An application of L-functions of imaginary quadratic fields

Let F₁(x, y),…, F_2h+1(x, y) be the representatives of equivalent classes of positive definite binary quadratic forms of discriminant ?q (q is a prime such that q ≡ 3 mod 4) with integer coefficients, then the number of integer solutions of F_i(x, y) = n (i = 1,…, 2h + 1) can be calculated for each natural number n using L-functions of imaginary quadratic field $\text{Q}$((?q)^1/2).     

Microwave spectroscopy of propynal in the v2 = 1 vibrational state by IR-MW triple resonance

Infrared-microwave triple resonance was applied to microwave spectroscopy of propynal, HCCCHO, in the v₂ = 1 vibrational state. Eleven microwave transitions were newly observed by using a Zeeman-tuned 3.51 μm HeXe laser as the infrared radiation source. The spectrum was analyzed including the 11 transitions previously observed by double resonance. A least-squares fit of the 13 low-J transitions revealed that the rotational constants in the K_?1 = 1 states were slightly different from those of the K_?1 = 0 states. A higher-order rotational resonance was proposed for explanation of the effect.     

Ghost-free formulation of quantum gravity in the light-cone gauge

By choosing the light-cone gauge, we remove all redundant components of the metric tensor as well as all Faddeev-Popov ghosts from the Einstein Lagrangian, from which Feynman rules for two independent transverse components can be immediately formulated. The 2 + 2 decomposition of the metric tensor proves to be simpler than the usual canonical 1 + 3 decomposition, so that all spurious components can be explicitly eliminated from the spectrum. Because the Lagrangian is now only a function of independent components, it is possible to study the unresolved problem of the functional measure for quantum gravity. We are presently studying the measure problem.     

Nonlinear viscoelasticity of polystyrene solutions. II. Non-Newtonian viscosity

The steady shear viscosity η(k) and the stress decay function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \eta \left({t,k} \right)$\end{document} (the shear stress divided by the rate of shear k after cessation of steady shear flow) were measured for concentrated solutions of polystyrene in diethyl phthalate. Ranges of molecular weight M and concentration c were 7.10 × 10⁵ to 7.62 × 10⁶ and 0.112–0.329 g/cm³, respectively. Measurements were performed with a rheometer of the cone-and-plate type in the range 10^?4 < k < 1 sec^?1. The Cox–Merz relation η(k) = |η^*(ω)|_ω=k was tested with the experimental result (|^*(ω)| is the magnitude of the complex viscosity). It was found to be applicable to solutions of relatively low M or c but not to those of high M and c. For the latter η(k) began to decrease at a lower rate of shear than |η^*(ω)|_ω=k did; the Cox–Merz law underestimated the effect of rate of shear. The stress decay function was assumed to have a functional form \documentclass{article}\pagestyle{empty}\begin{document}$\tilde \eta \left( {t,k} \right) = \sum {\eta _p \left( k \right)e^{ - t/\tau p\left( k \right)} } $\end{document} where τ₁ > τ₂ > …, and the values of τ₁, τ₂ η₁ and η₂ were determined for some solutions. The relaxation times τ₁ and τ₂ were found to be independent of k and equal to the relaxation times of linear viscoelasticity. At the limit of k → 0, η₁ and η₂ were approximately 60 and 20–30%, respectively, of η and the non-Newtonian behavior was due to large decreases of η₁ and η₂ with increasing k. It was shown that η₁(k) may be evaluated from the relaxation strength G₁(s) for the longest relaxation time of the strain-dependent relaxation modulus with a constitutive model for relatively high c–M systems as well as for low c–M systems.     

Forbidden bands in the photoelectron spectra of diatomic molecules

Configuration interaction CNDO/INDO calculations have been used to interpret weak bands which have been observed in the photoelectron spectra of gaseous N₂, CO and CS. These bands are due to photoionisation to states which are formally forbidden on the simple one-electron transition model. The more general implications of configuration interaction bands in polyatomic molecules are discussed, and some examples are suggested where it is believed that the effect may be important.     

A decidualized endometrial cyst in a pregnant woman: a case observed with a steady-state free precession imaging sequence

Decidual changes of the ectopic endometrial stroma during pregnancy are well known among pathologists and obstetricians. However, they appear very similar to endometrial cysts with malignant transformation when imaged. Balanced fast field echo (BFFE) is a steady-state free precession imaging sequence and its contrast is decided by the T1/T2 ratio. The authors report a case of a decidualized endometrial cyst in which mural nodules were isointense with the nomotopic decidualized endometrium on T1- and T2-weighted images and BFFE. Isointensity with the nomotopic endometrium is an MR characteristic that can differentiate a decidualized endometrial cyst from malignant transformation. BFFE is a good alternative sequence during pregnancy because of its shorter acquisition time and lower radiofrequency absorption.