Optimal decomposition method

Umeda, T., Shindo, A. and Tazaki, E., "Optimal Design of Chemical Process by Feasible Decomposition Method," I6EC Proc. Design and Development, Vol. 11, p 1, 1972. 

NCA-p-[18F]fluorotoluene, 1, has been obtained in up to 19% yield under optimized conditions5 by the modified Balz-Schieman decomposition method using BC14 anions (equation 2a). />-Toluidyldiazonium tetrachloroborate (2) served as the model compound to study the influence of solvents, anion activation agents and decomposition temperatures on the yields. The decomposition may occur via a homolytic or a heterolytic pathway (equation 2b). 

MILP-based Decomposition Method for the Optimal Scheduling of an Industrial Batch Plant... 

This paper has addressed the optimal periodic scheduling of an industrial batch plant from a new perspective. The aim has been to select a convenient number of equipment units so as to rninirnize the total equipment allocation cost and hence achieve a trade-off between a low makespan and high free capacity. A decomposition method based on a Resource-Task Network discrete-time formulation has been proposed that, when compared to the solution of the full problem, was able to reduce the total computational effort by one order of magnitude without severely compromising optimality. 

The optimal choice of preconditioner will ultimately depend on the computer architecture, in as much as some are more readily vectorizable or parallelizable. For example, the initial incomplete Cholesky decomposition methods work well on serial machines, but the forward and backward substitutions are not vectorizable. Simpler decompositions, such as diagonal scaling, run faster on machines like the Cray YMP. More complicated, vectorizable variations of the incomplete Cholesky decompositions have been developed (see, e.g., ref. 24) and are currently under investigation for their applicability to problems in biomolecular electrostatics. Studies of multigridding techniques are also very exciting. 

Measurement of the end products of nitric oxide decomposition involves the combined problems of determining (1) what the likely products are, (2) whether products are stable enough in biological systems to survive separation and analysis, and (3) developing and optimizing specific methods... 

MD simulations of polymer systems, in particular, require computation of two kinds of interactions bonded forces (bond length stretching, bond angle bending, torsional) and nonbonded forces (van der Waals and Coulombic). Parallel techniques developed [31-33] include the atom-decomposition (or replicated-datd) method, the force-decomposition method, and the spatial (domain)-decomposition method. The three methods differ only in the way atom coordinates are distributed among the processors to perform the necessary computations. Although all methods scale optimally with respect to computation, their different data layouts incur different interprocessor communication costs which affect the overall performance of each method. 

The sequential minimal optimization (SMO) algorithm is derived from the idea of the decomposition method to its extreme and the optimization for a minimal subset of just two points at each iteration. It was first devised by Platt [110], and applied to text categorization problems. SMO is a simple algorithm that can quickly solve the SVM QP problem without any extra matrix storage and without using numerical QP optimization steps at all. SMO decomposes the overall QP problem into QP sub-problems, using Osuna s theorem to ensure convergence. 

Unlike the common decomposition method, SMO will always alter only two Lagrange multipliers to move uphill in the objective function projected into the one-dimensional feasible subspace. In order to speed convergence, SMO uses heuristics to choose which two Lagrange multipliers to jointly optimize. 

All these technological and medical apvplications require that the nanoparticles are superparamagnetic with size smaller than 20 nm and the overall particle size distribution is narrow so that the part ides have uniform physical and chemical properties. In the last years, various methods for the preparation of such particles have been developed and optimized. High-quality monodisperse iron oxide nanopartides with high crystalline and narrow size distribution have been prepared by a high-temperature organic phase decomposition method. 

The expected time for a set-up is 1/18. In Table 6.3. we will give the choices for Xopi which give the optimal set according to the decomposition method, as well as the optimal set of available production times in the cyclic model. For these optimal values we will give the average delivery times and the profit P. 

Dianion formation from 2-methyl-2-propen-l-ol seems to be highly dependent on reaction conditions. Silylation of the dianion generated using a previously reported method was unsuccessful in our hands. The procedure described here for the metalation of the allylic alcohol is a modification of the one reported for formation of the dianion of 3-methyl-3-buten-l-ol The critical variant appears to be the polarity of the reaction medium. In solvents such as ether and hexane, substantial amounts (15-50%) of the vinyl-silane 3 are observed. Very poor yields of the desired product were obtained in dirnethoxyethane and hexamethylphosphoric triamide, presumably because of the decomposition of these solvents under these conditions. Empirically, the optimal solvent seems to be a mixture of ether and tetrahydrofuran in a ratio (v/v) varying from 1.4 to 2.2 in this case 3 becomes a very minor component. 

Abstract—Carbon nanotubules were produced in a large amount by catalytic decomposition of acetylene in the presence of various supported transition metal catalysts. The influence of different parameters such as the nature of the support, the size of active metal particles and the reaction conditions on the formation of nanotubules was studied. The process was optimized towards the production of nanotubules having the same diameters as the fullerene tubules obtained from the arc-discharge method. The separation of tubules from the substrate, their purification and opening were also investigated. 

Ab initio methods allow the nature of active sites to be elucidated and the influence of supports or solvents on the catalytic kinetics to be predicted. Neurock and coworkers have successfully coupled theory with atomic-scale simulations and have tracked the molecular transformations that occur over different surfaces to assess their catalytic activity and selectivity [95-98]. Relevant examples are the Pt-catalyzed NO decomposition and methanol oxidation. In case of NO decomposition, density functional theory calculations and kinetic Monte Carlo simulations substantially helped to optimize the composition of the nanocatalyst by alloying Pt with Au and creating a specific structure of the PtgAu7 particles. In catalytic methanol decomposition the elementary pathways were identified... 

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