Electromagnetic simulations of tunable terahertz metamaterial infiltrated with highly birefringent nematic liquid crystal

In this article electromagnetic simulations of tunable terahertz metamaterial infiltrated with nematic liquid crystal are described. A full-wave analysis technique based on the finite-difference time-domain (FDTD) method was done by employing QuickWave 3D electromagnetic solver. Scattering parameter analysis shows a resonant frequency shift of 0.8 THz obtained by reorienting the layered highly birefringent nematic liquid crystal. Effective refractive index for operation frequency varies from negative to positive values.     

Inclusion Compounds of Nitrosobenzenes with Cholic Acid and Deoxycholic Acid

The crystalline inclusion compounds of cholic acid (CA) and deoxycholic acid (DCA) with several nitrosobenzenes were prepared. The IR spectra and crystal structures of these compounds confirmed inclusion of the monomeric form of the C-nitroso compounds. The DCA compounds have 2 : 1 host:guest stoichiometry and P2₁ symmetry. Guest molecules are enclosed in channels and disordered. In the CA-nitrobenzene inclusion compound (1·CA) the host:guest stoichiometry is 1 : 1. The host molecules form typical CA bilayer aggregates and guest molecules are accommodated in helicoidal channels. The guest nitroso group is not coplanar with the phenyl ring; the torsion angle on the C–N bond is 8.6(8)°. The solid-state circular dichroism spectrum of 1·CA shows the negative Cotton effect at 780 nm corresponding to the n–^* electronic transition that can be associated with the P helicity of the guest molecule. The extremely weak magnitude of the Cotton effects exhibited by the DCA complexes points to a nearly planar arrangement of the NO group and the phenyl ring in the guest molecules.     

Visible‐Light Photoactive,Highly Efficient Triplet Sensitizers Based on Iodinated Aza‐BODIPYs: Synthesis,Photophysics and Redox Properties

A series of novel iodinated NO₂‐substituted aza‐BODIPYs have been synthesized and characterized. Highly desirable photophysical and photochemical properties were induced in NO₂‐substituted aza‐BODIPYs by iodination of the pyrrole rings. In particular, high values of singlet oxygen quantum yields (Φ_Δ) ranging from 0.79 to 0.85 were measured. The photooxygenation process proceeds via a Type II mechanism under the experimental conditions applied. The compounds studied exhibited an absorption band within the so‐called “therapeutic window”, with λ_max located between 645 nm to 672 nm. They were non‐fluorescent at room temperature with excited singlet‐state lifetimes within the picosecond range as measured by femtosecond transient absorption. Nanosecond laser flash photolysis experiments revealed T₁→T_n absorption spanning from ca. 400 nm to ca. 500 nm and allowed determination of the triplet‐state lifetimes. The estimated triplet lifetimes (τ_T) in deaerated acetonitrile ranged between 2.74 μs and 3.50 μs. As estimated by CV/DPV measurements, all iodinated aza‐BODIPYs studied exhibited one irreversible oxidation and two quasi‐reversible reductions processes. Estimation of the E_HOMO gave the value of ?6.06 to ?6.26 eV while the E_LUMO was found to be located at ca. ?4.6 eV. Thermogravimetric (TGA) analysis revealed that iodinated aza‐BODIPYs were stable up to approximately 300 °C. All compounds studied exhibit high photostability in toluene solution.     

Complete π-Facial Stereoselectivity in the TiCl4-Mediated [4 + 2] Cycloaddition of Cyclopentadiene to N,N′-fumaroyldi[(2R)-bornane-10,2-sultam]

Under the co-operative influence of two prosthetic groups, and independent of the TiCl₄ concentration, complete and constant diastereofacial π-selection was achieved during the [4 + 2] cycloaddition of cyclopentadiene to N,N′-fumaroyl-di[(2R)-bornane-10,2-sultam] ((?)- 1c ); reactive conformations are discussed.     

Column Chromatography and Preparative TLC for Isolation and Purification of Coumarins from Peucedanum verticillare L. Koch ex DC

JPC – Journal of Planar Chromatography – Modern TLC - Preparative separation and isolation of coumarins from petroleum ether and methanol extracts of the fruits and roots of Peucedanum...     

Diffusion in a Weakly Random Hamiltonian Flow

We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to obtain error estimates for the convergence of the solution of the stochastic acceleration problem to a momentum diffusion. We also apply our results to the system of random geometric acoustics equations and show that the energy density of the acoustic waves undergoes a spatial diffusion.     

On commutators of equivariant homeomorphisms

The long-standing problem of the perfectness of the compactly supported equivariant homeomorphism group on a G-manifold (with one orbit type) is solved in the affirmative. The proof is based on an argument different than that for the case of diffeomorphisms. The theorem is a starting point for computing H₁(HG(M)) for more complicated G-manifolds.     

The bicategories of corings

To a B-coring and a (B,A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projective on one side, together with a map of corings over the same base ring, lead to the notion of a module-morphism, which extends the notion of a morphism of corings (over different base rings). A module-morphism of corings induces functors between the categories of comodules. These functors are termed pull-back and push-out functors, respectively, and thus relate categories of comodules of different corings. We study when the pull-back functor is fully faithful and when it is an equivalence. A generalised descent associated to a morphism of corings is introduced. We define a category of module-morphisms, and show that push-out functors are naturally isomorphic to each other if and only if the corresponding module-morphisms are mutually isomorphic. All these topics are studied within a unifying language of bicategories and the extensive use is made of interpretation of corings as comonads in the bicategory Bim of bimodules and module-morphisms as 1-cells in the associated bicategories of comonads in Bim.     

Platonic Orthonormal Wavelets

We classify all orthonormal wavelets which occur in theL²space of the faces of a platonic solid.     

Stationarity of Lagrangian Velocity¶in Compressible Environments

We study the transport of a passive tracer particle by a random d-dimensional, Gaussian, compressible velocity field. It is well known, since the work of Lumley, see [13], and Port and Stone, see [20], that the observations of the velocity field from the moving particle, the so-called Lagrangian velocity process, are statistically stationary when the field itself is incompressible. In this paper we study the question of stationarity of Lagrangian observations in compressible environments. We show that, given sufficient temporal decorrelation of the velocity statistics, there exists a transformation of the original probability measure, under which the Lagrangian velocity process is time stationary. The transformed probability is equivalent to the original measure. As an application of this result we prove the law of large numbers for the particle trajectory. Received: 1 May 2001 / Accepted: 4 December 2001