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Table 1 Results for a Spectrum without Noise
"... In PAGE 5: ...06% 41.69% portional to the frequency (a in Figure 3 and Table1 ), was used. The synthetic and modeled spectra are very similar in the graph, but there is a large error in the Q parameter, around 20%, taking into account that the spectrum is not contaminated by noise (Table 1).... In PAGE 5: ...69% portional to the frequency (a in Figure 3 and Table 1), was used. The synthetic and modeled spectra are very similar in the graph, but there is a large error in the Q parameter, around 20%, taking into account that the spectrum is not contaminated by noise ( Table1 ). Errors in Xo and f0 are below 5%.... In PAGE 5: ... Doing the weight inversely proportional to the frequency leads to equalizing all the con- tributions of the spectrum (Prejean and Ellsworth, 2001), but we think the purpose is to discriminate between the contri- bution of the attenuation and that of the corner frequency, because of the trade-off between them. After that, the L2 norm of the log difference between the synthetic (observed, in a real case) and modeled spectra was tried, without weighting by the inverse of the frequency (b in Figure 3 and Table1 ). As can be observed, the improvement is notable.... ..."
Table 1: BNA: Basic network algebra .
"... In PAGE 5: ...g. axiom B10 in Table1 ) and notational convenience it is useful to use the block extensions of the feedback and of the above constants. Their meaning may be obtained using the identities in axioms R5{R6 and B6, B8{B9, A12{A19, respectively.... In PAGE 6: ... The algebraic structure de ned by the BNA axioms was introduced in [Ste86, CaS88 amp;89] under the name of bi ow; in the more sistematic notation used in [Ste94] it is also called a -ssmc with feedback.2 The algebraic structure de ned by axioms B1{B10 in Table1 and A1{A19 in Table 2 was introduced in [CaS91] under the name d -ssmc. Finally, the algebraic structure de ned by all the axioms in Tables 1 and 2 is called d -ssmc with feedback, cf.... In PAGE 6: ... [Ste86, CaS88 amp;89]. Correctness: Using the graphical interpretation of the operations and of the constants it is easy to see that the axioms in Table1 are correct with respect to graph isomorphism equivalence.... ..."
TABLE IV. Selected concepts of Algebra not necessarily known to those knowing numbers and selected theorems of Graph Theory not necessarily known to those knowing graphs
Table 1: Language and algebraic concepts of a VL 5
1997
"... In PAGE 5: ...entences based on graph grammar concepts. I.e. given a start graph which is an algebra wrt. to the corresponding speci cation, all sentences of a visual language can be derived by applying grammar rules formulated on the de ned symbols and links. Table1 illustrates the connection between the language and algebraic concepts we use within our approach.... ..."
Cited by 8
Table 3. Truth-table of Example Function for Computation of the KL Spectrum
"... In PAGE 4: ... Note that this func- tion can be considered to have a support variable set consisting of the binary-valued variable x1 and the ternary-valued variable x2, or, the single sextary- valued variable X. Also, a mapping is assigned to each domain value of f in Table3 although this is done arbitrarily. The general form of the adjacency matrix of the Cayley graph for functions with this... ..."
Table 1: Relationship of the Haar Spectrum and Out- put Probabilities
"... In PAGE 3: ... The following table contains symbols for each of the Haar coe cients, Hi, values that indicate the size of the constituent function range, i and n, and probability expressions that evaluate whether the function to be transformed and the constituent function simultaneously evaluate f x1 x2 fx1 x2 fx1 x3 fx1x2 x3 fx1x2 x3 fx1x2 x3 fx1x2 2 6 6 6 6 6 6 6 6 6 6 4 1 1 1 1 1 1 1 1 1 1 1 1 ?1 ?1 ?1 ?1 1 1 ?1 ?1 0 0 0 0 0 0 0 0 1 1 ?1 ?1 1 ?1 0 0 0 0 0 0 0 0 1 ?1 0 0 0 0 0 0 0 0 1 ?1 0 0 0 0 0 0 0 0 1 ?1 3 7 7 7 7 7 7 7 7 7 7 5 Figure 1: Example of Modi ed Haar Transformation Matrix for n = 3 to logic-0 (denoted as pm0), or evaluate to logic-1 (de- noted as pm1). Using the notation introduced in Table1 , we can write an algebraic equation to compute the value of the kth Haar spectral coe cient in terms of the out- put probabilities used to compute pm0 and pm1. Hk = 2n?i[2(pm0 + pm1) ? 1] (13) Table 1: Relationship of the Haar Spectrum and Out- put Probabilities... ..."
Table 2.1. Then the spectrum of P( ) has the pairing depicted in Table 2.2. Moreover, the algebraic, geometric, and partial multiplicities of the two eigenvalues in each such pair are equal. (Here, we allow = 0 and interpret 1= as the eigenvalue 1.) Table 2.2
2005
Cited by 9
Tables, equations, graphs, function machines, verbal and written descriptions are all used to analyze relationships. Graphing calculators provide excellent support for the tables, equations, and graphs. We summarise the interviews with DK who had completed two semesters of developmental algebra, receiving an A in both semesters.
1996
Cited by 2
Table 1. Dynkin diagrams corresponding to nite dimensional complex simple Lie algebras
"... In PAGE 27: ... Finite dimensional complex simple Lie algebras (2.1) Dynkin diagrams and Cartan matrices A Dynkin diagram is one of the graphs in Table1 . A Cartan matrix is one of the matrices in Table 2.... ..."
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