Discrete generating rule

As a rule, narrowband windows should be established to monitor at least these three distinct frequencies, i.e. lx, 2x, and 3x. In addition, narrowbands should be established to monitor the discrete frequencies generated by the couplings or joints used to connect the jackshaft to the driver and driven unit. 

Problem formulations [ 1-3 ] for designing lead-generation library under different constraints belong to a class of combinatorial resource allocation problems, which have been widely studied. They arise in many different applications such as minimum distortion problems in data compression (11), facility location problems (12), optimal quadrature rules and discretization of partial differential equations (13), locational optimization problems in control theory (9), pattern recognition (14), and neural networks... 

Figure 1. Catch-and-escape dilemma of SA type algorithms for a discrete two dimensional function X2). To escape local extrema, a certain minimal step-width must be observed by the configuration generator. The finite stepwidth at the same time makes it difficult to approach the exact extreme, (a) GSA configuration generator searches at a predefined radius with respect to the rule...

QED provides a framework for describing the role of the negative energy states in the Dirac theory and the divergences which arise in studies of electrodynamic interactions.83-85 In Section 2.3 it will be shown how the use of the algebraic approximation to generate a discrete representation of the Dirac spectrum has opened the way for the transcription of the rules of QED into practical algorithms for the study of many-electron systems. 

As a rule, primary data are generated as analog signals either in a discrete or a continuous mode (Figure 1.1). For example, monitoring the intensity of optical radiation by means of a photocell provides a continuous signal. Weak radiation, however, could be monitored by detecting individual photons by a photomultiplier. 

Just as the rule whereby a discrete-time chain evolves is defined by a matrix P, the transition matrix, the rule whereby a continuous-time chain evolves is defined by a matrix Q, the generator matrix. The off-diagonal entry q, i + j, of Q has the interpretation that q jh is approximately the probability that the chain, starting from state i at a time t, makes a transition to state j by time t + h, where h is small ... 

Rough set theory (RST), first introduced by Pawlak more than 20 years ago [6], is a set-based method that is well suited for dealing with a wide variety of discrete data that can be represented by DTs [7-11]. RST appears to be well suited to the problem at hand since, as will be seen in the sequel, it provides computationally tractable procedures for identifying minimal subsets of attributes, that is, genes, in this work [12,13]. These subsets of attributes maintain key relationships in the data that support the generation of simple linguistic rules. This procedure is similar in many ways to dimensionality reduction techniques that are routinely employed to continuous variables to reduce the size and complexity of mathematical models [14]. 

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