(qmin≦q≦qmax) on the path, creating a leaf node by appending an edge with an endmarker symbol #, if this new leaf node has not been previously inserted into the trie, signifying that the positional gram of length |s|−p+1 has a prefix gram of length q that ends at this leaf...
where the unknown functions x, y and z depend on 𝑡>0t>0, and the dot symbol denotes a derivative with respect to t. In this section, we also recall [31] some geometrical properties of the system (1). The considered system has a Hamilton–Poisson realization with the Hamiltonian 𝐻...
2.1. Symbol Definitions In this subsection, the basic symbols are introduced in detail. In this paper, nonbold lowercase letters refer to scalars; bold lowercase letters stand for vectors; bold capital letters represent matrices; bold calligraphic letters refer to tensors. For a third-order tensor...
where the symbol (*) denotes the conjunction operation. Equation (3) expresses that the exact PSF depends on the number of retained singular values. The truncation index 𝑁N is related to the accuracy of the solution and can be adopted in terms of the NDF. 2. The introduction of the a...
The empty set is denoted by the symbol ∅. Let Ω be a nonempty set in R n × R m , equipped with the Euclidean norm ∥ · ∥ . The closure, interior, and the convex hull of Ω are denoted by the symbols cl Ω , int Ω , and co Ω , respectively. For any ( z ¯ 1...
with 𝛿𝑖𝑗 denoting the Kronecker symbol. Furthermore, the associative flow rule is assumed to govern the plastic strain, 𝜀˙p𝑖𝑗=!𝛾∂𝑓∂𝜎𝑖𝑗=3𝛾𝜎′𝑖𝑗, (4) with a positive consistency parameter 𝛾∈ℝ>0 which can be related to the equivalent pl...
When applied to a 16-bit radicand (the number under the square root symbol), the proposed designs have the lowest error rates, normalized mean error distances, and mean relative error distances by at least 1.8x when compared to all previous methods using the same number of approximate cells....
where 𝐱∈ℂ𝑁×1 denotes the symbols to be modulated on N subcarriers. The mth subcarrier is with the frequency 𝑓𝑚=𝑓𝑐+𝑚Δ𝑓, where Δ𝑓 denotes the subcarrier spacing. The symbol duration is 𝑇=1Δ𝑓. Before transmission, the OFDM-IM is transformed as the time...
Such a symbol has the form 𝜎=(𝜎1,𝜎2)σ=(σ1,σ2) where 1≤𝜎1<𝜎2≤41≤σ1<σ2≤4. 𝜎σ 𝑑(𝜎)d(σ) (1,2)(1,2) 0 (1,3)(1,3) 1 (1,4)(1,4) 2 (2,3)(2,3) 2 (2,4)(2,4) 3 (3,4)(3,4) 4 Theorem 2. The (𝑛𝑘)nk sets 𝑒...
Such a symbol has the form 𝜎=(𝜎1,𝜎2)σ=(σ1,σ2) where 1≤𝜎1<𝜎2≤41≤σ1<σ2≤4. 𝜎σ 𝑑(𝜎)d(σ) (1,2)(1,2) 0 (1,3)(1,3) 1 (1,4)(1,4) 2 (2,3)(2,3) 2 (2,4)(2,4) 3 (3,4)(3,4) 4 Theorem 2. The (𝑛𝑘)nk sets 𝑒...