### Table 1 Sizes of non-regular orbits of subgroups

"... In PAGE 8: ...izes of multiples of (pm + 1)/2. Hence all orbits except one are regular. We summarize the results of the previous lemmas in the following theorem. Theorem 17 The sizes of non-regular orbits for any subgroup H of PSL(2, q) are as given in Table1 . (Subgroups with no non-regular orbits do not appear... ..."

### Table 1 Sizes of non-regular orbits of subgroups

"... In PAGE 8: ...izes of multiples of (pm + 1)=2. Hence all orbits except one are regular. We summarize the results of the previous lemmas in the following theorem. Theorem 17 The sizes of non-regular orbits for any subgroup H of PSL(2; q) are as given in Table1 . (Subgroups with no non-regular orbits do not appear... ..."

### Table 1: The Distance-Regular Graphs with an Eigenvalue of Multiplicity Four

"... In PAGE 13: ... Lemma 7.1 For the array listed in Table1 , it is impossible to realise this array by a distance-regular graph. Proof: There is only one array; such a graph would have 4 as an eigenvalue of multiplicity three and thus would have a representation in R3.... ..."

### Table 1. Examples of regular derivations: Gen - gender motion, ARel - relational adjectives, APos - possessive adjectives, Dim - diminutives, Augm - augmentatives

"... In PAGE 3: ...Table 1. Examples of regular derivations: Gen - gender motion, ARel - relational adjectives, APos - possessive adjectives, Dim - diminutives, Augm - augmentatives Consider the examples given in Table1 , listed according to the only complete explanatory dictionary of Serbian (RMSMH, 1967). Each column in the Table represents a noun denoting a profession that belongs to the inflective class N2.... In PAGE 3: ... Lemmas in table cells that are not represented in this dictionary are given in italic, while those not represented in the corpus are underlined. The unsystematic processing of lemmas in traditional lexicographic descriptions is illustrated by the examples from the Table1 . The basic lemmas, profesor, lektor, rektor, pekar can be expanded in a similar way by regular derivation, as seen in Table 1, but only some derived lemmas are represented in the explanatory dictionary, not necessarily those occurring in the corpus of contemporary Serbian2.... In PAGE 3: ... The unsystematic processing of lemmas in traditional lexicographic descriptions is illustrated by the examples from the Table 1. The basic lemmas, profesor, lektor, rektor, pekar can be expanded in a similar way by regular derivation, as seen in Table1 , but only some derived lemmas are represented in the explanatory dictionary, not necessarily those occurring in the corpus of contemporary Serbian2. For instance, lemma pekarov (Engl.... In PAGE 3: ... In general, regular derivations are the feature of inflective class rather than lemma itself, and thus they enhance it in a way that enables their classification in a similar manner as inflectional classes themselves. In other words, if the noun belongs to the class N2+Hum+Act, lemmas given in Table1 can be derived for it, which independently of the lemma itself always belong to the same, pre-existing class. The next important feature is that some suffixes that are used in regular derivation can change the meaning of the basic lemma.... ..."

### Table 2: The Distance-Regular Graphs with an Eigenvalue of Multiplicity Five

"... In PAGE 13: ... This process involves two steps. First, the acceptable arrays which are not realisable are listed in a table (Ta- ble 1, Table2 , and Table 3). For each of these arrays, we exhibit a feasibility condition from Section 6 which is violated.... In PAGE 15: ... Lemma 7.3 For each array listed in Table2 , it is impossible to realise this array by a distance-regular graph. Proof: Array 2-1: This array should correspond to a graph on twenty- eight vertices having diameter two.... ..."

### Table 3: Solutions of type 4n, n even We now describe a di erent type of construction for G-GDDs. Let G be a graph which is regular of degree d, i.e. so that every vertex is in exactly d edges of G. A 1-factor of G is a spanning subgraph of G which is regular of degree 1. A 1-factorization of G is a partition F1; : : :; Fd of the edges of G into 1- factors. By the Stern-Lenz lemma (see [5]), whenever gu is even, G(gu) has a 1-factorization. We use this to establish the following: Lemma 4.1 Let g 1 and u 2 be integers. If gu is even, then there is a fG21g-GDD of type (2g)u(g(u ? 1))1.

### Table 1: Non-regular bilateral generalized gamma density

2007

"... In PAGE 11: ... Lemma 4 implies that Hellinger rates in these cases do not depend on the value of . Table1 summarizes the results from an analysis of this example; detailed calculations are provided in Appendix B.2.... ..."

### Table 3: Table 6: The Distance-Regular Graphs with an Eigenvalue of Mul- tiplicity Six

"... In PAGE 13: ... This process involves two steps. First, the acceptable arrays which are not realisable are listed in a table (Ta- ble 1, Table 2, and Table3 ). For each of these arrays, we exhibit a feasibility condition from Section 6 which is violated.... In PAGE 18: ... Lemma 7.5 For each array listed in Table3 , it is impossible to realise this array by a distance-regular graph. Proof: The absolute bound for the number of vertices in a primitive distance- regular graph of diameter d having an eigenvalue of multiplicity seven is obtained from Inequality (4): n 6 + d 6 ! + 5 + d 6 !:... ..."

### Table 2. Elimination lemmas

2004

"... In PAGE 3: ... Note that the de- pendency graph of the constructions must be cycle free. To eliminate a point from the goal we need to apply one of the elimination lem- mas shown on Table2 on page 5. This table can be read as follows: To eliminate a point Y , choose the line corresponding to the way Y has been constructed, and apply the formula given in the column corresponding to the geometric quantity in which Y is used.... In PAGE 4: ... We rst translate the goal (A0B0 k AB) into its equivalent using the signed area: SA0B0A = SA0B0B Then we eliminate compound points from the goal starting by the last point in the order of their construction. The geometric quantities containing an oc- currence of B0 are SA0B0B and SA0B0A, B0 has been constructed using the rst construction on Table2 with = 1 2: SA0B0A = SAA0B0 = 1 2SAA0A + 1 2SAA0C = 1 2SAA0C and SA0B0B = SBA0B0 = 1 2SBA0A + 1 2SBA0C The new goal is SAA0C = SBA0A + SBA0C Now we eliminate A0 using: SCAA0 = 1 2SCAB + 1 2SCAC = 1 2SCAB SABA0 = 1 2SABB + 1 2SABC = 1... In PAGE 11: ... This tactic (called eliminate_all) rst searches the con- text for a point which is not used to build another point (a leaf in the dependency graph). Then for each occurrence of the point in the goal, it applies the right lemma from Table2 by nding in the context how the point has been constructed and which geometric quantity it appears in. Finally it removes the hypotheses stating how the point has been constructed from the context.... In PAGE 12: ...this classical reasoning step. As noted before, the elimination lemmas given in Table2 on page 5, do eliminate an occurrence of a point Y only if Y appears only one time in the geometric quantity (A,B,C and D must be di erent from Y ). If Y appears twice in S, this is not a problem because then the geometric quantity is zero, and so already eliminated by the simpli cation phase.... ..."

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