Hyperbolic Yamabe problem

In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the(1 + n)-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n = 2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem;while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.     

Solitary wave solution of the generalized Hirota–Satsuma coupled KdV system

In this research, we find the exact traveling wave solutions involving parameters of the generalized Hirota–Satsuma couple KdV system according to the modified simple equation method with the aid of Maple 16. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified simple equation method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented.     

Solitons and other solutions to a new coupled nonlinear Schrodinger type equation

In this paper, the first integral method combined with Liu's theorem is applied to integrate a new coupled nonlinear Schrodinger type equation. Using this combination, more new exact traveling wave solutions are obtained for the considered equation using ideas from the theory of commutative algebra. In addition, more solutions are also obtained via the application of semi-inverse variational principle due to Ji-Huan He. The used approaches with the help of symbolic computations via Mathematica 9, may provide a straightforward effective and powerful mathematical tools for solving nonlinear partial differential equations in mathematical physics.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

Asymptotic behavior toward the combination of contact discontinuity with rarefaction waves for 1-D compressible viscous gas with radiation

This paper is concerned with the large-time behavior toward the combination of two rarefaction waves and viscous contact wave for the Cauchy problem to a one-dimensional Navier–Stokes–Poisson coupled system, modeling the dynamics of a viscous gas in the presence of radiation. We show that the composite wave with small strength is asymptotically stable under partially large initial perturbations. The proofs are based on the more refined energy estimates to control the possible growth of the perturbations induced by two different waves and large data.     

Detection of acetone in the human breath as diabetes biomarker based on PPy/WO3 nanocomposite sensor by FFT continuous cyclic voltammetry method

This research represents a novel detection method of acetone level in the exhaled breath samples (RH=88 %) based on polypyrrole/tungsten oxide (PPy/WO₃) nanocomposite sensor. The PPy/WO₃ sensor was fabricated by the deposition of nanocomposite on/between interdigitated electrodes (IDEs) through electrospray coating and was then characterized by FE-SEM imaging. In this detection method, the coulometric signal of the sensor was calculated using Fast Fourier Continuous Cyclic Voltammetry (FFTCCV), where cyclic voltammetry (CV) was applied to the sensor in the defined potential rang and then charge changes of the sensor was obtained by integration of the current in all scanned potential ranges. FFTCCV method enhances the sensitivity of the sensor when exposed to the gas mixtures containing acetone. In addition to its fast coulometric response time (≤5 s) in the two linear ranges of 0.7–2.8 ppm and 2.8–28.2 ppm (R²=0.99), FFTCCV method provides the low detection limit of 70 ppb, and high sensitivity toward acetone at the optimum values of the parameters. The fabricated sensor showed great selectivity toward acetone when exposed to humid air and some exhaled gas like carbon dioxide, ammonia, methanol, ethanol and alkyl amines. The results were very satisfying as the sensor was capable to detect different acetone levels in human exhaled breath as non-invasive diagnosis of diabetes with a good correlation (R²≃0.9) to the routine blood sugar test taken by different commercial glucometers results.     

Sensitive Electrochemical Detection of Thiabendazole in Fruits Using Ag−MoS2 Electrode

Herein, Ag nanoparticles (NPs) modified MoS₂ (Ag−MoS₂) was applied to the surface of glassy carbon (GC) to produce a robust electrochemical sensor for the detection of thiabendazole, a common antifungal in the post-harvesting of fruits. Cyclic voltammetry studies confirmed thiabendazole exhibited an irreversible, diffusion-controlled process on Ag−MoS₂ with a two-fold increase in peak current than the pristine MoS_2. A square wave voltammetry was used for the detection of TBZ. The developed sensor exhibited a linear range between 1–10 μM with LOD down to 0.1 μM (S/N>3). Analysis of TBZ in mango and banana matrices gave a recovery of 91.6–100.4 % indicating the suitability of the sensor for food safety monitoring.     

A Photoelectrochemical Sensor for Firstly the Detection of Amlodipine Besylate Based on an MnC4Pc Coated ZnO Composite Materials

In this study, tetracarboxylic manganese phthalocyanine coated nano-zinc oxide (MnC₄Pc-ZnO) composite material was prepared by in-situ growth method and modified with indium tin oxide (ITO) glass electrode to construct a photoelectrochemical (PEC) sensor. A PEC sensor for the determination of amlodipine besylate (AB) was developed for the first time based on the principle of precipitation reaction between heavy metal ions and dihydropyridine and the recombination suppression effect of the material. The morphology and optical properties of the MnC₄Pc-ZnO composites were characterized by scanning electron microscopy (SEM) and ultraviolet-visible diffuse reflectance spectroscopy (UV-vis DRS). Chronoamperometry (i-t) and electrochemical impedance spectroscopy (EIS) were used to study the PEC behavior of ITO electrodes modified by MnC₄Pc-ZnO composite material. The study found that the MnC₄Pc-ZnO composite material has a good photocurrent response to AB, and there was a good linear relationship between the concentration range of 75 nM-250 μM, the linear equation was I(μA)=−5.2×10⁻⁸×lgC+3.2×10⁻⁸ (r=0.9947), a limit of detection (LOD) of 20 nM. In addition, MnC₄Pc-ZnO/ITO also has good selectivity and stability. The PEC sensor detects amlodipine besylate tablets, amlodipine besylate dispersible tablets, and biological samples, with standard addition recovery rates of 96.11 % and 103.96 %, respectively. The determination result has good accuracy, and the PEC sensor provides a new method for detecting AB.     

Determination of Mercury with a Miniature Sensor for Point-of-care Testing

In developing countries, subsistence gold mining entails mixing metallic mercury with crushed sediments to extract gold. In this approach, the gold−mercury amalgam is heated to evaporate mercury and obtain gold. Thus, the highly volatile mercury can be absorbed through inhalation, resulting in adverse health effects. Urinalysis can be used to detect mercury, which is excreted in urine and feces, and correlate exposure with toxic effects. The current gold standard analytical methods are based on fluorescence or inductively coupled plasma mass spectrometry methods, but are expensive, time consuming, and are not easily accessible in countries where testing is needed. In this work, we report on a miniature electrochemical sensor that can rapidly detect mercury in urine at levels well below the US Biological Exposure Index (BEI) limit of 50 ppb (μg/L). The sensor is based on a thin-film gold electrode and anodic stripping voltammetry electroanalytical approach. The sensor successfully detected mercury at trace levels in urine, with a limit of detection of ∼15 ppb Hg in the linear range of 20–80 ppb. With the low-cost disposable sensors and portable instrumentation, it is well suited for point-of-care applications.