Multivariate analysis of montmorillonite

Clay Minerals ◽  
1965 ◽  
Vol 6 (1) ◽  
pp. 59-70 ◽  
Author(s):  
J. H. Rayner
Keyword(s):  
Multivariate Analysis ◽  
Similarity Coefficient ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
One Dimensional ◽  
The Relationship

AbstractVarty & White's application of multivariate analysis to Grim & Kulbicki's measurements on montmorillonites has been re-examined and extended. Inconsistencies between their table of scored data and derived similarity table, and some unexplained errors in the similarity table, have only a small effect on their results. Similarities calculated from Grim & Kulbicki's data, using a different similarity coefficient, lead to a two dimensional representation which separates the groups of montmorillonites more clearly. The groups can be clearly separated even in a one dimensional representation, by changing the relationship between distance and similarity.

scholarly journals Estimation for Two-Dimensional Nonsymmetric Coherently Distributed Source in L-Shaped Arrays

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Tao Wu ◽  
Zhenghong Deng ◽  
Qingyue Gu ◽  
Jiwei Xu
Keyword(s):  
Expectation Maximization ◽  
Two Dimensional ◽  
Signal Distribution ◽  
Distributed Source ◽  
One Dimensional ◽  
Least Squares Estimators ◽  
Iterative Calculation ◽  
Symmetric Source ◽  
Relationship Of ◽  
The Relationship

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

DIAGRAMS FOR MAGNETOTELLURIC DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley
Keyword(s):  
Impedance Tensor ◽  
Two Dimensional ◽  
Magnetotelluric Data ◽  
One Dimensional ◽  
Magnetic Components ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
The Relationship ◽  
Special Case ◽  
Phase Differences

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].

scholarly journals A Two-Dimensional Genetic Algorithm and Its Application to Aircraft Scheduling Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Ming-Wen Tsai ◽  
Tzung-Pei Hong ◽  
Woo-Tsong Lin
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Scheduling Problem ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Time Table ◽  
Feasible Solutions ◽  
Crossover And Mutation ◽  
Airline Company

Genetic algorithms have become increasingly important for researchers in resolving difficult problems because they can provide feasible solutions in limited time. Using genetic algorithms to solve a problem involves first defining a representation that describes the problem states. Most previous studies have adopted one-dimensional representation. Some real problems are, however, naturally suitable to two-dimensional representation. Therefore, a two-dimensional encoding representation is designed and the traditional genetic algorithm is modified to fit the representation. Particularly, appropriate two-dimensional crossover and mutation operations are proposed to generate candidate chromosomes in the next generations. A two-dimensional repairing mechanism is also developed to adjust infeasible chromosomes to feasible ones. Finally, the proposed approach is used to solve the scheduling problem of assigning aircrafts to a time table in an airline company for demonstrating the effectiveness of the proposed genetic algorithm.

Measurement of Temperature and Heat Flux Changes During the Fixing Process in Electrophotographic Machines

1996 ◽  
Vol 118 (1) ◽  
pp. 150-154 ◽  
Author(s):  
T. Mitsuya ◽  
K. Masuda ◽  
Y. Hori
Keyword(s):  
Heat Flux ◽  
Print Quality ◽  
Two Dimensional ◽  
Temperature Changes ◽  
One Dimensional ◽  
Temperature Heat ◽  
Rapid Temperature ◽  
Pressure Changes ◽  
The Relationship ◽  
Electrophotographic Printing

Increasingly higher speeds of modern electrophotographic printing force examination of the problem of retaining sufficient fixing strength without deterioration of print quality. In the nip region between the two rollers where fixing occurs, the significant parameters are temperature, heat flux, and pressure changes. Their optimization is necessary to maintain both speed and print quality. Difficulty in analyzing the relationship among these parameters occurs because of the complexity of two-dimensional phenomena in a rotating field and the rapidity of changes. Experimental equipment to measure relative heat flux in the nip region during rapid temperature changes was designed. Two sensors are installed in the heat roller. An adiabatic piece is buried under sensor 1. Sensor 2, without an adiabatic piece, detects temperature. Sensor 1 is electrically heated and always at the same temperature as sensor 2. Heat flux changes are obtained by noting the electric power supplied to sensor 1. The equipment was fabricated and measurements were made. They indicate an intermittent two-dimensional heat flux. Because of this, temperature decreases rapidly before the entrance to the nip region. Estimates of two-dimensional effects are made and modified for a one-dimensional case. From them, the temperature field in the nip region for actual fixing conditions is calculated.

