In this talk we discuss explicit constructions of sequences with optimal $L_2$ discrepancy and explicit constructions of point sets with optimal $L_q$ discrepancy for $1 < q < \infty$. In 1954 Roth proved a lower bound for the $L_2$ discrepancy of finite point sets in the unit cube of arbitrary dimension. Later various authors extended Roth's result to lower bounds also for the $L_q$ discrepanc...

Explicit, implicit–explicit and Crank–Nicolson implicit–explicit numerical schemes for solving the generalized lubrication equation are derived. We prove that the implicit– explicit and Crank–Nicolson implicit–explicit numerical schemes are unconditionally stable. Numerical solutions obtained from both schemes are compared. Initial curves with both zero and finite contact angles are considered....

Explicit finite difference and finite element schemes are constructed to solve wave propagation, shock, and impact problems. The schemes rely on exponential functions and the solution of linearised Rlemann problems in order to reduce the effects of numerical dispersion and diffusion. The relationship of the new schemes to existing explicit schemes is analysed and numerical results and compariso...

Almost all finite graphs have the n-e.c. adjacency property, although until recently few explicit examples of such graphs were known. We survey some recently discovered families of explicit finite n-e.c. graphs, and present a new construction of strongly regular n-e.c. arising from affine planes.

ca2 (continuum analysis, 2- dimensional) is a computer program developed by the author. ca2 can solve a variety of complex geotechnical problems using explicit finite difference method. in this paper, an introduction will be given to the theoretical and numerical basis of the program and the capability of the code will be shown by solving a few interesting nonlinear and transient problems. fina...

We define in an axiomatic way scalar and fuzzy cardinalities of finite multisetsover ]0, 1], and we obtain explicit descriptions for them. We show that, for multisetsover ]0, 1] associated to finite fuzzy sets, the cardinalities defined in this paper areequivalent to the cardinalities of the corresponding fuzzy sets previously introducedin the literature. Finally, we also de...

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

The fractional step method is a technique that results in a computationally-efficient implementation of Navier–Stokes solvers. In the finite element-based models, it is often applied in conjunction with implicit time integration schemes. On the other hand, in the framework of finite difference and finite volume methods, the fractional step method had been successfully applied to obtain predicto...

although explicit and implicit knowledge of language learners are essential to theoretical and pedagogical debates in second language acquisition (sla), little research has addressed the effects of instructional interventions on the two knowledge types (r. ellis, 2005).this study examined the relative effectiveness of explicit and implicit types of form-focused instruction (ffi) on the acquisit...