scholarly journals XXIX. On the analytical theory of the conic

1862 ◽  
Vol 152 ◽  
pp. 639-662
Keyword(s):  
Linear Function ◽  
Constant Factor ◽  
Analytical Theory ◽  
The Other ◽  
Analytical Basis ◽  
Linear Factor

The decomposition into its linear factors of a decomposable quadric function cannot be effected in a symmetrical manner otherwise than by formulæ containing supernumerary arbitrary quantities; thus, for a binary quadric (which of course is always decomposable) we have ( a, b, c )( x, y ) 2 = 1/( a, b, c )( x 1 , y 1 ) 2 Prod. {( a, b, c )( x, y )( x 1 , y 1 ) ± √ ac - b 2 ( xy 1 - x 1 y )}; or the expression for a linear factor is 1/√( a, b, c )( x 1 , y 1 ) 2 {( a , b , a, b, c )( x, y )( x 1 , y 1 ) ± √ ac - b 2 ( xy 1 - x 1 y )}, which involves the arbitrary quantities ( x 1 , y 1 ). And this appears to be the reason why, in the analytical theory of the conic, the questions which involve the decomposition of a decomposable ternary quadric have been little or scarcely at all considered: thus, for instance, the expressions for the coordinates of the points of intersection of a conic by a line (or say the line-equations of the two ineunts), and the equations for the tangents (separate each from the other) drawn from a given point not on the conic, do not appear to have been obtained. These questions depend on the decomposition of a decom­posable ternary quadric, which decomposition itself depends on that for the simplest case, when the quadric is a perfect square. Or we may say that in the first instance they depend on the transformation of a given quadric function U = (*)( x, y, z ) 2 into the form W 2 + V, where W is a linear function, given save as to a constant factor (that is, W = 0 is the equation of a given line), and V is a decomposable quadric function, which is ultimately decomposed into its linear factors, = QR, so that we have U = W 2 + QR. The formula for this purpose, which is exhibited in the eight different forms I, II, III, IV, I(bis), Il(bis), Ill(bis), IV(bis), is the analytical basis of the whole theory; and the greater part of the memoir relates to the establishment of these forms. The solution of the geometrical questions above referred to is (as shown in the memoir) involved in and given immediately by these forms. It is also shown that the formulæ are greatly simplified in the case e. g. of tangents drawn to a conic from a point in a conic having double contact with the first-mentioned conic, and that in this case they lead to the linear Automorphic Transformation of the ternary quadric. The memoir concludes with some formulæ relating to the case of two conics, which however is treated of in only a cursory manner.

scholarly journals IV. On the analytical theory of the conic

1863 ◽  
Vol 12 ◽  
pp. 106-108
Keyword(s):  
Analytical Theory ◽  
The Other ◽  
Linear Factor

The decomposition into its linear factors of a decomposable quadric function cannot be effected in a symmetrical manner otherwise than by formulæ containing supernumerary arbitrary quantities; thus, for a binary quadric (which of course is always decomposable) we have ( a, b, c )( x, y ) 2 = 1/( a, b, c )( x', y' ) 2 Prod. { ( a, b, c )( x, y )( x', y' ) ± √ ac - b 2 ( xy' - x'y or the expression for a linear factor is 1 1/√( a, b, c )( x', y' ) 2 { ( a, b, c )( x, y )( x', y' ± √ ac - b 2 ( xy' - x'y ) }, which involves the arbitrary quantities ( x', y' ). And this appears to be the reason why, in the analytical theory of the conic, the questions which involve the decomposition of a decomposable ternary quadric have been little or scarcely at all considered: thus, for instance, the expressions for the coordinates of the points of intersection of a conic by a line (or, say, the line-equations of the two ineunts), and the equations for the tangents (separate each from the other) drawn from a given point not on the conic, do not appear to have been obtained.

scholarly journals Variation of MODIS reflectance and vegetation indices with viewing geometry and soybean development

2012 ◽  
Vol 84 (2) ◽  
pp. 263-274 ◽  
Author(s):  
Fábio M. Breunig ◽  
Lênio S. Galvão ◽  
Antônio R. Formaggio ◽  
José C.N. Epiphanio
Keyword(s):  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Vegetation Indices ◽  
Constant Factor ◽  
The Other ◽  
Large Field ◽  
Phenological Stages ◽  
Water Index ◽  
Growing Seasons ◽  
Moderate Resolution Imaging Spectroradiometer

