Counting combinatorial objects and determining the associated generating functions can be computationally very difficult and expensive when using exact numbers. Doing similar calculations modulo a prime can be orders of magnitude faster. We use two simple polygon models to illustrate this: we study the generating functions of (singly) punctured staircase polygons and imperfect staircase polygon...

Relational query processors derive much of their effectiveness from the awareness of specific table properties like sort order, size, or absence of duplicate tuples. This text applies (and adapts) this successful principle to database-supported XML and XPath processing: the relational system is made tree aware, i.e., tree properties like subtree size, intersection of paths, inclusion or disjoin...

The probability distribution of precipitation amount strongly depends on geography, climate zone, and time scale considered. Closed-form parametric distributions are not sufficiently flexible to provide accurate universal models for over different scales. In this paper we derive non-parametric estimates the cumulative function (CDF) wet periods. CDF obtained by integrating kernel density estima...

This Rapid Communication sets forth the mechanism by which mesoscale staircase structures condense to form macroscopic states of enhanced confinement. Density, vorticity, and turbulent potential enstrophy are the variables for this model. Formation of the staircase structures is due to inhomogeneous mixing of (generalized) potential vorticity (PV). Such mixing results in the local sharpening of...

Relational query processors derive much of their effectiveness from the awareness of specific table properties like sort order, size, or absence of duplicate tuples. This text applies (and adapts) this successful principle to database-supported XML and XPath processing: the relational system is made tree aware, i.e., tree properties like subtree size, intersection of paths, inclusion or disjoin...

In this talk, matrix inequality characterizations for the positive realness of descriptor systems are introduced. Hence, the celebrated positive real lemma for standard state space systems is established for descriptor systems. In addition, the lossless positive realness of both standard state space systems and descriptor systems are characterized explicitly based on the controllable staircase ...

A novel MatLab-based diffraction tool for the investigation of scattered fields around a two-dimensional Perfectly Electric Conductor (PEC) wedge is introduced. Analytical (Exact by Integral, as well as some High Frequency Asymptotic (HFA) techniques) and numerical (Finite-Difference Time-Domain (FDTD)) models are included. The FDTD staircase modeling problems are removed by the application of ...

In this paper, the finite-difference time-domain (FDTD) method is applied to calculate the resonant frequency of dielectric resonators (DR’s) with curved surface. The contour-path integral FDTD (CFDTD) is modified to deal with the curved surface of the dielectric body while the traditional rectangular cells are maintained. Results are compared with theoretical values and staircase approximation...

The exertion of stairclimbing has been studied in 10 normal young men, 10 healthy middle-aged men, and 10 middle-aged men with chronic bronchitis. Subjects climbed a staircase with a total vertical ascent of 40.8 m. They were allowed to adopt the most comfortable pattern of ascent, the patients having to stop at intervales for rest pauses. Work rate was determined by timing the raising body wei...

We explain how the moments of the (weight function of the) Askey Wilson polynomials are related to the enumeration of the staircase tableaux introduced by the first and fourth authors [11, 12]. This gives us a direct combinatorial formula for these moments, which is related to, but more elegant than the formula given in [11]. Then we use techniques developed by Ismail and the third author to gi...