On the asymptotic behavior of solutions of certain integro-differential equations

The authors present conditions under which every positive solution $x(t)$ of the integro--differential equation $x^{\prime \prime }(t)=a(t)+\int_{c}^{t}(t-s)^{\alpha-1}[e(s)+k(t,s)f(s,x(s))]ds, \quad c>1, \ \alpha >0,$ satisfies $x(t)=O(tA(t))\textrm{ as }t\rightarrow \infty,$ i.e, $\limsup_{t\rightarrow \infty }\frac{x(t)}{tA(t)}<\infty, \textrm{where} \ A(t)=\int_{c}^{t}a(s)ds.$ From the results obtained, they derive a technique that can be applied to some related integro--differential equations that are equivalent to certain fractional differential equations of Caputo type of any order.     

Seven‐Step Continuous Flow Synthesis of Linezolid Without Intermediate Purification

Herein, the blockbuster antibacterial drug linezolid is synthesized from simple starting blocks by a convergent continuous flow sequence involving seven (7) chemical transformations. This is the highest total number of distinct reaction steps ever performed in continuous flow without conducting solvent exchanges or intermediate purification. Linezolid was obtained in 73 % isolated yield in a total residence time of 27 minutes, corresponding to a throughput of 816 mg h^?1.     

Metal 3D‐printed catalytic jet and flame ionization detection for in situ trace carbon oxides analysis by gas chromatography

A gas chromatographic approach for the determination and quantification of trace levels of carbon oxides in gas phase matrices for in situ or near‐line/at‐line analysis has been successfully developed. Catalytic conversion of the target compounds to methane via the methanation process was conducted inside a metal 3D‐printed jet that also acted as a hydrogen burner for the flame ionization detector. Modifications made to a field transportable gas chromatograph enabled the leveraging of advantaged microfluidic‐enhanced chromatography capability for improved chromatographic performance and serviceability. The compatibility with adsorption chromatography technology was demonstrated with in‐house constructed columns. Sustained reliable conversion efficiencies of greater than 99% with respectable peak symmetries were attained at 400°C. Quantification of carbon monoxide and carbon dioxide at a parts‐per‐million level over a range from 0.2 ppm to 5% v/v for both compounds with a respectable precision of less than 3% relative standard deviation for peak area (n = 10) and a detection limit of 0.1 ppm v/v was achieved. Linearity with correlation coefficients of R² greater than 0.9995 and measured recoveries of >99% for spike tests were achieved. The 3D‐printed steel jet was found to be reliable and resilient against potential contamination from the matrices owing to the in situ backflushing capability.     

On the oscillation of fourth order strongly superlinear and strongly sublinear dynamic equations

We establish some new criteria for the oscillation of fourth order nonlinear dynamic equations on a time scale. We investigate the case of strongly superlinear and the case of strongly sublinear equations subject to various conditions. Some examples are given here to illustrate our main results.     

Simulating bubble dynamics in a buoyant system

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid–based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge.     

Multidimensional gas chromatography with capillary flow technology and LTM-GC

2-D GC is a logical and cost effective extension to 1-D GC for improving the separation resolution, selectivity, and peak capacity of an analytical system. The advent of electronic pressure control systems that are accurate to the third decimal place, combined with recently innovated chromatographic devices such as capillary flow technology, has eliminated many deficiencies encountered in current conventional 2-D GC by making the technique reliable and simple to implement in both production and research analytical facilities. Low thermal mass GC (LTM-GC) was successfully integrated with capillary flow technology to further enhance overall 2-D GC chromatographic system performance by providing not only faster throughput via rapid heating and cooling, but independent temperature control for each dimension to maximize separation power. As an example, despite the enhanced peak capacity obtained from conventional 2-D GC, alkyl naphthalene isomers such as 2,3-dimethyl and 1,4-dimethyl naphthalene coeluted. These two critical compounds were well resolved (R = 5.2) using 2-D GC with LTM-GC with a similar analytical time. This paper demonstrates the benefits of combining capillary flow technology with LTM-GC to provide major enhancements to conventional 2-D GC. The synergy of these techniques is highlighted with practical industrial applications.     

Isomer discrimination of polycyclic aromatic hydrocarbons in the Murchison meteorite by resonant ionization

We have used two-color resonant two-photon ionization (2C-R2PI) mass spectrometry to discriminate between isomers of polycyclic aromatic hydrocarbons in the Murchison meteorite. We measured the 2C-R2PI spectra of chrysene and triphenylene seeded in a supersonic jet by laser desorption. Since each isomer differs in its R2PI spectrum, we can distinguish between isomers using wavelength dependent ionization and mass spectrometry. We found both chrysene and triphenylene in sublimates from carbonaceous residue obtained by acid demineralization of the Murchison meteorite. Their R2PI mass spectra show only the molecular ion, even though these samples contain a complex inventory of organic molecules.     

Synthesis of new amidino-substituted 2-aminothiophenoles: mild basic ring opening of benzothiazole

The efficient synthesis of new amidino, N-isopropylamidino, 2-imidazolinyl substituted benzothiazoles and 2-aminothiophenoles by the Pinner reaction is described. The novel ring opening of benzothiazole with ammonia and ethylenediamine was found, and a plausible reaction mechanism proposed. The ring opening with ethylenediamine is selective and applicable to compounds bearing hydrolytically and amonolytically unstable substituents. Different amidino-substituted 2-aminothiophenoles were isolated in zwitterionic and disulfide form and their structures were determined by X-ray crystal structure analysis.     

Batch Fermentation Model of Propionic Acid Production by Propionibacterium acidipropionici in Different Carbon Sources

Propionic acid (PA) is widely used as additive in animal feed and also in the manufacturing of cellulose-based plastics, herbicides, and perfumes. Salts of propionic acid are used as preservative in food. PA is mainly produced by chemical synthesis. Nowadays, PA production by fermentation of low-cost industrial wastes or renewable sources has been an interesting alternative. In the present investigation, PA production by Propionibacterium acidipropionici ATCC 4965 was studied using a basal medium with sugarcane molasses (BMSM), glycerol or lactate (BML) in small batch fermentation at 30 and 36 degrees C. Bacterial growth was carried out under low dissolved oxygen concentration and without pH control. Results indicated that P. acidipropionici produced more biomass in BMSM than in other media at 30 degrees C (7.55 g l(-1)) as well as at 36 degrees C (3.71 g l(-1)). PA and biomass production were higher at 30 degrees C than at 36 degrees C in all cases studied. The best productivity was obtained by using BML (0.113 g l(-1) h(-1)), although the yielding of this metabolite was higher when using glycerol as carbon source (0.724 g g(-1)) because there was no detection of acetic acid. By the way, when using the other two carbon sources, acetic acid emerged as an undesirable by-product for further PA purification.