Directional effects introduce a variability in reflectance and vegetation index determination, especially when large field-of-view sensors are used (e.g., Moderate Resolution Imaging Spectroradiometer - MODIS). In this study, we evaluated directional effects on MODIS reflectance and four vegetation indices (Normalized Difference Vegetation Index - NDVI; Enhanced Vegetation Index - EVI; Normalized Difference Water Index - NDWI1640 and NDWI2120) with the soybean development in two growing seasons (2004-2005 and 2005-2006). To keep the reproductive stage for a given cultivar as a constant factor while varying viewing geometry, pairs of images obtained in close dates and opposite view angles were analyzed. By using a non-parametric statistics with bootstrapping and by normalizing these indices for angular differences among viewing directions, their sensitivities to directional effects were studied. Results showed that the variation in MODIS reflectance between consecutive phenological stages was generally smaller than that resultant from viewing geometry for closed canopies. The contrary was observed for incomplete canopies. The reflectance of the first seven MODIS bands was higher in the backscattering. Except for the EVI, the other vegetation indices had larger values in the forward scattering direction. Directional effects decreased with canopy closure. The NDVI was lesser affected by directional effects than the other indices, presenting the smallest differences between viewing directions for fixed phenological stages.

scholarly journals The principal magnetic susceptibilities of neodymium sulphate octahydrate at low temperatures

1939 ◽  
Vol 170 (941) ◽  
pp. 266-271 ◽  
Keyword(s):  
Low Temperatures ◽  
Room Temperature ◽  
Energy Levels ◽  
Constant Factor ◽  
The Other ◽  
Crystalline Field ◽  
Cubic Symmetry ◽  
The Subject ◽  
The Difference ◽  
The One

The magnetic and other related properties of neodymium sulphate have been the subject of numerous investigations in recent years, but there is still a remarkable conflict of evidence on all the essential points. The two available determinations of the susceptibility of the powdered salt at low temperatures, those of Gorter and de Haas (1931) from 290 to 14° K and of Selwood (1933) from 343 to 83° K both fit the expression X ( T + 45) = constant over the range of temperature common to both, but the constants are not the same and the susceptibilities at room temperature differ by 11%. The fact that the two sets of results can be converted the one into the other by multiplying throughout by a constant factor suggested that the difference in the observed susceptibilities was due to some error of calibration. It could, however, also be due to the different purity of the samples examined though the explanation of the occurrence of the constant factor is then by no means obvious. From their analysis of the absorption spectrum of crystals of neodymium sulphate octahydrate Spedding and others (1937) conclude that the crystalline field around the Nd+++ ion is predominantly cubic in character since they find three energy levels at 0, 77 and 260 cm. -1 .* Calculations of the susceptibility from these levels reproduce Selwood’s value at room temperature but give no agreement with the observations-at other temperatures. On the other hand, Penney and Schlapp (1932) have shown that Gorter and de Haas’s results fit well on the curve calculated for a crystalline field of cubic symmetry and such a strength that the resultant three levels lie at 0, 238 and 834 cm. -1 , an overall spacing almost three times as great as Spedding’s.

Multiple-Instance Classification via Generalized Eigenvalue Proximal SVM

2010 ◽  
Vol 143-144 ◽  
pp. 1235-1239
Author(s):  
Zhen Wang ◽  
Dong Mei Li
Keyword(s):  
Linear Function ◽  
Classification Problem ◽  
Real Space ◽  
Local Solution ◽  
The Other ◽  
Computational Results ◽  
Finite Dimensional ◽  
Generalized Eigenvalue ◽  
Bilinear Constraints ◽  
Nonparallel Planes

The multiple-instance classification problem is formulated using a linear or nonlinear kernel as the minimization of a linear function in a finite dimensional real space subject to linear and bilinear constraints by SVM-based methods. This paper presents a new multiple-instance classifier that determines two nonparallel planes by solving generalized eigenvalue proximal SVM. Our method converges in a few iterations to a local solution. Computational results on a number of datasets indicate that the proposed algorithm is competitive with the other SVM-based methods in multiple-instance classification.

