Regularity of the Rotation Number for the One-Dimensional Time-Continuous Schr?dinger Equation

Starting from results already obtained for quasi-periodic co-cycles in $SL(2, \mathbb R),$ we show that the rotation number of the one-dimensional time-continuous Schr?dinger equation with Diophantine frequencies and a small analytic potential has the behavior of a $\frac{1}{2}-$ H?lder function. We give also a sub-exponential estimate of the length of the gaps which depends on its label given by the gap-labeling theorem.     

Joint project of fishery and poultry - A bioeconomic model

This paper considers the optimal joint harvest of prawns and poultry in a linked bioeconomic system. Through the cultivation process, poultry and prawns are reciprocal predators of one another. Prawns of non-marketable quality are fed to the birds, and birds which perish (in greater numbers in the face of increased density) are fed to prawns, along with a lot of other things that one does not usually consider prawns to eat (hogs, broken rice, etc.). The paper derives optimality conditions for the joint “effort” imposed in each of these industries, where effort is somehow analogous to the control variable in classical Gordon-Schaefer fishery problems. Growth of both species is governed by parameters as well as externally applied nutrients and the biomass of the other species available as supplemental nutrition. Analysis of the boundedness of this dynamical system is discussed. The conditions for local and global stability are derived. Finally, an optimal harvesting policy is discussed by applying Pontryagin’s Maximal Principle. Due to linearity of the objective function with respect to the control variable, the solution is bang-bang in this control and the best policy is to reach the singular equilibrium as quickly as possible by switching to the singular control.     

Recent synthetic methodologies for pyridopyrazines: An update

Abstract

Among heterocyclic compounds, pyridopyrazines are the scaffolds that have gained considerable attention on academic and industrial level due to their widespread applications as intermediates in the preparation of advanced and biologically potent pharmaceutical materials. Many pyridopyrazine derivatives are available in market to cure various pharmacological disorders. These candidates can be synthesized via a number of synthetic routes using various reagents like cyclocondensation of diaminopyridines with carbonyl compounds or their derivatives etc. In the present review, we have elaborated all these protocols along with different factors and reaction conditions such as use of metal catalyst, solvent-free and microwave irradiation, one-pot synthesis etc. that have resulted in high regioselectivity and yields. The review focuses on the synthetic methodologies developed in the last decade for different pyridopyrazine derivatives.     

Time-dependent density functional theory investigations on structural modification in carbazole-based organic photosensitizers to improve electron injection in dye-sensitized solar cell

The time-dependent density functional theory approach, implemented at hybrid-B3LYP, GGA-PBE, and density functional-based tight binding levels of theory, was used to model photoinjection in organic dye/TiO₂ quantum dot to explore the prospects of improvement of dye-sensitized solar cell (DSSC). The photosensitizer used in this study consisted of six carbazole-based organic dyes, a cyanoacrylic acid group as an acceptor and an oligothiophene π-bridge spacer. The modifications were made in the dyes by increasing the length of the spacer by adding thiophene and oxadiazole rings at different positions of the donor-acceptor bridge. The structural variations appeared to alter the electronic and optical properties of dyes studied via energy levels and excitation spectra. The UV-Vis spectra calculated for all the dyes in solvents exhibited a red shift in spectral peaks with an increase in the polarity of the solvents. The findings of the study pointed toward the indirect photoinjection of the dye-(TiO₂)₉₆ complex for six different dyes. The substitution of the oxadiazole ring at the center and addition of a thiophene ring at the edge of the spacer produced two dyes that exhibited the lowest injection energies of 0.11 and 0.17 eV, along with the regeneration energies of 1.18 and 1.12 eV, respectively. The dyes reported here may have promising applications in photoanode for enhancing the performance of DSSC.     

Projective synchronization of time‒delayed chaotic systems with unknown parameters using adaptive control method

The present article aims to study the projective synchronization between two identical and non?identical time?delayed chaotic systems with fully unknown parameters. Here the asymptotical and global synchronization are achieved by means of adaptive control approach based on Lyapunov–Krasovskii functional theory. The proposed technique is successfully applied to investigate the projective synchronization for the pairs of time?delayed chaotic systems amongst advanced Lorenz system as drive system with multiple delay Rössler system and time?delayed Chua's oscillator as response system. An adaptive controller and parameter update laws for unknown parameters are designed so that the drive system is controlled to be the response system. Numerical simulation results, depicted graphically, are carried out using Runge–Kutta Method for delay?differential equations, showing that the design of controller and the adaptive parameter laws are very effective and reliable and can be applied for synchronization of time?delayed chaotic systems. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Organic-Paradodecatungstate Hybrid Compound: Synthesis, Characterization and Crystal Structure

