Rvachev function

Abstract: A novel mathematical model for determining the electrical characteristics in a dc energized duct type electrostatic precipitator is described. The method is a quasi-analytical one, based on solving the current continuity equation by finite-difference method and Poisson's equation by variational principle with the help of Rvachev functions (R-functions). The methodology described represents a valuable design tool for simulating and comparing the voltage-current characteristics of different wire-plate precipitator configurations before optimizing the geometric parameters namely shape of the corona wire, shape of the collection electrodes, wire cross-section, wire-wire and wire-plate spacing. The proposed method will be useful in trying innovative ideas in the design aspect of a wire-duct precipitator. Other significant features of this method are reduced problem domain, less memory space, and faster convergence. The proposed method has been validated with published experimental results and the agreement is excellent. A comparison of electrical characteristics has been made for different sizes and shapes of corona wire and also for various configurations of the wire-plate precipitators.

Abstract: The proposed method for classifying clusters of patterns in complex non-convex, disconnected domains using Radial Basis Function Neural Networks (RBFNNs) enhanced with the Rvachev Function Method (RFM) is presented with numerical examples R-functions are used to construct complex pattern cluster domain, parameters of which are applied to RBFNNs to establish boundaries for classification The error functional is a convex quadratic one with respect to weight functions which take weight values on the discrete connectors between neurons Activation function of neurons of RBFNNs is the sgn(·) function and, therefore, the error function is non-smooth The delta learning rule during training phase is applied The sub-gradient of the discretized error function is used rather than its gradient, because it is not smooth The application of the RFM allows for the creation, implementation, and resolution of large heterogeneous NNs capable to solving diverse sets of classification problems with greater accuracy

Abstract: We present a Rvachev function method with the Chebysev collocation for the stability analysis of fluid flow. The strategy is to construct an approximate solution that satisfies all boundary conditions exactly. As an example, we consider the stability problem of the two-dimensional flow of an incompressible viscous liquid near a circular cylinder. The results coincide well with the reference data. The method is simpler than the widely used spectral/hp element method, in particular because it does not require mesh generation, and the collocation algorithm does not handle the boundary conditions or any geometric information.

Abstract: A noved method for reducing a training data set in the context of nonparametric classification is proposed. The new method is based on the method of R-clouds. The advantage of the R-cloud classification method introduced recently are being investigated. A data set reduction approach using Rvachev function-based represetation of the separating boundary is proposed. The R-cloud method was found instructive and practical in a number of engineering problems related to pattern classification. The method of key vectors extraction uses the property of the normal R-cloud boundary to evaluate the distance from the sample to the separating boundary.