Formation and transformation of Pb2SiO4

A new modification of Pb₂SiO₄ was formed by the simultaneous hydrolysis of lead and silicon alkoxides, followed by washing and drying. It has a     

A study of the K = 3nA1 - A2 centrifugal splitting in the 3ν2 and 4ν2 states of PH3 using a difference-frequency laser system

A frequency tunable infrared source has been constructed by using the (Ar-laser) - (dyelaser) difference frequency method developed by Pine and applied to the observation of the overtone bands of PH₃ 3ν₂ ← 0 and 4ν₂ ← ν₂ in the 3.4 μm region and 4ν₂ ← 0 in the 1.6-μm region. A Stark modulation method was used to increase the sensitivity of detection. For transitions which were well modulated, the minimum detectable absorption coefficient was estimated to be ～3 × 10^?7 cm^?1 using a 3-m cell. Emphasis was placed on the observation of the A₁-A₂ splitting for K = 3n rotational levels. For the 3ν₂ state splittings were observed for K = 3, 6, and 9 because PH₃ is a very nearly spherical top in this state. The magnitude and the J dependence of the observed K = 3n splittings have been analyzed by using a normal symmetric rotor Hamiltonian and a centrifugal distortion term of the form $\text{τ}{}_{\mathrm{xxxz}}\text{[(J}{}_{\mathrm{+}}{}^3\text{+ J}{}_{\mathrm{?}}{}^3\text{)J}{}_{\mathrm{z}}\text{+ J}{}_{\mathrm{z}}\text{(J}{}_{\mathrm{+}}{}^3\text{+ J}{}_{\mathrm{?}}{}^3\text{)]}\text{4}$.     

Unipotent Algebraic Affine Supergroups and Nilpotent Lie Superalgebras

We characterize hereditary (as coalgebras) Hopf algebras by the property of ‘equivariant smoothness’, and apply the result to generalize to the super-context, the category equivalence, due to Hochschild, between the unipotent algebraic affine groups and the finite-dimensional nilpotent Lie algebras, in characteristic zero. The global dimension of commutative Hopf algebras, regarded as coalgebras, is also discussed. Presented by S. Montgomery Mathematics Subject Classification (2000) 16W30.     

ΔK = 2 transitions in H2CO and D2CO

Weak transitions of the type ΔJ = ± 1, $\text{Δ}\text{K}{}_{\mathrm{a}}\text{= ? 2}$, ΔK_c = ± 3 have been observed in H₂CO and D₂CO by the millimeterwave double resonance method and also by direct absorption with a Stark modulated spectrometer. The addition of these new transitions in a least-squares analysis, in which all previously known microwave and millimeterwave data are also included, results in an improved set of rotational and distortion constants.     

Channeled spectropolarimetry using a coherent white-light continuum

We carry out polarization measurements using a coherent white-light continuum as a light source for channeled spectropolarimetry. The white-light continuum, whose spectrum ranges from the UV to the IR region, is generated in Kr gas by a terawatt femtosecond laser system. The complete set of Stokes parameters from 450-700 nm are reconstructed from one spectral measurement. Also, the effectiveness of channeled spectropolarimetry using a coherent white-light continuum is experimentally demonstrated with a highly attenuating sample whose transmittance is as low as 10(-6).     

Global solvability for abstract semilinear evolution equations

The Cauchy problem for the abstract semilinear evolution equation u^′(t) = Au (t) + B (u (t)) + C (u (t)) is discussed in a general Banach space X. Here A is the so‐called Hille‐Yosida operator in X, B is a differentiable operator from D (A) into X, and C is a locally Lipschitz continuous operator from D (A) into itself. A vectorvalued functional defined only on X is used and appropriate conditions on the nonlinear operators B and C are imposed so that a vector‐valued functional defined on the domain of the operator A may be constructed in order to specify the growth of a global solution. The advantage of our formulation lies in the fact that it is possible to obtain a global solution by checking some energy inequalities concerning only low order derivatives (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)