Exact BPS solutions of multi-walls are obtained in five-dimensional supergravity. The solutions contain 2n parameters similarly to the moduli space of the corresponding global SUSY models and have a smooth limit of vanishing gravitational coupling. The models are constructed as gravitational deformations of massive T CP nonlinear sigma models by using the off-shell formulation of supergravity a...

The classical Busemann-Petty problem (1956) asks, whether origin-symmetric convex bodies in R with smaller hyperplane central sections necessarily have smaller volumes. It is known, that the answer is affirmative if n ≤ 4 and negative if n > 4. The same question can be asked when volumes of hyperplane sections are replaced by other comparison functions having geometric meaning. We give unified ...

We extend Jordan’s notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two orthogonal projections in the matrices over the real, complex or quaternionic field (or skew field). From this we derive an algorithm to turn almost commuting projections into commuting projections that minimizes the sum of the displacements of the two projections. ...

The research reported in this paper is motivated by the study of stability for linear dynamical systems with quaternionic coefficients. These systems can be used to model several physical phenomena, for instance, in areas such as robotics and quantum mechanics. More concretely, quaternions are a powerful tool in the description of rotations [1]. There are situations, especially in robotics, whe...

We consider Bézier-like formulas with weights in quaternion and geometric (Clifford) algebra for parametrizing rational curves and surfaces. The simplest non-trivial quaternionic case of bilinear formulas for surface patches is studied in detail. Such formulas reproduce well known biquadratic parametrizations of principal Dupin cyclide patches, and are characterized in general as special Darbou...

I point out critical errors in the paper “Bell’s Theorem Versus Local Realism a Quaternionic Model of Physical Space” by J. Christian, published IEEE Access. Christian’s fact contains several conflicting models. None them form counterexamples to Bell’s theorem. Most is devoted model based on detection loophole due Pearle (1970).

The universal hypermultiplet arises as a subsector of every Calabi-Yau compactifica-tion of M-theory or Type II string theory. Classically its moduli space is the quaternionic space SU (2, 1)/U (2). We show that this moduli space receives a one-loop correction proportional to the Euler character of the Calabi-Yau, which can locally be absorbed by a certain constant shift of the fields. The corr...

The quaternionic representation of ham images, treating RGB colour components as a single unit instead of as separate components, is very effective. The advantage of using quaternion arithmetic is that the perceptually richer colour images can be represented and analyzed as a single entity, improving the accuracy of pattern recognition models. The quaternionic singular value decomposition (SVD)...

In this paper, we study the multiple-access channel where users employ space–time block codes (STBC). The problem is formulated in the context of an intersymbol interference (ISI) multiple-access channel which occurs for transmission over frequency-selective channels. The algebraic structure of the STBC is utilized to design joint interference suppression, equalization, and decoding schemes. Ea...

The paper compares the features of three extensions of the notion of the Gabor’s analytic signal for 2-D signals: the analytic signals with single-quadrant spectra (AS), the quaternionic signals with quaternionic single-quadrant spectra (QS) and the monogenic signals (MS). A good platform of comparison are the polar representations of the AS and the QS and the spherical coordinate representatio...