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| | ====Table 9==== | | ====Table 9==== |
| | | | |
| − | <font face="courier new">
| + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%" |
| − | {| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:left; width:96%" | |
| | |+ '''Table 9. Higher Order Differential Features''' | | |+ '''Table 9. Higher Order Differential Features''' |
| − | | width=50% |
| + | | |
| − | {| cellpadding="4"
| + | <p><math>\begin{array}{lllll} |
| − | | <font face="lucida calligraphy">A</font>
| + | \operatorname{d}^0 \mathcal{A} |
| − | | =
| + | & = & \{a_1, \ldots, a_n\} |
| − | | d<sup>0</sup><font face="lucida calligraphy">A</font>
| + | & = & \mathcal{A} \\ |
| − | | =
| + | \operatorname{d}^1 \mathcal{A} |
| − | | {''a''<sub>1</sub>,
| + | & = & \{\operatorname{d}a_1, \ldots, \operatorname{d}a_n\} |
| − | | …,
| + | & = & \operatorname{d}\mathcal{A} \\ |
| − | | ''a''<sub>''n''</sub>}
| + | \end{array}</math></p> |
| − | |-
| + | <p><math>\begin{array}{lll} |
| − | | d<font face="lucida calligraphy">A</font>
| + | \operatorname{d}^k \mathcal{A} |
| − | | =
| + | & = & \{\operatorname{d}^k a_1, \ldots, \operatorname{d}^k a_n\} \\ |
| − | | d<sup>1</sup><font face="lucida calligraphy">A</font>
| + | \operatorname{d}^* \mathcal{A} |
| − | | =
| + | & = & \{\operatorname{d}^0 \mathcal{A}, \ldots, \operatorname{d}^k \mathcal{A}, \ldots \} \\ |
| − | | {d''a''<sub>1</sub>,
| + | \end{array}</math></p> |
| − | | …,
| + | | |
| − | | d''a''<sub>''n''</sub>}
| + | <p><math>\begin{array}{lll} |
| − | |-
| + | \operatorname{E}^0 \mathcal{A} |
| − | |
| + | & = & \operatorname{d}^0 \mathcal{A} \\ |
| − | |
| + | \operatorname{E}^1 \mathcal{A} |
| − | | d<sup>''k''</sup><font face="lucida calligraphy">A</font>
| + | & = & \operatorname{d}^0 \mathcal{A}\ \cup\ \operatorname{d}^1 \mathcal{A} \\ |
| − | | =
| + | \operatorname{E}^k \mathcal{A} |
| − | | {d<sup>''k''</sup>''a''<sub>''1''</sub>,
| + | & = & \operatorname{d}^0 \mathcal{A}\ \cup\ \ldots\ \cup\ \operatorname{d}^k \mathcal{A} \\ |
| − | | …,
| + | \operatorname{E}^\infty \mathcal{A} |
| − | | d<sup>''k''</sup>''a''<sub>''n''</sub>}
| + | & = & \bigcup\ \operatorname{d}^* \mathcal{A} \\ |
| − | |-
| + | \end{array}</math></p> |
| − | | d<sup>*</sup><font face="lucida calligraphy">A</font>
| + | |}<br> |
| − | | =
| |
| − | | {d<sup>0</sup><font face="lucida calligraphy">A</font>,
| |
| − | | …,
| |
| − | | d<sup>''k''</sup><font face="lucida calligraphy">A</font>,
| |
| − | | …}
| |
| − | |}
| |
| − | | width=50% |
| |
| − | {| cellpadding="4" | |
| − | | E<sup>0</sup><font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | d<sup>0</sup><font face="lucida calligraphy">A</font>
| |
| − | |-
| |
| − | | E<sup>1</sup><font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | d<sup>0</sup><font face="lucida calligraphy">A</font> ∪ d<sup>1</sup><font face="lucida calligraphy">A</font>
| |
| − | |-
| |
| − | | E<sup>''k''</sup><font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | d<sup>0</sup><font face="lucida calligraphy">A</font> ∪ … ∪ d<sup>''k''</sup><font face="lucida calligraphy">A</font>
| |
| − | |-
| |
| − | | E<sup>∞</sup><font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | ∪ d<sup>*</sup><font face="lucida calligraphy">A</font>
| |
| − | |}
| |
| − | |}
| |
| − | </font><br>
| |
| − | | |
| − | <font face="courier new">
| |
| − | {| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:left; width:96%" | |
| − | |+ '''Table 9. Higher Order Differential Features'''
| |
| − | | width=50% |
| |
| − | {| cellpadding="4" | |
| − | | <font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | d<sup>0</sup><font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | {''a''<sub>1</sub>,
| |
| − | | …,
| |
| − | | ''a''<sub>''n''</sub>}
| |
| − | |-
| |
| − | | d<font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | d<sup>1</sup><font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | {d''a''<sub>1</sub>,
| |
| − | | …,
| |
| − | | d''a''<sub>''n''</sub>}
| |
| − | |-
| |
| − | |
| |
| − | |
| |
| − | | d<sup>''k''</sup><font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | {d<sup>''k''</sup>''a''<sub>''1''</sub>,
| |
| − | | …,
| |
| − | | d<sup>''k''</sup>''a''<sub>''n''</sub>}
| |
| − | |-
| |
| − | | d<sup>*</sup><font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | {d<sup>0</sup><font face="lucida calligraphy">A</font>,
| |
| − | | …, | |
| − | | d<sup>''k''</sup><font face="lucida calligraphy">A</font>,
| |
| − | | …}
| |
| − | |}
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| − | | width=50% |
| |
| − | {| cellpadding="4" | |
| − | | E<sup>0</sup><font face="lucida calligraphy">A</font>
| |
| − | | =
| |
| − | | d<sup>0</sup><font face="lucida calligraphy">A</font>
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| − | |-
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| − | | E<sup>1</sup><font face="lucida calligraphy">A</font>
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| − | | =
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| − | | d<sup>0</sup><font face="lucida calligraphy">A</font> ∪ d<sup>1</sup><font face="lucida calligraphy">A</font>
| |
| − | |-
| |
| − | | E<sup>''k''</sup><font face="lucida calligraphy">A</font>
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| − | | =
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| − | | d<sup>0</sup><font face="lucida calligraphy">A</font> ∪ … ∪ d<sup>''k''</sup><font face="lucida calligraphy">A</font>
| |
| − | |-
| |
| − | | E<sup>∞</sup><font face="lucida calligraphy">A</font>
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| − | | =
| |
| − | | ∪ d<sup>*</sup><font face="lucida calligraphy">A</font>
| |
| − | |} | |
| − | |}
| |
| − | </font><br>
| |