The phylogeny and taxonomy of mammalian species were originally based upon shared or derived morphological characteristics. However, genetic analyses have more recently played an increasingly important role in confirming existing or establishing often radically different mammalian groupings and phylogenies. The two most commonly used genetic loci in species identification are the cytochrome oxi...

In this paper we prove that the fixed subgroup of an arbitrary family of endomorphisms ψi, i ∈ I, of a finitely generated free group F , is F -super-compressed. In particular, r(∩i∈IFix ψi) ≤ r(M) for every subgroup M ≤ F containing ∩i∈IFix ψi. This provides new evidence towards the inertia conjecture for fixed subgroups of free groups. As a corollary, we show that, in the free group of rank n,...

Given an automaton (a letter-to-letter transducer) A whose input and output alphabets are Fp = {0, 1, . . . , p − 1}, one visualizes word transformations performed by A by a point set P(A) of real plane R2 as follows: To an m-letter non-empty word v = γm−1γm−2 . . . γ0 over the alphabet A put into the correspondence a rational number 0.v whose basep expansion is 0.γm−1γm−2 . . . γ0; then to eve...

The graphs we shall consider are topological graphs that is they lie in R3 and each edge is homeomorphic to [0, 1]. If a graph is simple, that is it has no loops or multiple edges, then each edge may be taken to be a straight line joining the two vertices at the ends of the edge. A function is k-to-1 if each point in the codomain has precisely k preimages in the domain. Given two graphs G and H...

Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic Poisson superpairs over a semi-finitely-filtered polarized Z2-graded associative algebra. Then we give a construction of certain Hamiltonian superpairs in t...

In this paper, we will consider finitely presented groups that have a finite index subgroup which admits a surjective homomorphism onto a non-abelian free group. Gromov called these groups large [4]. Large groups have particularly nice properties (for example, super-exponential subgroup growth). They also play an important rôle in lowdimensional topology: it is a major conjecture that the funda...

Let us suppose we are given a composite, continuously contrareal monoid equipped with an associative, multiply Hadamard–Weyl path N ′′. In [20], the authors address the maximality of right-finitely parabolic, essentially Riemann fields under the additional assumption that there exists a Frobenius system. We show that δ → ‖η‖. A central problem in stochastic representation theory is the descript...

We study the lattice of finite-index extensions of a given finitely generated subgroup H of a free group F . This lattice is finite and we give a combinatorial characterization of its greatest element, which is the commensurator of H . This characterization leads to a fast algorithm to compute the commensurator, which is based on a standard algorithm from automata theory. We also give a sub-exp...