Mercerization, definition

Sisson has traced the evolution of current concepts of the crystalline part of cellulose structures. The fiber diagram obtained by X-ray diffraction is now known to be produced by a series of elementary crystals, called crystallites, which have a definite arrangement with respect to the fiber axis. It is also known that the crystallites in regenerated cellulose may be oriented to varying degrees with respect to the fiber axis and that the crystallites in regenerated cellulose and mercerized cotton differ from those in native fibers. These hydrate type crystallites appear to be more reactive chemically than the native type. 

Between the NH3-treated samples and the mercerized ones, no significant difference in DP has been found after posthydrolysis, while the residue value of the NH3-treated samples was definitely lower. 

These rather simple considerations explain most of our experimental results—for example, the behavior of thermally treated samples, the different influences of dry and wet disintegration on acid and enzymatic hydrolysis, or the pronounced increase in accessibility to acid hydrolysis as compared to enzymatic degradation by treatment with liquid NH3. No definite interpretation can be given so far of the unexpected strong increase in weight loss during enzymatic degradation after a previous mercerization. 

In both the dual solution and decision function, only the inner product in the attribute space and the kernel function based on attributes appear, but not the elements of the very high dimensional feature space. The constraints in the dual solution imply that only the attributes closest to the hyperplane, the so-called SVs, are involved in the expressions for weights w. Data points that are not SVs have no influence and slight variations in them (for example caused by noise) will not affect the solution, provides a more quantitative leverage against noise in data that may prevent linear separation in feature space [42]. Imposing the requirement that the kernel satisfies Mercer s conditions (K(xj, must be positive semi-definite)... 

Let us observe this theorem, the positivity condition I K(x,z)/(x)/(z)dxdz > 0, V/ 6 Z2 (X), corresponds to the positive semi-definite condition in the finite case, this gives the second characterization of a kernel function that is proved to be most useful when we come to constructing kernels. We use the term kernel to refer to function satisfying this property, but in the literature these are often called Mercer kernel. 

If the kernel fC is a symmetric positive definite function, which satisfies the Mercer s conditions... 

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