Rhodium(I) catalyzed four-component reaction of Fischer alkenyl carbene complexes and 1,1-diphenylallene

Alkyl substituted chromium Fischer carbene complexes react with 1,1-diphenylallene in the presence of rhodium(I) catalysts (10 mol%) to yield highly substituted dienyl indenone derivatives. In this process a catalytic chromium(0)-rhodium(I) exchange occurs, four new C-C bonds are created, and four-components (two allenes, the carbene ligand and one CO ligand) are joined in a chemo- and regioselective manner.     

Capillary electrophoretic determination of triamterene, methotrexate, and creatinine in human urine

A capillary zone electrophoresis (CZE) method using a fused-silica capillary (60.2 cm x 75 microm ID) was investigated for the determination of triamterene (TRI), methotrexate (MTX), and creatinine (CREA) in human urine. The separation was performed using a hydrodynamic injection time of 7 s (0.5 psi), a voltage of 25 kV, a capillary temperature of 30 degrees C, and 40 mM phosphoric acid adjusted to pH 2.25 by addition of triethanolamine as separation electrolyte. Under these conditions, analysis takes about 15 min. A linear response over the 0.5-15.0 mg L(-1) concentration range was found for TRI and MTX, and 0.5-80.0 mg L(-1) for CREA. Dilution of the sample (water:urine, 1:1 for TRI and MTX, and 1:25 for CREA determination) was the only step necessary prior to analysis by electrophoresis. The developed method is easy, rapid, and sensitive and has been applied to determine triamterene,methotrexate, and creatinine in urine samples with satisfactory results.     

Control of the Diels-Alder-Addition Regioselectivity by Remote Olefins. Syntheses and Cycloadditions of 2,3,5-Trimethylidenebicyclo[2.2.1]heptane and 2,3,5,6,7-Pentamethylidenebicyclo[2.2.2]octane

The syntheses of 2,3,5-trimethylidenebicyclo[2.2.1]heptane ( 1 ) and 2,3,5,6,7-pentamethylidenebicyclo[2.2.2]-octane ( 2 ) are reported. The Diels-Alder additions of the diene moieties of these polyenes can be regioselective, probably because of a possible transannular interaction between the homoconjugated methylidene and s-cis-buta-diene groups.     

Regularity of solutions and interfaces of a generalized porous medium equation inR N

Summary We consider the Cauchy problem for the generalized porous medium equation u_t=(u) where u=u(x, t), xRⁿ and t>0, and the initial datum u(x, 0) is assumed to be nonnegative, integrable mid to nave compact support. The nonlinearity (u) is a C¹ function defined for uO which grows like a power of u. Our assumptions generalize the porous medium case, (u)=u^m, m>1, and also include the equation of the Marshak waves. This problem has finite speed of propagation. We estimate the rate of growth of the support of the solution with precise estimates for t 0 and t. Our main result deals with the regularity of the solutions. We show that after a certain time t₀ the pressure, defined by v=(u), with (u)=(u)/u and (0)=0, is a Lipschitz-continuous function of x and t and the interface is a Lipschitz-continuous surface in R^N+1; the solution u is Hölder continuous for all times t> 0.Both authors partially supported by CAICYT, Project 2805-83. The second author also supported by USA-Spain Joint Research Grant CCB-8402023.     

Harmonic maps from compact Kähler manifolds to exceptional hyperbolic spaces

It has been conjectured that a lattice in a noncompact group of real rank one, other than SU(1,n), cannot be isomorphic to the fundamental group of a compact Kähler manifold; moreover, it is known to be true for SO(1,n). In this note it is shown that this conjecture also holds for the case of uniform lattices in F_4(?20), the group of isometries of the Cayley hyperbolic plane. The result is a consequence of a classification theorem for harmonic maps between Kähler and Cayley hyperbolic manifolds.     

