Shape index

Chi indices for the various isomers of hexane. (Figure adapted in part from Hall L H and L B Kier 1991. The ir Connectivity Chi Indexes and Kappa Shape Indexes in Structure-property Modeling. In Lipkowitz K B and id (Editors) Reviews in Computational Chemistiy Volume 2. New York, VCH Publishers, pp. 367-422.)... 

LH Hall, LB Kier. The molecular connectivity chi indexes and kappa shape indexes in structure-property modeling. In KB Lipkowitz, DB Boyd, eds. Reviews in Computational Chemistry, Vol. 2. New York VCH, 1991, pp 367-422. 

The HlV-1 protease is responsible for processing the protein precursors to the enzymes (integrase, protease and reverse transcriptase) and the structural proteins of the HIV-1 virus. Maw and Hall found that topological indices provide rehable QSAR models for the IC50 data of 32 HIV-1 protease inhibitors [29]. The best QSAR model, with r = 0.86, s=0.60 and q = 0.79, was obtained with the shape index Ka, the connechvity index the sum of HE-state indices for ah groups that act as... 

Y. Xie, P.K. Hopke and D. Wienke, Airborne particle classification with a combination of chemical composition and shape index utilizing an adaptive resonance artificial neural network. Environ. Sci. Technol., 28 (1994) 1399-1407. 

Comparative Molecular Field Analysis (CoMFA), 6 16 16 755-757 pharmacophore generation and validation, 6 12 Comparative Molecular Shape Indexes Analysis (CoMSIA), J0 327t,... 

Lowell H. Hall and Lemont B. Kier, The Molecular Connectivity Chi Indexes and Kappa Shape Indexes in Structure-Property Modeling. 

The data containing 324 descriptor values of 88 molecules was given as an input to VSMP program, to build models based on three and four descriptors, keeping the interdescriptor correlation below 0.75. The best three-descriptors model, Eq. 80, was based on descriptors 254 (atomic type E-state index), 311 (AlogP98), and 320 (2D Van der Waals surface area) with a correlation coefficient, r, of 0.8425, and the cross-validated correlation coefficient, q, of 0.8239. The correlation coefficients of the other two VSMP models, Eqs. 81 and 82 were 0.8411 and 0.8329, respectively. Significantly, the descriptors 254 and 311 were selected in all the best three-descriptors models of VSMP. The three descriptors, in the models 80, 81, and 82 were 320, 144 (Kappa shape index of order 1), and 30 (topological Xu index), respectively. 

The model sufficiently conforms to the change in the shape index with longer treatment time, and it was proved that processing particulate materials of smaller ductility, the particle shape is more adjustable stepwise in terms of the shape index. 

The unevenness coefficient of particle surface decreased with larger shape index and had a critical value. Therefore, the particle shape modification process was considered in such a way that the submicro uneven particle surface was smoothed at first and, in consequence, the macro shape was processed to be spherical. 

Figure 13.3.10 shows the typical spheroidal deformation of stainless steel particles with treatment time. As compared with the result of copper particles, the rate of spheroidal deformation was lower. Thus, the stainless steel particles were easier for stepwise adjustment of the shape index with treatment time. 

Refinements, parameterization, and the complete COSMO-RS 113 7.1.4 Local shape index... 

Particle shape index is defined as the projected area of the particle divided by the area of a circle having a diameter equivalent to the maximum projected length of the particle. 

Randic branching index, or molecular connectivity Kappa shape index Hammett constant Dipole moment... 

Kier, L.B., A shape index from molecular graphs, Quant. Struct.-Act. Relat., 4, 109-116, 1985. 

L. B. Kier and L. H. Hall, Molecular Connectivity in Chemistry and Drug Research, Academic Press, New York, 1976. L. H. Hall and L. B. Kier, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1991, pp. 367-422. The Molecular Connectivity Chi Indexes and Kappa Shape Indexes in Structure-Property Modeling. 

Shurcliff, Wm. A., Curve Shape Index for Identification by Means of Spec-... 

Some work has shown a direct correlation between shape factor and the flow properties of powders. The flowability of fine powders, as measured by a shear-cell as well as by Carr s method, was found to increase with increasing sphericity, where the sphericity is indicated by a shape index approaching one, as measured by an image analyzer. Huber and co-workers derived an equuation in which flow rate was correlated to the volume specific surface as measured by laser diffractometry. Reasonable predictions were made for individual powders as well as binary and ternary mixtures. 

Power consumption or torque fluctuations are influenced by granule properties (PSD, shape index, and apparent density) and the granulation time. Fluctuation of torque/power consumption and intensity of spectrum obtained by FFT analysis can be used for end-point determination. 

A first Petitjean shape index is a topological anisometry descriptor [Petitjean, 1992], also called a graph-theoretical shape coefficient h, defined as ... 

Kier, L.B. (1985). A Shape Index from Molecular Graphs. Quant.Struct-Act.Relat., 4,109-116. 

Kier, L.B. (1986a). Distinguishing Atom Differences in a Molecular Graph Shape Index. Quant Struct-ActRelat, 5,7-12. 

Fig. 43. (a) Effect of order of reaction on plots of reaction rate against temperature for constant heating rate, frequency factor and activation energy. EjR = 20,000, lnA = 16.0. From ref. 350. (b) Method of measuring reaction order from the shape index of dta peak. Shape index S = alb. 

Morphologically, seeds of S. chirayita and S. angustifoiia differ in their external features i.e., colour, weight, length, width shape index and size index. These distinguishing characteristics features can be utilized for proper identification and reduce the chance of adulteration. 

Mature seeds were collected from all of the five distantly located populations of S. chirayita and S. cmgustifolia from west Himalaya (Table 1). Seeds obtained from different individuals were pooled for each population. The morphology of seed was studied by recording seed length, seed width, size index and shape index in three replicates of ten seeds each from each population (Sharma et al., 2000). 

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