On the beam propagation through active media

An analytical iterative procedure has been established to determine the amplitude of a laser beam propagating through an active medium. The treatment is valid for both homogeneous and inhomogeneous broadening, and for arbitrary inhomogeneities of the parameters characterizing the active medium, namely, the refractive index, the small-signal gain and the saturation intensity. After a supplementary approximation, a thin-sheet gain approach is derived from the first iteration. The formalism enables us to provide analytical criteria for evaluating both the accuracy of each iteration and the propagation distances for which the thin-sheet solution can be used. This revised version was published online in November 2006 with corrections to the Cover Date.     

Determination of molecular configuration by debye length modulation

Silicon nanowire field effect transistors (FETs) have emerged as ultrasensitive, label-free biodetectors that operate by sensing bound surface charge. However, the ionic strength of the environment (i.e., the Debye length of the solution) dictates the effective magnitude of the surface charge. Here, we show that control of the Debye length determines the spatial extent of sensed bound surface charge on the sensor. We apply this technique to different methods of antibody immobilization, demonstrating different effective distances of induced charge from the sensor surface.     

ADM-Padé solutions for generalized Burgers and Burgers-Huxley systems with two coupled equations

We present an approximate numerical solution to generalized Burgers and Burgers-Huxley systems with two coupled equations using the ADM-Padé technique which is a combination of the Adomian decomposition method and Padé approximation. The Padé technique is used to enhance the accuracy and speed up the convergence rate of the truncated series solution produced by the ADM. Results are given in graphical form for explicit examples of the two systems.     

On non-commutative noetherian local rings, non-commutative geometry and particle physics

In this note we find the necessary and sufficient conditions which implies that the Dilworth number of non-commutative noetherian local ring equals one. In addition we discuss briefly connections to non-commutative geometry, theory and particle physics.     

Ionization and electroreduction of some benzthiazin-4-one azodyes

pKa values of a series of the titled compounds (2 a–g) together with a model compound3 have been determined spectrophotometrically in alcoholic buffered media. These values were correlated to different sets. The polarographic behaviour of the parent2 a and its nitro derivative2 g was studied in detail. The obtained data showed that2 a is reduced via a 2-electron process to the corresponding hydrazo from which was stabilized through hydrogen bonding.

---

Ionisierung und Elektroreduktion einiger Benzthiazin-4-on-Azofarbstoffe

Zusammenfassung Es wurden diepKa-Werte einer Serie der Titelverbindungen (2 a–g) zusammen mit einer Modellverbindung3 spektrophotometrisch in alkoholischer gepufferter Lösung bestimmt. Diese Werte wurden mit verschiedenen Sets von -Werten korreliert. Das polarographische Verhalten der Stammverbindung2 a und deren Nitroderivat2 g wurde im Detail untersucht. Die Daten zeigen, daß2 a über einen Zweielektronenprozeß zur entsprechenden Hydrazo-Verbindung reduziert wird, die durch Wasserstoffbrücken stabilisiert ist.

     

Multivariate experimental design: towards more reliable electrochemical detection

Design of an experiment approach has recently become an urgent requirement for different experimental measurements. Not only owing to the increased expenses for purchasing chemicals and equipment but also to reduce time required to conduct several one-variable at a time experiments to optimize the operating conditions of an experimental design. Design of experiments has excellent applicability in the analytical process related to method development based on multiple variants used for pharmaceutical, food, and environmental analysis. Application of experimental design has become effective to identify and optimize the significant factors and to achieve adequate results using few experimental trials. Electrochemical sensors represent a class of fast, reliable, and economic tools in analytical chemistry, with vast applicability to different fields. This review aims at presenting the most recently used screening and optimization designs during (2019–2021) for the fabrication and operation variables of electrochemical sensors and how can they be efficiently correlated.     

Synthetic studies using unsaturated and active phosphonium salts. A convenient preparation of furano‐ and pyrano[2,3‐c]pyridazines and substituted quinolines

By applying vinyl‐ ( 3 ) and allyltriphenylphosphonium bromides ( 9 ) to 4‐cyano‐5,6‐difur‐2′yl‐2H‐pyridazin‐3‐one ( 1 ) the corresponding fused 5,8‐oxazolo‐ 6, 12 (∼37%) and pyrano‐ 8 , 13 , 14 (∼20%) derivatives are isolated whereas with alkylphosphonium bromides 15a,b fused furans 17a,b (22%) and isopyrroles 18a,b (∼45%) are obtained. On the other hand, the reaction of 2‐[(benzylidene)amino]‐benzonitrile ( 2 ) with 3 and 9 yielded benzoazepines 20 and 21 (∼56%). With 15a,b , quinolines 23a,b (∼46%) and quinazoline 25 (∼24%) are obtained. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:56–64, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20065     

The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid

The present paper presents a general treatment of the transient thermoelastic stresses in a rotating nonhomogeneous anisotropic solid under compressive initial stress. The system of fundamental equations is solved by means of a boundary element method (BEM) and the numerical calculations are carried out for the temperature, displacement components and stress components. The results indicate that the effects of inhomogeneity and initial stress are very pronounced.     

Construction and Implementation of NMR Quantum Logic Gates for Two Spin Systems

The implementation of small prototype quantum computers has been studied through ensemble quantum computing via NMR measurements. In such laboratory studies it is convenient to have access to a wide array of logic gates. Here a systematic approach to reduce the logic gate to an NMR pulse sequence is introduced. This approach views the truth table for a quantum logic operation as a permutation matrix that corresponds to a propagator for an NMR transition. This propagator is then used as the starting point for the derivation of a pulse sequence. Pulse sequences for all the permutations of a four level system are reported along with implementations of representative examples on a two spin-1/2 system, 13C-labeled chloroform.