### Table 1. (cont.) Sporadic Examples of Zw of Index 1 I 10 Index w

"... In PAGE 19: ...Table1 . Sporadic Examples of Zw of Index 1 I 10 Index w Monomials of fw d b2 K-E 1 (1,2,3,5) z10 0 ; z5 1; z3 2z1; z2 3; : : : (17) 10 9 ? 1 (1,3,5,7) z15 0 ; z5 1; z3 2; z2 3z0; : : : (19) 15 9 ? 1 (1,3,5,8) z16 0 ; z5 1z0; z3 2z0; z2 3; : : : (20) 16 10 ? 1 (2,3,5,9) z9 0; z6 1; z3 2z1; z2 3; : : : (13) 18 7 Y 1 (3,3,5,5) g5(z0; z1); f3(z2; z3) 15 5 Y 1 (3,5,7,11) z6 0z2; z5 1; z2 2z3; z2 3z0; : : : (8) 25 5 Y 1 (3,5,7,14) z7 0z2; z5 1z0; g2(z2 2; z3); : : : (9) 28 6 Y 1 (3,5,11,18) g2(z6 0; z3); z5 1z2; z3 2z0; : : : (10) 36 6 Y 1 (5,14,17,21) z7 0z3; z4 1; z3 2z0; z2 3z1; z5 0z1z2 56 4 Y 1 (5,19,27,31) z10 0 z3; z4 1z0; z3 2; z2 3z1; z7 0z1z2 81 3 Y 1 (5,19,27,50) z20 0 ; z10 0 z3; z2 3; z5 1z0; z3 2z1; z7 0z2 1z3 100 4 Y 1 (7,11,27,37) z10 0 z1; z4 1z3; z3 2; z3 3z0 81 3 Y 1 (7,11,27,44) z11 0 z1; z3 2z0; z8 1; z4 1z3; z2 3; z4 0z3 1z2 88 4 Y 1 (9,15,17,20) z5 0z1; z4 1; z3 2z0; z3 3 60 3 Y 1 (9,15,23,23) z6 0z1; z4 1z0; z3 2; z2 2z3; z3; z2z2 3; z3 3 69 5 Y 1 (11,29,39,49) z8 0z2; z4 1z0; z3 2; z2 3z1 127 3 Y 1 (11,49,69,128) z17 0 z2; z5 1z0; z4 2; z2 2z3; z2 3 256 2 Y 1 (13,23,35,57) z8 0z1; z4 1z2; z2 2z3; z2 3z0 127 3 Y 1 (13,35,81,128) z17 0 z1; z5 1z2; z3 2z0; z2 3 256 2 Y 2 (2,3,4,5) z6 0; z4 1; z3 2; z2 3z0; : : : (10) 12 5 ? 2 (2,3,4,7) z7 0; z4 1z0; z3 2z0; z2 3; : : : (11) 14 6 ? 2 (3,4,5,10) z5 0z2; z5 1; z4 2; z2 3; : : : (9) 20 5 Y 2 (3,4,6,7) g3(z2 0; z2); z3 1z2; z2 3z1; z0z3z2 1; z2 0z3 1 18 6 ? 2 (3,4,10,15) z10 0 ; z5 1z3; z3 2; z2 3; : : : (10) 30 7 Y 2 (3,7,8,13) z7 0z2; z3 1z2; z2 2z3; z2 3z0; z5 0z1; z3 0z1z3; z2 0z1z2 2 29 5 ? 2 (3,10,11,19) z10 0 z3; z3 1z2; z2 2z3; z2 3z0; z7 0z2 1; z4 0z1z3; z3 0z1z3 2 41 5 ? 2 (5,13,19,22) z7 0z3; z4 1z0; z3 2; z2 3z1; z5 0z1z2 57 3 Y 2 (5,13,19,35) z14 0 ; z7 0z3; z2 3; z5 1z0; z3 2z1; z5 0z2 1z2 70 3 Y 2 (6,9,10,13) z6 0; z4 1; z3 2z0; z2 3z2; z3 0z2 1 36 4 Y 2 (7,8,19,25) z7 0z1; z4 1z3; z3 2; z2 3z0; z2 0z3 1z2 57 3 Y 2 (7,8,19,32) z8 0z1; z8 1; z4 1z3; z2 3; z3 2z0; z0z3 2; z3 0z3 1z2 64 4 Y 2 (9,12,13,16) z4 0z1; z4 1; z3 2z0; z3 3 48 3 Y 2 (9,12,19,19) z5 0z1; z4 1z0; z3 2; z2 2z3; z2z3 3; z3 3 57 5 Y 2 (9,19,24,31) z9 0; z3 1z2; z3 2z0; z2 3z1 81 3 Y 2 (10,19,35,43) z7 0z2; z5 1z0; z3 2; z2 3z1 105 3 Y 2 (11,21,28,47) z7 0z2; z5 1; z3 2z1; z2 3z0 105 3 Y 2 (11,25,32,41) z6 0z3; z3 1z2; z3 2z0; z2 3z1 107 3 Y 2 (11,25,34,43) z10 0 ; z4 1z0; z2 2z3; z2 3z1 111 3 Y 2 (11,43,61,113) z15 0 z2; z5 1z0; z3 2z1; z2 3 226 2 Y 2 (13,18,45,61) z9 0z1; z5 1z2; z3 2; z2 3z0 135 3 Y... In PAGE 22: ... But I I?n D 2 j ? KZwj so this completes the proof of the lemma. The analysis of most of the sporadic examples of Table1 is easily done with help of Corollary 3.7 which can restated for this purpose as: Corollary 5.... In PAGE 31: ...f degree wi. The simplest situation occurs when f1 = f2 = f3 are forced to vanish. Then Gw = (C )3 is the smallest it can possibly be as P(w) is toric. This is, in fact, common to many examples of the log del Pezzo suraces of Table1 . More precisely, we have Lemma 7.... In PAGE 33: ...As mentioned previously for the log del Pezzo surfaces with a Y in the last column of Table1 and the tables of Theorem 4.5, there is a unique homothety class of Kahler-Einstein metrics corresponding to each point of Md w: But the question remains whether two inequivalent Kahler-Einstein structures can share the same Riemannian metric.... ..."

