On real matrices with positive definite symmetric component

Inequalities concerning real square matrices A with positive definite symmetric component A+A^*are derived from certain inertia relations which hold for any complex (not necessarily real) square matrices A with positive definite

A+A^*     

A numerical study of oblique shock wave reflections over wedges in an ideal quantum gas

The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection, simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and observed. Both Bose–Einstein and Fermi–Dirac gases are considered.      

A rutherford scattering study of the diffusion of heavy metal impurities in silicon to ion-damaged surface layers

Rutherford backscattering of 1.75 and 2 MeV ⁴He⁺ ions has been utilized to study the high temperature gettering of Fe, Co, Ni, Cu and Au from silicon by ion-damaged surface layers. In a typical experiment a metal film was evaporated onto one side of a silicon wafer (125 microm thick) which had received ion implantation damage (10¹⁶/cm² Si⁺ ions at 100 keV) on the opposite side; the wafer was then annealed at 900°C, usually for 30 min. The results of such experiments show that the metals studied may be divided into two classes, those which are gettered slowly - Fe, Co, and Au, and those gettered rapidly - Cu and Ni. Fe, Co, and Au were found at levels of 1×10¹³?1×10¹⁴/cm² in the damaged layer, whereas Cu and Ni appeared at levels of 6×10¹⁴ to 5 ×10¹⁶cm². The gettered level of Au, one of the “slow” group, was increased ten-fold by an equal increase in the anneal time to 300 min. The gettered Cu and Au exhibited double peaks in the scattered ion spectra, corresponding to metal concentrated at the most heavily damaged region (end of range for Si implant) and also at the outer surface, with a separation of ~ 1300 Å. A simple model is proposed to explain the slow and fast gettering, based on published interstitial diffusivities and solubilities of the five elements studied.Rutherford scattering has proven to be well suited for the quantitative identification of low levels of impurities on Si surfaces and for impurities gettered at damaged layers close to the surface.     

Availability Analysis of Repairable <Emphasis Type="Italic">N</Emphasis>-Server <Emphasis Type="Italic">n</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>-Replicated Systems

We develop an exact closed-form expression for the steady-state availability of a repairable, N-server system in which the ith server contains n _i identical, reconfigurable, breakdown-prone units. Our approach, which follows from the Markov chain balance equations and the recursive properties of Hessenberg matrix determinants, is simpler than previously proposed matrix geometric approaches, and can readily be adapted to the availability analysis of more complicated structures. We illustrate this by computing the steady-state availability of a mixed parallel-serial gracefully degrading replicated system.     

Self-sustained oscillations between two tandem cylinders at Reynolds number 1,000

This study focuses on the self-sustained oscillatory flow characteristics between two tandem circular cylinders of equal diameter placed in a uniform inflow. The Reynolds number (Re _D ), based on the cylinder diameter, was around 1,000 and all experiments were performed in a recirculating water channel. The streamwise distance between two tandem cylinders ranged within 1.5 ≤ X _c/D ≤ 7.0. Here X _c denotes the center-to-center distance between two tandem cylinders. For all experiments studied herein, quantitative velocity measurements were performed using hot-film anemometer and the LDV system. The laser sheet technique was employed for qualitative flow visualization. The wavelet transform was applied to elucidate the temporal variation and phase difference between two spectral components of the velocity signals detected in the flow field. The remarkable finding was that when two tandem circular cylinders were spaced at a distance within 4.5 ≤ X _c/D ≤ 5.5, two symmetrical unstable shear layers with a certain wavelength were observed to impinge onto the downstream cylinder. The responding frequency (f _u ), measured between these two cylinders, was much higher than the natural shedding frequency behind a single isolated cylinder at the same Re _D . This responding frequency decreased as the distance X _c/D increased. Not until X _c/D ≥ 6.0, did it recover to the natural shedding frequency behind a single isolated cylinder. Between two tandem cylinders, the Strouhal numbers (St _c = f _u X _c/U_c) maintained a nearly constant value of 3, indicating the self-sustained oscillating flow characteristics with a wavelength X _c/3. Here U _c is the convection speed of the unstable shear layers between two tandem cylinders. At Re _D = 1,000, the self-sustained oscillating characteristics between two tandem circular cylinders were proven to exhibit a sustained flow pattern, not just a sporadic phenomenon.     

Synthesis and thermotropic behaviour of liquid crystals containing tolane-based mesogenic units

Tolane-based liquid crystal materials with three different terminal groups: trifluoromethyltolanes, cyanotolanes, and nitrotolanes, and with different chain lengths of alkenyloxy groups, have been synthesized. The phase behaviour of these liquid crystal materials has been characterized by differential scanning calorimetry, optical polarized light microscopy and X-ray diffraction. The mesophase behaviour of the materials was shown to be significantly influenced by the polarity of the terminal groups. The trifluoromethyltolanes exhibit an enantiotropic smectic E mesophase and the cyanotolanes exhibit a monotropic nematic mesophase. The most polar among the three types of liquid crystal material; the nitrotolanes do not display any liquid crystalline phases, except for the homologue with an eleven methylene unit chain.     

Sample stacking for determination of aromatic acid impurities by microemulsion electrokinetic chromatography

In this study, a sample stacking step coupled with microemulsion electrokinetic chromatography (MEEKC) was used to detect and analyze nine aromatic acids (benzoic acid (BA), isophthalic acid (IPA), terephthalic acid (TPA), p-toluic acid (p-TA), 4-carboxylbenzaldehyde (4-CBA), trimesic acid (TSA), trimellitic acid (TMA), o-phthalic acid (OPA), and hemimellitic acid (HMA)) which are common impurities produced during aromatic acid synthesis. First, the presence of both acid and water plugs at the front of the capillary improved the reproducibility in retention time and peak intensity of the tested analytes in the stacking method. Second, the pH and the electrolyte type of acidic plug and sample matrix were found to be the predominant influences on the aromatic acid stacking. The detection limits of these aromatic acids were reduced to the range of 0.00007-0.00032 μg mL⁻¹ by this optimal sample stacking step. This proposed on-line concentration MEEKC method was able to detect trace levels of aromatic acid impurities in commercial aromatic acid products that were not previously possible by the normal MEEKC method. Furthermore, these results in comparison with our previous studies on sample stacking MEEKC method indicated that all acidic species were concentrated by this simple stacking procedure. The sensitivity enhancement, however, was highly dependent on the types of functional groups present in the structures of analytes, and the enhancement was in the order of first the compounds carrying both carboxy and hydroxy groups (e.g. phenolic acid), followed by carboxylic acid compounds (e.g. aromatic acid), and then phenol compounds (e.g. polyphenol).     

Indole synthesis: palladium-catalyzed C-H bond amination via reduction of nitroalkenes with carbon monoxide

Nitroalkenes have been called ‘chemical chameleons’ due to their versatility in numerous synthetic transformations. Herein, we describe the first transition metal-catalyzed transformation of conjugated nitroalkenes into indoles. Under mild reaction conditions (1 atm carbon monoxide, 110 °C), palladium catalyzes the reductive cyclization of nitroalkenes to form a putative nitrosoalkene intermediate, which then rearranges to provide 3-arylindoles in high yields. Notably, this novel C-H bond amination takes advantage of carbon monoxide as an inexpensive stoichiometric reductant and produces carbon dioxide as the major byproduct.