Polyelectrolyte Solutions with Multivalent Salts

We investigate the thermodynamic properties of a polyelectrolyte solution in a presence of {\it multivalent} salts. The polyions are modeled as rigid cylinders with the charge distributed uniformly along the major axis. The solution, besides the polyions, contain monovalent and divalent counterions as well as monovalent coions. The strong electrostatic attraction existing between the polyions and the counterions results in formation of clusters consisting of one polyion and a number of associated monovalent and divalent counterions. The theory presented in the paper allows us to explicitly construct the Helmholtz free energy of a polyelectrolyte solution. The characteristic cluster size, as well as any other thermodynamic property can then be determined by an appropriate operation on the free energy

Complex Formation Between Polyelectrolytes and Ionic Surfactants

The interaction between polyelectrolyte and ionic surfactant is of great importance in different areas of chemistry and biology. In this paper we present a theory of polyelectrolyte ionic-surfactant solutions. The new theory successfully explains the cooperative transition observed experimentally, in which the condensed counterions are replaced by ionic-surfactants. The transition is found to occur at surfactant densities much lower than those for a similar transition in non-ionic polymer-surfactant solutions. Possible application of DNA surfactant complex formation to polynucleotide delivery systems is also mentioned.Comment: 5 pages, latex, 3 figure

Rational acyclic resolutions

Let X be a compactum such that dim_Q X 1. We prove that there is a Q-acyclic resolution r: Z-->X from a compactum Z of dim < n+1. This allows us to give a complete description of all the cases when for a compactum X and an abelian group G such that dim_G X 1 there is a G-acyclic resolution r: Z-->X from a compactum Z of dim < n+1.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-12.abs.htm

Maps to the projective plane

We prove the projective plane \rp^2 is an absolute extensor of a finite-dimensional metric space $X$ if and only if the cohomological dimension mod 2 of $X$ does not exceed 1. This solves one of the remaining difficult problems (posed by A.N.Dranishnikov) in extension theory. One of the main tools is the computation of the fundamental group of the function space \Map(\rp^n,\rp^{n+1}) (based at inclusion) as being isomorphic to either $\Z_4$ or $\Z_2\oplus\Z_2$ for $n\ge 1$. Double surgery and the above fact yield the proof.Comment: 17 page

The exceptional set in Vojta's conjecture for algebraic points of bounded degree

We study the dependence on various parameters of the exceptional set in Vojta's conjecture. In particular, by making use of certain elliptic surfaces, we answer in the negative the often-raised question of whether Vojta's conjecture holds when extended to all algebraic points (that is, if the conjecture holds without fixing a bound on the degree of the algebraic points)