Cited by 12

### Table 4: Difference in 11-point averaged precision between hybrid term indexing and other indexing strategies, for title queries.

"... In PAGE 4: ...2.2 Is Hybrid Term Indexing Better? Table4 shows the 11-point averaged precision of hybrid term indexing minus that of other indexing strategies for title queries. On average, there was an insignificant better precision of 0.... ..."

### Table 1: Input format parameters. In either case, there must be provisions for including the correct starting page number in the pre-formatted version of index. 3 Index Processing The index processor performs the tasks indicated above | permutation, page number merg- ing, subindexing, style handling, and other special e ects. In order to achieve format and formatter independence, the index processor must be able to accept raw index terms des- ignated by di erent keywords and delimiters. Likewise, it must be able to generate output in a speci c style so that the result can be processed by the corresponding formatter. The intended tasks can be performed in multiple passes: First the input format le and output style le are scanned and analyzed. Entries in the input le are then processed. Next, all legal entries are sorted. Finally, the output index is generated in the last pass. The remainder of this section discusses the essential attributes for input formats and output styles and points out relevant issues for sorting and generating the entries.

1988

"... In PAGE 12: ...Input Format Table1 is a summary of the input format that consists of a list of lt;speci er, attribute gt; pairs. These attributes are the essential tokens and delimiters needed in scanning the input index le.... ..."