Seepage flow in unconfined aquifers

1975 ◽  
Vol 71 (1) ◽  
pp. 181-192 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Flow Rate ◽  
Seepage Flow ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Unconfined Aquifers ◽  
Source Line ◽  
Theory Yield ◽  
The Relationship

The paper concerns one- and two-dimensional models of steady seepage flow in unconfined aquifers and the relationship between them. The first part gives a new proof of Charnyi's result that one- and two-dimensional theory yield the same value for the flow rate in a horizontal aquifer or porous bed between vertical ends and shows the extent to which it can be generalized to non-uniform or anisotropic media. The second part solves the highly two-dimensional problem of flow from a line source (line of springs) in an otherwise impermeable, sloping stratum and compares the result with the predictions of a one-dimensional Dupuit–Pavlovsky approach. Confirmatory experiments using the Hele Shaw analogue of seepage flow are also reported.

The Sahara

2017 ◽  
Author(s):  
Barbara E. Barich
Keyword(s):  
Human Body ◽  
Manufacturing Process ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
Three Dimensional Representation ◽  
The Difference ◽  
Symbolic Content ◽  
The Relationship

This chapter discusses the collection of objects, in clay and stone, from various pastoral Saharan sites whose original core area lay between Libya (Tadrart Acacus) and Algeria (Tassili- n-Ajjer). The chapter starts from the general theme of the relationship between the figurines and the subjects they represent, and the difference between two-dimensional and three-dimensional representation. It goes on to discuss the manufacturing process of the clay specimens (dating from between 7000 and 4000 years ago) and the significance of the changes introduced by the Neolithic. Most of the items studied fall into the category of zoomorphic figurines, with only two anthropomorphic examples, and find in the depiction of cattle their most striking subject. These representations possess an evident symbolic content which must be framed within the pastoral ideology of the Saharan Neolithic. In the anthropomorphic figurines the representation of the human body also plays the role of recapturing the sense of wholeness.

Measurement of Straightness for Two-Dimensional Translatory Stage

2010 ◽  
Vol 437 ◽  
pp. 194-197
Author(s):  
Ryoshu Furutani ◽  
Masakazu Watanabe
Keyword(s):  
Laser Interferometer ◽  
Probe Method ◽  
Two Dimensional ◽  
Profile Error ◽  
Reference Mirror ◽  
One Dimensional ◽  
Dimensional Measurement ◽  
Adjustment Error ◽  
Profile Errors ◽  
The Relationship

The large scaled and high accurate 2D-stage is necessary for nanomanufacturing. In order to measure the position of stage, two direction sensors are used. These sensors measure the displacement from the metrological frame. However in nanometer application, as the profile error of metrological frame is comparable with the accuracy of 2D-stage, it is not negligible. Therefore the measuring result includes the displacement of stages and the profile error of metrological frame. So the multi-probe method is applied in one-dimensional measurement to separate the displacement error from the profile error of the metrological frame. In the multi-probe method, the zero adjustment error cannot be removed. So this article proposes a new method which separates the displacement of 2D-stage from the profile errors of the metrological frames in two directions. In this article, as the laser interferometer is used as the sensor, the measuring data is assumed as the shape of the axis of stages mixed with the profile error of the reference mirror in laser interferometer. The relationship during the measuring data, the shape of the axis and the profile error is described. The shape of axis of stage and the profile error of mirror are derived from the measuring result in experiment.

PUSHDOWN RECOGNIZERS FOR ARRAY PATTERN

1989 ◽  
Vol 03 (03n04) ◽  
pp. 377-392
Author(s):  
H. J. LIN ◽  
P. S. P. WANG
Keyword(s):  
Two Dimensional ◽  
One Dimensional ◽  
Array Pattern ◽  
The Relationship ◽  
Context Free ◽  
Pushdown Automata

We investigate the factors that make it difficult to generalize pushdown automata for one-dimensional strings to two-dimensional arrays. Then we resolve the problems and construct two-dimensional pushdown array automata (PDAA). The relationship between isometric context-free array languages and pushdown array automata is established. Several examples of array automata are presented, and a pushdown array automaton is tested on VAX8650/VMS using PASCAL.

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