Interpolation for nonlinear BVP in circular membrane with known upper and lower solutions

AbstractA successive nonextrapolatory linear interpolation is described to solve a singular two-point boundary value problem arising in circular membrane theory. The problem is associated with a second-order nonlinear ordinary differential equation for which the upper and lower bounds of the solution is analytically established/known. The importance and the scope of these bounds in solving the problem is stressed. Also depicted graphically are the lower and upper solutions as well as the true and iterated solutions. In addition, discussed are the reasons why linear interpolation, and not nonlinear interpolation or bisection which are possible procedures, has been employed

A note on higher-order nondifferentiable symmetric duality in multiobjective programming

AbstractIn this work, we establish a strong duality theorem for Mond–Weir type multiobjective higher-order nondifferentiable symmetric dual programs. This fills some gaps in the work of Chen [X. Chen, Higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290 (2004) 423–435]

Fabrication of Low-Roughness Au/Ti/ SiO2/Si Substrates for Nanopatterning of 16-Mercapto Hexadecanoic Acid (MHA) by Dip-Pen-Nanolithography

Silicon based low-roughness Au/Ti/SiO2/Si substrates were fabricated using standard IC fabrication processes. Evolution of surface roughness during substrate fabrication process was studied. Fabrication process steps, namely, thermal oxidation and e-beam evaporation for ultra-thin Ti(~ 5 nm)/Au(22 nm) films, were optimized to result in surface r.m.s roughness ~ 0.2 m and ~ 1.0 nm, after thermal oxidation and Ti/Au deposition steps respectively. Surface roughness was estimated by atomic force microscope (AFM) imaging and image analysis. Nano-patterning experiments using thiol based 16-MHA molecular-ink on fabricated substrates were carried out, under controlled environment conditions, by dip-pen-nanolithography (DPN) technique. Minimum line-width ~ 60 nm and circular dots radius ~ 175 nm were patterned. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2779

Obstructive Granulomatous Bronchiolitis Obliterans due to Mycobacterium tuberculosis

Bronchiolitis obliterans is an uncommon cause of obstructive airway disease in adults characterised by progressive irreversible airway obstruction. Granulomatous bronchiolitis is a rare entity and tuberculosis presenting as bronchiolitis is distinctly uncommon. The authors present a case of tubercular granulomatous bronchiolitis obliterans, confirmed on histopathology, who responded completely to anti-tubercular chemotherapy

Determination of Copper, Total Chromium and Silver in Impregnated Carbon

Carbon samples were impregnated with ammonical solutions of silver salt alone and in combination with Cu and Cr salts. The impregnated samples were characterised for Cu, total Cr and Ag. Copper was extracted as CuCl/sub 2/ using concentrated HCl and Cr with NaOH. Silver was extracted from impregnated carbon using HNO3 and sodium thiosulphate (Na/sub 2/S/sub 2/O/sub 3/-5H/sub 2/0) and ashed impregnated carbons using aqua regia. The extracted metals in their solutions were quantitatively determined by titrimetric method and atomic absorption spectroscopy. The results were within acceptable limits of error. Sodium thiosulphate is recommended for extraction of Ag, as it accomplishes complete leaching of Ag faster than the other extracting agents

A FRACTIONAL INTEGRAL OPERATOR INVOLVING THE MITTAG-LEFFLER TYPE FUNCTION WITH FOUR PARAMETERS

In this paper our main aim is establishing a fractional integration formula (of pathway type) involving the Mittag-Leffler type function with four parameters $_{\zeta,\eta}E_{\mu,\nu} [z]$ which is recently introduced by Garg, Sharma and Manohar [Thai J. Math. (2015)].  Some interesting special cases of the main result are also considered and shown to be connected with certain known ones