Subtleties in data analysis related to the size of critical region

We comment on the analysis of the critical behavior of a layered driven diffusive system recently done by Achahbar and Marro. We discuss why we believe their method of taking the thermodynamic limit and determining the order-parameter exponent leads to unreliable estimates.     

On some global well-posedness and asymptotic results for quasilinear parabolic equations

We prove that the quasilinear parabolic initial-boundary value problem (1.1) below is globally well-posed in a class of high order Sobolev solutions, and that these solutions possess compact, regular attractors ast+.     

A Construction of Partial Difference Sets in {\mathbb{Z}}_{p^{2 \times } } {\mathbb{Z}}_{p^{2 \times \cdot \cdot \cdot \times } } {\mathbb{Z}}_{p^2 }

In this paper, we give a construction of partial difference sets in _p ² x _p ² x ... x _p ²using some finite local rings.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe work of this paper was done when the authors visited the University of Hong Kong.     

Synthesis and Structural Studies of Platinum Complexes Containing Monodentate, Bridging, and Chelating Formamidine Ligands

The reactions of K(2)PtCl(4) with N,N'-diphenylformamidine (HDPhF) and N,N'-di-p-tolylformamidine (HDTolF) produce the trans square-planar compounds PtCl(2)(HDPhF)(2), 1a, and PtCl(2)(HDTolF)(2), 1b. Compound 1a crystallizes as yellow parallelepipeds in the space group P2(1)/c with two independent molecules in the asymmetric unit and unit cell dimensions a = 23.427(7) ?, b = 16.677(6) ?, c = 12.980(4) ?, and beta = 96.10(2) degrees. These compounds are soluble in common organic solvents and have been used as starting materials for the preparation of diplatinum compounds. Treatment of 1a and 1b with NaOMe and the halide abstraction reagent TlPF(6) produces the compounds Pt(2)(&mgr;-DArF)(2)(eta(2)-DArF)(2), Ar = Ph (2a) and Tol (2b), respectively. Compound 2a crystallizes as yellow rods in the space group P&onemacr; with unit cell dimensions a = 12.296(3) ?, b = 12.310(4) ?, c = 15.374(4) ?, alpha = 90.75(2) degrees, beta = 91.02(2) degrees, and gamma = 110.20(2) degrees. Compound 2b crystallizes with a molecule of THF, as yellow rods in the space group P2(1)/c with a = 17.883(3) ?, b = 14.517(3) ?, c = 22.581(3) ?, and beta = 98.17(1) degrees. These compounds contain two cis bridging formamidinato ligands and two formamidinato ligands that are chelated to separate Pt centers. Upon heating, they further react to give the tetrabridged compounds Pt(2)(&mgr;-DArF)(4), Ar = Ph (3a), Tol (3b). Compound 3a crystallizes as orange cubes in the cubic space group I432 with a = 19.671(1) ?. On going from the bis-bridged, bis-chelate structure in 2a to the tetrabridged structure in 3a, the metal-metal separation decreases from 2.910(1) to 2.649(1) ?. Both 2band 3b have been oxidized to give the Pt(II)-Pt(III) compound Pt(2)(&mgr;-DTolF)(4)(PF(6)), 4. Compound 4 crystallizes as cubes in the tetragonal space group P4/ncc with a = 14.392(1) ? and c = 14.436(1) ?. The Pt-Pt distance in 4 is 2.5304(6) ?.     

On generalized quadratic equations in three prime variables

Leta ₁,a ₂ anda ₃ be any nonzero integers which are relatively prime and not all negative. In this paper, as a parallel problem of [11] for each integerk≥2, we consider the setE(X) of positive integersb≤X which satisfy the condition of congruent solubility and that the equation $$a_1 p_1^2 + a_2 p_2^2 + a_3 p_3^k = b$$ is insoluble in primesp _j. We obtain CardE(X)≤X ^1-ε. Our result extends the wellknown classical results (by Legendre and Gauss and byDavenport andHeilbronn [2]) on the equation $$x_1^2 + x_2^2 + x_3^k = b$$ in integral variablesx _j with the above bound for CardE(X) better than that in [2].