New Theta-Function Identities of Level 6 in the Spirit of Ramanujan

Mathematical Notes - Michael Somos discovered several theta-function identities of various levels by computer and offered no proof for them. These identities highly resemble some of...     

Comparative computational appraisal of supercritical CO2-based natural circulation loop: effect of heat-exchanger and isothermal wall

Journal of Thermal Analysis and Calorimetry - Natural circulation loop (NCL) is a geometrically simple heat transfer device in which fluid flow occurs due to density gradient of loop fluid, induced...     

Effect of balanced and unbalanced magnetron sputtering processes on the properties of SnO2 thin films

A comparative study has been carried on the role of balanced magnetron (BM) and unbalanced magnetron (UBM) sputtering processes on the properties of SnO₂ thin films. The oxygen partial pressure, substrate temperature and deposition pressure were kept 20%, 700 °C and 30 mTorr, respectively and the applied RF power varied in the range of 150–250 W. It is observed that the UBM deposition causes significant effect on the structural, electrical and optical properties of SnO₂ thin films than BM as evidenced by X-ray diffraction, C-V, Spectroscopic Ellipsometer and Photoluminescence measurements. The value of band gap (E_g) of the films deposited at 150 W in UBM is found as E_g = 3.83 eV which is much higher than the value of E_g = 3.69 eV as observed in BM sputtering indicating that UBM sputtering results in good crystalline quality. Further, the C-V measurements of SnO₂ thin films deposited using UBM at high power 250 W show hysteresis with large flat band shift indicating that these thin films can be used for the fabrication of memory device. The observed results have been attributed to different mechanisms which exist simultaneously under unbalanced magnetron sputtering due to ion bombardment of growing SnO₂ thin film by energetic Ar+ ions.     

Structure‐controlled growth of ZnO nanonails by thermal evaporation technique

Wurtzite ZnO nanonail structures have been grown on sapphire substrate by simple thermal evaporation of Zn powder in oxygen ambient. Growth parameters such as growth temperature and oxygen gas flow have been examined for the growth of nanonail structure. It is found that the nanonail structures repeatedly grow under a certain relation between the growth temperature and the oxygen flow. Also, at higher growth temperature, the nanonails grow in the form of branched‐structures. The grown ZnO nanonails have hexagonally well‐faceted cap and grow mostly perpendicular to the sapphire substrate. Excellent luminescence properties of a strong UV emission peak with negligible green band have been obtained at room temperature. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantitative capillary gel electrophoresis assay of phosphorothioate oligonucleotides in pharmaceutical formulations

Quantitative capillary gel electrophoresis (QCGE) has been developed for the accurate quantitation of a 21-mer phosphorothioate oligonucleotide, ISIS 2922, and its degradation products in an intravitreal formulation. The electrokinetic mode of injection employed by CGE necessitates formulation of the external reference standard in a sample matrix similar to that of the drug product and the use of an internal standard for improved accuracy and precision. The analytical method detailed in this paper has demonstrated the necessary accuracy, precision, linearity, range, selectivity and ruggedness for use in routine drug product analysis and stability monitoring of phosphorothioate oligonucleotides.     

Nega-base periodic decimals

Some properties of the periods of prime-reciprocals in a general negative base representation are described.     

Equilibrium in a finite capacity M/M/1 queue with unknown service rates consisting of strategic and non-strategic customers

Queueing Systems - We consider an $$M/M/1/{\overline{N}}$$ observable non-customer-intensive service queueing system with unknown service rates consisting of strategic impatient customers who make...     

Methodological inaccuracies in clinical aortic valve severity assessment: insights from computational fluid dynamic modeling of CT-derived aortic valve anatomy

Aortic stenosis is the most common valvular heart disease. Assessing the contribution of the valve as a portion to total ventricular load is essential for the aging population. A CT scan for one patient was used to create one in vivo tricuspid aortic valve geometry and assessed with computational fluid dynamics (CFD). CFD simulated the pressure, velocity, and flow rate, which were used to assess the Gorlin formula and continuity equation, current clinical diagnostic standards. The results demonstrate an underestimation of the anatomic orifice area (AOA) by Gorlin formula and overestimation of AOA by the continuity equation, using peak velocities, as would be measured clinically by Doppler echocardiography. As a result, we suggest that the Gorlin formula is unable to achieve the intended estimation of AOA and largely underestimates AOA at the critical low-flow states present in heart failure. The disparity in the use of echocardiography with the continuity equation is due to the variation in velocity profile between the outflow tract and the valve orifice. Comparison of time-averaged orifice areas by Gorlin and continuity with instantaneous orifice areas by planimetry can mask the errors of these methods, which is a result of the assumption that the blood flow is inviscid.     

Partition identities arising from Somos’s theta function identities

In this paper, we establish certain partition identities for theta function identities of level 14 discovered by M. Somos.