With a detailed investigation of n linear algebraic equations Bx = b, we find that the scaled residual dynamics for y ∈ Sn−1 is equipped with four structures: the Jordan dynamics, the rotation group SO(n), a generalized Hamiltonian formulation, as well as a metric bracket system. Therefore, it is the first time that we can compute the steplength used in the iterative method by a novel algorithm...

For graphs G and H , a homomorphism from G to H is a function φ : V (G) → V (H), which maps vertices adjacent in G to adjacent vertices of H . A homomorphism is locally injective if no two vertices with a common neighbor are mapped to a single vertex in H . Many cases of graph homomorphism and locally injective graph homomorphism are NPcomplete, so there is little hope to design polynomial-time...

S OF PAPERS SUBMITTED FOR PRESENTATION TO THE SOCIETY The following papers have been submitted to the Secretary and the Associate Secretaries of the Society for presentation at meetings of the Society. They are numbered serially throughout this volume. Cross references to them in the reports of the meetings will give the number of this volume, the number of this issue, and the serial number of ...

Given a Young diagram λ and the set Hλ of partitions of {1, 2, . . . , |λ|} of shape λ, we analyze a particular S|λ|-module homomorphism QH λ → QHλ ′ to show that QHλ is a submodule of QHλ ′ whenever λ is a hook (n, 1, 1, . . . , 1) with m rows, n ≥ m, or any diagram with two rows.

We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping theorem are discussed. The construction is illustrated by a simple example of calculus and joint spectrum of two non-commuting selfadjoint n× n matrices.

The aim of this paper is to endow a monoid structure on the set S of all oriented knots(links) under the operation ⊎ , called addition of knots. Moreover, we prove that there exists a homomorphism of monoids between (Sd, ⊎ ) to (N, +), where Sd is a subset of S with an extra condition and N is the monoid of non negative integers under usual addition.

We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane R = k〈x, y〉/(xy − yx− y). Complete description of irreducible components of the representation variety mod(R,n) obtained for any dimension n, it is shown that the variety is equidimensional. The influence of the property of the non-commutati...

Introduction: Obesity is a worldwide health concern, which has been on an alarming trend in Jordan. Obesity leads to several chronic disorders and adversely affects the figure. Furthermore, it is considered to be a severe health threat during adolescence and early adulthood. People in Jordan tend to consume the foods that are rapidly prepared, and such dietary habits are referr...