Parametric CR-umbilical locus of ellipsoids in C2

For every real numbers $a?1$, $b?1$ with $(a,b)\ne (1,1)$, the curve parametrized by $\theta \in \mathbb{R}$ valued in ${\mathbb{C}}^2?{\mathbb{R}}^4$

$\gamma :\theta ?(x(\theta )+\sqrt{?1}y(\theta ),u(\theta )+\sqrt{?1}v(\theta ))$

with components:

$\begin{array}{c}x(\theta ):=\sqrt{\frac{a?1}{a(ab?1)}}\cos ?\theta ,y(\theta ):=\sqrt{\frac{b(a?1)}{ab?1}}\sin ?\theta ,\hfill \\ u(\theta ):=\sqrt{\frac{b?1}{b(ab?1)}}\sin ?\theta ,v(\theta ):=?\sqrt{\frac{a(b?1)}{ab?1}}\cos ?\theta ,\hfill \end{array}$

has image contained in the CR-umbilical locus:

$\gamma (\mathbb{R})?\mathsf{UmbCR}\left({\mathsf{E}}_{a,b}\right)?{\mathsf{E}}_{a,b}$

of the ellipsoid ${\mathsf{E}}_{a,b}?{\mathbb{C}}^2$ of equation $a{x}^2+y^2+b{u}^2+v^2=1$, where the CR-umbilical locus of a Levi nondegenerate hypersurface $M^3?{\mathbb{C}}^2$ is the set of points at which the Cartan curvature of M vanishes.     

Effective surface potential method for calculating surface states

A novel formalism (the effective surface potential method) is developed for calculating surface states. Like the Green function method of Kalkstein and Soven and the transfer matrix method of Falicov and Yndurain, the technique is exact for simple tight binding Hamiltonians. As well as offering an alternative viewpoint, the present method provides a simple analytic expression describing the surface states. At each point k_s in the surface Brillouin zone the semi-infinite solid is viewed as an effective linear chain where each element of the chain is a planar layer. The solution to the linear chain problem can be expressed in terms of an effective potential h(k_s,E) at each energy E. A number of examples are presented in detail; “sp^d” Hamiltonians for a linear chain (d = 1), the honeycomb lattice (d = 2), the 111 surface of silicon (d = 3), and a dissected Bethe lattice. Various exact results are given, e.g. the extremities of surface state bands and the surface density of states of p-like (delta function) bands. The results of Kalkstein and Soven for the 100 surface of a simple cubic solid with a perturbation on the surface layer are rederived.     

Self-organized superlattice formation during crystal growth from continuous beam fluxes

Alloy superlattice structures consisting of alternating Si-rich and C-rich layers form spontaneously during gas-source molecular beam epitaxy of Si(1-y)C(y) on Si(001) from constant Si2H6 and CH3SiH3 precursor fluxes at T(s)=725-750 degrees C. The self-organized patterning is due to a complex interaction among competing surface reactions. During growth of the initial Si-rich layer, strain-driven C segregation to the subsurface results in charge transfer from surface Si atom dangling bonds to C backbonds. This decreases the Si2H6 sticking probability, and, hence, the instantaneous deposition rate, thereby enhancing C segregation. The Si-rich layer continues until a critical C coverage is reached allowing nucleation of a C-rich layer which grows until the excess subsurface C is depleted. The process then repeats with periods tunable through the choice of T(s) and y(avg).     

Electrophoretic flow of interacting polymer chains: Effects of temperature,polymer concentration,and porosity

Using a Monte Carlo simulation in three dimensions, we studied the variation of the root-meansquare (rms) displacement (R_rms) of polymer chains with time and the rates of their mass transfer (j) as a function of biased field (B), polymer concentration (p), chain length (L_c), porosity (p_s), and temperature (T). In homogeneous/annealed system, the rms displacement of the chains shows a drift-like behavior, R_rms ∼ t, in the asymptotic time regime preceded by a subdiffusive power-law (R_rms ∼ t^k, with k < 1/2) at high p. The subdiffusive regime expands on increasing L_c and p but reduces on increasing T or B. In quenched porous media, the drift-like behavior of R_rms persists at low barrier concentration (p_b) and high T. However, at high p_b and/or low T, chains relax into a subdrift and/or subdiffusive behavior especially with high p or long L_c. Flow of chains is measured via an effective permeability (σ) using a linear response assumption. In annealed system, σ increases monotonically with B at high T and low p but varies nonmonotonically at low T, high p and high L_c. We find that σ decays with L_c, σ ∼ L, where α depends on B, p and T with a typical value a α ∼ 0.43−0.64 for p = 0.1-0.3 at B = 0.5. Further, σ decays with p, σ ∼ − Cp with a decay rate C sensitive to T and B. In quenched porous media, even at low pb and high T, σ varies nonmonotonically with bias, i.e., the increase of σ is followed by decay on increasing the bias beyond a characteristic value (B_c). This characteristic bias seems to decrease logarithmically with barrier concentration, B_c ∼ −klnp_b. The prefactor k depends on the chain length, k ≈ 0.35 for shorter chains (L_c = 20, 40) and ≈ 0.15 for longer chains (L_c = 60). Scaling dependence of σ on L_c similar to that in annealed system is also observed in porous media with different values of exponent α. The current density shows a nonlinear power-law response, j ∼ B^σ, with a nonuniversal exponent δ ≈ 1.10−1.39 at high temperatures and low barrier concentrations.     

