On Asymptotic Dimension of Groups Acting on Trees

We prove the following.THEOREM. Let be the fundamental group of a finite graph of groups with finitely generated vertex groups G _v having asdim G _v n for all vertices v. Then asdim n+1.This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product.     

Electrochemical characterization of cationic surfactants’ adsorption on a disturbed n-alkanethiolate self-assembled monolayer-modified polycrystalline gold electrode

The adsorption of cetyltrimethylammonium bromide (CTAB) on disturbed n-alkanethiolate self-assembled monolayers (SAMs) was investigated by electrochemical methods with potassium ferricyanide [K₃Fe(CN)₆] as a probe. Compared with the completely restrained signal at ordinary compact n-alkanethiolate SAMs, the electrochemical response of K₃Fe(CN)₆ at the disturbed n-alkanethiolate SAMs was partly restored and became progressively reversible in the presence of increasing concentrations of CTAB, which was employed to characterize the adsorption of cationic surfactants on hydrophobic SAMs. The effect of CTAB concentration on electrochemical impedance spectroscopy (EIS) plots indicated that CTAB experienced two different types of adsorptive behavior at the disturbed n-alkanethiolate SAMs: monomer adsorption at low concentrations below 1×10^–6 M and monolayer adsorption at CTAB concentrations above 1×10^–5 M. The adsorption of a series of cationic surfactants with similar structures to CTAB on disturbed n-alkanethiolate SAMs was also explored. These surfactants had similar adsorptive behavior and showed nearly linear adsorption characteristics with the length of their hydrophobic tails.     

Trees, parking functions, syzygies, and deformations of monomial ideals

For a graph , we construct two algebras whose dimensions are both equal to the number of spanning trees of . One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis elements correspond to -parking functions that naturally came up in the abelian sandpile model. These ideals are instances of the general class of monotone monomial ideals and their deformations. We show that the Hilbert series of a monotone monomial ideal is always bounded by the Hilbert series of its deformation. Then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals. In some cases these resolutions coincide with Scarf resolutions. We prove several formulas for Hilbert series of monotone monomial ideals and investigate when they are equal to Hilbert series of deformations. In the appendix we discuss the abelian sandpile model.

     

Smooth solutions to a class of free boundary parabolic problems

We establish existence, uniqueness, and regularity results for solutions to a class of free boundary parabolic problems, including the free boundary heat equation which arises in the so-called ``focusing problem' in the mathematical theory of combustion. Such solutions are proved to be smooth with respect to time for positive , if the data are smooth.

     

Free Wreath Product by the Quantum Permutation Group

Let A be a compact quantum group, let nN ^* and let A _aut(X _n ) be the quantum permutation group on n letters. A free wreath product construction A*_w A _aut(X _n ) is introduced. This construction provides new examples of quantum groups, and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph.     

On the dynamics of generic non-Abelian free actions

We investigate some global generic properties of the dynamics associated to non-Abelian free actions in certain special cases. The main properties considered in this paper are related to the existence of dense orbits, to ergodicity and to topological rigidity. We first deal with them in the case of conservative homeomorphisms of a manifold and C ¹-diffeomorphisms of a surface. Groups of analytic diffeomorphisms of a manifold which, in addition, contain a Morse-Smale element and possess a generating set close to the identity are considered as well. From our discussion we also derive the existence of a rigidity phenomenon for groups of skew-products which is opposed to the phenomenon present in Furstenbergs celebrated example of a minimal diffeomorphism that is not ergodic (cf. [Ma]).     

Equivalence Principle Measurements

Over the centuries there have been many experimental tests of the universality of free-fall. To date, these measurements have established the equivalence between inertial and gravitational mass to high precision, justifying its use as a foundation stone of general relativity by Einstein. There is a surprising richness in the variety of techniques and choice of test bodies which have been used so far, and a brief review is presented. However, future space experiments promise much better precision in this measurement and STEP is presented in some detail as one of a number of such missions. Using pairs of concentric free-falling proof-masses, STEP will be able to test the Equivalence Principle (EP) to a sensitivity at least five orders of magnitude better than currently achievable on ground. The EP is a founding principle of general relativity and STEP is the most sensitive experiment of this type planned so far, aiming at 1 part in 10¹⁸.     

Thermosensitive poly(methyl methacrylate) emulsion prepared in the presence of poly(vinyl alcohol) with a cloud point as a protective colloid

An emulsion of poly(methyl methacrylate) (PMMA) was prepared using poly(vinyl alcohol) (PVA) of low degree of hydrolysis with a cloud point as a protective colloid. The behaviour of an aqueous solution of PVA with 80% degree of hydrolysis was first investigated in terms of the Huggins constant in viscometry. MMA was polymerized using the PVA at 20 °C, where no abnormality in the aqueous PVA was observed. The change in transmittance of the emulsion observed with a UV–vis photometer revealed that in the case of UV light of wavelength 370 nm, the transmittance decreased markedly at around 30 °C with an increase in temperature, and then increased with a decrease in temperature. The thermosensitive property resulted from PVA with a low degree of hydrolysis with a cloud point, at a higher temperature of which the PVA loses solubility in water owing to weakening of the hydrogen bond between PVA molecules and water.     

Monosized cationic nanoparticles prepared by emulsifer-free emulsion polymerization

Monosized poly(styrene/N-[3-(dimethylamino)propyl]methacrylamide/poly(ethylene glycol) ethyl ether methacrylate) [poly(St/PEG-EEM/DMAPM)] cationic nanoparticles were synthesized by emulsifier-free emulsion polymerization conducted in the presence of a cationic initiator, 2,2-azobis(2-methylpropionamidine) dihydrochloride (APDH or V-50). Particle sizes and surface charge densities were measured with a Zeta Sizer. The structure of the terpolymers was determined by Fourier transform IR and ¹H NMR spectroscopies. The amounts of the main monomer (St), cationic comonomer (DMAPM), stabilizer (PEG-EEM), and initiator (APDH), and the water-to-monomer phase ratio were all effective on both the average size and the surface charge of the nanoparicles. The average particle size was in the range 75–400 nm depending on the recipe applied; it decreased on increasing the amount of DMAP or PEG-EEM or the water-to-monomer phase ratio in the feed, while it increased with increasing St or APDH content. These nanoparticles were quite monodisperse with a polydispersity index of 1.008–1.14.