An organic–inorganic hybrid compound Na₂(HAn)₈[H₂W₁₂O₄₂]·16H₂O (HAn: p-anisidinium, C₇H₁₀NO) has been synthesized under soft acidic conditions and characterized by infrared and UV–visible spectroscopies, thermogravimetric analysis, cyclic voltammetry and single crystal X-ray diffraction. The compound crystallizes in the monoclinic P2₁/n space group with a = 10.1920(4) Å, b = 34.2901(9) Å, c = 14.0745(5) Å, β = 95.830(3)°, V = 4,893.4(3) Å³ and Z = 4. The compound exhibits a 2D supramolecular structure formed by alternated [paradodecatungstate/Na] and p-anisidinium layers. The catalytic activity of the compound for oxidation of cyclooctene with H₂O₂ was proved and gives rise to good reaction yield.     

Dirhodium(II) Compounds with Bridging Thienylphosphines: Studies on Reversible P,C/P,S Coordination

Monocyclometalated compound [Rh₂{(C₈H₄S)P(C₈H₅S)₂}(CH₃CO₂H)₂(O₂CCH₃)₃] ( 1 a ) and bis‐cyclometalated compound [Rh₂{(C₈H₄S)P(C₈H₅S)₂}₂(CH₃CO₂H)₂(O₂CCH₃)₂] ( 2 a ) have been isolated from the reaction of dirhodium tetraacetate and tris(2‐benzo[b]thienyl)phosphine ( 2 BTP ) using low acidic solutions. By contrast, in pure acetic acid the reaction of Rh₂(O₂CCH₃)₄ with 2 BTP and tris(2‐thienyl)phosphine ( 2 TP ), followed by replacement of the axial acetate ligands by chlorides, led to [Rh₂{(2‐C₈H₅ S )P(2‐C₈H₅S)₂}₂Cl₂(O₂CCH₃)₂] ( 3 b ) and [Rh₂{(2‐C₄H₃ S )P(C₄H₃S)₂}₂Cl₂(O₂CCH₃)₂] ( 5 b ), respectively. These new dirhodium(II) compounds possess equatorial bridging ligands in a phosphorous–sulfur (P,S) coordination mode. The reversible switching between the P,C and P,S bonding mode of the phosphine has been studied in the monocyclometalated [Rh₂{(C₄H₂S)P(C₄H₃S)₂}(CH₃CO₂H)₂(O₂CCH₃)₃] ( 6 a ), which was selectively transformed into compound [Rh₂{(2‐C₄H₃ S )P(C₄H₃S)₂}(CF₃SO₃)(CH₃CO₂H)(O₂CCH₃)₃] ( 7 c ) in triflic acid media. Remarkably, compound 7 c reverts to the starting compound 6 a upon treatment with sodium acetate. Theoretical DFT calculations for both the P,C/P,S rearrangement and the base‐promoted reversion have been performed to explain the experimental findings. Data suggest the P,C/P,S rearrangement occurs by means of a “concerted protonation–demetalation mechanism” followed by η² coordination of the thienyl ring and subsequent isomerization to the S‐η¹‐coordination mode. In the reversion reaction, the base coordinated at the axial position would promote a concerted metalation–deprotonation mechanism.     

Fukuyama reduction,Fukuyama coupling and Fukuyama–Mitsunobu alkylation: recent developments and synthetic applications

Fukuyama reaction for the synthesis of multifunctional aldehydes, secondary amines and ketones has gained considerable importance in synthetic organic chemistry because of mild reaction conditions. The use of thioesters in both Fukuyama aldehydes and ketones synthesis is highly attractive for organic chemists as they are easily accessible from corresponding carboxylic acids. Fukuyama–Mitsunobu reaction utilizes 2-nitrobenzenesulfonyl (Ns) for the protection/activation/deprotection of primary amines to afford secondary amines in good yields and high enantioselectivities. This review presents recent synthetic developments and applications of Fukuyama reaction for the synthesis of aldehydes, secondary amines and ketones.

Graphic abstract

     

Growth of Yb3+-doped KY3F10 concentration gradient crystal fiber by laser-heated pedestal growth (LHPG) technique

Crystal fiber of cubic Yb³⁺-doped KY₃F₁₀ has been grown. Both, mono-doped and concentration gradient fibers were grown by laser-heated pedestal growth (LHPG) method under argon atmosphere. The preparation of feed rod materials under CF₄ atmosphere prior to LHPG is efficient to obtain oxygen-free fluorides. Yb³⁺-doped KY₃F₁₀ crystals have excellent spectroscopic properties, weak self-quenching property and can be expected for solid-state laser application.