Kernel analysis

Shinzawa, H., Iwahashi, M., Noda, I. Ozaki. Y. (2008a). Asynchronous Kernel Analysis for Binary Mixture Solutions of Ethanol and Carboxylic Acids. Journal of Molecular Structure, Vol. 883-884, No. 30, pp. 27-30... 

Fatal cyanide poisoning occurred in a 3-year-old girl who ingested an unspecified number of apricot kernels. Analysis of apricot kernels from the same lot that caused the poisoning showed an average of 2.15 mg cyanide per kernel (Gunders et al. 1969). 

To nnderstand the internal molecnlar motions, we have placed great store in classical mechanics to obtain a picture of the dynamics of the molecnle and to predict associated patterns that can be observed in quantum spectra. Of course, the classical picture is at best an imprecise image, becanse the molecnlar dynamics are intrinsically quantum mechanical. Nonetheless, the classical metaphor mnst surely possess a large kernel of truth. The classical stnichire brought out by the bifiircation analysis has accounted for real patterns seen in wavefimctions and also for patterns observed in spectra, snch as the existence of local mode doublets, and the... 

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... 

All the kernels are empirical, or semiempirical and must be fitted to plant or laboratory data. The kernel proposed by Adetayo and Ennis is consistent with the granulation regime analysis described above (see section on growth) and is therefore recommended ... 

In Eq (25), the integration kernel function K x)= rr x is smooth everywhere except the singularity point (x = 0). In a numerical analysis, the integration has to be evaluated in discrete form over a grid with the mesh size h... 

Even when the patterns are known to cluster, there remain difficult issues that must be addressed before a kernel-based approach can be used effectively. Two of the more fundamental conceptual issues are the number and size of clusters that should be used to characterize the pattern classes. These are issues for which there are no hard and fast answers. Despite the application of well-developed statistical methods, including squared-error indices and variance analysis, determining the number and size of clusters remains extremely formidable. 

Other integral transforms are obtained with the use of the kernels e" or xk among the infinite number of possibilities. The former yields the Laplace transform, which is of particular importance in the analysis of electrical circuits and the solution of certain differential equations. The latter was already introduced in the discussion of the gamma function (Section 5.5.4). 

Since FAS can be produced either from vegetable oil based or petrochemical-based fatty alcohol (Fig. 4.9), both types have been evaluated in a life-cycle analysis with a positive overall result for the natural based product. With vegetable-based fatty alcohol sulfate, the analysis starts with the harvesting of the oil fruits (palm kernels or coconuts) and their processing to isolate the desired plant oil. Subsequent transesterification and hydrogenation of the methyl ester intermediates lead to the fatty alcohols, which are finally sulfated to produce the desired product. Based on this analysis the environmental impact of vegetable oil based fatty alcohol sulfate compared with the petrochemical based product is as follows ... 

Dong, Y. Steffenson, B. J. Mirocha, C. J. Analysis of Ergosterol in Single Kernel and Ground Grain by Gas Chromatography-Mass Spectrometry. /. Agric. Food Chem. 2006, 54, 4121-4125. 

Table 8 Mean Recalls at 5% for Similarity Searching (SS), Conventional Turbo Similarity Searching using Croup Fusion (TSS-CF) and Turbo Similarity Searching using Substructural Analysis (TSS-SSA) and Binary Kernel Discrimination (TSS-BKD)...

The key physics of our model (see Eqs. (9) and (10)) is contained in the nonlocal diffusion kernels which occur after integrating over the atomic processes which produce step fluctuations. We have calculated these kernels for a variety of physically interesting cases (see Appendix C) and have related the parameters in those kernels to atomic energy barriers (see Appendix B). The model used here is close in spirit to the work of Pimpinelli et al. [13], who developed a scaling analysis based on diffusion ideas. The theory of Einstein and co-workers and Bales and Zangwill is based on an equihbrated gas of atoms on each terrace. The concentration of this gas of atoms obeys Laplace s equation just as our probability P does. To make complete contact between the two methods however, we would need to treat the effect of a gas of atoms on the diffusion probabilities we have studied. Actually there are two effects that could be included. (1) The effect of step roughness on P(J) - we checked this numerically and foimd it to be quite small and (2) The effect of atom interactions on the terrace - This leads to the tracer diffusion problem. It is known that in the presence of interactions, Laplace s equation still holds for the calculation of P(t), but there is a concentration... 

---