Property smoothing parameter

This two-dimensional RDF descriptor is calculated depending on the distance r and an additional property p. In this case, p is a property difference calculated in the same fashion as the Cartesian distance r, in fact, p can be regarded as a property distance. Mnch in the same way as B influences the resolution of the distance dimension, the property-smoothing parameter D affects the resolution — and, thus, the half-peak width — in the property dimension. D is measured in inverse squared units [p l of the property p. ... 

Property Smoothing Parameter (D) is an exponential factor that defines the width of the Gaussian distribution around a peak in the property space of a multidimensional RDF descriptor. It can be interpreted as measure of deviation describing the uncertainty of atoms properties within a molecule. 

Steinhauer and Gasteiger [30] developed a new 3D descriptor based on the idea of radial distribution functions (RDFs), which is well known in physics and physico-chemistry in general and in X-ray diffraction in particular [31], The radial distribution function code (RDF code) is closely related to the 3D-MoRSE code. The RDF code is calculated by Eq. (25), where/is a scaling factor, N is the number of atoms in the molecule, p/ and pj are properties of the atoms i and/ B is a smoothing parameter, and Tij is the distance between the atoms i and j g(r) is usually calculated at a number of discrete points within defined intervals [32, 33]. 

By including characteristic atomic properties, A. of atoms i andj, the RDF code can be used in different tasks to fit the requirements of the information to be represented. The exponential term contains the distance r j between the atoms i andj and the smoothing parameter fl, which defines the probability distribution of the individual distances. The function g(r) was calculated at a number of discrete points with defined intervals. 

Years of development have led to a standardized system for objective evaluation of fabric hand (129). This, the Kawabata evaluation system (KES), consists of four basic testing machines a tensile and shear tester, a bending tester, a compression tester, and a surface tester for measuring friction and surface roughness. To complete the evaluation, fabric weight and thickness are determined. The measurements result in 16 different hand parameters or characteristic values, which have been correlated to appraisals of fabric hand by panels of experts (121). Translation formulas have also been developed based on required levels of each hand property for specific end uses (129). The properties include stiffness, smoothness, and fullness levels as well as the total hand value. In more recent years, abundant research has been documented concerning hand assessment (130—133). 

The known oxidation states of plutonium present a 5f -series, starting from f1 [Pu(VII)] up to f5 [Pu(III)]. But contrary to the 4f - and 5f series across the period table, where the properties can be described by some smooth varying parameters, changing of the oxidation states influences the electronic properties drastically. Due to the large range of available oxidation states plutonium represents a favorable element among the actinides to study these effects. 

To the contrary, mnlticomponent nonmetallic systems such as mixed oxides often provide the possibility for a smooth or discontinuous variation of electrophysical parameters, and thns for some adjustment of their catalytic properties. In a number of cases, one can do without expensive platinum catalysts, instead using nonmetallic catalysts. Serious research into the properties of nonmetallic catalytic electrodes was initiated in the 1960s in connection with broader efforts to realize various kinds of fuel cells. 

Our goal is to estimate the function P(r) from the set of discrete observations Y(tj). We use a nonparametric approach, whereby we seek to estimate the function without supposing a particular functional form or parameterization. We require that our estimated function be relatively smooth, yet consistent with the measured data. These competing properties are satisfied by selecting the function that minimizes, for an appropriate value of the regularization parameter X, the performance index ... 

The physical characteristics of the powder and the mechanical properties of the electrode made from these powders were seen to be among key important parameters. Some physical characteristics of the LBG1025 and its typical Scanning Electron Microscope image can be found in Table 3. The SEM shows a flaky, rounded edge smooth morphology. 

We have described above the evolution of the magnetic properties of the [Cp2M (dmit)]AsFg salts upon isomorphous Mo/W substitution. Another possibility offered by this attractive series is the isomorphous substitution of the counter ion, that is PFg- vs AsF6 vs Sbl- fi. Electrocrystallization experiments conducted with [Cp2Mo(dmit)] and the three different electrolytes afforded an isomorphous series, with a smooth evolution of the unit cell parameters with the anion size [32], This cell expansion with the anion size leads to decreased intermolecular interactions between the [Cp2Mo(dmit)]+ radical cation, as clearly seen in Table 2 from the decreased Curie-Weiss temperatures and Neel temperatures (associated with the transition they all exhibit to an AF ground state). 

