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Using the path model and the theory of crystals, we generalize the concept of patterns to arbitrary complex semi-simple algebraic groups.
      
Then it is shown that for many (and perhaps all) pairs E, F, of wavelet sets, the corresponding MSF wavelets can be connected by a continuous path in L2(?) of MSF wavelets for which the Fourier transform has support contained in E ∪ F.
      
Smooth Frame-Path Termination for Higher Order Sigma-Delta Quantization
      
The frames under consideration are obtained from regular sampling of a path in a Hilbert space.
      
In the continuous sample path case precise error bounds are derived.
      
This approximation method is used to develop a simulation method of the sample path of linear fractional stable motions.
      
Computational complexity of (2,2) path chromatic number problem
      
Is there a normalPk coloring usingr colors for a given graph? This problem is called the (k, r) path chromatic number problem of graphs.
      
This paper proves that the (2,2) path chromatic number problem of graphs with maximum degree 4 is NP-complete.
      
The uniqueness of the geodesic by its initial values severely restricts the choice of the fiber path and is an obstacle to the production of optimized structures.
      
A routing in a network assigns to each ordered pair of nodes a fixed path.
      
The author proves that the set of points where the Chung type LIL fails for the path of the infinite series of independent Ornstein-Uhlenbeck processes is a random fractal, and eval-uates its Hausdorff dimension.
      
Under a kind of utility function and production function, we prove that these conditions are satisfied and the economy at least has an optimal growth path.
      
By numerical analysis, the fertility decreases with the per capita capital and per capita consumption increasing and increases with the per capita capital and per capita consumption decreasing on the economic growth path are obtained.
      
A note on sample path properties of lp-valued Gaussian processes
      
sample path properties for lp-valued Gaussian processes with stationary increments under some more general conditions are established.
      
The cutwidth problem for a graph G is to embed G into a path such that the maximum number of overlap edges is minimized.
      
The cutwidth problem for a graph G is to embed G into a path Pn such that the maximum number of overlap edges (i.e., the congestion) is minimized.
      
An increasing nonconsecutive path in a labeled graph (G, L) is a path (u1, u2, ..., uk), k≥1, in G such that L(ui)+1>amp;lt;L(ui+1) for all i=1, 2, ..., k-1.
      
An increasing nonconsecutive path in a labeled graph (G, L) is either a path (u1, u2, …, uk) (k ≥ 2) in G such that L(ui) + 2 ≤ L(ui+1) for all i = 1, 2, …, k - 1 or a path of order 1.
      
 

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