Nonlinear characteristic boundary conditions based on multidimensional wave modeling are proposed for twoand three-dimensional full compressible Navier-Stokes equations with/without scalar transport equations. This model is consistent with the physics of flows and transport properties. Based on the theory of characteristics, the multidimensional flows can be decomposed into acoustic, entropy, a...

Locally narrow-band images can be modeled as two-dimensional (2D) spatial AM–FM signals with several applications in image texture analysis and computer vision. We formulate an image-demodulation problem and present a solution based on the multidimensional energy operator Fs f d ­ k=fk2 2 f=2f . This nonlinear operator is a multidimensional extension of the one-dimensional (1D) energy-tracking ...

We analyze the theoretical properties of an adaptive Legendre-Galerkin method in the multidimensional case. After the recent investigations for Fourier-Galerkin methods in a periodic box and for Legendre-Galerkin methods in the one dimensional setting, the present study represents a further step towards a mathematically rigorous understanding of adaptive spectral/hp discretizations of elliptic ...

This letter addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented in those frameworks that provides an explicit functional link between the reservoir architecture and its performance in the execution of a specific task. S...

Compositional model theory serves as an alternative approach to multidimensional probability distribution representation and processing. Every compositional model over a finite non-empty set of variables N is uniquely defined by its generating sequence – an ordered set of low-dimensional probability distributions. A generating sequence structure induces a system of conditional independence stat...

Data warehouses, multidimensional databases, and OLAP tools are based on the multidimensional (MD) modeling. Lately, several approaches have been proposed to easily capture main MD properties at the conceptual level. These conceptual MD models, together with a precise management of metadata, are the core of any related tool implementation. However, the broad diversity of MD models and managemen...

Multidimensional Synchronous Dataflow (MDSDF) [15][7] is a model of computation that has been proposed for specifying multidimensional multirate signal processing systems such as image and video processing algorithms. The model is an extension of synchronous dataflow (SDF) [14] and has all of the desirable properties of the SDF model such as static schedulability, exposition of data and functio...