The effect of pH and complexation on redox reactions between RS• radicals and flavins

1984 ◽  
Vol 62 (1) ◽  
pp. 171-177 ◽  
Author(s):  
Rizwan Ahmad ◽  
David A. Armstrong
Keyword(s):  
Redox Potential ◽  
Linear Function ◽  
Redox Reactions ◽  
Flavin Adenine Dinucleotide ◽  
Protonated Form ◽  
Redox Properties ◽  
The Other ◽  
Effect Of Ph ◽  
Other Hand ◽  
High Redox Potential

Elementary considerations indicate that thiol radicals, RS•, should have a high redox potential [Formula: see text][Formula: see text]However, the equilibrium [4],[Formula: see text]which is established in the presence of excess RS−, would convert RS•to [Formula: see text] which is a reducing species. Experimentally it was demonstrated that thiol radicals made by γ radiolysis of β-mercaptoethanol solutions effected two-electron oxidation of dihydroflavin FlH2 at pH 6.3 and of FlH− at pH 8. On the other hand, [Formula: see text] readily reduced Fl to FlH2 or FlH− as expected. At pH 9, photostationary states were established after a few minutes radiolysis and the ratios [FlH−]ss/[Fl]ss were a function of [Formula: see text] The main reactions occurring were:[Formula: see text]The values of k19 and k22 were both large. The ratio k19/k22 was ∼0.8 for lumiflavin and ∼0.3 for flavin adenine dinucleotide. The cyclic disulphide anions of lipoamide and dithiothreitol [Formula: see text] also effected two-electron reductions of flavins. However, the protonated form of [Formula: see text] oxidized FlH2, and the photostationary ratio [FlH−]ss/[Fl]ss was an approximate linear function of [Formula: see text]. The implications of the observed changes in redox properties of sulphur radicals on complexation with RS− and protonation were briefly considered.Des considérations élémentaires indiquent que les radicaux thiyles, RS•, doivent avoir un potentiel rédox élevé [Formula: see text][Formula: see text]

scholarly journals Bootstrap Percolation in High Dimensions

2010 ◽  
Vol 19 (5-6) ◽  
pp. 643-692 ◽  
Author(s):  
JÓZSEF BALOGH ◽  
BÉLA BOLLOBÁS ◽  
ROBERT MORRIS
Keyword(s):  
Positive Root ◽  
Constant Factor ◽  
The Other ◽  
Bootstrap Percolation ◽  
Main Question ◽  
Critical Probability ◽  
High Dimensions ◽  
Critical Window ◽  
Fixed Constant ◽  
Image Position

In r-neighbour bootstrap percolation on a graph G, a set of initially infected vertices A ⊂ V(G) is chosen independently at random, with density p, and new vertices are subsequently infected if they have at least r infected neighbours. The set A is said to percolate if eventually all vertices are infected. Our aim is to understand this process on the grid, [n]d, for arbitrary functions n = n(t), d = d(t) and r = r(t), as t → ∞. The main question is to determine the critical probability pc([n]d, r) at which percolation becomes likely, and to give bounds on the size of the critical window. In this paper we study this problem when r = 2, for all functions n and d satisfying d ≫ log n.The bootstrap process has been extensively studied on [n]d when d is a fixed constant and 2 ⩽ r ⩽ d, and in these cases pc([n]d, r) has recently been determined up to a factor of 1 + o(1) as n → ∞. At the other end of the scale, Balogh and Bollobás determined pc([2]d, 2) up to a constant factor, and Balogh, Bollobás and Morris determined pc([n]d, d) asymptotically if d ≥ (log log n)2+ϵ, and gave much sharper bounds for the hypercube.Here we prove the following result. Let λ be the smallest positive root of the equation so λ ≈ 1.166. Then if d is sufficiently large, and moreover as d → ∞, for every function n = n(d) with d ≫ log n.

On perceiving morality and potency: Social values and the effects of person perception in a give‐some dilemma

1989 ◽  
Vol 3 (3) ◽  
pp. 209-225 ◽  
Author(s):  
Paul A. M. Van Lange ◽  
Wim B. G. Liebrand
Keyword(s):  
Linear Function ◽  
Person Perception ◽  
Social Values ◽  
Social Value ◽  
The Other ◽  
Quadratic Trend ◽  
Major Purpose ◽  
Significant Quadratic Trend

