Cut-power correlation

Infrared, Raman, microwave, and double resonance techniques turn out to offer nicely complementary tools, which usually can and have to be complemented by quantum chemical calculations. In both experiment and theory, progress over the last 10 years has been enormous. The relationship between theory and experiment is symbiotic, as the elementary systems represent benchmarks for rigorous quantum treatments of clear-cut observables. Even the simplest cases such as methanol dimer still present challenges, which can only be met by high-level electron correlation and nuclear motion approaches in many dimensions. On the experimental side, infrared spectroscopy is most powerful for the O—H stretching dynamics, whereas double resonance techniques offer selectivity and Raman scattering profits from other selection rules. A few challenges for accurate theoretical treatments in this field are listed in Table I. 

The power of the TMA technique is the capability of performing a series of analyses of thousands of specimens in a parallel fashion. Sections cut from the array allow parallel detection of DNA, FISH, mRNA, or IHC targets in each of the hundreds of specimens in the array. This allows consecutive analyses of a large number of molecular markers and construction of a database of correlated genotype or phenotypic characteristics of the tumor type being evaluated. 

In theoretical studies, one usually deals with two simple models for the solvent relaxation, namely, the Debye model with the Lorentzian form of the frequency dependence, and the Ohmic model with an exponential cut-off [71, 85, 188, 203]. The Debye model can work well at low frequencies (long times) but it predicts nonanalytic behavior of the time correlation function at time zero. Exponential cut-off function takes care of this problem. Generalized sub- and super-Ohmic models are sometimes considered, characterized by a power dependence on CO (the dependence is linear for the usual Ohmic model) and the same exponential cut-off [203]. All these models admit analytical solutions for the ET rate in the Golden Rule limit [46,48]. One sometimes includes discrete modes or shifted Debye modes to mimic certain properties of the real spectrum [188]. In going beyond the Golden Rule limit, simplified models are considered, such as a frequency-independent (strict Ohmic) bath [71, 85, 203], or a sluggish (adiabatic)... 

The values for specific pressure u are normally obtained through orthogonal metal-cutting experiments. Specific pressure is related to and correlates well with shear stress r, for a given metal. The unit power is sensitive to material properties (e.g., hardness), rake angle, depth of cut, and feed, whereas is sensitive to material properties only. Specific power can be used to estimate the motor power required to perform a machining operation for a given material. 

The pair correlation function of fractal aggregates reflects their self-similarity for medium interpaiticle distances (a r Rg) hy a power-law relationship (Eq. (4.8)). At large arguments (r > Rg), the pair correlation function decays steeply, which can be modelled by a cut-off function. For medium and large arguments, one obtains ... 

According to the results of trend analysis and test for the serial correlation, it is clear that the assumption of iid is normally not valid for the TBFs of the cutting arms of the drum shearer machine. The assumption that the power law process adequately describes the TBFs of this system was validated and confirmed by graphical method. Since the failure rate of this system is increasing, the preventive maintenance is suitable strategy for this system. 

As different as the various types of chemical information are, the uses of the various data analysis methods also differ. When experimental data are based on clear-cut physical concepts, explicit mathematical relationships can be derived. More complex relationships such as the ones inherent in the correlations between structure and spectral data ask for powerful modeling techniques. Chemical reactions are under a variety of influences and, therefore, the analysis of common features of chemical reactions faces even more severe problems. 

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