114,983 research outputs found

    Polyelectrolyte Solutions with Multivalent Salts

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    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

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    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

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    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

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    We prove the projective plane \rp^2 is an absolute extensor of a finite-dimensional metric space XX if and only if the cohomological dimension mod 2 of XX 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 Z4\Z_4 or Z2Z2\Z_2\oplus\Z_2 for n1n\ge 1. Double surgery and the above fact yield the proof.Comment: 17 page

    Current Trends in School Finance Reform Litigation: A Commentary

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    Cost of Survival for Large Rapidity Gaps

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    In this talk, given at "RunII QCD and weak boson WS", we report on calculations of the survival probability of the large rapidity gap (LRG) processes and its energy behaviour.Comment: 4 pages, 3 figure

    Universal acyclic resolutions for arbitrary coefficient groups

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    We prove that for every compactum XX and every integer n2n \geq 2 there are a compactum ZZ of dimn+1\dim \leq n+1 and a surjective UVn1UV^{n-1}-map r: Z \lo X such that for every abelian group GG and every integer k2k \geq 2 such that dimGXkn\dim_G X \leq k \leq n we have dimGZk\dim_G Z \leq k and rr is GG-acyclic
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