In this work, a novel colour quantization approach has been applied to the JSEG texture segmentation using quaternion algebra. As rule, fundamental vectors of space are derived by inverting three RGB directions in complex hyperplanes. proposed system, is represented as because algebra provides very intuitive means working with homogeneous coordinates. This representation views pixel point three...

An abelian surface A over a field K has potential quaternionic multiplication if the ring End K̄ (A) of geometric endomorphisms of A is an order in an indefinite rational division quaternion algebra. In this brief note, we study the possible structures of the ring of endomorphisms of these surfaces and we provide explicit examples of Jacobians of curves of genus two which show that our result is...

We prove a coordinatization theorem for unital alternative algebras containing $2\\times 2$ matrix algebra with the same identity element 1. This solves an old problem announced by Nathan Jacobson on description of generalized quaternion $\\mathbb{H}$ 1, case when is split. In particular, this basic field finite or algebraically closed.

Few-shot segmentation (FSS) aims to segment unseen classes given only a few annotated samples. Encouraging progress has been made for FSS by leveraging semantic features learned from base with sufficient training samples represent novel classes. The correlation-based methods lack the ability consider interaction of two subspace matching scores due inherent nature real-valued 2D convolutions. In...

In this paper, we study the restricted singular-value decomposition (RSVD) for three quaternion tensors under Einstein product, and give higher-order RSVD over algebra, which can achieve simultaneous singular value of tensors. Moreover, algorithm computing What is more, present a new blind color video watermarking scheme based on forth-order our numerical example demonstrates effectiveness fram...

There are essential arithmetical differences between algebras which satisfy the i?-condition (i?-algebras) and those which do not, especially with regard to class-number properties (Eichler [l, 2, 3]). The meaning of the i?-condition in the case n = 2 is as follows. Both k and A are simple algebras over the field ko of rational numbers, of orders m and 4m, respectively, over &oSuppose ko is ext...

Reducible matrices are closely associated with the connection of directed graph and can be used in stochastic processes, biology others. In this paper, we investigate reducible solution to a system matrix equations over Hamilton quaternion algebra. We establish necessary sufficient conditions for have derive formula general when it is solvable. Finally, present numerical example illustrate main...

We define an invariant of torsors under adjoint linear algebraic groups of type Cn—equivalently, central simple algebras of degree 2n with symplectic involution—for n divisible by 4 that takes values in H(k, μ2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple alg...