Exploring the Mathematics of Bouncing Balls

2010 ◽  
Vol 104 (3) ◽  
pp. 192-198
Author(s):  
Natalya Vinogradova ◽  
Larry G. Blaine
Keyword(s):  
Experimental Data ◽  
Quadratic Equations ◽  
Geometric Sums

Simple equipment—stopwatches, tape measures, and golf balls—allows students to explore geometric sums and quadratic equations and analyze experimental data.

Optimization of l-Asparaginase Production by Isolated Aspergillus niger C4 from Sesame (black) Oil Cake under SSF using Box–Behnken Design in Column Bioreactor

2013 ◽  
Vol 11 (1) ◽  
pp. 103-109 ◽  
Author(s):  
Kiran Babu Uppuluri ◽  
Ravi Kumar V. R. Dasari ◽  
Vinod Sajja ◽  
Annie Shanan Jacob ◽  
D. Sri Rami Reddy
Keyword(s):  
Experimental Data ◽  
Aspergillus Niger ◽  
Response Surfaces ◽  
Design Matrix ◽  
Process Variables ◽  
Box Behnken Design ◽  
Quadratic Equations ◽  
Black Oil ◽  
Column Bioreactor ◽  
Bed Thickness

Abstract l-Asparaginase production was investigated in the isolated Aspergillus niger C4 on sesame (black) oil cake using solid state fermentation in a column bioreactor. The main objective of the present study is optimizing the environmental conditions for l-Asparaginase production in a column bioreactor. In order to determine the effect of process variables on the yield of l-Asparaginase, by the way of response surface methodology, an experimental plan (Box–Behnken design) involving a design matrix of 15 trails was sketched. The design results were fitted with response surfaces. Empirical quadratic equations were fitted to the experimental data (BBD) relevant to the yields of l-Asparaginase, with three chosen variables (aeration, bed thickness and temperature). The statistical analysis revealed a maximum l-Asparaginase yield of 310 U/gds at the points where aeration, bed thickness and temperature were 0.44 vvm, 17.35 cm and 29.31°C, respectively.

Microdiffraction Patterns of Small Metallic Particles II; Theoretical Analysis

1982 ◽  
Vol 40 ◽  
pp. 668-669
Author(s):  
A. Gómez ◽  
P. Schabes-Retchkiman ◽  
M. José-Yacamán ◽  
T. Ocaña
Keyword(s):  
Experimental Data ◽  
Electron Diffraction ◽  
Theoretical Analysis ◽  
Size Range ◽  
Dynamical Theory ◽  
Metallic Particles ◽  
Splitting Effect

The splitting effect that is observed in microdiffraction pat-terns of small metallic particles in the size range 50-500 Å can be understood using the dynamical theory of electron diffraction for the case of a crystal containing a finite wedge. For the experimental data we refer to part I of this work in these proceedings.

Evidence for ordered Fe3Ni

1987 ◽  
Vol 45 ◽  
pp. 216-217
Author(s):  
K.B. Reuter ◽  
D.B. Williams ◽  
J.I. Goldstein
Keyword(s):  
Experimental Data ◽  
Martensitic Transformation ◽  
Electron Diffraction ◽  
Room Temperature ◽  
Direct Evidence ◽  
Transformation Product ◽  
Iron Meteorites ◽  
X Ray ◽  
Ni Content ◽  
Temperature Transformation

In the Fe-Ni system, although ordered FeNi and ordered Ni3Fe are experimentally well established, direct evidence for ordered Fe3Ni is unconvincing. Little experimental data for Fe3Ni exists because diffusion is sluggish at temperatures below 400°C and because alloys containing less than 29 wt% Ni undergo a martensitic transformation at room temperature. Fe-Ni phases in iron meteorites were examined in this study because iron meteorites have cooled at slow rates of about 10°C/106 years, allowing phase transformations below 400°C to occur. One low temperature transformation product, called clear taenite 2 (CT2), was of particular interest because it contains less than 30 wtZ Ni and is not martensitic. Because CT2 is only a few microns in size, the structure and Ni content were determined through electron diffraction and x-ray microanalysis. A Philips EM400T operated at 120 kV, equipped with a Tracor Northern 2000 multichannel analyzer, was used.

