In the Goemans-Williamson semidefinite relaxation of MAX-CUT, the gradient of the dual barrier objective function has a term of the form diag(Z), where Z is the slack matrix. The purpose of this note is to show that this term can be computed in time and space proportional to the time and space for computing a sparse Cholesky factor of Z using an algorithm due to Erisman and Tinney. The algorith...

The synthesis of Li1.1Co0.3Fe2.1O4 ferrite nanoparticles has been synthesized by the citrate auto-combustion method. distribution cations on A-site and B-site is studied X-ray diffraction High-Resolution Transmission Electron Microscopy. Williamson–Hall analysis Debye–Scherrer method are used to study individual contributions crystallite sizes peak broadening Li1.1Co0.3Fe2.1O4. estimated size i...

in this paper, a boussinesq equation is solved by using the adomian's decomposition method, modified adomian's decomposition method and homotopy analysis method. the approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. the existence and uniqueness of the solution and the convergence of the propose...

we report on the synthesis, morphology, chemically and structurally of tio2-cuo-sio2 nanostructure with different precursors molar ratio and calcined temperatures. in the present work, ternary reactive powders in the tio2-cuo-sio2 systems have been obtained using the sol-gel method, by the simultaneous gelation of all cations. the compounds and other elements change in special chemical and phys...

in this research, mechanical alloying was used to synthesize ultrafine grained aa2024 and aa2024-b4c powders in an attrition mill under argon atmosphere up to 50 h with the rotational speed of 400 rpm. in order to determine the grain size of the matrix, x-ray diffraction test and williamson–hall method was used. after mechanical alloying, hot pressing and hot extrusion were used for densificati...

The objective of this work is to study the Williamson fluid flow with a chemically reactive species.The governing equations of Williamson model in two dimensional flows are constructed by using scaling transformation under a Reynolds and Weissenberg numbers approximation. The analytic solution of the system of nonlinear ordinary differential equations (ODEs) is constructed in the series form by...

Scanning Hall Probe Microscopy (SHPM) is a scanning probe microscopy technique developed to observe and image magnetic fields locally. This method is based on application of the Hall Effect, supplied by a micro hall probe attached to the end of cantilever as a sensor.  SHPM provides direct quantitative information on the magnetic state of a material and can also image magnetic induction under a...

In the present paper, nanometer scale hydroxyapatite powders with a rod-like shape, were prepared using combined ultrasonic and microwave heating-based method. Subsequent annealing of as-synthesized at 800 ℃ for 2 h produced nanoparticles rectangular granular morphology. The particles characterized X-ray diffraction Fourier transform infrared spectroscopy methods. Also, nanoparticle ...