Octad Orbits for Certain Subgroups of

Using Curtis’s MOG [3], we display the orbits and orbit representatives for various subgroups of the Mathieu group acting on the octads of the Steiner system This information is deployed in [8] and [9] to study a graph associated with the largest simple Fischer group.

Some Classes of Quantale Morphisms

This paper concerns some types of coherent quantale morphisms: Baer, minimalisant, quasi rigid, quasi r- and quasi morphisms. Firstly, we study how the reticulation functor preserves the properties that define these types of quantale morphisms. Secondly, we prove some characterization theorems for quasi rigid, quasi r- and quasi morphisms. These theorems extend some results existing in the literature of ring extensions and frame extensions.

k Part Partitions of Integers

This paper presents formulas (together with their proofs) determining 3 and 4 part partitions of any integer. These formulas were derived using the properties of the floor function and Bernoulli formulas for various powers of finite sums of the floor function series. This made it possible to obtain above formulas in a much simpler way than most traditional methods.

The Point-Line Collinearity Graph of the Maximal 2-Local Geometry – the First Three Discs

The disc structure of the point-line collinearity graph for the maximal 2-local geometry associated with the largest simple Fischer group is investigated. For an arbitrary vertex of this graph the first three discs are determined. Additionally a fragment of the fourth disc is uncovered.

Cohomology and Conformal Derivations of Bihom-Lie Conformal Superalgebras

In this paper, we introduce the notion of BiHom-Lie conformal superalgebras. We develop its representation theory and define the cohomology group with coefficients in a module. Finally, we introduce conformal derivations of BiHom-Lie conformal superalgebras and study some of their properties.

Relations Between Ranks of Matrix Polynomials

We show that the sum of the ranks of two matrix polynomials is the same as the sum of the rank of the matrix obtained by applying the greatest common divisor of the polynomials, with the rank of the matrix obtained by applying the least common multiple of the polynomials. Many applications, for older or more recent problems, of this result are obtained.

On Skew Fibonacci Matrices

In this paper we mainly define the skew Fibonacci sequence and skew Fibonacci matrices, and give the eigenvalues of skew Fibonacci matrices. Furthermore, we present some conditions for a matrix to be a skew Fibonacci matrix.

On a Class of Indefinite KAC-Moody Algebras

In this paper, we study a special class of indefinite Kac-Moody algebras. Based on the study of hyperbolic Kac-Moody algebras, we give the definition of type Kac-Moody algebras and study some properties of this special type Kac-Moody algebras.

Convergence of Generalized Collatz Problem in k-Adic Field

In this article, we define a new series transformation called transformation and probe into its fixed point and periodicity. We extend the number field of the transform period problem to a wider field. Different constraints are imposed on then different periodic columns are formed after finite transformations. We obtain that their periodic sequences are and respectively after derivation. As an application, it can provide a reference for C problems in more complex algebraic systems.