depositions occur predominantly in li...

The Neumann problem for the Poisson equation is considered in a domain Ωε ⊂ R with boundary components posed at a small distance ε > 0 so that in the limit, as ε → 0, the components touch each other at the point O with the tangency exponent 2m ≥ 2. Asymptotics of the solution uε and the Dirichlet integral ‖∇xuε; L(Ωε)‖ are evaluated and it is shown that main asymptotic term of uε and the existe...

We study [2m−1, 2m]-binary linear codes whose weights lie between w0 and 2m−w0, where w0 takes the highest possible value. Primitive cyclic codes with two zeros whose dual satisfies this property actually correspond to almost bent power functions and to pairs of maximum-length sequences with preferred crosscorrelation. We prove that, for odd m, these codes are completely characterized by their ...

For every positive integer m, we construct a symmetric (v, k, λ)-design with parameters v = h((2h−1) 2m−1) h−1 , k = h(2h − 1)2m−1, and λ = h(h − 1)(2h − 1)2m−2, where h = ±3 · 2 and |2h − 1| is a prime power. For m ≥ 2 and d ≥ 1, these parameter values were previously undecided. The tools used in the construction are balanced generalized weighing matrices and regular Hadamard matrices of order...

The functions m := j j 2m d if d is odd, and m := j j 2m d log j j if d is even, are known as surface splines, and are commonly used in the interpolation or approximation of smooth functions. We show that if one's domain is the unit ball in R, then the approximation order of the translates of m is at most m. This is in contrast to the case when the domain is all of R where it is known that the ...

For each complex number $\nu$, an associative symplectic reflection algebra $\mathcal H:= H_{1,\nu}(I_2(2m+1))$, based on the group generated by root system $I_2(2m+1)$, has $m$-dimensional space of traces and $(m+1)$-dimensional supertraces. A (super)trace $sp$ is said to be degenerate if corresponding bilinear (super)symmetric form $B_{sp}(x,y)=sp(xy)$ degenerate. We find all values parameter...