The present study examines a two‐person give‐some dilemma characterized by the conflict between the pursuit of own benefits (not giving) and collective benefits (giving). The major purpose was two‐fold: (a) to examine the effects of person perceptions manipulated along the dimensions of morality (goodness) and potency (strength) on co‐operation, and (b) to examine whether pre‐existing differences between individuals in their preference for specific self‐other outcome distributions (social values) would modify the effects of person perception. First, we predicted and found that across social values the degree of co‐operative behaviour increased as a linear function of the extent to which the other was seen as moral. Concerning the perceptions in terms of potency, we found a significant quadratic trend; another seen as moderate on potency elicited more co‐operative behaviour than another seen as either high or low on potency. These effects of person perception were not moderated by social value. More interesting was the finding that even though persons classified as pro‐social (co‐operators and altruists) and pro‐self (individualists and competitors) held about the same expectation about the magnitude of another's co‐operation, pro‐socials behaved more co‐operatively than pro‐selfs. This suggests that under certain conditions behavioural differences between pro‐socials and pro‐selfs are not conditional upon expectational differences between those two social values.

Influence of Ageing and Lint Accumulation on the Fastening Strength of Hook and Loop Fasteners

1992 ◽  
Vol 62 (12) ◽  
pp. 766-770 ◽  
Author(s):  
Alison R. Taylor ◽  
Nigel A. G. Johnson ◽  
Bruce Dowdell
Keyword(s):  
Linear Function ◽  
The Other ◽  
Other Hand ◽  
Opening And Closing

Two possible causes of deterioration in the fastening performance of hook and loop fasteners have been investigated. The performance, quantified by various shear and peel forces, fell by less than 20% over 5000 cycles of repeated opening and closing. On the other hand, accumulated lint caused a serious loss of performance, which was nearly a linear function of the mass of lint among the hooks.

A Comparison of Performance in a Surface Wiring Task Using Laboratory and Plant Subjects

1986 ◽  
Vol 30 (4) ◽  
pp. 393-397
Author(s):  
Ram R. Bishu ◽  
Colin G. Drury
Keyword(s):  
Linear Function ◽  
The Other ◽  
Significant Group ◽  
Input Information ◽  
Amount Of Information ◽  
Performance Time ◽  
Instruction Sheet ◽  
Group Effects

Industrial surface wiring tasks, in which operators read from an instruction sheet and wire accordingly, involve processing of a considerable amount of information (20–30 bits/stimulus). Two groups of subjects, one inexperienced laboratory trained and the other experienced plant operators, participated in an experiment comprising both single and multimove tasks. Significant group effects were observed on both the tasks. Two main differences were observed between the plant and the laboratory subjects. The plant subjects were slower but more accurate in performing the multimove task. The second difference was that the laborabory subjects were performing similarly on both the tasks, their performance time being a linear function of input information. On the contrary, the plant subjects did not view multimove tasks as an extension of the single move tasks. Their processing rates for the single and multimove tasks were radically different.

scholarly journals The IAU Nutation Theory and Perspectives of its Change

1995 ◽  
Vol 10 ◽  
pp. 247-248
Author(s):  
D. McCarthy ◽  
V. Dehant
Keyword(s):  
Celestial Mechanics ◽  
Analytical Theory ◽  
The Other ◽  
General Assembly ◽  
Other Hand ◽  
Order Of Magnitude ◽  
Rigid Earth ◽  
The One ◽  
Nutation Series ◽  
Whole Earth

The IAU General Assembly has adopted in 1980 a nutation series, on the one hand, based on rigid Earth’s contributions theorically computed from celestial mechanics, and on the other hand, based on non-rigid Earth’s contributions theoretically computed from Earth deformation equations using geophysical parameters.1.From the previous papers (see Session 1) of this Joint Discussion, we know that there are differences of this adopted theory with respect to the observations of precession and nutations. These differences can reach several mas, which is well above the present accuracy of the observations.2.From previous papers (see Session 2) and from the posters, we also know that there exist new rigid-Earth nutations (Kinoshita-Souchay, Roosbeek, Hartmann) of which the accuracy has increased by one order of magnitude.3.From Session 3 papers, we know that there are some additional geophysical effects that are not yet taken into account in Wahr’s nutation theory adopted in 1980 by the IAU which have a contribution at a level above the present precision of the observations. These additional geophysical aspects can be accounted for either from a semi-analytical theory (like Mathews, Herring, Shapiro and Buffett are doing), or from an integration of deformation equations through the whole Earth (Dehant, Wahr).

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