On the asymptotic behaviour of solution for the generalized double dispersion equation

In this article, we investigate the Cauchy problem for the generalized double dispersion equation in n-dimensional space. We establish the decay estimates of solution to the corresponding linear equation. Under smallness condition on the initial data, we prove the global existence and asymptotic behaviour of the small amplitude solution in the time-weighted Sobolev space by the contraction mapping principle.     

Spaces of Ideal Convergent Sequences of Bounded Linear Operators

Abstract

The notation of I–convergence was introduced and studied by Kostyrko, Macaj, Salat, and Wilczynski. Recently, the concept of I–convergent for a sequence of bounded linear operators has been studied by Khan and Shafiq. This has motivated us to introduce and study some new spaces of double sequences of bounded linear operators and their basic topological and algebraic properties of these spaces. And we study some of their basic topological and algebraic properties of these spaces. We prove some inclusion relations on these spaces.     

Monitoring of progestins: Development of immunochemical methods for purification and detection of levonorgestrel

A polyclonal antibody (Ab) for the progestin levonorgestrel (LNG) was generated, and immunochemical assays for its detection, clean-up and concentration were developed. A highly specific microplate diagnostic assay for the detection of LNG was developed that used the enzyme linked immunosorbent assay (ELISA) method. The LNG ELISA developed was sensitive and reproducible; it exhibited I₅₀ and I₂₀ values of 3.3 ± 1.8 ng mL⁻¹ and 0.6 ± 0.4 ng mL⁻¹, respectively, and the Abs did not cross react with any of the tested steroid hormones. The above Abs were used to develop a sol-gel-based immunoaffinity purification (IAP) method for concentration and clean-up of LNG that is compatible with subsequent immunochemical or instrumental chemical analytical procedures, such as liquid chromatography followed by mass spectrometry (LC-MS/MS). Development of the columns included successful entrapment of Abs within a tetramethoxysilane (TMOS)-based SiO₂ polymer network. The Abs could bind the free analyte from solution, and the bound analyte could be easily eluted from the sol-gel matrix at high recoveries. The Ab selectivity towards the antigen was high, in both ELISA and the sol-gel columns, but the entrapped Abs cross-reacted with two other steroid hormones - ethynylestradiol (EE2) and nortestosterone (NT) - which share similar epitopes with LNG, despite the lack of cross reactivity in the ELISA. The validity of the method was investigated by LC-MS/MS and a good analytical correlation was obtained.     

Thermoresponsive PPEGMEA‐g‐PPEGEEMA well‐defined double hydrophilic graft copolymer synthesized by successive SET‐LRP and ATRP

A series of well‐defined double hydrophilic graft copolymers containing poly[poly(ethylene glycol) methyl ether acrylate] (PPEGMEA) backbone and poly[poly(ethylene glycol) ethyl ether methacrylate] (PPEGEEMA) side chains were synthesized by the combination of single electron transfer‐living radical polymerization (SET‐LRP) and atom transfer radical polymerization (ATRP). The backbone was first prepared by SET‐LRP of poly(ethylene glycol) methyl ether acrylate macromonomer using CuBr/tris(2‐(dimethylamino)ethyl)amine as catalytic system. The obtained comb copolymer was treated with lithium diisopropylamide and 2‐bromoisobutyryl bromide to give PPEGMEA‐Br macroinitiator. Finally, PPEGMEA‐g‐PPEGEEMA graft copolymers were synthesized by ATRP of poly(ethylene glycol) ethyl ether methacrylate macromonomer using PPEGMEA‐Br macroinitiator via the grafting‐from route. The molecular weights of both the backbone and the side chains were controllable and the molecular weight distributions kept narrow (M_w/M_n ≤ 1.20). This kind of double hydrophilic copolymer was found to be stimuli‐responsive to both temperature and ion (0.3 M Cl^? and SO). © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 647–655, 2010     

