Well- and Ill-Posedness Issues for a Class of 2D Wave Equation with Exponential Growth

Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, we prove the propagation of the regularity in the Sobolev spaces HS（IR^2） with s 〉 1. Finally, an ill-posedness result is obtained in HS（IR^2） for s 〈 1.     

Optimized bandwidth allocation in broadband wireless access networks

Towards satisfying the requirements of International Mobile Telecommunications–Advanced, both the Institute of Electrical and Electronics Engineers (IEEE) and Third Generation Partnership Project (3GPP) introduced revolutionary wireless technologies, exploiting advanced technologies and architectures. Both IEEE's 802.16 (Worldwide Interoperability for Microwave Access (WiMAX)) and 3GPP's Long Term Evolution have been introduced to accommodate the increasing demand for mobile services and applications. To realize the true potential of these technologies, however, opportunistic frameworks for radio resource management must be designed to exploit the adaptive nature of mobile traffic. The utility optimized quality‐of‐service (QoS) framework proposed in this paper for the mobile WiMAX networks achieves this objective. To maintain support for QoS guarantees, the framework capitalizes on the adaptive nature of WiMAX traffic by individually linking connections with a utility function designed to both uphold the end users’ perceived performance and determine bandwidth allocations by a search tree maximization algorithm. In doing so, bandwidth utilization is maximized for all active connections, and blocking and dropping probabilities for new and handover calls, respectively, are minimized. The framework is evaluated through an extensive simulation model and is shown to outperform state‐of‐the‐art solutions. Copyright © 2014 John Wiley & Sons, Ltd.     

Spatiotemporal Control over Molecular Delivery and Cellular Encapsulation from Electropolymerized Micro‐ and Nanopatterned Surfaces

Bioactive, patterned micro‐ and nanoscale surfaces that can be spatially engineered for three‐dimensional ligand presentation and sustained release of signaling molecules represent a critical advance for the development of next‐generation diagnostic and therapeutic devices. Lithography is ideally suited to patterning such surfaces due to its precise, easily scalable, high‐throughput nature; however, to date polymers patterned by these techniques have not demonstrated the capacity for sustained release of bioactive agents. Here a class of lithographically defined, electropolymerized polymers with monodisperse micro‐ and nanopatterned features capable of sustained release of bioactive drugs and proteins is demonstrated. It is shown that precise control can be achieved over the loading capacity and release rates of encapsulated agents and this aspect is illustrated using a fabricated surface releasing a model antigen (ovalbumin) and a cytokine (interleukin‐2) for induction of a specific immune response. Furthermore, the ability of this technique to enable three‐dimensional control over cellular encapsulation is demonstrated. The efficacy of the described approach is buttressed by its simplicity, versatility, and reproducibility, rendering it ideally suited for biomaterials engineering.     

Alkyl heterocycles in heterocyclic synthesis (II): Novel synthesis of isoquinoline,thiazolopyridine, and thieno[2,3‐b]pyridine derivatives

Treating 5‐(4‐phenylcarboxamido)‐3‐cyano‐4‐methylpyridin‐2(1H)thione ( 3 ) with elemental sulfur yielded thienopyridine 4 . Compound 4 reacts with acrylonitrile to give isoquinoline 7 . Compound 7 was also, prepared from 3 and methylenemalononitrile. Reaction of 3 with dimethylacetylene dicarboxylate (DMAD) gave the pyridothiazole 9 . Also, 3 reacted with N,N‐dimethylchloroacetamide ( 10 ) to afford compound 11 which further reacted with the reagents 12 , 13 and 14 providing the thieno[2,3‐b]pyridine derivatives 15 , 16 and 17 respectively.     

Studies with Alkylheterocycles: Novel Synthesis of Functionally Substituted Isoquinoline and Pyridopyridines Derivatives

Several isoquinolines were prepared via reacting pyridine 4 with cinnamonitriles 5a‐c or 5d‐f . Treating 4 with elemental sulphur yielded thienopyridine 9. 9 reacts with acrylonitrile to give isoquinoline 12. 12 was also prepared from 4 and methylenemalononitrile. Condensation of 4 with aromatic aldehydes gave the arylidine 13. 13 afforded the pyridine 14 and 15 on treating it with NH₄OH and AcOH/HCl, respectively.     

Molecular dynamics and conduction mechanism of poly(vinyl chloride-co-vinyl acetate-co-2-hydroxypropyl acrylate) terpolymer containing ionic liquid

Dielectric spectroscopy (DS) measurements were performed to probe the segmental dynamics and ion mobility of poly(vinyl chloride-co-vinyl acetate-co-2-hydroxypropyl acrylate) terpolymer dopped with different amounts of tetrabutylammonium tetrafluoroborate ([TBA] [BF₄]) ionic liquid (IL). Differential scanning calorimetry (DSC) was also employed to trace the change in the glass transition temperature (T_g) at different loads of IL. The DSC measurements revealed a remarkable reduction in the PVVH T_g from 344 to 310 K just by adding 20 wt% of IL. The DS measurements revealed three relaxation processes named α, β₁, and β₂. The α-process is related to the segmental motion of PVVH while the β₁ and β₂ are due to the restricted local dynamics of side chains. The segmental relaxation times (α-relaxation) speed up with increasing the concentration of IL due to the plasticization effect of IL on polymer chains. The temperature dependence of α-relaxation follows the Vogel-Fulcher-Tammann (VFT) relation with dynamic glass transition between 323 and 294 K in agreement with the DSC measurements. The β₁ and β₂-relaxations have an Arrhenius temperature dependence. The temperature dependence of ionic conductivity obeys the VFT behavior indicating the coupling between the segmental motion of PVVH chains and ion transport. Polaronic tunneling is the predominant conduction mechanism in PVVH and its composites. The specific capacitance increases with increasing both the temperature and IL concentration.     

