Least-squares Analysis of Fabric Data: A Note on Conical, Cylindroidal and Near–cylindroidal Folds

1971 ◽  
Vol 8 (6) ◽  
pp. 694-697 ◽  
Author(s):  
C. S. Venkitasubramanyan
Keyword(s):  
Least Squares ◽  
Stereographic Projection ◽  
Rotation Axis ◽  
Computational Procedure ◽  
Apical Angle ◽  
Small Circle ◽  
Best Fitting ◽  
Fabric Diagrams ◽  
The Mean

A cylinder and a plane may be considered as special limiting cases for a right circular cone as the semi-apical angle approaches 0° and 90° respectively (Loudon 1964, Kelley 1966). If these forms are viewed as surfaces generated by an array of lines in space, the rotation axis for the array (the axis of the "cone") can be determined from the orientations of the surface-generating lines by a single computational procedure, using least-squares criterion. The mean angle between the rotation axis and the surface-generating lines will be the semi-apical angle of the cone. However, if this method for determination of the semi-apical angle of the cone, and therefore the best-fitting small circle, is extended to fabric diagrams, in which an array of lines may only statistically describe a great circle or small circle on a stereographic projection, ambiguities arise in certain cases and the semi-apical angle obtained may not be the true semi-apical angle. The difficulty arises because the poles to foliation surfaces are arbitrarily assigned "senses".

scholarly journals Simultaneous Determination of Several Fiber Contents in Blended Fabrics by Near-Infrared Spectroscopy and Multivariate Calibration

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Hui Chen ◽  
Zan Lin ◽  
Chao Tan
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Near Infrared ◽  
Multivariate Calibration ◽  
Nir Spectroscopy ◽  
Nondestructive Method ◽  
Full Spectrum ◽  
Lattice Design ◽  
The Mean

The qualitative and quantitative determination of the components of textile fibers takes an important position in quality control. A fast and nondestructive method of simultaneously analyzing four fiber components in blended fabrics was studied by near-infrared (NIR) spectroscopy combined with multivariate calibration. Two sample sets including 39 and 25 samples were designed by simplex mixture lattice design methods and used for experiment. Four components include wool, polyester, polyacrylonitrile, and nylon and their mixture is one of the most popular formulas of textiles. Uninformative variable elimination-partial least squares (UVEPLS) and the full-spectrum partial least squares (PLS) were used as the tool. On the test set, the mean standard error of prediction (SEP) and the mean ratio of the standard deviation of the response variable and SEP (RPD) of the full-spectrum PLS model and UVEPLS model were 0.38, 0.32 and 7.6, 8.3, respectively. This result reveals that the UVEPLS can construct local models with acceptable and better performance than the full-spectrum PLS. It indicates that this method is valuable for nondestructive analysis in the field of wool content detection since it can avoid time-consuming, costly, and laborious wet chemical analysis.

Determination of the water regulation capacity of a typic hapludands by means of humidity retention curves and the modeling of its hydrophysical properties

2019 ◽  
Vol 21 (1) ◽  
Author(s):  
Cindy L. Argote-Sanchez ◽  
Juliana M. Lozano-Santa ◽  
Aldemar Reyes-Trujillo
Keyword(s):  
Organic Matter ◽  
Laboratory Finding ◽  
High Capacity ◽  
Water Regulation ◽  
A Value ◽  
Best Fitting ◽  
The Mean ◽  
Valle Del Cauca ◽  
Fitting Model

In the watershed Centella , located in the upper river basin of the Dagua - Valle del Cauca, in nine farms with association coffee - banana, coffee - guamo, cane panelera and pastures, the water regulation capacity of the soil was studied by means of humidity retention curves obtained in the laboratory and by modeling its hydrophysical properties in Hydrus 2D. Properties such as texture, bulk density, porosity, organic matter, hydraulic conductivity, infiltration and humidity were determined. Subsequently, moistureretention curves were simulated using the hydraulic models of Van Genuchten, Brooks and Corey, Van Genuchten modified and Kosugi, evaluating the average errors and the dispersion of the data. Agreed to the results it is possible to point out that the soil under study has a high capacity for moisture retention ( > 18%), consequence of the high content of clays ( > 41%) and organic matter ( > 5%), characteristics of the Andisols of the Valle del Cauca. Finally, the best fitting model was compared statistically with the data of the curves obtained in the laboratory, finding that Van Genuchten and Van Genuchten models modified, are the most appropriate for obtaining the retention curves from the hydrophysical properties since they presented a lower mean error (ME) with a value not higher than -0.11 cm3 / cm3 and a value of the square root of the mean square error (RMSE) less than 0.11 cm3 / cm3.