Short diastereoselective synthesis of the C1-C13 (AB spiroacetal) and C17-C28 fragments (CD spiroacetal) of spongistatin 1 and 2 through double chain-elongation reactions

A unique and practical synthetic sequence for rapid access to polyketides and to further the spiroacetals derived from them, which utilizes a bidirectional Hosomi-Sakurai allylation approach around key allylsilanes in the synthesis of the AB and CD ring systems of spongistatin 1 and 2, is reported. The synthesis of the AB spiroacetal 9 requires 13 steps, with a longest linear sequence of seven steps in an overall yield of 27%. The synthesis of the CD spiroacetal 13 requires 15 steps, with a longest linear sequence of 11 steps in an overall yield of 30%. Both syntheses start from but-3-enol.     

Electrochemical Oxidation of Epinephrine and Uric Acid at a Layered Double Hydroxide Film Modified Glassy Carbon Electrode and Its Application

Increasing attention has been paid to layered double hydroxide (LDH) film modified electrode attributing to its desirable properties for fabrication of electrochemical sensor. In this paper, the Zn‐Al LDH film modified glassy carbon electrode was characterized by electrochemical methods. The enhanced electrocatalytic currents and well‐separated potentials for epinephrine (EP) and uric acid (UA) were observed at the as‐prepared electrode. Under selected condition, the differential pulse voltammetry response of the modified electrode to EP (or UA) shows a linear concentration range of 0.5 μM to 0.3 mM (or 2 μM to 0.4 mM) in the presence of 10.0 μM UA (or 20.0 μM EP). At a signal‐to‐noise ratio of 3, the calculated limits of detection are 0.13 μM and 0.66 μM, respectively. The proposed method has been performed to successfully detect EP and UA in analysis of real samples, such as in EP injection solution and human urine samples.     

Crystal structures and phonon modes of Ba(Ca1/2W1/2)O3, Ba(Ca1/2Mo1/2)O3 and Ba(Sr1/2W1/2)O3 complex perovskites investigated by Raman scattering

This work investigates the crystal structures and phonon modes of Ba(Ca_1/2W_1/2)O₃, Ba(Ca_1/2Mo_1/2)O₃ and Ba(Sr_1/2W_1/2)O₃ perovskites by Raman spectroscopy. The samples were produced by conventional solid‐state processing at 1200 °C. X‐ray diffraction showed that single‐phase homogeneous materials were produced, which are cubic or pseudo‐cubic in symmetry. The existing controversies in the literature for these complex perovskites were investigated by comparing experimental Raman data with group‐theory analysis. Ceramics with Ca and W or Mo were found to be cubic, space group Fm3 m. For these materials, four Raman‐active bands were observed and the fitting parameters showed that the Ba(Ca_1/2Mo_1/2)O₃ ceramic presents bands at lower wavenumbers if compared with the Ba(Ca_1/2W_1/2)O₃ sample. For the Ba(Sr_1/2W_1/2)O₃ material, two hypotheses were investigated for monoclinic or triclinic structures. The experimental results showed 12 Raman‐active modes for this ceramic, which is in perfect agreement with the theoretical predictions for a monoclinic (I2/m) structure. Copyright © 2009 John Wiley & Sons, Ltd.     

Broadband non-collinear double QPM optical parametric amplification in mid-infrared wave

