We present two left-to-right integer recodings which can be used to perform scalar multiplication with a fixed sequence of operations. These recodings make it possible to have a simple power analysis resistant implementation of a group-based cryptosystem without using unified formulas or introducing dummy operations. This approach is very useful for groups in which the doubling step are less ex...

A real finite dimensional space with indefinite scalar product having v − negative squares and v+ positive ones is considered. The paper presents a classification of operators that are normal with respect to this product for the cases min{v − , v+} = 1, 2. The approach to be used here was developed in the papers [1] and [2], where the similar classification was obtained for complex spaces with ...

For a square integrable vector-valued process f on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for f are presented. The process f is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for f involving the biorthogo...

The spectral factorization problem of a scalar coercive spectral density is considered in the framework of the CallierDesoer algebra of distributed parameter system transfer functions. Criteria for the infinite product representation of a coercive spectral density and for the convergence of infinite product representations of spectral factors, i.e. for the convergence of the symmetric extractio...

A model for the ux of a passive scalar by the subgrid motions in the largeeddy simulation of turbulent ow is proposed within the framework of the stretched-vortex subgrid stress model. The model is based on an analytical solution for the winding of a scalar eld by an elemental subgrid vortex. This gives a tensor gradient-di usion expression for the local ux of the scalar with subgrid turbulent ...

The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus additional scalar fields. Grassmann nature is being enforced by allowing measure to take both positive and negative values, and also by introducing a vector space t...

We study compactifications of Einstein gravity on product spaces in vacuum and their acceleration phases. Scalar potentials for the dimensionally reduced effective theory are found to be of exponential form and exact solutions are obtained for a class of product spaces. The inflation in our solutions is not sufficient for the early universe. We comment on the possibility of obtaining sufficient...

Concepts of the inner product and conjugate of matrix of complex numbers are defined here. Operations such as addition, subtraction, scalar multiplication and inner product are introduced using correspondent definitions of the conjugate of a matrix of a complex field. Many equations for such operations consist like a case of the conjugate of matrix of a field and some operations on the set of s...

In this article, we consider pair frames in Banach spaces and   introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as   special kinds of (Banach) pair frames.  Some frame-like inequalities  for (Banach)  pair frames are presented. The elements that participant  in the construction of (Ba...