X-Ray Spectroscopy in the Clinical Laboratory

1962 ◽  
Vol 8 (1) ◽  
pp. 17-34 ◽  
Author(s):  
Samuel Natelson ◽  
Bertrum Sheid
Keyword(s):  
Filter Paper ◽  
Proportional Counter ◽  
Clinical Laboratory ◽  
Ether Extract ◽  
Ray Method ◽  
Small Circle ◽  
X Ray ◽  
The Mean ◽  
Inorganic Iodine

Abstract A procedure is described for the determination of protein-bound iodine of human serum with the X-ray spectrometer. The protein-bound iodine is extracted from serum at acid pH with alcohol-ether (3:1) solution. Evaporation of this extract results in the loss of the inorganic iodine. The residue is extracted with ammoniacal methanol, evaporated on filter paper, and exposed to the X-ray field. The Lα radiation is evaluated using the flow proportional counter. An instrument is described for evaporating the ammoniacal methanol in a confined area on the paper. The residue from the alcohol-ether extract may also be digested, with the liberated iodine distilled onto a small circle of filter paper (in a simple apparatus described) and the filter paper exposed to the X-ray field. The procedure requires 2 ml. of serum. Levels obtained by this method are somewhat lower than those obtained by an ashing procedure followed by the ceric-arsenite reaction. The X-ray method is more precise than the conventional procedures. In preliminary studies, the mean normal value found by this method was 4.7 µg./100 ml. of serum, with a range of ± 0.6 (2 σ).

Detection of Circulating Tissue Factor and Factor VII in a Normal Population

1996 ◽  
Vol 75 (05) ◽  
pp. 772-777 ◽  
Author(s):  
Sybille Albrecht ◽  
Matthias Kotzsch ◽  
Gabriele Siegert ◽  
Thomas Luther ◽  
Heinz Großmann ◽  
...  
Keyword(s):  
Tissue Factor ◽  
Normal Population ◽  
Mean Value ◽  
Factor Vii ◽  
Significant Difference ◽  
Age Dependent ◽  
The Mean ◽  
Highly Correlated ◽  
And Gender

SummaryThe plasma tissue factor (TF) concentration was correlated to factor VII concentration (FVIIag) and factor VII activity (FVIIc) in 498 healthy volunteers ranging in age from 17 to 64 years. Immunoassays using monoclonal antibodies (mAbs) were developed for the determination of TF and FVIIag in plasma. The mAbs and the test systems were characterized. The mean value of the TF concentration was 172 ± 135 pg/ml. TF showed no age- and gender-related differences. For the total population, FVIIc, determined by a clotting test, was 110 ± 15% and the factor VIlag was 0.77 ± 0.19 μg/ml. FVII activity was significantly increased with age, whereas the concentration demonstrated no correlation to age in this population. FVII concentration is highly correlated with the activity as measured by clotting assay using rabbit thromboplastin. The ratio between FVIIc and FVIIag was not age-dependent, but demonstrated a significant difference between men and women. Between TF and FVII we could not detect a correlation.

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

Determination of Plasminogen in Clots and Thrombi

1966 ◽  
Vol 16 (01/02) ◽  
pp. 038-050 ◽  
Author(s):  
Ulla Hedner ◽  
Inga Marie Nilsson ◽  
B Robertson
Keyword(s):  
Mean Value ◽  
Main Mechanism ◽  
Clot Lysis ◽  
Post Mortem ◽  
Digestion Time ◽  
Normal Volunteers ◽  
Casein Solution ◽  
The Mean

SummaryThe plasminogen content was determined by a casein method in plasma and serum from 20 normal volunteers. The mean plasminogen content was found to be 10.1 ACU (the arbitrary caseinolytic unit defined in such a way that using a 3% casein solution and a digestion time of 20 min. at 37°C, 10 ACU gave an extinction of 0.300). No difference between serum and plasma regarding the plasminogen content was found.Plasminogen was determined in drained and drained plus washed clots prepared from 2 ml plasma. The highest values found in the drained clots were 0.9 ACU/clot and 0.2 ACU/clot in the drained plus washed clots.Plasminogen was also determined in drained and drained plus washed clots prepared from plasma with added purified plasminogen. The plasminogen was recovered in the washing fluid. According to these tests, then, purified added plasminogen is washed out of the clots.The plasminogen content of 20 thrombi obtained post mortem was also determined. The mean value was found to be 0.7 ACU/cm thrombus. Judging from our results, the “intrinsic clot lysis theory” is not the main mechanism of clot dissolution.