The properties of optical parametric amplification (OPA) based on non-collinear double quasi-phase matching (NDQPM) with single periodically poled KTP (PPKTP) have been investigated theoretically. The NDQPM includes two different non-linear processes: one is optical parametric generation (OPG) and the other is difference frequency generation (DFG). The investigation of our numerical simulation focuses on the gain bandwidth of dependence upon non-collinear angle, grating period and crystal temperature. At a certain non-collinear angle and grating period with fixed temperature, there exists a broadest gain bandwidths of output mid-infrared pulse at 526 nm pump wavelength and certain signal wavelength in PPKTP. These are an optimal values of non-collinear angles and grating period. By accurately tuning the non-collinear angle or temperature near the optimal non-collinear angle, broadband mid-infrared tuning is obtained and an optimal operation of NDQPM can be realized. In this paper, the solutions of the coupled equations of the cascaded processes were discussed, and the spatial-temporal frequency (STF) band of the output idler pulse is analyzed by taking angular dispersion of amplified pulse beam into account. The idler pulse with a certain angular dispersion can improve the OPA bandwidth significantly. So, optical parametric chirped-pulse amplification can be realized in this configuration. For a broadband NDQPM both the acceptance angles and the acceptance temperature are smaller and the gain bandwidth is sensitive to non-collinear angles and temperature, it is important to control the precision of the non-collinear angles and the temperature in experiment.     

Sensitive and Facile Determination of Catechol and Hydroquinone Simultaneously Under Coexistence of Resorcinol with a Zn/Al Layered Double Hydroxide Film Modified Glassy Carbon Electrode

A stable dihydroxybenzene sensor was fabricated by electrochemical deposition of Zn/Al layered double hydroxide film on glassy carbon electrode (LDHf/GCE). The sensitive and facile electrochemical method for the simultaneous determination of catechol (CA) and hydroquinone (HQ) under coexistence of resorcinol (RE) has been achieved at the LDHf/GCE in phosphate buffer solution (pH 6.5). Under the optimized conditions, the differential pulse voltammetry response of the modified electrode to CA (or HQ) shows a linear concentration range of 0.6 μM to 6.0 mM (or 3.2 μM to 2.4 mM) with a correlation coefficient of 0.9987 (or 0.9992) and the calculated limit of detection is 0.1 μM (or 1.0 μM) at a signal‐to‐noise ratio of 3. In the presence of 50 μM isomer, the linear concentration ranges for CA and HQ are 3.0 μM to 1.5 mM and 12.0 μM to 0.8 mM, respectively. The detection limits are 1.2 μM and 9.0 μM. Further, the proposed method has been performed to successfully detect dihydroxybenzene isomers in analysis of real samples, such as water and tea.     

The relation between the potential of zero charge and work function for <Emphasis Type="Italic">sp</Emphasis>-metals

It is shown that for numerous sp-metals there exists no unified work function (W _e) dependence of the potential of zero charge E _{q = 0} and the potential drop characterizing the metal lyophilic behavior Δ _M ^Hg E _chem) _{q = 0}. The reason is that the metal work function is by no means the only factor affecting the value of E _{q = 0}. The quantities E _{q = 0} and (Δ _M ^Hg E _chem) _{q = 0} depend also on the distance of the solvent dipoles’ closest approach to metal surfaces (d _ms) in the absence of the metal-solvent chemisorption interaction. When the metal-solvent chemisorption interaction is involved, this distance affects the degree of overlapping of the metal’s acceptor levels and the upper occupied donor levels in the solvent molecules. To reliably investigate the effect of any of these factors on E _{q = 0}, the other one should be fixed up. It is shown, by example of Ga-, Bi-Gaand Sn-Ga-electrodes, as well as Pb-Ga-, In-Ga-, and Cd-Ga-electrodes demonstrating very close values of the “electrochemical work function” that the metal-solvent chemisorption interaction becomes stronger with the decreasing of d _ms. The influence of this factor is intensified with the increasing of the solvent’s donor number DN. The W _e dependence of E _{q = 0} and (Δ _M ^Hg E _chem) _{q = 0} can be traced by example of metals with nearly equal d _ms values, e.g., Tl-Ga, In-Ga, and Ga. In all studied solvents, the deviation of E _{q = 0} from W _e increased in the series Tl-Ga < In-Ga < Ga, that is, with the increasing of the metal’s work function in vacuum. The effect is intensified with the increasing of the solvent’s DN. The obtained results agree with the concept of donor-acceptor nature of the metal-solvent chemisorption interaction.