Wavelet processing and digital interferometric contrast to improve reconstructions from X‐ray Gabor holograms

In this work, the application of an undecimated wavelet transformation together with digital interferometric contrast to improve the resulting reconstructions in a digital hard X‐ray Gabor holographic microscope is shown. Specifically, the starlet transform is used together with digital Zernike contrast. With this contrast, the results show that only a small set of scales from the hologram are, in effect, useful, and it is possible to enhance the details of the reconstruction.     

Solvable lattice models related to the vector representation of classical simple Lie algebras

A series of solvable lattice models with face interaction are introduced on the basis of the affine Lie algebraX _n ⁽¹⁾ =A _n ⁽¹⁾ ,B _n ⁽¹⁾ ,C _n ⁽¹⁾ ,D _n ⁽¹⁾ . The local states taken on by the fluctuation variables are the dominant integral weights ofX _n ⁽¹⁾ of a fixed level. Adjacent local states are subject to a condition related to the vector representation ofX _n . The Boltzmann weights are parametrized by elliptic theta functions and solve the star-triangle relation.     

Exact coexistence surfaces containing double critical points for a three-component solution on the Bethe,honeycomb, and square lattices

A model is considered in which the bonds of a lattice are covered by rodlike molecules. Neighboring molecular ends interact with orientation-dependent interactions. The model exhibits closed -loop phase diagrams and double critical points. Exact coexistence surfaces are calculated for the model on the Bethe, honeycomb, and square lattices. The nature of the doubling of the critical exponent near a double critical point is calculated. The behavior of the critical line in the neighborhood of a double critical point is calculated exactly.     

Certain Families of Elliptic Functions Defined by <Emphasis Type="Italic">q</Emphasis>-Series

We introduce certain families of elliptic functions involving the Weierstrass ℘-function via q-series systematically and investigate their analytic and algebraic properties. Especially, we give examples of non-linear algebraic ordinary differential equations satisfied by some such elliptic functions. 2000 Mathematics Subject Classification: Primary–11M36, 33E05     

Hierarchic Natures and Dynamics of Photoinduced Structural Phase Transition in Non-Degenerate Charge Density Wave States Via Successive Photoexcitations

We investigate the adiabatic and dynamical natures of the lattice relaxation of excitons in strongly coupled electron-phonon (e-ph) systems using the extended Peierls-Hubbard model, so as to clarify the possible mechanisms of the photoinduced structural phase transition (PISPT) via multi-photon. Focusing on the growth process of relaxed domains that is induced by multi-photoexcitation, we calculate the adiabatic potential energy surfaces relevant to the nonlinear lattice relaxations of excitons in this process. Calculated potentials lead to an essential model of a multi-stepwise potential-crossing (MSPC) system that is composed of many displaced harmonic oscillators as an elementary process of the domain growth in the strongly coupled e-ph systems. We also investigate the dynamical natures in such MSPC systems calculating the time-developments the excited wave packet in this system using the density operator. It is concluded from calculated results that the system possibly develops from the lowest-energy potential state to the higher ones by the effect of the photoexcitations followed by the lattice relaxations.     

Hierarchy of the Selberg Zeta Functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Mathematics Subject Classifications (2000). Primary 11M36, Secondary 33B15     

Scanning ion conductance microscopy for imaging biological samples in liquid: a comparative study with atomic force microscopy and scanning electron microscopy

The present study was designed to show the applicability of scanning ion conductance microscopy (SICM) for imaging different types of biological samples. For this purpose, we first applied SICM to image collagen fibrils and showed the usefulness of the approach-retract scanning (ARS)/hopping mode for such samples with steep slopes. Comparison of SICM images with those obtained by AFM revealed that the ARS/hopping SICM mode can probe the surface topography of collagen fibrils and chromosomes at nanoscale resolution under liquid conditions. In addition, we successfully imaged cultured HeLa cells, with 15 μm in height by ARS/hopping SICM mode. Because SICM can obtain non-contact (or force-free) images, delicate cellular projections were visualized on the surface of the fixed cell. SICM imaging of live HeLa cells further demonstrated its applicability to study the morphological dynamics associated with biological processes on the time scale of minutes under liquid conditions. We further applied SICM for imaging the luminal surface of the trachea and succeeded in visualizing the surface of both ciliated and non-ciliated cells. These SICM images were comparable with those obtained by scanning electron microscopy. Although the dynamic mode of AFM provides better resolution than the ARS/hopping mode of SICM in some samples, only the latter can obtain contact-free images of samples with steep slopes, rendering it an important tool for observing live cells as well as unfixed or fixed soft samples with complicated shapes. Taken together, we demonstrate that SICM imaging, especially using an ARS/hopping mode, is a useful technique with unique capabilities for imaging the three-dimensional topography of a range of biological samples under physiologically relevant aqueous conditions.