EELS white line intensities calculated for the 3d and 4d metals

1989 ◽  
Vol 47 ◽  
pp. 388-389
Author(s):  
C. C. Ahn ◽  
D. H. Pearson ◽  
P. Rez ◽  
B. Fultz
Keyword(s):  
Experimental Data ◽  
Line Intensity ◽  
Transition Probabilities ◽  
Initial Increase ◽  
White Line ◽  
Hartree Fock ◽  
Line Intensities ◽  
Integrated Intensity ◽  
X Ray Absorption ◽  
The Continuum

Previous experimental measurements of the total white line intensities from L2,3 energy loss spectra of 3d transition metals reported a linear dependence of the white line intensity on 3d occupancy. These results are inconsistent, however, with behavior inferred from relativistic one electron Dirac-Fock calculations, which show an initial increase followed by a decrease of total white line intensity across the 3d series. This inconsistency with experimental data is especially puzzling in light of work by Thole, et al., which successfully calculates x-ray absorption spectra of the lanthanide M4,5 white lines by employing a less rigorous Hartree-Fock calculation with relativistic corrections based on the work of Cowan. When restricted to transitions allowed by dipole selection rules, the calculated spectra of the lanthanide M4,5 white lines show a decreasing intensity as a function of Z that was consistent with the available experimental data.Here we report the results of Dirac-Fock calculations of the L2,3 white lines of the 3d and 4d elements, and compare the results to the experimental work of Pearson et al. In a previous study, similar calculations helped to account for the non-statistical behavior of L3/L2 ratios of the 3d metals. We assumed that all metals had a single 4s electron. Because these calculations provide absolute transition probabilities, to compare the calculated white line intensities to the experimental data, we normalized the calculated intensities to the intensity of the continuum above the L3 edges. The continuum intensity was obtained by Hartree-Slater calculations, and the normalization factor for the white line intensities was the integrated intensity in an energy window of fixed width and position above the L3 edge of each element.

A fuzzy neural network approach for modeling the growth kinetics of FeB and Fe2B layers during the boronizing process

2018 ◽  
Vol 106 (6) ◽  
pp. 603 ◽  
Author(s):  
Bendaoud Mebarek ◽  
Mourad Keddam
Keyword(s):  
Neural Network ◽  
Experimental Data ◽  
Fuzzy Neural Network ◽  
Treatment Time ◽  
Calculation Model ◽  
Average Error ◽  
Network Approach ◽  
Neural Network Approach ◽  
Fuzzy Neural ◽  
Kinetics Of

In this paper, we develop a boronizing process simulation model based on fuzzy neural network (FNN) approach for estimating the thickness of the FeB and Fe2B layers. The model represents a synthesis of two artificial intelligence techniques; the fuzzy logic and the neural network. Characteristics of the fuzzy neural network approach for the modelling of boronizing process are presented in this study. In order to validate the results of our calculation model, we have used the learning base of experimental data of the powder-pack boronizing of Fe-15Cr alloy in the temperature range from 800 to 1050 °C and for a treatment time ranging from 0.5 to 12 h. The obtained results show that it is possible to estimate the influence of different process parameters. Comparing the results obtained by the artificial neural network to experimental data, the average error generated from the fuzzy neural network was 3% for the FeB layer and 3.5% for the Fe2B layer. The results obtained from the fuzzy neural network approach are in agreement with the experimental data. Finally, the utilization of fuzzy neural network approach is well adapted for the boronizing kinetics of Fe-15Cr alloy.

Use of Posterior Probabilities to Evaluate Methods of Discriminant Analysis

1981 ◽  
Vol 20 (04) ◽  
pp. 207-212 ◽  
Author(s):  
J. Hermans ◽  
B. van Zomeren ◽  
J. W. Raatgever ◽  
P. J. Sterk ◽  
J. D. F. Habbema
Keyword(s):  
Experimental Data ◽  
Discriminant Analysis ◽  
Posterior Probabilities

By means of a case study the choice between several methods of discriminant analysis is presented. Experimental data of a two-groups problem with one or two variables is analysed. The different methods are compared according to posterior probabilities which can be computed for each subject and which are the basis of discriminant analysis. These posterior probabilities are analysed graphically as well as numerically.

Analysis of athletes’ stadium stress source based on improved layered K-means algorithm

2020 ◽  
Vol 39 (4) ◽  
pp. 5905-5914
Author(s):  
Chen Gong
Keyword(s):  
Experimental Data ◽  
Machine Learning Algorithms ◽  
User Preference ◽  
Experimental Comparison ◽  
Actual Situation ◽  
Medical Field ◽  
Pressure Source ◽  
Preference Model ◽  
Related Research ◽  
Analysis System

Most of the research on stressors is in the medical field, and there are few analysis of athletes’ stressors, so it can not provide reference for the analysis of athletes’ stressors. Based on this, this study combines machine learning algorithms to analyze the pressure source of athletes’ stadium. In terms of data collection, it is mainly obtained through questionnaire survey and interview form, and it is used as experimental data after passing the test. In order to improve the performance of the algorithm, this paper combines the known K-Means algorithm with the layering algorithm to form a new improved layered K-Means algorithm. At the same time, this paper analyzes the performance of the improved hierarchical K-Means algorithm through experimental comparison and compares the clustering results. In addition, the analysis system corresponding to the algorithm is constructed based on the actual situation, the algorithm is applied to practice, and the user preference model is constructed. Finally, this article helps athletes find stressors and find ways to reduce stressors through personalized recommendations. The research shows that the algorithm of this study is reliable and has certain practical effects and can provide theoretical reference for subsequent related research.

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