Asymptotic enumeration of some RNA secondary structures

In this paper, we derive recursions of some RNA secondary structures with certain properties under two new representations. Furthermore, by making use of methods of asymptotic analysis and generating functions we present asymptotic enumeration of these RNA secondary structures.     

Uniform reducibility of representability problems for algebraic structures

Given a countable algebraic structure \(\mathfrak{B}\) with no degree we find sufficient conditions for the existence of a countable structure \(\mathfrak{A}\) with the following properties: (1) for every isomorphic copy of \(\mathfrak{A}\) there is an isomorphic copy of \(\mathfrak{A}\) Turing reducible to the former; (2) there is no uniform effective procedure for generating a copy of \(\mathfrak{A}\) given a copy of \(\mathfrak{B}\) even having been enriched with an arbitrary finite tuple of constants.     

RNA secondary structure, permutations, and statistics

We construct a permutation representation for RNA secondary structure. We also introduce some basic combinatorial statistics for RNA secondary structure and relate them to permutation statistics when appropriate. These statistics allow us to quantify some structural phenomena in RNA secondary structure.     

Chern-flat and Ricci-flat invariant almost Hermitian structures

We study left-invariant almost Hermitian structures on homogeneous spaces having either flat Chern connection or flat Ricci–Chern form. Many examples are carefully described, and a classification is given in low dimensions.     

Reflexive representability and stable metrics

It is well-known that a topological group can be represented as a group of isometries of a reflexive Banach space if and only if its topology is induced by weakly almost periodic functions [see Megrelishvili (Operator topologies and reflexive representability. Nuclear groups and Lie groups (Madrid 1999). Res. Exp. Math., vol. 24, pp. 197?C208. Heldermann, Lemgo, 2001; Topological transformation groups: selected topics. In: Pearl E (ed) Open Problems in Topology II. Elsevier, Amsterdam 2007), Shtern (Russian J. Math. Phys. 2(1):131?C132, 1994)]. We show that for a metrisable group this is equivalent to the property that its metric is uniformly equivalent to a stable metric in the sense of Krivine and Maurey (Isr J Math 39(4):273?C295, 1981). This result is used to give a partial negative answer to a problem of Megrelishvili.     

Conjugacy classes,characters and products of elements

Recently, Baumslag and Wiegold proved that a finite group G is nilpotent if and only if for every of coprime order. Motivated by this result, we study the groups with the property that and those with the property that for every and every nontrivial of pairwise coprime order. We also consider several ways of weakening the hypothesis on x and y. While the result of Baumslag and Wiegold is completely elementary, some of our arguments here depend on (parts of) the classification of finite simple groups.     

Left invariant contact structures on Lie groups

Amongst other results, we perform a ‘contactization’ method to construct, in every odd dimension, many contact Lie groups with a discrete center, unlike the usual (classical) contactization which only produces Lie groups with a non-discrete center. We discuss some applications and consequences of such a construction, construct several examples and derive some properties. We give classification results in low dimensions. A complete list is supplied in dimension 5. In any odd dimension greater than 5, there are infinitely many locally non-isomorphic solvable contact Lie groups. We also characterize solvable contact Lie algebras whose derived ideal has codimension one. For simplicity, most of the results are given in the Lie algebra version.     

Transversely holomorphic structures with many invariant hypersurfaces

In this paper we show that a transversely holomorphic foliation in a compact manifold $M$ having an infinite number of invariant hypersurfaces admits a basic transversely meromorphic first integral $f:M?\overline{\mathbb{C}}$.     

Conjugacy classes and finite p-groups

Let G be a finite p-group, where p is a prime number, and a ∈ G. Denote by Cl(a) = {gag⁻¹| g ∈ G} the conjugacy class of a in G. Assume that |Cl(a)| = pⁿ. Then Cl(a) Cl(a⁻¹) = {xy | x ∈ Cl(a), y ∈ Cl(a⁻¹)} is the union of at least n(p − 1) + 1 distinct conjugacy classes of G. Received: 16 December 2004     

Order representability in groups and vector spaces

In the present paper, first we study in a systematic way the numerical representation problem for total preorders defined either on groups or on real vector spaces. Then, we consider groups and real vector spaces equipped with a topology, and analyze the fulfillment of the so-called continuous representability property; the latter meaning that every continuous total preorder defined on the given topological space admits a continuous real-valued order-preserving function. We also explore the analogous cases as above for total preorders that are compatible with the given algebraic structure, looking for real-valued, continuous or not, order-preserving functions that, in addition, are algebraic homomorphisms.     

L-topological vector spaces and families of L-fuzzy pseudo-norms

In this paper, the concept of a family of L-fuzzy pseudo-norms on vector spaces is proposed and the characterization of L-vector topologies in terms of a family of L-fuzzy pseudo-norms is presented. As applications of the characterization, the Hausdorff separation property, convergence of molecule nets and boundedness of L-sets in L-topological vector spaces are investigated.     

Representability and local representability of algebraic theories

A finitary monosorted algebraic theory is called locally representable (or representable) in a category with finite products if every its initial segment is the domain of a full faithful finite-products-preserving functor into (or if itself is the domain of such a functor). The question of when local representability implies representability is discussed, and theories for which local representability always implies representability are fully characterized. Received December 20, 1996; accepted in final form March 19, 1998.     

Closed Conjugacy Classes,Closed Orbits and Structure of Algebraic Groups

In this paper we prove that if an affine algebraic group (in characteristic zero) has all its conjugacy classes closed, then it is nilpotent. A classical result (called sometimes the Kostant-Rosenlicht Theorem) guarantees that if an affine algebraic group G is unipotent, then all its orbits on affine varieties are closed. We prove the converse of that theorem in arbitrary characteristics.     

Conjugacy Classes,Class Sums and Character Tables for Hopf Algebras

We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ^?2 where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS ₃), which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums.