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3 Result(s) for 'Scaling'
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1.
PFG-NMR Studies of Linear and Dendritic Polymers
James E. Hanson, Sibel Alkan, Hershel Lackey, Judith B. Cain
Journal of Polymer and Biopolymer Physics Chemistry. 2018 6 (1). doi: 10.12691/jpbpc-6-1-3
Keywords: dendrimers, pulsed field gradient NMR, diffusion coefficients, Scaling law, hydrodynamic radii
Context: Diffusion coefficients were measured by pulsed-field gradient NMR for low molecular weight linear polystyrenes in THF and for a broader molecular weight range of linear polystyrenes in chloroform and for PAMAM dendrimers up to generation methanol. Radii were calculated from the measured diffusion coefficients using the Stokes-Einstein relationship. The linear polystyrenes displayed a relationship between radius and molecular weight that followed the expected power law. From simple theoretical considerations, the dendritic polymers were expected to follow a logarithmic relationship between radius and molecular weight. The PAMAM dendrimers gave reasonable fits to both a power law and a logarithmic relationship from generation 0 to generation 3 (the power law gave a slightly better fit), but displayed a turnover with generation 4, which gave a smaller Stokes radius than generation 3. These results were compared with earlier results from poly (aryl ether) monodendrons, where the relationship was ambiguous between a power law and a logarithmic relationship.
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2.
Improving the Statistical Capacity Index: A Statistical Approach
Dharmaratne MA, Attygalle MDT
American Journal of Applied Mathematics and Statistics. 2018 6 (3). doi: 10.12691/ajams-6-3-1
Keywords: nonlinear principal component analysis, optimal Scaling , statistical capacity index
Context: Good quality, timely and accurate statistics lie at the heart of a country's effort to improve development effectiveness. As a response to the challenge of measuring the institutional capacity of a country in producing timely and accurate statistics, the World Bank developed its framework for the Statistical Capacity Index (SCI). Although the World Bank's framework is acknowledged for its simplistic approach, it has received extensive critique for the ad-hoc allocation of weights. This research attempts to find a solution to this criticism using a statistical methodology. Country information used by the World Bank to create the SCI for the year 2014 was considered. The data consisted information on 25 categorical variables out of which 16 were binary variables and 9 were ordinal variables. Nonlinear Principal Component Analysis (NLPCA) was conducted on the categorical data to reduce the observed variables to uncorrelated principal components. Consequently, the optimally scaled variables were used as input for factor analysis with principal component extraction. The results of the factor analysis were used to weight the new SCI. The dimension, availability and periodicity of economic and financial indicators explained most of the variance in the data set. The research proposes a simpler version of the new SCI with only 23 variables. In the proposed new index, the variables enrolment reporting to UNESCO, gender equality in education and primary completion indicators were the three variables receiving the largest weight. These three indicators measure the periodicity of reporting data on educational statistics to UNESCO; periodicity of observing the gross enrolment rate of girls to boys in primary and secondary education; and periodicity of observing the PCR indicator which is the number of children reaching the last year of primary school net of repeaters respectively. This research represents the first attempt to create a SCI using multivariate statistical techniques and especially index construction with NLPCA. The research concluded with a comparison of the proposed new index and the index created by the World Bank, which justified that the proposed index be used as a solution for the arbitrary allocation of weights in creating the SCI.
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3.
Geometric Transformations in the Design of Assembly Systems
Milan Fiľo, Jaromír Markovič, Gabriela Ižaríková, Peter Trebuňa
American Journal of Mechanical Engineering. 2013 1 (7). doi: 10.12691/ajme-1-7-56
Keywords: modeling, assembly systems, Scaling
Context: The design of the assembly systems is an important role optimizing the spatial resolution. An important tool for the problem solving is approaches to mathematics based modeling. The article presents the basic geometric transformations to identify the location.
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