This paper presents a comparative study on the application of different numerical methods for the solution of the dynamic bi-variate population balance equation (PBE) in batch particulate systems. Specifically, particulate processes operating under the combined action of particle aggregation and/or particle growth are examined. In order to solve the bi-variate PBE the Galerkin finite element me...

We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers the second kind that we studied previous work. prove bi-variate polynomial version some known results on standard Bernoulli polynomials, as addition formula and binomial formula. also result allows us to obtain identities from identities, use this several involving products and/or polynomials....

In this note we estimate the asymptotic rates for the L2-error decay and the storage cost when approximating 2πperiodic, d-variate functions from isotropic and mixed Sobolev classes by the recent hierarchical tensor format as introduced by Hackbusch and Kühn. To this end, we survey some results on bilinear approximation due to Temlyakov. The approach taken in this paper improves and generalizes...

A new multilayer preceptor initialization method is proposed and compared experimentally with a traditional random initialization method. An operator maps training-set vectors into a two-variate space, inspects bi-variate training-set vectors and controls the complexity of the decision boundary. Simulations with sixteen real-world pattern classi®cation tasks have shown that in small-scale patte...

Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in the non-parametric model will have two different non-parametric regression functions. Therefore, we...

Knowledge of traditional medicine is important for the formation a person's activity in using medicine. Preliminary studies conducted show level public knowledge about less category. This can be caused by lack desire to seek information and education from health workers. For this reason, educational media such as e-booklets are needed. study aims see after being given an e-booklet. uses preexpe...