Morvan and Stirling have proved that the context-sensitive languages are exactly the traces of graphs defined by transducers with labelled final states. We prove that this result is still true if we restrict to the traces of graphs defined by synchronized transducers with labelled final states. From their construction, we deduce that the context-sensitive languages are the languages of path lab...

We consider two notions describing how one finite graph may be larger than another. Using them, we prove several theorems for such pairs that compare the number of spanning trees, the return probabilities of random walks, and the number of independent sets, among other combinatorial quantities. Our methods involve inequalities for determinants, for traces of functions of operators, and for entr...

We consider two types of Besov spaces on the Koch curve, defined by traces and with the help of the snowflaked transform. We compare these spaces and give their characterization in terms of Daubechies wavelets.

  Background: Nonspecific symptoms are common in all areas of medicine. Patients and caregivers can be frustrated when an illness cannot be reduced to a discrete pathophysiological process that corresponds with the symptoms. We therefore asked the following questions: 1) Which demographic factors and psychological comorbidities are associated with change from an initial diagnosis of nonspecific...

this paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. first, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. this new algorithm ca...

We present a novel ice/firn core melter system that uses fraction collectors to collect discrete, high-resolution (<1 cm/sample possible), continuous, coregistered meltwater samples for analysis of eight major ions by ion chromatography (IC), >32 trace elements by inductively coupled plasma sectorfield mass spectrometry (ICP-SMS), and stable oxygen and hydrogen isotopes by isotope ratio mass sp...

This set of notes will try to set down in one coherent place, a general set of equations for calculating changes of major element, reactive trace element and U-series nuclides in an open system. Given the continuous form of the equations we will also deal with scaling and discrete forms using Semi-Lagrangian advection schemes. The key to these derivations will be using general conservation of m...

This paper describes a comprehensive and systematic framework for building mixed continuous/discrete, i.e., hybrid physical system models. Hybrid models are a natural representation for embedded systems (physical systems with digital controllers) and for complex physical systems whose behavior is simplified by introducing discrete transitions to replace fast, often nonlinear dynamics. In this p...

We present a systematic and constructive methodology to devise various hybridized discontinuous Galerkin (HDG) methods for linearized shallow water equations. At the heart of our development is an upwind HDG framework obtained by hybridizing the upwind flux in the standard discontinuous Galerkin (DG) approach. The chief idea is to first break the uniqueness of the upwind flux across element bou...