Theory of coherent,degenerate two-photon absorption and emission

The theory of the coherent, two-photon resonant interaction of a monochromatic field with N atoms is given. It is seen that the dynamics of the atom-field system can be completely determined when the field is “strong”. Two specific examples are given: (i) two-photon absorption by atoms in ground state, and (ii) stimulated two-photon emission by fully excited atoms, assuming a coherent field in both cases. In case (ii), the field shows photon-antibunching after the decay of half of the atoms. The merits of our approach are shown by comparing with other treatments. Our results can also be applied to certain degenerate four-wave mixing processes which are described by a similar Hamiltonian.     

A concise, enantioselective approach to (-)-quinic acid

[reaction: see text] An expedient, enantioselective synthesis of a key precursor to (-)-quinic acid has been achieved from an ephedrine-derived morpholine-dione. The salient features of this approach are a highly diastereoselective conversion of the dione to a dialkenyl morpholinone and a subsequent ring-closing metathesis reaction. Removal of the ephedrine portion generates an enantiomerically enriched hydroxycyclohexene carboxamide that is readily converted to the quinic acid precursor.     

First enantioselective organocatalytic allylation of simple aldimines with allyltrichlorosilane

A new organocatalytic system, novel chiral bisformamide and in situ generated L-proline-derived allylsilane reagent , which converts different aldimines to homoallylic amines in good to high yields (up to 95%) and good enantioselectivities (up to 85% ee) has been described.     

Further exploration of antimicrobial ketodihydronicotinic acid derivatives by multiple parallel syntheses

A synthetic reexamination of a series of ketodihydronicotinic acid class antibacterial agents was undertaken in an attempt to improve their therapeutic potential. A convenient new synthesis was developed involving hetero Diels-Alder chemistry producing 74 new analogs in a multiple parallel synthetic manner and these were examined in vitro for their antimicrobial potential. Several compounds demonstrated significant broad-spectrum activity against clinically derived bacterial strains but previously known 1-(2,4-difluorophenyl)-6-(4-dimethylaminophenyl)-4-pyridone-3-carboxylic acid (7) remained the most potent compound in this class. Cross-resistance with ciprofloxacin supported a commonality of mode of action. Permiabilization of Escherichia coli cells by polymyxin B significantly enhanced potency with these agents suggesting that poor cellular uptake was primarily responsible for the disappointing activity against bacteria that some of the analogs exhibited.     

An analysis for heat equations arises in diffusion process using new Yang-Abdel-Aty-Cattani fractional operator

The heat equation is parabolic partial differential equation and occurs in the characterization of diffusion progress. In the present work, a new fractional operator based on the Rabotnov fractional-exponential kernel is considered. Next, we conferred some fascinating and original properties of nominated new fractional derivative with some integral transform operators where all results are significant. The fundamental target of the proposed work is to solve the multidimensional heat equations of arbitrary order by using analytical approach homotopy perturbation transform method and residual power series method, where new fractional operator has been taken in new Yang-Abdel-Aty-Cattani (YAC) sense. The obtained results indicate that solution converges to the original solution in language of generalized Mittag-Leffler function. Three numerical examples are discussed to draw an effective attention to reveal the proficiency and adaptability of the recommended methods on new YAC operator.     

