The number of spanning trees of plane graphs with reflective symmetry

A plane graph is called symmetric if it is invariant under the reflection across some straight line (called symmetry axis). Let G be a symmetric plane graph. We prove that if there is no edge in G intersected by its symmetry axis then the number of spanning trees of G can be expressed in terms of the product of the number of spanning trees of two smaller graphs, each of which has about half the number of vertices of G.     

Characterization of PbSe1−xTex thin films

The lead salts and their alloys are extremely interesting semiconductors due to their technological importance. The fabrication of devices with alloys of these compounds possessing detecting and lasing capabilities has been an important recent technological development. The high quality polycrystalline thin films of PbSe_1−xTe_x with variable composition (0≤x≤1) have been deposited onto ultra clean glass substrates by vacuum evaporation technique. As deposited films were annealed in vacuum at 350 K. The optical, electrical and structural properties of PbSe_1−xTe_x thin films have been examined. The optical constants (absorption coefficient and bandgap) of the films were determined by absorbance measurements in the wavelength range 2500-5000 nm using Fourier transform infrared spectrophotometer. The dc conductivity and activation energy of the films were measured in the temperature range 300-380 K. The X-ray diffraction patterns were used to determine the sample quality, crystal structure and lattice parameter of the films.     

Domains of infinitesimal generators of automorphism flows

We present a systematic characterization of the domain of a generator of a one parameter group on certain C∗-subalgebras of via finite-dimensional estimates. Our approach yields an example of a densely defined closed symmetric derivation on a C∗-subalgebras of whose domain is not closed with respect to the C¹-functional calculus. This completes and complements the earlier example of McIntosh (J. Funct. Anal. 30 (1977) 264). Our methods are partly based on the theory of adjoint C₀-semigroups.     

Minimal volume with length bounded below

We study a broad class of problems where volume is minimized among metrics on a smooth, compact Riemannian manifold that keep the length of a fixed set of curves bounded below. They can be seen as a generalization of isosystolic inequalities. Necessary and sufficient conditions are given for continuous minima in a conformal class and necessary conditions are given for local minima.     

Comparison results for the volume of geodesic celestial spheres in Lorentzian manifolds

Volume comparison results are obtained for the volume of geodesic celestial spheres in Lorentzian manifolds and the corresponding objects in Lorentzian space forms. Also, as a rigidity result it is shown that the volume of geodesic celestial spheres is independent of the instantaneous observer if and only if the spacetime has constant curvature.     

Neutron electric dipole moment measurement with a buffer gas comagnetometer

A neutron EDM measurement with a comagnetometer is discussed. For magnetometry, polarized xenon atoms are injected into a cylindrical cell where a cylindrically symmetric magnetic field and an electric field are applied for the EDM measurement. The geometric phase effect (GPE), which originates from particle motion in a magnetic field gradient, is analyzed in terms of the Dyson series. The motion of the xenon atom is largely suppressed because of a small mean free path. The field gradient is controlled by means of NMR measurements, where the false effect of Earth?s rotation is removed. As a result, the GPE is reduced below 10⁻²⁸e cm${10}^{-28}e\text{cm}$.     

C4- and D4-Modules via perspective direct summands

In this article, we study the C4- and D4-modules in terms of perspective direct summands, providing new characterizations and results. Endomorphism rings of C4-modules and extensions of right C4-rings are also investigated. Decompositions of C4-modules with restricted ACC on direct summands and D4-modules with restricted DCC on direct summands are obtained.     

Unusual conformational preferences of 1,3‐dimethyl‐3‐isopropoxy‐3‐silapiperidine

The conformational analysis of the first representative of the Si‐alkoxy substituted six‐membered Si,N‐heterocycles, 1,3‐dimethyl‐3‐isopropoxy‐3‐silapiperidine, was performed by low‐temperature ¹H and ¹³C NMR spectroscopy and DFT theoretical calculations. In contrast to the expectations from the conformational energies of methyl and alkoxy substituents, the Me_axi‐PrO_eq conformer was found to predominate in the conformational equilibrium in the ratio Me_axi‐PrO_eq : Me_eqi‐PrO_ax of ca. 2 : 1 as from the ¹H and ¹³C NMR study. The thermodynamic parameters obtained by the complete line shape analysis showed that the main contribution to the barrier to ring inversion originates from the entropy term of the free energy of activation. Copyright © 2012 John Wiley & Sons, Ltd.     

Slow molecular processes in a nematic liquid crystal confined to random porous network formed by aerosil particles

Frequency dispersion measurements of proton spin–lattice relaxation rates (R ₁) of liquid crystal 4-propyl-4′-pentylazoxybenzene in bulk and confined samples (in random porous network of aerosil nano-particles) are reported in isotropic and nematic phases. Significant low-frequency increase in R ₁ in confined samples indicates slow molecular reorientations mediated by translational displacements near the adsorbing porous surface. The resulting dispersion behavior of R ₁ (～ω ^{? p} ) reflects the nature of the random surface (p?=?0.5 for equi-partition of the diffusive modes). The observed temperature-independent exponent in the isotropic phase (p?=?0.34) indicates the abundance of low-wavelength surface modes. Its temperature-dependent higher values in the nematic phase (from 0.59 to 0.65 on cooling), and increased spin–lattice coupling via this mechanism, show progressive onset of longer wavelength modes. A detailed analysis shows the effect of confinement on the order director fluctuations, molecular reorientations, and translational diffusion of the molecules.     

Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis

In this paper, we present a method of higher-order analysis on bifurcation of small limit cycles around an elementary center of integrable systems under perturbations. This method is equivalent to higher-order Melinikov function approach used for studying bifurcation of limit cycles around a center but simpler. Attention is focused on planar cubic polynomial systems and particularly it is shown that the system studied by ?o?a?dek (1995) [24] can indeed have eleven limit cycles under perturbations at least up to 7th order. Moreover, the pattern of numbers of limit cycles produced near the center is discussed up to 39th-order perturbations, and no more than eleven limit cycles are found.