The concept of transparency order (denoted by TO) is an important criterion of (n, m)-functions to resist against differential power analysis (DPA). In this paper, we give several transparency order relationships of s...
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The concept of transparency order (denoted by TO) is an important criterion of (n, m)-functions to resist against differential power analysis (DPA). In this paper, we give several transparency order relationships of some Boolean functions. We give the lower bound on the transparency order for Boolean function, and obtain the transparency order relationship between one Boolean function and its decomposition Boolean functions. Furthermore, we deduce one relationship among TO(f circle plus g), TO(f), TO(g) and TO(fg) for any n-variable Boolean functions f, g. Finally, we study the transparency order for the sum function and for the product function between two variable-disjoint Boolean functions, and calculate the transparency order distributions of 4-variable and 5-variable balanced Boolean functions, respectively.
For decomposing foliar litter in forest systems the pattern for accumulated mass loss vs time varies among litter species and environments. Thus, decomposition may be complete (100% accumulated mass loss) or the rate ...
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For decomposing foliar litter in forest systems the pattern for accumulated mass loss vs time varies among litter species and environments. Thus, decomposition may be complete (100% accumulated mass loss) or the rate may cease and proceed at such a low rate that a limit value for decomposition may be estimated. Such limit values have been found to range from 42% accumulated mass loss to 100%, resulting in stable fractions of 58 and 0%, respectively. To support a discussion about pattern we need causal relationships and I have used a conceptual model with three decomposition stages as a reference and discuss that in relation to two nutrients that influence the degradation of lignin and lignified tissue. Whereas a high nitrogen (N) concentration may have a stimulating effect on degradation of holocellulose in the early stage the same high N concentration may retard the degradation of lignified tissue in the late stage and the higher the N concentration the stronger the retardation. Through the enzyme manganese peroxidase (MnP), manganese (Mn) stimulates lignin degradation and thus the lignified fraction of litter. A high level of Mn appears to support a further degradation of the lignified tissue and thus results in a high limit value, whereas a high N has been related to a low value. The aim behind this review is to: (i) identify specific factors that may influence the pattern of accumulated mass loss and thus the type of regression model that describes the data;and (ii) present a possible climate influence on decomposition pattern. To this purpose we need to discuss a possible variation in pattern following the variation in concentrations of the two nutrients N and Mn. Concentrations of N and Mn in newly shed litter are both influenced by site climate, with N increasing and Mn decreasing with increasing mean annual temperature (MAT) and increasing annual actual evapotranspiration (AET). Thus, climate becomes at least an indirect regulating factor for decomposition p
Several asymptotic expansions are given for the generalized incomplete gamma function Gamma(alpha, x;b) = integral(x)(infinity)t(alpha-1)e(-t-b/t)dt, x > 0, Re b greater than or equal to 0, b not equal 0, as x tend...
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Several asymptotic expansions are given for the generalized incomplete gamma function Gamma(alpha, x;b) = integral(x)(infinity)t(alpha-1)e(-t-b/t)dt, x > 0, Re b greater than or equal to 0, b not equal 0, as x tends to infinity, where the real paramete alpha is allowed to take negative values. In the case b = -i omega, omega > 0, we obtain the expansions of the decomposition functions C-Gamma(alpha, x;omega) and S-Gamma(alpha,x;omega). Closed form expressions are also given for alpha = -3/2, -5/2, ... (C) Academic Press.
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