On the SIG-Dimension of Trees Under the L ∞-Metric

Let ${{\mathcal P},}$ where ${|{\mathcal P}| \geq 2,}$ be a set of points in d-dimensional space with a given metric ρ. For a point ${p \in {\mathcal P},}$ let r _p be the distance of p with respect to ρ from its nearest neighbor in ${{\mathcal P}.}$ Let B(p,r _p ) be the open ball with respect to ρ centered at p and having the radius r _p . We define the sphere-of-influence graph (SIG) of ${{\mathcal P}}$ as the intersection graph of the family of sets ${\{B(p,r_p)\ | \ p\in {\mathcal P}\}.}$ Given a graph G, a set of points ${{\mathcal P}_G}$ in d-dimensional space with the metric ρ is called a d-dimensional SIG-representation of G, if G is isomorphic to the SIG of ${{\mathcal P}_G.}$ It is known that the absence of isolated vertices is a necessary and sufficient condition for a graph to have a SIG-representation under the L _∞-metric in some space of finite dimension. The SIG-dimension under the L _∞-metric of a graph G without isolated vertices is defined to be the minimum positive integer d such that G has a d-dimensional SIG-representation under the L _∞-metric. It is denoted by SIG _∞(G). We study the SIG-dimension of trees under the L _∞-metric and almost completely answer an open problem posed by Michael and Quint (Discrete Appl Math 127:447–460, 2003). Let T be a tree with at least two vertices. For each ${v\in V(T),}$ let leaf-degree(v) denote the number of neighbors of v that are leaves. We define the maximum leaf-degree as ${\alpha(T) = \max_{x \in V(T)}}$ leaf-degree(x). Let ${ S = \{v\in V(T)\|\}}$ leaf-degree{(v) = α}. If |S| = 1, we define β(T) = α(T) ? 1. Otherwise define β(T) = α(T). We show that for a tree ${T, SIG_\infty(T) = \lceil \log_2(\beta + 2)\rceil}$ where β = β (T), provided β is not of the form 2 ^k ? 1, for some positive integer k ≥ 1. If β = 2 ^k ? 1, then ${SIG_\infty (T) \in \{k, k+1\}.}$ We show that both values are possible.     

Quantification of Flavonoids,Phenols and Antioxidant Potential from Dropped Citrus reticulata Blanco Fruits Influenced by Drying Techniques

Physiologically dropped immature Citrus reticulata Blanco fruits are regarded as waste and discarded in the citrus orchard but are a good source of bioactive compounds including flavonoids, antioxidants and total phenols. A study was undertaken to identify and quantify these bioactive compounds and to investigate the influence of different drying techniques, namely freeze drying and hot air oven drying, on flavonoids namely flavanone glycosides, antioxidant potential and total phenol content in immature dropped fruits of Citrus reticulata Blanco. Flavonoids were quantified in high-performance liquid chromatography (HPLC). The antioxidant activity were investigated with three assays azino-bis [3-ethylbenzthiazoline-6-sulfonic acid]) (ABTS), 2,2-diphenyl-1-picrylhydrazyl radical (DPPH), Ferric Reducing Ability of Plasma (FRAP) and total phenol content was determined. Freeze dried samples of 12 and 14 mm size retained maximum hesperidin flavonoid content (27.03% and 27.20%) as compared to the hot air dried samples (17.99%) and retained higher phenolic content ranged from 50.54–54.19 mg GAEL⁻¹. The antioxidant activity in freeze dried fruits was from 12.21–13.55 mM L⁻¹ Trolox and 15.27–16.72 mM L⁻¹ Trolox with ABTS, DPPH assay and FRAP values ranging from 7.31–9.07 mM L⁻¹ Trolox. Significant positive correlation was found between the flavonoid hesperidin with antioxidant assays and total phenolic content (TPC). The results showed that waste citrus fruits can act as potential source of bioflavonoids, especially hesperidin, and antioxidants for pharmaceutical as well as nutraceutical industry.     

LES of spatially developing turbulent boundary layer over a concave surface

We revisit the problem of a spatially developing turbulent boundary layer over a concave surface. Unlike previous investigations, we simulate the combined effects of streamline curvature as well as curvature-induced pressure gradients on the turbulence. Our focus is on investigating the response of the turbulent boundary layer to the sudden onset of curvature and the destabilising influence of concave surface in the presence of pressure gradients. This is of interest for evaluating the turbulence closure models. At the beginning of the curve, the momentum thickness Reynolds number is 1520 and the ratio of the boundary layer thickness to the radius of curvature is δ₀/R = 0.055. The radial profiles of the mean velocity and turbulence statistics at different locations along the concave surface are presented. Our recently proposed curvature-corrected Reynolds Averaged Navier-Stokes (RANS) model is assessed in an a posteriori sense and the improvements obtained over the base model are reported. From the large Eddy simulation (LES) results, it was found that the maximum influence of concave curvature is on the wall-normal component of the Reynolds stress. The budgets of wall-normal Reynolds stress also confirmed this observation. At the onset of curvature, the effect of adverse pressure gradient is found to be predominant. This decreases the skin friction levels below that in the flat section.