Combined distribution function

Fig. 3 Combined distribution functions showing the hydrogen bond geometry between the atom C2 of the [C2mim] cation and the (a) oxygen atoms of the [OAc] anion, (b) [Cl] anion, (c) nitrogen atom of the [SCN] anion, and (d) sulfur atom of the [SCN] anion. The black area defines the regions where the criteria to form a hydrogen bond used in this publication are fulfilled, i.e., the distance C2-Y is lower than the sum of the Van der Waals radii and the angle a(C2-H2-Y) is larger than 160°...

Fig. 5 Combined distribution functions showing the bridging behavior of one imidazolium cation via the H2,4,5 ring protons to two different anions (a) an oxygen of two [OAc]- anions, (b) two [Cl]- anions and (c) a sulfur or a nitrogen atom of two [SCN]- anions [80]...

Integration of the expression for the combined distribution function ovor all rmentations gives the probability of finding a molecule in a particular conformation irrespective of its (mentation (see EQN (45)) as... 

A combination of physicochemical, topological, and geometric information is used to encode the environment of a proton, The geometric information is based on (local) proton radial distribution function (RDF) descriptors and characterizes the 3D environment of the proton. Counterpropagation neural networks established the relationship between protons and their h NMR chemical shifts (for details of neural networks, see Section 9,5). Four different types of protons were... 

Notice that those distribution functions that satisfy Eq. (4-179) still constitute a convex set, so that optimization of the E,R curve is still straightforward by numerical methods. It is to be observed that the choice of an F(x) satisfying a constraint such as Eq. (4-179) defines an ensemble of codes the individual codes in the ensemble will not necessarily satisfy the constraint. This is unimportant practically since each digit of each code word is chosen independently over the ensemble thus it is most unlikely that the average power of a code will differ drastically from the average power of the ensemble. It is possible to combine the central limit theorem and the techniques used in the last two paragraphs of Section 4.7 to show that a code exists for which each code word satisfies... 

Dorko et al. [442] have used the Weibull distribution function for the consideration of reactions in which decomposition is accompanied by melting. Following a procedure described by Kao [446], they used a mixed Weibull function, written as a linear combination of separate functions, viz. 

Similar treatments of the terms in Eq. (19) containing vy and vz will yield exact analogues of Eq. (29) for f(vy) and f(vz). Since the product of the three one-dimensional distribution functions gives the three-dimensional distribution function, i.e., F(v) = f(vx)f(vy)f(vz), we may combine Eq. (29) with similar expressions for the y and z velocity components to give... 

Structured products, such as cosmetics, detergents, surfactant foams, inks, paints, drugs, foods and agrochemicals, combine several functions and properties in a single product. Design of these structured products involve the creation and the control of the particle size distribution in operations such as crystallization, precipitation, generation of aerosols, and nanoparticles as well as... 

An early model for slip of fluids in tubes is due to Maxwell [62], wherein the velocity distribution function parallel to the wall is a linear combination of... 

When we wanted to numerically fit experimental PFGE data of water diffusion in a water-in-oil emulsion, we found that for a beginner in this field the literature is quite confusing. First, all three expressions for diffusion in a sphere with reflecting walls are somewhat different and lead to very different fitting results, especially when the formulas are combined with a radius distribution function. Since the derivation of the published expressions needs some tedious algebra (which has not been published), it is not trivial to check the derivation in order to establish which expression is the correct one. Here we use a numerical approach to decide which expression is correct. 

Computational methods combined with a novel approach in the application of scattering physics were recently employed by Barbi et al. in a synchrotron SAXS study of the nanostructure of Nafion as a function of mechanical load. A new method of multidimensional chord-distribution function (CDF) analysis was used to visualize the multiphase nano-... 

Theoretical investigations of the problem were carried out on the base of the mathematical model, combining both deterministic and stochastic approaches to turbulent combustion of organic dust-air mixtures modeling. To simulate the gas-phase flow, the k-e model is used with account of mass, momentum, and energy fluxes from the particles phase. The equations of motion for particles take into account random turbulent pulsations in the gas flow. The mean characteristics of those pulsations and the probability distribution functions are determined with the help of solutions obtained within the frame of the k-e model. 

Using the separation of the pair-distribution function nf into its uncorrelated and correlated parts, Eq. (284), and noting that the combination... 

For polymerizations where termination occurs by a combination of coupbng, disproportionation, and chain transfer, one can obtain the size distribution by a weighted combination of the two sets of distribution functions presented above. Thus the weight distribution can be obtained as... 

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