Solutions in hand for the reference pairs, it is useful to write out empirical smoothing expressions for the rectilinear densities, reduced density differences, and reduced vapor pressures as functions of Tr and a, following which prediction of reduced liquid densities and vapor pressures is straightforward for systems where Tex and a (equivalently co) are known. If, in addition, the critical property IE s, ln(Tc /Tc), ln(PcVPc), and ln(pcVPc), are available from experiment, theory, or empirical correlation, one can calculate the molar density and vapor pressure IE s for 0.5 < Tr < 1, provided, for VPIE, that Aa/a is known or can be estimated. Thus to calculate liquid density IE s one uses the observed IE on Tc, ln(Tc /Tc), to find (Tr /Tr) at any temperature of interest, and employs the smoothing relations (or numerically solves Equation 13.1) to obtain (pR /pR). Since (MpIE)R = ln(pR /pR) = ln[(p /pc )/(p/pc)] it follows that ln(p7p)(MpIE)R- -ln(pcVpc). For VPIE s one proceeds similarly, substituting reduced temperatures, critical pressures and Aa/a into the smoothing equations to find ln(P /P)RED and thence ln(P /P), since ln(P /P) = I n( Pr /Pr) + In (Pc /Pc)- The approach outlined for molar density IE cannot be used to rationalize the vapor pressure IE without the introduction of isotope dependent system parameters Aa/a. 

It is also not practical to expect that a single equation will correlate simultaneously the properties of NaCl with hexane, since there are too many differences between them. When we study the properties within a homologous series, such as the normal paraffins that differ only in the number of —CH2—units, we isolate only one parameter to study. In many cases, the molecular properties change smoothly with the number of units, which can be used as the predictor. The one-parameter populations set out in table 5.4 are frequently used. 

The crystal property perhaps most sensitive to structure is density and, conversely, the increase in density of a crystal with pressure is accompanied by significant structural changes. The latter can be of two types - either a smooth variation of the free parameters of the structure with pressure, or a first-order transition to a new structure type. 

Extrusion parameters, such as basket temperature, extrusion rate, and die design, can be adjusted to suit a particular formulation and granule size. This is an empirical process based on experience. Extrusion characteristics represent an intimate interplay between press parameters and dough properties, the latter predominating. What is wanted is maximum production rate of a smooth, dense, homogeneous strand of these qualities, smoothness is perhaps most sensitive to extrusion conditions. 

Multiplying the transform by the window w[0,n-l] shown in Fig. 4.6 this property is preserved, and hence the inverse transform of the product is purely real. The window (or low-pass filter) is described in terms of two parameters, the index NS of the frequency where smoothing is started, and the smothing factor SM that determines the slope of the decreasing part of the window as shown on Fig. 4.6. The transform of the smoothed function is then the product [f] [W]. To obtain the smoothed derivative of f, we multiply this product by... 

In contrast to the mechanical and rheological properties of materials, which have defined physical meanings, no such definitions exist for the psychophysical assessment of equivalent textural properties of foods. To identify material properties, or combinations of these, which are able to model sensory assessments requires a mixture of theory and experimentation. Scientific studies of food texture began during the twentieth century by the analysis of the rheological properties of liquid or semi-solid foods. In particular Kokini14 combined theoretical and experimental approaches in order to identify appropriate rheological parameters from which to derive mathematical models for textural attributes of liquid and semi-solid foods, namely, thickness, smoothness and creaminess. 

The majority of the above examples are non-rough (structurally unstable) systems. The rough dynamic systems on the plane cannot demonstrate the properties shown by the above examples. If Tt is specified by a rough individual (without parameters) system on the plane, there cannot exist th, rj2 slow relaxations and rh 2,3 and tj3 slow relaxations can take place only simultaneously. This can be confirmed by the results given below and the data of some classical studies concerning smooth rough two-dimensional systems [20, 21],... 

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