SERUM TRIIODOTHYRONINE DETERMINATION BY SATURATION ANALYSIS

1973 ◽  
Vol 72 (4) ◽  
pp. 714-726 ◽  
Author(s):  
A. Burger ◽  
B. Miller ◽  
C. Sakoloff ◽  
M. B. Vallotton
Keyword(s):  
Ionic Strength ◽  
Limit Of Detection ◽  
Improved Method ◽  
Accuracy Of Measurement ◽  
Tracer Amount ◽  
The Mean ◽  
Physiological Values ◽  
Hyperthyroid Patients ◽  
Solvent Blank

ABSTRACT An improved method for the determination of serum triiodothyronine (T3) has been developed. After addition of a tracer amount of the hormone, T3 was extracted from 1 ml serum under conditions of pH and ionic strength which favoured T3 extraction (89%) over thyroxine (T4) extraction (58%). Chromatography of the extracted material on Sephadex LH-20 separated T3 completely from residual T4. The T3 eluate was dried, then re-dissolved in 0.5 ml NaOH 0.04 n. To 0.2 ml duplicate aliquots, a standard amount of TBG was added for the competitive protein analysis. After one hour incubation at 4°C, separation of bound from free T3 was achieved on small Sephadex G-25 columns. Overall recovery was 67 ± 10.8% and correction for the loss was made. The solvent blank was 37 ± 27 (sd) ng/100 ml. Accuracy of measurement of known quantities of T3 added to serum was 98.4%. The coefficient of variation within the assay was 6.2% and between the assays it was 11.4%. The limit of detection (0.1 ng) corresponded to a concentration of 25 ng/100 ml. T4 added to serum did not interfere with T3 determination until high non-physiological values were reached. The mean ± sd serum T3 in 54 euthyroid subjects was 153 ± 58 ng/100 ml and in 24 hyperthyroid patients it was 428 ±186 ng/100 ml; 4 out of the 24 hyperthyroid values were within 2 sd of the mean euthyroid group. All the values found in the euthyroid group were well above the limit of detection of the method.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

Determination of Pyridostigmine Bromide in Presence of its Related Impurities by Four Modified Classical Least Square Based Models: A Comparative Study

2020 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
Ibrahim A. Naguib ◽  
Fatma F. Abdallah ◽  
Aml A. Emam ◽  
Eglal A. Abdelaleem
Keyword(s):  
Comparative Study ◽  
Least Squares ◽  
Orthogonal Projection ◽  
Predictive Ability ◽  
Least Square ◽  
Projection To Latent Structures ◽  
Preprocessing Method ◽  
Spectral Residual ◽  
Latent Structures

: Quantitative determination of pyridostigmine bromide in the presence of its two related substances; impurity A and impurity B was considered as a case study to construct the comparison. Introduction: Novel manipulations of the well-known classical least squares multivariate calibration model were explained in detail as a comparative analytical study in this research work. In addition to the application of plain classical least squares model, two preprocessing steps were tried, where prior to modeling with classical least squares, first derivatization and orthogonal projection to latent structures were applied to produce two novel manipulations of the classical least square-based model. Moreover, spectral residual augmented classical least squares model is included in the present comparative study. Methods: 3 factor 4 level design was implemented constructing a training set of 16 mixtures with different concentrations of the studied components. To investigate the predictive ability of the studied models; a test set consisting of 9 mixtures was constructed. Results: The key performance indicator of this comparative study was the root mean square error of prediction for the independent test set mixtures, where it was found 1.367 when classical least squares applied with no preprocessing method, 1.352 when first derivative data was implemented, 0.2100 when orthogonal projection to latent structures preprocessing method was applied and 0.2747 when spectral residual augmented classical least squares was performed. Conclusion: Coupling of classical least squares model with orthogonal projection to latent structures preprocessing method produced significant improvement of the predictive ability of it.

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