scholarly journals On the Direct Sum Conjecture in the Straight Line Model

1998 ◽  
Vol 14 (1) ◽  
pp. 49-62 ◽  
Author(s):  
Nader H. Bshouty
Keyword(s):  
Line Model ◽  
Direct Sum ◽  
Straight Line

Estimates of Gastrocnemius Muscle Length During Simulated Pathological Gait

2013 ◽  
Vol 29 (2) ◽  
pp. 127-134 ◽  
Author(s):  
Smita Rao ◽  
Fred Dietz ◽  
H. John Yack
Keyword(s):  
Gastrocnemius Muscle ◽  
Muscle Length ◽  
Gait Pattern ◽  
Line Model ◽  
Gait Patterns ◽  
Segmented Model ◽  
Normal Gait ◽  
Straight Line ◽  
Crouch Gait ◽  
Pathological Gait

The purpose of this study was to compare estimates of gastrocnemius muscle length (GML) obtained using a segmented versus straight-line model in children. Kinematic data were acquired on eleven typically developing children as they walked under the following conditions: normal gait, crouch gait, equinus gait, and crouch with equinus gait. Maximum and minimum GML, and GML change were calculated using two models: straight-line and segmented. A two-way RMANOVA was used to compare GML characteristics. Results indicated that maximum GML and GML change during simulated pathological gait patterns were influenced by model used to calculate gastrocnemius muscle length (interaction: P = .004 and P = .026). Maximum GML was lower in the simulated gait patterns compared with normal gait (P < .001). Maximum GML was higher with the segmented model compared with the straight-line model (P = .030). Using either model, GML change in equinus gait and crouch with equinus gait was lower compared with normal gait (P < .001). Overall, minimum GML estimated with the segmented model was higher compared with the straight-line model (P < .01). The key findings of our study indicate that GML is significantly affected by both gait pattern and method of estimation. The GML estimates tended to be lower with the straight-line model versus the segmented model.

Probabilistic and least-squares inference of the parameters of a straight-line model

Metrologia ◽  
2007 ◽  
Vol 44 (5) ◽  
pp. 379-384 ◽  
Author(s):  
Ignacio Lira ◽  
Clemens Elster ◽  
Wolfgang Wöger
Keyword(s):  
Least Squares ◽  
Line Model ◽  
Straight Line

scholarly journals Comparing Methods for Calculating Nano Crystal Size of Natural Hydroxyapatite Using X-Ray Diffraction

Nanomaterials ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1627 ◽  
Author(s):  
Marzieh Rabiei ◽  
Arvydas Palevicius ◽  
Ahmad Monshi ◽  
Sohrab Nasiri ◽  
Andrius Vilkauskas ◽  
...  
Keyword(s):  
Crystal Size ◽  
Gas Adsorption ◽  
Deformation Model ◽  
Check Point ◽  
Line Model ◽  
Uniform Deformation ◽  
Straight Line Passing ◽  
Straight Line ◽  
Xrd Patterns ◽  
Scherrer Method

We report on a comparison of methods based on XRD patterns for calculating crystal size. In this case, XRD peaks were extracted from hydroxyapatite obtained from cow, pig, and chicken bones. Hydroxyapatite was synthesized through the thermal treatment of natural bones at 950 °C. XRD patterns were selected by adjustment of X-Pert software for each method and for calculating the size of the crystals. Methods consisted of Scherrer (three models), Monshi–Scherrer, three models of Williamson–Hall (namely the Uniform Deformation Model (UDM), the Uniform Stress Deformation Model (USDM), and the Uniform Deformation Energy Density Model (UDEDM)), Halder–Wanger (H-W), and the Size Strain Plot Method (SSP). These methods have been used and compared together. The sizes of crystallites obtained by the XRD patterns in each method for hydroxyapatite from cow, pig, and chicken were 1371, 457, and 196 nm in the Scherrer method when considering all of the available peaks together (straight line model). A new model (straight line passing the origin) gave 60, 60, and 53 nm, which shows much improvement. The average model gave 56, 58, and 52 nm, for each of the three approaches, respectively, for cow, pig, and chicken. The Monshi–Scherrer method gave 60, 60, and 57 nm. Values of 56, 62, and 65 nm were given by the UDM method. The values calculated by the USDM method were 60, 62, and 62 nm. The values of 62, 62, and 65 nm were given by the UDEDM method for cow, pig, and chicken, respectively. Furthermore, the crystal size value was 4 nm for all samples in the H-W method. Values were also calculated as 43, 62, and 57 nm in the SSP method for cow, pig, and chicken tandemly. According to the comparison of values in each method, the Scherrer method (straight line model) for considering all peaks led to unreasonable values. Nevertheless, other values were in the acceptable range, similar to the reported values in the literature. Experimental analyses, such as specific surface area by gas adsorption (Brunauer–Emmett–Teller (BET)) and Transmission Electron Microscopy (TEM), were utilized. In the final comparison, parameters of accuracy, ease of calculations, having a check point for the researcher, and difference between the obtained values and experimental analysis by BET and TEM were considered. The Monshi–Scherrer method provided ease of calculation and a decrease in errors by applying least squares to the linear plot. There is a check point for this line that the slope must not be far from one. Then, the intercept gives the most accurate crystal size. In this study, the setup of values for BET (56, 52, and 49 nm) was also similar to the Monshi–Scherrer method and the use of it in research studies of nanotechnology is advised.

A Straight Line Model for Multiplication

1966 ◽  
Vol 59 (4) ◽  
pp. 342-347
Author(s):  
Donald Fukuda ◽  
Edwin Mookini ◽  
James K. M. Siu
Keyword(s):  
Subject Matter ◽  
Secondary Mathematics ◽  
Line Model ◽  
Modern Approach ◽  
Linear Relations ◽  
Straight Line ◽  
Basic Concepts ◽  
Average Students

IN THE abundant material of modern elementary and secondary mathematics, there appears little to comfort teachers who are unfamiliar with the modern approach and students who have difficulty mastering the highly axiomatic development of subject matter. To overcome these handicaps, this unit of study is presented with the hope of offering structurally sound mathematics at a level which is intuitively discoverable and comprehensible by “average” students. (As this unit was being written, the material was tried in several classrooms by the writers.) This approach allows these students to discover some basic concepts of mathematics through linear relations.

Kinematics and Statics Including Cable Sag for Large Cable-Suspended Robots

2016 ◽  
Author(s):  
Dheerendra Sridhar ◽  
Robert L. Williams
Keyword(s):  
Comparative Analysis ◽  
Modeling And Simulation ◽  
Large Scale ◽  
Robot System ◽  
Line Model ◽  
Actuation Redundancy ◽  
Cable Length ◽  
Qualitative And Quantitative ◽  
Straight Line ◽  
Quantitative Results

Cable sag can have significant effects on the cable length computation in a cable-suspended robot and this is more pronounced in large-scale outdoor systems. This requires modeling the cable as a catenary instead of an approximated straight-line model. Furthermore, when there is actuation redundancy involved, the modeling and simulation of the system becomes much more complex, requiring optimizing routines to solve the problem. A cable-sag-compensated (catenary) model was implemented in simulation for an example large outdoor cable-suspended robot system to solve the coupled kinematics and statics problems. This involved optimization of cable tensions and finding the errors involved in the cable length. A comparative analysis between the straight-line and cable sag model is presented, the main contribution of this paper. Based on the qualitative and quantitative results obtained, recommendations were made on the choice of model and solution methodologies.

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