Cohomological non-rigidity of generalized real Bott manifolds of height 2

We investigate when two generalized real Bott manifolds of height 2 have isomorphic cohomology rings with Z/2 coefficients and also when they are diffeomorphic. It turns out that cohomology rings with Z/2 coefficients do not distinguish those manifolds up to diffeomorphism in general. This gives a counterexample to the cohomological rigidity problem for real toric manifolds posed in \cite{ka-ma08}. We also prove that generalized real Bott manifolds of height 2 are diffeomorphic if they are homotopy equivalent

Estimation of Phonon Dispersion Relations Using Correlation Effects Among Thermal Displacements of Atoms

Neutron diffraction measurement of powder α-Fe sample at 295 K was carried out at the high resolution powder diffractometer installed at Japan Proton Accelerator Research Complex (J-PARC). Crystal parameters were determined from Rietveld analysis. The correlation effects among thermal displacements of atoms were estimated from a generalized equation based on the results of fomer diffuse scattering analysis. The force constants among atoms were obtained using an equation for transforming of the correlation effects to force constants. The force constants and the crystal structure of α-Fe were used to estimate the phonon dispersion relations, phonon density of states, and specific heat by computer simulation. The obtained force constants among first-nearest-neighboring atoms is 2.3 eV/Å2 at 295 K and the specific heat is 185 meV/K at 150 K. The calculated phonon dispersion relations and specific heat of α-Fe are similar to those obtained from inelastic neutron scattering and specific heat measurements, respectively. Received: 04 October 2014; Revised: 22 January 2015; Accepted: 30 March 201

Estimation of Phonon Dispersion Relations Using Correlation Effects Among Thermal Displacements of Atoms

Neutron diffraction measurement of powder α-Fe sample at 295 K was carried out at the high resolution powder diffractometer installed at Japan Proton Accelerator Research Complex (J-PARC). Crystal parameters were determined from Rietveld analysis. The correlation effects among thermal displacements of atoms were estimated from a generalized equation based on the results of fomer diffuse scattering analysis. The force constants among atoms were obtained using an equation for transforming of the correlation effects to force constants. The force constants and the crystal structure of α-Fe were used to estimate the phonon dispersion relations, phonon density of states, and specific heat by computer simulation. The obtained force constants among first-nearest-neighboring atoms is 2.3 eV/Å2 at 295 K and the specific heat is 185 meV/K at 150 K. The calculated phonon dispersion relations and specific heat of α-Fe are similar to those obtained from inelastic neutron scattering and specific heat measurements, respectively. Received: 04 October 2014; Revised: 22 January 2015; Accepted: 30 March 201

5-dimensional contact SO(3)-manifolds and Dehn twists

In this paper the 5-dimensional contact SO(3)-manifolds are classified up to equivariant contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that all simply connected 5-manifoldswith singular orbits are realized by a Brieskorn manifold with exponents (k,2,2,2). The standard contact structure on such a manifold gives right-handed Dehn twists, and a second contact structure defined in the article gives left-handed twists.Comment: 16 pages, 1 figure; simplification of arguments by restricting classification to coorientation preserving contactomorphism

A Computational Model of the Ionic Currents, Ca2+ Dynamics and Action Potentials Underlying Contraction of Isolated Uterine Smooth Muscle

Uterine contractions during labor are discretely regulated by rhythmic action potentials (AP) of varying duration and form that serve to determine calcium-dependent force production. We have employed a computational biology approach to develop a fuller understanding of the complexity of excitation-contraction (E-C) coupling of uterine smooth muscle cells (USMC). Our overall aim is to establish a mathematical platform of sufficient biophysical detail to quantitatively describe known uterine E-C coupling parameters and thereby inform future empirical investigations of physiological and pathophysiological mechanisms governing normal and dysfunctional labors. From published and unpublished data we construct mathematical models for fourteen ionic currents of USMCs: currents (L- and T-type), current, an hyperpolarization-activated current, three voltage-gated currents, two -activated current, -activated current, non-specific cation current, - exchanger, - pump and background current. The magnitudes and kinetics of each current system in a spindle shaped single cell with a specified surface area∶volume ratio is described by differential equations, in terms of maximal conductances, electrochemical gradient, voltage-dependent activation/inactivation gating variables and temporal changes in intracellular computed from known fluxes. These quantifications are validated by the reconstruction of the individual experimental ionic currents obtained under voltage-clamp. Phasic contraction is modeled in relation to the time constant of changing . This integrated model is validated by its reconstruction of the different USMC AP configurations (spikes, plateau and bursts of spikes), the change from bursting to plateau type AP produced by estradiol and of simultaneous experimental recordings of spontaneous AP, and phasic force. In summary, our advanced mathematical model provides a powerful tool to investigate the physiological ionic mechanisms underlying the genesis of uterine electrical E-C coupling of labor and parturition. This will furnish the evolution of descriptive and predictive quantitative models of myometrial electrogenesis at the whole cell and tissue levels