Then there exist positive constants (K_{1}), (K_{2}) such that biglVert bigl nabla^{m}u, nabla^{m}d bigr bigrVert _{q, lambda}leq K_{1}bigl(K_{2} vert tilde{beta} vert bigr)^{2m}t^{-frac{m}{2sigma} -frac{1}{2sigma}(2sigma-1-frac{n-lambda}{q})}, (1.6) where (tilde{beta}inmathbb{N}_{0}^{n}) is a multi-index and (| tilde{beta}|=m).
Tao and Hung [44] identified three types of models: composite index, multi-level index and multi-dimension matrix models.
Here we use the multi-index notations,,, and, for,, where is the set of non-negative integers and.
As before, we are using multi-index notation and the numbers (lambda _i) are the eigenvalues of (y in M) on the basis vectors (e_i) so that (lambda _i > 1) for all (i,).
Tables 3 and 4 show the result of the multi-index classification by MLPs and SVMs of RP and HDO, in light and darkness condition, respectively.
(iii) Multi-Symbol Transmitted Reference (MSTR) with and where is a multi-symbol block index and. .
Multi-Symbol Differential Encoder (MSDE) [17] with and where is a multi-symbol block index and.
In the following, we list three kinds of encoders: (i) Transmitted Reference (TR) [12] with = 1 if is even, otherwise =. (ii) Multi-Symbol Differential Encoder (MSDE) [17] with and where is a multi-symbol block index and.
Support for multi-lingual indexing and searching in Solr, especially Chinese, Japanese, and Korean languages.
After the above-mentioned update, the multi-layer-index and data table are kept up to date.
We shall use index k to denote the categorical levels of X i and multi-index j for the combination of parent states of X i, and with slight abuse of notation shall write k ∈ X i and j ∈ Pa i.
