The Darboux-Type Theorems for ∂-Symplectic and ∂-Contact Structures

A -symplectic structure on a complex manifold M of complex dimension2n is given by a smooth -closed (2, 0)-form such that ⁿ is nonvanishing. We prove that a version of the Darboux theorem isvalid for such a structure: locally can be represented as _i=1 ⁿ f _i f _{n + i} for appropriate smooth complex valuedfunctions f ₁, ..., f _2n . We also present a contact version of this theorem.     

Chemically active substitutional nitrogen impurity in carbon nanotubes

We investigate the nitrogen substitutional impurity in semiconducting zigzag and metallic armchair single-wall carbon nanotubes using ab initio density functional theory. At low concentrations (less than 1 at. %), the defect state in a semiconducting tube becomes spatially localized and develops a flat energy level in the band gap. Such a localized state makes the impurity site chemically and electronically active. We find that if two neighboring tubes have their impurities facing one another, an intertube covalent bond forms. This finding opens an intriguing possibility for tunnel junctions, as well as the functionalization of suitably doped carbon nanotubes by selectively forming chemical bonds with ligands at the impurity site. If the intertube bond density is high enough, a highly packed bundle of interlinked single-wall nanotubes can form.     

Brief review of emerging photovoltaic absorbers

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Nonlinear analysis of digital images and Doppler measurements for trophoblastic tumor

Cancer can be viewed as a complex adaptive system. Complex adaptive systems can be described mathematically by nonlinear (chaos) theory including asymmetry, fractal structure and autocorrelation factor. Taking into consideration spatial irregularity and heterogeneity of internal structures of tumor cells, we examined deterministic chaos of trophoblastic tumor for organ, cellular, molecular levels on digital images and their Doppler measurements of blood flow. The digital images were tested by evaluation of contours deformation level and quantitative heterogeneous pattern. The suggested algorithm for estimation of spatial chaos in digital medical image is based on calculation of the skew and the spread parameters, fractal dimension and autocorrelation function. Ultrasound images demonstrated higher values of the skew parameter for the uterus of choriocarcinoma patients than hydatidiform mole and healthy individuals. The registered changes in nonlinear dynamics of uterine artery blood flow are tending to diminish deterministic chaotic process in choriocarcinoma. Nonlinear analysis of cell images for chorionic villi and tumor supressor gene p16 evidenced the tendency of increase in spatial chaos for patients with choriocarcinoma. The concept of deterministic chaos is hierarchical for the host during trophoblastic disease.     

Synthesis of 1R‐1H‐Imidazo[1,2‐a]pyridin‐4‐ium‐8‐olate Derivatives

A new method based on reaction of 4‐bromobut‐2‐enoates with N‐alkylimidazoles was proposed for obtaining 1R‐1H‐imidazo[1,2‐a]pyridin‐4‐ium‐8‐olate and 1‐R‐8‐methoxy‐1H‐imidazo[1,2‐a]pyridin‐4‐ium derivatives. The structures of synthesized compounds were confirmed by ¹H, ¹³C NMR, elemental analysis, and X‐ray data.     

Application of a portable nuclear magnetic resonance surface probe to porous media

A portable nuclear magnetic resonance (NMR) surface probe was used to determine the time-dependent self-diffusion coefficient D(t) of water molecules in two fluid-filled porous media. The measuring equipment and the inhomogeneous magnetic fields in the sensitive volume of the probe are described. It is discussed how to evaluate D(t) using a surface probe from the primary and stimulated echoes generated in three-pulse experiments. Furthermore, the evaluation of D(t) allows one to determine the geometrical structure of porous materials.     

Studies of electrochemical properties of compacted clays by concentration potential method

The development of concentration (membrane) potential upon step-wise change in salt concentration has been studied for diaphragms made of various strongly compacted clays (montmorillonite, illite, kaolinite) equilibrated with 0.1 M NaCl solution. Porous ceramic filters were used to confine the clays mechanically to be able to achieve high extent of compaction (dry density approximately 2000 kg/m3). A theoretical analysis has revealed that the relaxation pattern is primarily controlled by the properties of porous filters and only slightly depends on the clay properties. At the same time, quasi-stationary values of concentration potential are directly related to the electrochemical perm-selectivity of clay. This property has revealed considerable differences in the electrochemical behaviour of various clays used in this study. This has been attributed to the differences in the micro-structure of clays, in particular to the existence or nonexistence of the so-called interlayer water where cations may retain some mobility. It has also been shown that in clays with high electrochemical perm-selectivity, one can expect a strong increase in the diffusivity of cationic radio-tracers with decreasing ionic strength of equilibrium electrolyte solution. At the same time, low electrochemical perm-selectivity means no noticeable dependence of this kind. The correctness of this observation has been corroborated by the comparison of our findings with the literature data on the diffusion of cationic radio-tracers through compacted montmorillonite (high perm-selectivity) and kaolinite (low perm-selectivity). To check the self-consistency of our approach, we have also carried out sample measurements of diffusion of cationic and anionic radio-tracers through compacted illite. It has been found that the measured effective diffusion coefficients were in excellent agreement with the electrochemical perm-selectivity estimated for this clay from the measurements of concentration potential.     

Three-dimensional distribution function theory for the prediction of protein-ligand binding sites and affinities: application to the binding of noble gases to hen egg-white lysozyme in aqueous solution

The three-dimensional distribution function theory of molecular liquids is applied to lysozyme in mixtures of water and noble gases. The results indicate that the theory has the capability of predicting the protein-ligand binding sites and affinities. First, it is shown that the theory successfully reproduces the binding sites of xenon found by X-ray crystallography. Then, the ability of the theory to predict the size selectivity of noble gases is demonstrated. The effect of water on the selectivity is clarified by a theoretical analysis. Finally, it is demonstrated that the dose-response curve, which is employed in experiments for examining the binding affinity, is realized by the theory.