Pair function for the rectangular Ising ferromagnet

A representation of the pair correlation function for the rectangular Ising model in zero magnetic field is derived using a new spinor technique; this enables the scaling limit to be established, as well as several analytical properties of the scaling functions.Supported by the Fonds National Suisse de la Recherche Scientifique, by the National Science Foundation Grant No. PHY76-17191, and by the National Research Council of Canada Grant No. NRC A9344     

Continuity of invariant measures for families of maps

Let {τ_r} be the family of maps from [0,1] into [0,1] with properties similar to those of τ_r(x) = rx(1 ? x), 0 ≤ r ≤ 4. The limiting behaviour of orbits {τ_r^j(x)}_j^∞ = 1 is a complicated and discontinuous function of the parameter r. The stochastic approximation to the difference equation x_{n + 1} = τ_r(x_n), x_{n + 1} = τ_r(x_n) + W, where W is a fixed random variable independent of r and x_n, is considered. It is shown that this Markov process admits a unique absolutely continuous invariant measure μ_r and, furthermore, that the map r → μ_r is continuous. Such a result is important in applications, since slight changes in the shape of τ_r no longer cause discontinuous consequences in the limiting behaviour of the system.     

Wetting effects at a grain boundary

We consider a tier of weakened bonds along the center line of a two-dimensional Ising ferromagnet strip as a model of a grain boundary. When an interface traverses such a strip at an angle, whether or not there is a continuous pinning-depinning transition at subcritical temperature depends on this angle and the degree of bond weakening. We also study the relaxation of such a system to its equilibrium state using continuous time Monte Carlo simulation with Kawasaki dynamics; this reveals a matter transport mechanism confined to the grain boundary.     

Photo-lithographically impregnated and molecularly imprinted polymer thin film for biosensor applications

A voltammetric sensor for albuterol was investigated where we combined the techniques of microfabrication and molecular imprinting to construct on-chip devices using photoirradiation of cross-linkable polymers. Molecularly imprinted polymer was coated as a thin film onto the gold working electrode on chip and the analyte was directly quantified by differential pulse voltammetric measurements.     

A value on ′AN

We prove here the existence of a value (of norm 1) on the spaces N A and even A N, the closure in the variation distance of the linear space spanned by all games f, where is a non-atomic, non-negative finitely additive measure of mass 1 and f a real-valued function on [0,1] which satisfies a much weaker continuity at zero and one. 1991 Mathematics Subject Classification. 90A08, 90A07This research was in part supported by the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Prime Ministers Science Policy Office.     

On a superatomic Boolean algebra which is not generated by a well-founded sublattice

Let b denote the unboundedness number of ω^ω. That is, b is the smallest cardinality of a subset such that for everyg∈ω^ω there isf ∈ F such that {n: g(n) ≤ f(n)}is infinite. A Boolean algebraB is wellgenerated, if it has a well-founded sublatticeL such thatL generatesB. We show that it is consistent with ZFC that , and there is a Boolean algebraB such thatB is not well-generated, andB is superatomic with cardinal sequence 〈ℵ₀, ℵ₁, ℵ₁, 1〉. This result is motivated by the fact that if the cardinal sequence of a Boolean algebraB is 〈ℵ₀, ℵ₀, λ, 1〉, andB is not well-generated, then λ≥b.     

Some rings are hereditary rings

LetR be a bounded Noetherian Prime ring. The Asano-Michler theorem shows thatR is a bounded Dedekind ring if every prime ideal ofR is invertible. We provide a simple proof of the Asano-Michler theorem, and we suggest some possible generalizations. We also prove that if the proper residue rings ofR areQF-rings thenR is a bounded Dedekind ring, and generalize this result toLD-rings.     

Hydrothermal synthesis, structure and thermal stability of diamine templated layered uranyl-vanadates

Six new layered uranyl vanadates (NH₄)₂[(UO₂)₂V₂O₈] (1), (H₂EN)[(UO₂)₂V₂O₈] (2), (H₂DAP)[(UO₂)₂V₂O₈] (3), (H₂PIP)[(UO₂)₂(VO₄)₂].0,8H₂O (4), (H₂DMPIP)[(UO₂)₂V₂O₈] (5), (H₂DABCO)[(UO₂)₂(VO₄)₂] (6) were prepared from mild-hydrothermal reactions using 1,2-ethylenediamine (EN); 1,3-diaminopropane (DAP); piperazine (PIP); 1-methylpiperazine (MPIP); 1,4-diazabicyclo[2,2,2]octane (DABCO). The structures of 1, 4, 5 and 6 were solved using single-crystal X-ray diffraction data while the structural models of 2 and 3 were established from powder X-ray diffraction data. In compounds 1, 2, 3 and 5, the uranyl-vanadate layers are built from dimers of edge-shared UO₇ pentagonal bipyramids and dimers of edge-shared VO₅ square pyramids further connected through edge-sharing. In 1 and 3, the layers are identical to that occurring in the carnotite group of uranyl-vanadates. In 2 and 5, the V₂O₈ dimers differ in orientation leading to a new type of layer. The layers of compound 4 and 6 are built from chains of edge-shared UO₇ pentagonal bipyramids connected by VO₄ tetrahedra and are of uranophane-type anion topology. For the six compounds, the ammonium or organoammonium cation resides in the space between the inorganic layers. Crystallographic data: 1 monoclinic, space group P2₁/c with a=6.894(2), b=8.384(3), c=10.473(4) Å and β=106.066(5)°, 2 monoclinic, space group P2₁/a with a=13.9816(6), b=8.6165(3), c=10.4237(3) Å and γ=93.125(3)°, 3 orthorhombic, space group Pmcn with a=14.7363(8), b=8.6379(4) and c=10.4385(4) Å, 4 monoclinic, space group C2/m with a=15.619(2), b=7.1802(8), c=6.9157(8) Å and β=101.500(2)°, 5 monoclinic, space group P2₁/b with a=9.315(2), b=8.617(2), c=10.5246(2) Å and γ=114.776(2)°, 6 monoclinic, space group C2/m with a=17.440(2), b=7.1904(9), c=6.8990(8) Å and β=98.196(2)°.