Cited by 7

### Table 1: Input format parameters. In either case, there must be provisions for including the correct starting page number in the pre-formatted version of index. 3 Index Processing The index processor performs the tasks indicated above | permutation, page number merg- ing, subindexing, style handling, and other special e ects. In order to achieve format and formatter independence, the index processor must be able to accept raw index terms des- ignated by di erent keywords and delimiters. Likewise, it must be able to generate output in a speci c style so that the result can be processed by the corresponding formatter. The intended tasks can be performed in multiple passes: First the input format le and output style le are scanned and analyzed. Entries in the input le are then processed. Next, all legal entries are sorted. Finally, the output index is generated in the last pass. The remainder of this section discusses the essential attributes for input formats and output styles and points out relevant issues for sorting and generating the entries.

1988

"... In PAGE 12: ...Input Format Table1 is a summary of the input format that consists of a list of lt;speci er, attribute gt; pairs. These attributes are the essential tokens and delimiters needed in scanning the input index le.... ..."

Cited by 7

### Table 2. Average Index Terms per Document

2004

"... In PAGE 6: ... 5.1 Dimensionality Reduction The results presented in Table2 , show that RFA reduces the dimensionality of the affected documents space to a great extent. The reduction is obtained while preserving or improving the retrieval effectiveness of the system augmented with RFA (see results in Sections 5.... In PAGE 6: ... The retrieval systems ST, BR, BB and BS are considered together since none of them possesses a dimensionality reduction technique. In fact for the BR, BB and BS systems the dimensionality is even higher than the one presented in Table2 , because of the introduction of new terms. First column of Table 2 shows the minimum dimensionality, which in fact corresponds to the ST system.... In PAGE 6: ... In fact for the BR, BB and BS systems the dimensionality is even higher than the one presented in Table 2, because of the introduction of new terms. First column of Table2 shows the minimum dimensionality, which in fact corresponds to the ST system. 5.... ..."

Cited by 1

### Table 4: Switch points for natural Hermite moment index for various cluster separations and number of terms in the approximation (truncation point). Cluster Separation

1996

Cited by 5

### Table 4: Switch points for natural Hermite moment index for various cluster separations and number of terms in the approximation (truncation point). Cluster Separation

1996

Cited by 5

### Table 3: Switch points for natural Hermite moment index for various cluster separations and number of terms in the approximation (truncation point). Cluster Separation

### Table 1. Brief database schema and statistics of index terms per document

"... In PAGE 6: ... Figure 3 shows the 1,296th example item which con- sists of @DOCUMENT(record delimiter), TITLE, AU- THOR, JOURNAL, VOLUME, NUMBER, PAGE START, PAGE END, PUBDATE(publish date), ABSTRACT and KEYWORDS. Table1 shows average term counts in every section in the text collection (a section is the equivalent to a eld or column in database world). Remind that to keep the lexicographical order of the terms in an inverted le, usually a vocabulary data structure is separated from the postings list, and in the KRISTAL-IRMS postings lists are further separated physically into two parts, postings of document identi ers with term frequencies and exact locations in the documents.... In PAGE 6: ... Remind that to keep the lexicographical order of the terms in an inverted le, usually a vocabulary data structure is separated from the postings list, and in the KRISTAL-IRMS postings lists are further separated physically into two parts, postings of document identi ers with term frequencies and exact locations in the documents. Now refer to Table1 where a document con- tains more than one hundred unique terms, which means... In PAGE 7: ...cess three disk data structures the vocabulary list, posting list and location list for each unique term from the input document. As shown in Table1 , KRISTAL-IRMS supports data types such as string (var char equivalent but with length limit of 2GB (Usually DB has 4K limit); KSTRING in KRISTAL nomenclature), character array (KCHAR[]), integer (KINT), and oat (KFLOAT), of which index type can be any one among INDEX AS IS (whole section value as an indexing unit), INDEX NUMERIC (indexing section value as a oating point), INDEX BY CHAR (char level in- dexing), INDEX BY TOKEN (token level indexing), several more indexing types for Korean and Chinese characters, and a few other types related to biological sequences such as DNA and proteins. In the auxiliary strategies, the non-contiguous nature of postings lists, being separated in the main index and auxil- iary index, may result in deteriorated postings access, com- pared with contiguous posting lists.... ..."