The main statistics used in rough set data analysis, the approximation quality, is of limited value when there is a choice of competing models for predicting a decision variable. In keeping within the rough set philosophy of non–invasive data analysis, we present three model selection criteria, using information theoretic entropy in the spirit of the minimum description length principle. Our ma...

This paper is intended to reveal some new aspects of the principle of work and energy in its differential form. A theorem is given to state the principle of work and energy in differential form that can be applied alone to build up all the dynamical equations of a special class of MDOF mechanical systems. Some illustrations and discussions are presented to demonstrate the refined applicability ...

We establish the variational principle of Kolmogorov-Petrovsky-Piskunov (KPP) front speeds in temporally random shear flows with sufficiently decaying correlations. A key quantity in the variational principle is the almost sure Lyapunov exponent of a heat operator with random potential. To prove the variational principle, we use the comparison principle of solutions, the path integral represent...

Viscosity solutions are suitable notions in the study of nonlinear PDEs justified by estimates established via the maximum principle or the comparison principle. Here we prove that the isoperimetric profile functions of Riemannian manifolds with Ricci lower bound are viscosity supersolutions of some nonlinear differential equations. From these one can derive the isoperimetric inequalities of Lé...

Solids can exist in polygonal shapes with boundaries unions of flat pieces called facets. Analyzing the growth of such crystalline shapes is an important problem in materials science. In this paper we derive equations that govern the evolution of such shapes; we formulate the corresponding initial-value problem variationally; and we use this formulation to establish a comparison principle for c...

This paper examines four single-winner election methods, denoted here as Woodall, Benham, Smith-AV, and Tideman, that all make use of both Condorcet’s pairwise comparison principle and Hare’s elimination and reallocation principle used in the alternative vote. These methods have many significant properties in common, including Smith efficiency and relatively strong resistance to strategic manip...

This paper briefly describes the basic principle of wavelet packet analysis, and on this basis introduces the general principle of wavelet packet transformation for signal den-noising. The dynamic EEG data under +Gz acceleration is made a de-noising treatment by using wavelet packet transformation, and the de-noising effects with different thresholds are made a comparison. The study verifies th...