Fermat's Equation in Matrices

The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.

Description Reduction for Restricted Sets of (0,1) Matrices

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Algorithmic Minimization of Non-zero Entries in 0,1-Matrices

In this paper we present algorithms which work on pairs of 0,1- matrices which multiply again a matrix of zero and one entries. When applied over a pair, the algorithms change the number of non-zero entries present in the matrices, meanwhile their product remains unchanged. We establish the conditions under which the number of 1s decreases. We recursively define as well pairs of matrices which product is a specific matrix and such that by applying on them these algorithms, we minimize the total number of non-zero entries present in both matrices. These matrices may be interpreted as solutions for a well known information retrieval problem, and in this case the number of 1 entries represent the complexity of the retrieve and information update operations.

Technology of Classification of Electronic Documents Based on the Theory of Disturbance of Pseudoinverse Matrices

Technology of classification of electronic documents based on the theory of disturbance of pseudoinverse matrices was proposed.

Differential Balanced Trees and (0,1) Matrices

* The research was supported by INTAS 00-397 and 00-626 Projects.

Canonical Objects in Classes of (n, V)-Groupoids

AMS Subj. Classification: 03C05, 08B20

A Basis for Z-Graded Identities of Matrices over Infinite Fields

2000 Mathematics Subject Classification: 16R10, 16R20, 16R50

Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices

000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55.

Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices

2000 Mathematics Subject Classification: 42C05.

A Representation of Binary Matrices

Христина Костадинова, Красимир Йорджев - В статията се обсъжда представянето на произволна бинарна матрица с помощта на последователност от цели неотрицателни числа. Разгледани са някои предимства и недостатъци на това представяне като алтернатива на стандартното, общоприето представяне чрез двумерен масив. Показано е, че представянето на бинарните матрици с помощта на наредени n-торки от естествени числа води до по-бързи алгоритми и до съществена икономия на оперативна памет. Използуван е апарата на обектно-ориентираното програмиране със синтаксиса и семантиката на езика C++.

Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators

2010 Mathematics Subject Classification: 35Q15, 31A25, 37K10, 35Q58.

Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring

2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.

On Majorization for Matrices

In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences.

The Direct and Inverse Spectral Problems for some Banded Matrices

2000 Mathematics Subject Classification: 15A29.

Regulating the expression of eEF1A to decipher its non canonical functions in eukaryotic cells

The canonical function of eEF1A is delivery of the aminoacylated tRNA to the A site of the ribosome during protein translation, however, it is also known to be an actin binding protein. As well as this actin binding function, eEF1A has been shown to be involved in other cellular processes such as cell proliferation and apoptosis. It has long been thought that the actin cytoskeleton and protein synthesis are linked and eEF1A has been suggested to be a candidate protein to form this link, though very little is understood about the relationship between its two functions. Overexpression of eEF1A has also been shown to be implicated in many different types of cancers, especially cancers that are metastatic, therefore it is important to further understand how eEF1A can affect both translation and the organisation of the actin cytoskeleton. To this end, we aimed to determine the effects of reduced expression of eEF1A on both translation and its non canonical functions in CHO cells. We have shown that reduced expression of eEF1A in this cell system results in no change in protein synthesis, however results in an increased number of actin stress fibres and other proteins associated with these fibres such as myosin IIA, paxillin and vinculin. Cell motility and attachment are also affected by this reduction in eEF1A protein expression. The organisational and motility phenotypes were found to be specific to eEF1A by transforming the cells with plasmids containing either human eEF1A1 or eEF1A2. Though the mechanisms by which these effects are regulated have not yet been established, this data provides evidence to show that the translation and actin binding functions of eEF1A are independent of each other as well as being suggestive of a role for eEF1A in cell motility as supported by the observation that overexpression of eEF1A protein tends to be associated with the cancer cells that are metastatic.