Related papers: Further results on modularity in evolution algebra…

In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.

We give an account of Mazur's proof that, for an elliptic curve over $\mathbb{Q}$, if it admits a nonconstant mapping from $X(N)$ defined over the complex numbers $\mathbb{C}$, for some $N$, then it also admits a nonconstant mapping from…

We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all…

Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the…

This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where…

Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…

We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties of the involution. It is shown that this quadratic form can…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…

Let A be an algebra in a variety V. We study the modulization of a pointed A-overalgebra P, show that it is totally in any variety that P is totally in, and apply this theory to the construction of the enveloping ringoid Z[A,V].

In this paper, we give a relation between the Hilbert multiplicity and the irreducible multiplicity. As an application, we characterize Ulrich modules in term of the irreducible multiplicity.

The ubiquity of modules in biological networks may result from an evolutionary benefit of a modular organization. For instance, modularity may increase the rate of adaptive evolution, because modules can be easily combined into new…

We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.

We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables obtaining several new classes of evolution equations with…

An important aspect in the theory of algebras with polynomial identities is the study of the asymptotic behavior of the codimension sequence $c_n(A),\, n\geq 1,$ which measures the growth of polynomial identities of a given algebra $A$. In…

Changing base composition during the evolution of biological sequences can mislead some of the phylogenetic inference techniques in current use. However, detecting whether such a process has occurred may be difficult, since convergent…

In this paper, we systematically investigate the nilpotentizer and nilpotent graph for a Lie superalgebra over the field of characteristic not equal to 2. First, we establish some fundamental properties of the nilpotentizer. Next, we show…

We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of pull-back morphisms and of base-preserving morphisms…