We study context-free grammars whose generated language is bounded (that is, subset of some expression w ̊ 1 . . . w ̊ d called bounded expression). We investigate the underlying generating process of such language and show that there exists a bounded expression u1 . . . um over the production rules, such that the language is generated only by sequences of production rules conforming to the bound...

We study the triangle bounded by the antiparallels to the sidelines of a given triangle ABC through the intercepts of the trilinear polar of a point P other than the centroid G. We show that this triangle is perspective with the reference triangle, and also study the condition of concurrency of the antiparallels. Finally, we also study the configuration of induced GP -lines and obtain an intere...

where Ω is an open bounded set of R and W and V are two non-negative continuous functions vanishing at α, β and α, β, respectively. In the previous functional, we fix a = 2 − p and u is a scalar density function, Tu denotes its trace on ∂Ω, d(x, ∂Ω) stands for the distance function to the boundary ∂Ω. We show that the singular limit of the energies Fε leads to a coupled problem of bulk and surf...

In this paper we will focus on a parabolic degenerate system with respect to unknown functions u and w on a bounded domain of the two-dimensional Euclidean space. This system appears as a mathematical model for some biological processes. Global existence and uniqueness of a nonnegative classical Hölder continuous solution are proved. The last part of the paper is devoted to the study of the asy...

Many wave propagation phenomena of classical physics are governed by equations of the Schrödinger form iDtu *=Aw where (1) A iEtà-i't* AêDj. (E(x) and the Aj are Hermitian matrices, E(x) is positive definite and the Aj are constant.) The time-evolution of such phenomena is described by a group of unitary operators exp(-itA) on the Hilbert space 3C with the energy norm (2) \\u\\l f u(x)*E(x)u(x)...

For her love, support and sense of humor. iii ACKNOWLEDGEMENTS This work could not have been completed without the help of many people. My advisor, Ellen Zegura, has been a constant source of motivation. Her ability to cut to the core of complex issues has never ceased to surprise and inspire me. Matt Sanders and Russ Clark have provided much appreciated friendship and stimulating discussion. M...

Introduction. The problems encountered in building a driver assistance system are numerous. The collection of information about real environment by sensors is erroneous and incomplete. When the sensors are mounted on a moving observer it is difficult to find out whether a detected motion was caused by ego-motion or by an independent object moving. The collected data can be analyzed by several a...

The spacing of streaks of low-speed fluid has been studied experimentally in a wall-bounded turbulent flow in which sinusoidal unsteadiness was superposed on an otherwise steady mainstream over a range of frequencies. The modulation of phase-conditioned streak spacing about its mean value does not follow the steady wall-flow relation of hu Av equal to a constant. Instead, it is quite accurately...