The geometric structures of proteins are vital to the understanding of biochemical interactions. However, there is much yet to be understood about the spatial arrangements of the chains of amino acids making up any given protein. In particular, while conventional analysis tools like the Ramachandran plot supply some insight into the local relative orientation of pairs of amino acid residues, th...

The subject of this paper is the Brauer group of a nonsingular complex projective variety. More specifically, we study the question of whether a 2-torsion element of the cohomological Brauer group is representable by a quaternion algebra over the generic point. Using intersection theory – on schemes and on algebraic stacks – we are able to describe an obstruction to such a representation, and t...

We propose a method that identifies a mode of Rayleigh waves and separates it from body waves and from other modes, using quaternions to represent multicomponent data. Being well known the abilities of quaternions to handle rotations in space, we use previous results derived from Le Bihan and Mars [1] to prove that a Rayleigh-wave mode recorded by an array of vector-sensors can be approximated ...

In this paper we introduce convolution theorem for the Fourier transform (FT) of two complex functions. We show that the correlation theorem for the FT can be derived using properties of convolution. We develop this idea to derive the correlation theorem for the quaternion Fourier transform (QFT) of the two quaternion functions.

We extend the Siegel-Weil formula to all quaternion dual pairs. Applications include the classification problem of skew hermitian forms over a quaternion algebra over a number field and a product formula for the weighted average of the representation numbers of a skew hermitian form by another skew hermitian form.

We shown the quaternion orders OZ[2] ' ( √ 2,−1)Z[2] and OZ[3] ' (3+2 √ 3,−1)Z[3] that appear in applications of the coding theory [2] are not maximal orders in the quaternion algebras AQ(2) ' ( √ 2,−1)Q(2) and AQ(3) ' (3 + 2 √ 3,−1)Q(3), respectively. Furthermore, we identify the maximal orders that containing these orders.

We describe some constructions of orthonormal lattices in totally real subfields of cyclotomic fields, obtained by endowing their ring of integers with a trace form. We also describe constructions of quaternion division algebras over such fields. Orthonormal lattices and quaternion division algebras over totally real fields find use in wireless networks in ultra wideband communication, and we d...

The first mathematician who studied quaternion extensions (H8-extensions for short) was Dedekind [6]; he gave Q( √ (2 + √ 2)(3 + √ 6) ) as an example. The question whether given quadratic or biquadratic number fields can be embedded in a quaternion extension was extensively studied by Rosenblüth [32], Reichardt [31], Witt [36], and Damey and Martinet [5]; see Ledet [19] and the surveys [15] and...

We show that, in quaternion quantum mechanics with a complex geometry, the minimal four Higgs of the unbroken electroweak theory naturally determine the quaternion invariance group which corresponds to the Glashow group. Consequently, we are able to identify the physical significance of the anomalous Higgs scalar solutions. We introduce and discuss the complex projection of the Lagrangian density.

In this paper, we give an optimal lower bound for the eigenvalues of the basic Dirac operator on a quaternion-Kähler foliations. The limiting case is characterized by the existence of quaternion-Kähler Killing spinors. We end this paper by giving some examples.