Effect of potassium permanganate on morphological,structural and electro-optical properties of graphene oxide thin films

This work investigated the effect of Potassium Permanganate (KMnO₄) on graphene oxide (GO) properties, especially on electrical properties. The GO thin films were deposited on a glass substrate using drop casting technique and were analysed by using various type of spectroscopy (e.g. Scanning Electron Microscopy (SEM), Ultra- Violet Visible (UV–VIS), Fourier Transform Infrared (FTIR), X-Ray Diffraction (XRD), optical band gap, Raman Spectroscopy). Furthermore, the electrical experiments were carried out by using current–voltage (I-V) characteristic. The GO thin film with 4.5 g of KMnO₄ resulted in higher conductivity which is 3.11 × 10^?4 S/cm while GO with 2.5 g and 3.5 g of KMnO₄ achieve 2.47 × 10^?9 S/cm and 1.07 × 10^?7 S/cm, respectively. This further affects the morphological (SEM), optical (band gap, UV–Vis, FTIR, and Raman), and crystalline structural (XRD) properties of the GO thin films. The morphological, elemental, optical, and structural data confirmed that the properties of GO is affected by different amount of KMnO₄ oxidizing agent, which revealed that GO can potentially be implemented for electrical and electronic devices.     

Improving a Natural Enzyme Activity through Incorporation of Unnatural Amino Acids

The bacterial phosphotriesterases catalyze hydrolysis of the pesticide paraoxon with very fast turnover rates and are thought to be near to their evolutionary limit for this activity. To test whether the naturally evolved turnover rate could be improved through the incorporation of unnatural amino acids and to probe the role of peripheral active site residues in nonchemical steps of the catalytic cycle (substrate binding and product release), we replaced the naturally occurring tyrosine amino acid at position 309 with unnatural L-(7-hydroxycoumarin-4-yl)ethylglycine (Hco) and L-(7-methylcoumarin-4-yl)ethylglycine amino acids, as well as leucine, phenylalanine, and tryptophan. Kinetic analysis suggests that the 7-hydroxyl group of Hco, particularly in its deprotonated state, contributes to an increase in the rate-limiting product release step of substrate turnover as a result of its electrostatic repulsion of the negatively charged 4-nitrophenolate product of paraoxon hydrolysis. The 8-11-fold improvement of this already highly efficient catalyst through a single rationally designed mutation using an unnatural amino acid stands in contrast to the difficulty in improving this native activity through screening hundreds of thousands of mutants with natural amino acids. These results demonstrate that designer amino acids provide easy access to new and valuable sequence and functional space for the engineering and evolution of existing enzyme functions.     

Comparative analysis of essential oils from eight herbal medicines with pungent flavor and cool nature by GC–MS and chemometric resolution methods

Systematic comparative research was conducted on essential oils from eight traditional Chinese medicines (TCM) of pungent flavor and cool nature because the essential oils are the main active ingredients of herbs of this kind. The work was based on their component analysis by gas chromatography–mass spectrometry (GC–MS), on their retention indices, as well as on chemometric resolution methods. A total of 144 compounds were tentatively identified, accounting for 69.0% to 91.8% of the total essential oils. It is worth noting that there are 67 compounds in at least three of these eight essential oils. Moreover, many biologically active compounds, such as hexanal, α‐pinene, camphene, β‐pinene, p‐cymene, limonene, eucalyptol, (Z)‐ocimene, γ‐terpinene, camphor, p‐menthone, 4‐terpineol, α‐terpineol, carvone, eugenol, caryophyllene, β‐farnesene, α‐curcumene, β‐selinene, δ‐cadinene, caryophyllene oxide, cedrol, n‐hexadecanoic acid, benzaldehyde, benzeneacetaldehyde, phthalic acid diisobutyl ester, linoleic acid, tetradecanoic acid, (Z,Z,Z)‐9,12,15‐octadecatrienoic acid, eucalyptol, pentadecanoic acid, hexadecanoic acid methyl ester, linoleic acid methyl ester, exist in at least four of the eight essential oils. These results might help us to understand why the eight herbs are all of pungent flavor and cool nature according to the theory of TCM, and may provide a useful chemical basis for future research on herbs of this kind.