Visualization of supersonic screeching jets using a phase conditioned focusing schlieren system

This study describes a technique that combines the benefits of focusing schlieren and phase conditioning. Focusing schlieren blurs and drops contrast of non-critical features whereas phase conditioning emphasizes periodic flow features, and their combination produces unique results. The supersonic jets that we studied produced an intense tone referred to as screech. The measured screech tone signal was used as input to the phase conditioning circuit that adjusted the strobing light source to the vertical synchronization pulse of a CCD camera. The sharp video images obtained by this technique could either be frozen or continuously swept through one period of screech to acquire a slow motion video record of the jet unsteadiness. Two cases were visualized in this study: first, an underexpanded jet from a convergent rectangular nozzle at various fully expanded Mach numbers. Second, a supersonic jet emerging from a convergent-divergent rectangular nozzle at a design Mach number of 1.4, artificially excited by impingement tones. The results of this study illustrate the usefulness of this system in visualizing oscillatory flows.The authors would like to thank Dr. Edward J. Rice for his contributions including the design of the impingement obstacles. The efforts of Brentley C. Nowlin (NASA Lewis), and James E. Little (NYMA Inc.) in the design and construction of the strobe trigger mechanism are highly appreciated. We also thank Janet Ivancic (NASA Lewis Photo Lab) for the image enhancement.     

A colorimetric method for the determination of carboxylic acids

A new colorimetric method for the determination of carboxylic acids using bromocresol green reagent is established. The formed color follows Beer's Lambert law and is stable for 24 hr. The method is successfully applied for measuring the disappearance of volatile fatty acids in P. oxalicum culture media. The method is reproducable and is used also for the quantitative determination of carboxylic acids in Dowex 1-X8 eluates. A linear relationship between the pK₁ of different carboxylic acids and the calculated molar extinction coefficients of the color formed at 440 nm is demonstrated.     

Some singular value and unitarily invariant norm inequalities for Hilbert space operators

In this paper, we prove some singular value inequalities for sum and product of operators. Also, we obtain several generalizations of recent inequalities. Moreover, as applications we establish some unitarily invariant norm and trace inequalities for operators which provide refinements of previous results.     

Structural studies and biological evaluation of Co (II), Ni (II) and Cu (II) complexes of carbohydrazone derived from ethyl acetoacetate in addition to crystallographic description of La (III) or Sm (III) catalytic activity abnormal product

New carbohydrazone ligand derived from the condensation of carbohydrazide and ethyl acetoacetate, diethyl 3,3′‐(carbonylbis (hydrazin‐2‐yl‐1‐ylidene))(3E,3′E)‐dibutyrate (H₄EBC), and its divalent Co, Ni and Cu chelates have been isolated and characterized utilizing convenient methods. ¹H‐NMR spectrum of H₄EBC revealed the abundance of the enol isomer in solution, which was the opposite to what was shown by the solid IR. This was supported by comparing the theoretical IR of both keto and enol forms. In [Ni(H₄EBC)Cl₂(H₂O)]·2H₂O, H₄EBC acts as a neutral NON tridentate ligand via the (C=O)_carbonyl oxygen atom besides the two (C=N)_azomethine nitrogen atoms, while in [Co(H₄EBC)Cl₂(2H₂O)]·2H₂O, H₄EBC behaves as a neutral NN bidentate ligand through the two azomethine groups. Magnetic measurements inherent to their electronic spectra show that both Ni (II) and Co (II) chelates have octahedron coordination frameworks. On the other hand, the ligand behaves as a binegative tetradentate in [Cu₂(H₄EBC)Cl₂]·H₂O via the deprotonated (C=O)_carbonyl groups of the ethyl acetoacetate framework and the two (C=N)_azomethine groups. In the latter complex, the carbonyl group of the carbohydrazide moiety is converted to hydroxyl group. Cu (II) complex has a tetrahedral geometry according to ESR and electronic spectral data. The reaction of H₄EBC with SmCl₃·6H₂O or LnCl₃·7H₂O gave single crystals of abnormal product (C₁₆H₁₆N₄O₄). The packing diagram of this crystal has a chain structure. The photoluminescence spectra of [Cu ₂ (H ₄ EBC)Cl ₂ ]·H ₂ O , [Co(H ₄ EBC)Cl ₂ (H ₂ O) ₂ ]·2H ₂ O and [Ni(H ₄ EBC)Cl ₂ (H ₂ O)]·2H ₂ O display emission broad‐bands at 342, 321 and 337 nm, respectively. The microbial behavior of the synthesized moieties was investigated against various bacterial and fungal strains. [Cu₂(H₄EBC)Cl₂]·H₂O complex shows the same activity as ampicillin towards Escherichia coli and Staphylococcus aureus with inhibition zones of 26 and 22 mm, respectively. Antioxidant activity is determined using bleomycin‐dependent DNA damage assay besides erythrocyte hemolysis. Finally, in vitro cytotoxic activities against two different cell lines have been examined.     

Thermally Stable and Organo-soluble Polyamides Containing Triazine Rings and Ether Linkages in the Main Chain: Synthesis and Characterization

In order to synthesize new polyamide(PA) 5 and copolyamides(Co PA) 7a-7d, a new-type of dicarboxylic acid containing triazine ring was successfully synthesized from 2,4-dichloro-6-methoxy-s-triazine 1 and 4-aminobenzoic acid. New polyamide 5 containing triazine moiety was prepared from 4,4'-(6-methoxy-1,3,5-triazine-2,4-diyl)bis(azanediyl)dibenzoic acid 3 and 4,4′-diaminodiphenylether by direct polycondensation reaction. Then new series thermally stable copolyamides 7a-7d with high solubility in common organic solvents were synthesized from the direct polycondensation reaction of diacid 3 as a first monomer, aliphatic-aromatic diacids 6a-6d as second diacids and 4,4′-diaminodiphenylether. All of the above polymers were fully characterized by 1H-NMR and FTIR spectroscopy, elemental analysis(CHN), inherent viscosity, solubility tests, gel permeation chromatography(GPC), differential scanning calorimetry(DSC) and thermogravimetric analysis(TGA). The resulted Co PAs 7a-7d have shown good inherent viscosities, solubility and thermal properties.     

Orthogonal polynomials and continued fractions arising from contiguous relations and generalizations of Kummer and q-Kummer identities

The Ramanujan Journal - In this paper, we show formally how can we generate continued fractions starting from three-term contiguous relations. Then as examples, starting from certain contiguous...