Optimization of Mathematical Functions Using Gradient Descent Based Algorithms

Optimization problem involves minimizing or maximizing some given quantity for certain constraints. Various real-life problems require the use of optimization techniques to find a suitable solution. These include both, minimizing or maximizing a function. The various approaches used in mathematics include methods like Linear Programming Problems (LPP), Genetic Programming, Particle Swarm Optimization, Differential Evolution Algorithms, and Gradient Descent. All these methods have some drawbacks and/or are not suitable for every scenario. Gradient Descent optimization can only be used for optimization when the goal is to find the minimum and the function at hand is differentiable and convex. The Gradient Descent algorithm is applicable only in the case stated above. This makes it an algorithm which specializes in that task, whereas the other algorithms are applicable in a much wider range of problems. A major application of the Gradient Descent algorithm is in minimizing the loss functions in machine learning and deep learning algorithms. In such cases, Gradient Descent helps to optimize very complex mathematical functions. However, the Gradient Descent algorithm has a lot of drawbacks. To overcome these drawbacks, several variants and improvements of the standard Gradient Descent algorithm have been employed which help to minimize the function at a faster rate and with more accuracy. In this paper, we will discuss some of these Gradient Descent based optimization algorithms

Preparation and spectroscopic studies of Hydroxyapatite embedded in Poly(N-Vinylpyrrolidone) matrix

Pure HAp powder was prepared by precipitation and HAp/PVP composites were prepared by casting technique. X-ray diffraction was performed to examine the crystallinity and the complexation between HAp and PVP when the amount of HAp increased. XRD and EDX analysis showed that the concentration 15 wt% is the most confirmation for the formation of HAp. SEM shows more than one form of HAp such as plates, needles and bundles in the morphological structure of pure HAp and 15 wt% of HAp. Two main weight loss regions and two peaks were observed in TGA and DSC thermograms that reveal reduction in the thermal stability of the prepared samples as HAp content increases. The activation energy of the films was decreased with increasing the concentration of HAp. DSC thermographs of the samples show that the values of the glass transition temperatures are decreased with increasing the content of HAp filler which suggest that HAp filler act as plasticizer. The conductivity–temperature plots show linear variation, which suggests an Arrhenius behavior. The conductivity increases with adding HAp content for low concentrations while decreased for the critical concentration (15 wt %) which confirms the XRD results

Synthesis and Characterization of Core-shell ZrO2/PAAEM/PS Nanoparticles

This work demonstrates the synthesis of core-shell ZrO2/PAAEM/PS nanoparticles through a combination of sol–gel method and emulsifier-free emulsion polymerizaiton. By this method, the modified nanometer ZrO2cores were prepared by chemical modification at a molecular level of zirconium propoxide with monomer of acetoacetoxyethylmethacrylate (AAEM), and then copolymerized with vinyl monomer to form uniform-size hybrid nanoparticles with diameter of around 250 nm. The morphology, composition, and thermal stability of the core-shell particles were characterized by various techniques including transmission electron microscopy (TEM), X-ray diffractometer (XRD), Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), and thermal-gravimetry analyzer (TGA). The results indicate that the inorganic–organic nanocomposites exhibit good thermal stability with the maximum decomposition temperature of ~447 °C. This approach would be useful for the synthesis of other inorganic–organic nanocomposites with desired functionalities

Manajemen multibudaya: kecakapan baru demi sukses global

xiii, 272 p.; 22 cm

Manajemen Multibudaya : Kecakapan Baru demi Sukses Global

Jakartaxv, 272 hlm.; 23 cm