Derivative and Derivative Ratio Spectrophotometric Analysis of Antihypertensive Ternary Mixture of Amiloride Hydrochloride,Hydrochlorothiazide and Timolol Maleate

Two simple, rapid and reliable spectrophotometric methods are described for the resolution of the three‐component mixture of amiloride hydrochloride (AMD), hydrochlorothiazide (HCT) and timolol maleate (TIM). The first method involves the use of derivative spectrophotometry with the zero‐crossing technique where AMD was easily determined using its ⁰D and ¹D(Δλ = 6) amplitudes at 365 and 385 nm, respectively, while HCT and TIM were determined by measuring the ³D(Δλ = 6) amplitude at 265 nm and the ¹D(Δλ = 8) amplitude at 315.4 nm, respectively. The second method involves the application of the ratio‐spectra zero‐crossing first and second derivative spectrophotometry where two points have been used for the quantification of each compound. For the determination of AMD, HCT was used as divisor and the ¹DD (Δλ = 4) and ²DD (Δλ = 6) values at 299.4 and 311 nm, respectively, were plotted against AMD concentration; while — by using TIM as divisor — the ²DD (Δλ = 6) amplitudes at 264.2 and 290 nm were found to be proportional to HCT concentration. TIM was assayed in the mixture using its ¹DD (Δλ = 6) amplitudes at 289.8 nm (Divisor was AMD) and 314.8 nm (Divisor was HCT). Synthetic mixtures of different proportions and laboratory‐made tablets were assayed by the proposed methods and the results revealed good accuracy and repeatability of the developed methods.     

Kinetic Spectrophotometric Analysis and Spectrofluorimetric Analysis of Ciprofloxacin Hydrochloride and Norfloxacin in Pharmaceutical Preparations Using 4‐Chloro‐7‐Nitrobenzo‐2‐Oxa‐1,3‐Diazole (NBD‐Cl)

Simple, reliable, sensitive and accurate kinetic spectrophotometric and spectrofluorimetric methods were proposed for the determination of ciprofloxacin hydrochloride (CPX) and norfloxacin (NRX) in pure form and in pharmaceuticals. The methods are based on coupling the studied drugs with 4‐chloro‐7‐nitrobenzo‐2‐oxa‐1,3‐diazole (NBD‐Cl) in the presence of alkaline borate buffer. Spectrophotometric measurement was achieved by recording the absorbance at 477 nm after a fixed time of 20 and 15 min on a water bath adjusted at 70 ± 1 °C for CPX and NRX, respectively. The same product exhibited emission peaks at 540 nm. The different experimental parameters affecting the development and stability of the color were carefully studied and optimized. The absorbance concentration plots were linear over the ranges 3‐18 and 2.5‐15.0 μg/mL for CPX and NRX, respectively, while the fluorescence concentration plots were linear over the ranges 0.06‐0.36 and 0.05‐0.30 μg/mL for CPX and NRX, respectively. The limit of detection of the kinetic method was about 0.2 μg/mL for both drugs while the fluorescence measurement enabled their detection at a concentration of about 0.012 μg/mL. The proposed methods were successfully applied for the assay of the two drugs in their commercial products. The results obtained were statistically compared with those obtained by reference HPLC and spectrophotometric methods. The stoichiometry of the reaction was determined and the reaction pathway was postulated.     

Synthesis of a peptide nucleic acid with a novel 1‐methyl‐6‐mercaptopurine base

A novel peptide nucleic acid (PNA) monomer 16 containing a novel 1‐methyl‐6‐mercaptopurine base was synthesized by coupling the in situ generated acid chloride of (1‐methyl‐6‐mercaptopurin‐9‐yl)acetic acid ( 6 ) into an L‐lysine backbone ( 13 ) using 10% CCl₄ in pyridine and Ph₃P. Compound 6 was synthesized from 6‐mercapto‐1‐methylpurine and ethylbromoacetate in the presence of NaH followed by alkaline hydrolysis and subsequent neutralization with a cation exchange resin. The L‐lysine backbone ( 13 ) was obtained by the reaction of N?‐CBZ‐L‐lysine allyl ester with Boc‐aminoactaldehyde in the presence of NaBH₃CN under reductive amination conditions. Oligomerization of the monomer 16 to PNA analogues was achieved using BOC‐BHA‐PEG‐PS resin as a solid support and the in situ generated acid chloride of 16 by 10% CCl₄ in DCM in the presence of Ph₃P.