Higher-dimensional analogs of the predictable degree property and column reducedness are defined, and it is proved that the two properties are equivalent. It is shown that every multidimensional convolutional code has, what is called, a minimal reduced polynomial resolution. It is uniquely determined (up to isomorphism) and leads to a number of important integer invariants of the code generaliz...

We use the behavioural approach to de®ne and characterize control-lable and uncontrollable poles and zeros of multidimensional (nD) linear systems. We show a strong relationship between controllable poles and zeros and properties of the transfer function matrix, and we give characterizations of uncontrollable poles and zeros, in particular demonstrating that these have an input decoupling prope...

We study a four-level atomic system with electromagnetically induced transparency with giant chi(3) and chi(5) susceptibilities of opposite signs. This system will allow us to obtain multidimensional solitons and light condensates with surface tension properties analogous to those of usual liquids.

Structural properties of stochastic dynamic programs are essential to understanding the nature of the solutions and in deriving appropriate approximation techniques. We concentrate on a class of multidimensional Markov decision processes and derive sufficient conditions for the monotonicity of the value functions. We illustrate our result in the case of the Multiproduct Batch Dispatch (MBD) pro...

Evidence is presented that properties of objects, or events, or man-made artifacts in the natural world are clustered in a multidimensional space. Hence observations made by different sense modalities can be highly correlated. Such clustering favors perceptual inference, increasing its robustness, as well as supporting generalizations.

We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on Rn. The correspondence between multidimensional Diophantine approximation and dynamics of lattices in Euclidean spaces is discussed in an elementary way, and several recent results obtained by means of this correspon...

We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces. Mathematics Subject Classification 2000: 46E30, 46B25.

If our mutlidimensional vectors "live" in some appropriate multidimensional space (See Greenberg) we need some properties vector norms A natural question about a vector is, how "long" is it? We might want to know this for a physical reason, say mean velocity, or for an abstract comparision.

We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of “symmetric measure”: exchangeability and the Gibbs property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.

The aim of this study was to identify the tactile dimensions in the discrimination of light-weight wool fabrics. The participants judged the overall similarity between 21 light-weight wool fabrics using free sorting tasks. The fabrics were evaluated using active touch with limited exploratory procedure. Multidimensional scaling (MDS) was used to generate the perceptual space, revealing one dime...