Structural and magnetic phase transitions in Pr2NiO4

Neutron powder diffraction and magnetization measurements have been performed in stoichiometric Pr₂NiO₄₊(0), which at room temperature (RT) is orthorhombic (Bmab). Ni²⁺ becomes three dimensionally (3D) antiferromagnetically ordered atT _N 325K, with a propagation vectork=[100], and spins oriented along thea axis (parallel to the propagation vector). The magnetic structure belongs to the _7g (––+)-representation (g _x mode, Shubnikov groupB _pmab') ofBmab, and a magnetic moment of 1.5 _B is measured at 155K. This compound undergoes two different structural phase transitions. First, going down in temperature, Pr₂NiO₄ transforms by a first order phase transition from orthorhombic (Bmab) to tetragonal (P4₂/ncm) atT _c1115K. At high temperature, we can predict a transformation from orthorhombic (Bmab) to tetragonal (I4/mmm) in a continuous way. The extrapolated temperature for this second structural transition isT _c21500±100K. The low temperature structural transformation allows a change in the magnetic structure which forT<T _c1 is better described in the orthorhombic symmetry. Just belowT _c1 the magnetic structure is described by the: _3g (–+)-representation ofPccn(g_xc_yf_z mode, Shubnikov groupPccn), this magnetic phase begins to disappear going down in temperature and at the same time a new magnetic phase grows. This new magnetic structure is described by the _1g ofPccn (c _xg_ya_z mode, Shubnikov groupPccn). Both magnetic structures coexist in a certain temperature range. At 1.5 K thec _xg_ya_z mode represents the total of the magnetic ordering. To reproduce the observed magnetic intensities we are forced to consider that Pr³⁺ is polarized below 40 K, with a magnetic structure which is coupled to the Ni sublattices (i.e. _1g and _3g ). The magnetic moment at low temperature for Pr is about 1.28 _B .     

Convergence to equilibrium of critical branching particle systems and superprocesses,and related nonlinear partial differential equations

We consider a class of multitype particle systems in ^d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).     

Nontrivial periodic solutions of a nonlinear beam equation

We consider the existence of a nontrivial solution of the following equation: where g is a nondecreasing function defined on R¹, satisfies g(O) = O, and some other additional conditions. Our results and methods are quite similar to those associated with recent work on the nonlinear wave equation [1]-[8]: .     

Molecular dynamics in the smectic a and C phases in a long-chain ferroelectric liquid crystal: 2H NMR, dielectric properties, and a theoretical treatment

In this work, the rotational-diffusion coefficients D(parallel) and D(perpendicular) for the ferroelectric smectogen (+)-(S)-4-[4'-(1-methylheptyloxy)] biphenyl 4-(10-undecenyloxy)benzoate have been studied by means of 2H NMR spectroscopy in the smectic C phase, using a new theoretical approach (Domenici,V.; Geppi, M.; Veracini, C. A. Chem. Phys. Lett. 2003, 382, 518). The analysis of spin-lattice relaxation times has been performed in terms of the diffusional constant and the activation energy of the internal and overall molecular-reorientational motions, and the results are compared to the smectic A (SmA) phase. Moreover, from the 2H NMR data in the SmA phase, the dielectric permittivity and the dielectric relaxation time functions are investigated using a theoretical approach. The longitudinal and transverse components of the real Rchigammaomega and imaginary chigammaomega (gamma = parallel, perpendicular) parts of the complex susceptibility tensor and the nematic-like rotational-viscosity coefficients, lambda2 and lambda5, are calculated.     

Viscosimetric Study of Some Cyclic Ethers with Benzene, Toluene, or Halobenzene

Experimental viscosities and the corresponding viscosity deviations for the binary mixtures of a cyclic ether (tetrahydrofuran, tetrahydropyran, 2-methyltetrahydrofuran, or 2,5-dimethyltetrahydrofuran) with benzene, toluene, fluorobenzene, or chlorobenzene are given at 25°C. The kinematic viscosities and the corresponding densities were measured with an uncertainty of ±10^{– 4} mm²-s^{– 1} and ±(5×10^{– 3}) kg-m^{– 3}, respectively. The viscosity data were correlated by the equations of Grunberg–Nissan, McAllister, and Heric. On the other hand, the results have been compared to the predictions, by the method proposed by Asfour.