### Table 2 Basic equations on processes (p; p1; p2; p3 2 P )

1995

"... In PAGE 3: ... De nition 1 P = S0 i Pi is the set of process expressions, where the Pi are constructed inductively as shown in Table 1. Expressions in P are (by de nition) equal if they are equal under the equations of Table2 . PP is the set of program process expressions PP = f( _ v1; : : : ; _ vk; u1; : : : ul) p j v1; : : : ; vk 2 V ; u1; : : : ; ul 2 A [ V [ X; p 2 Ppg where Pp is the set of all p 2 P that do not contain any a 2 A.... In PAGE 4: ...n creation of an Actor. This mail address represents the only reference to the new Actor. Actions are composed by the binary operators , + and jj, where has the highest and jj the lowest priority. As Table2 shows, all three operators are associative. + and jj are commutative.... In PAGE 4: ... The empty process quot; is the neutral element for sequential and parallel composition, but not for alternative composition. The equations in Table2 are su cient for this paper, although some equalities that intuitively hold in our model cannot be derived from them. An example of a simple bu er demonstrates the use of our formalism: Bu 7! () put( _ v1) (get( _ v2) v2:return(v1) + use( _ v3) v3(v1)) Bu () `Bu apos; is a process name; `put apos;, `get apos;, `return apos; and `use apos; are message names; v1, v2 and v3 are variables.... In PAGE 7: ... As in Table 4 through Table 7, we denote elements of T , T [ Z, fv:z; z j v 2 V ; z 2 Zg and fv:t; v:z; z j v 2 V ; t 2 Ti; z 2 Zg by t, s, c and d (sometimes quoted or indexed), respectively. The resemblance between process and type expressions can easily be seen by a com- parison of Table 1 with Table 4 and Table2 with Table 5. This resemblance is intended: It is easy to transform a type expression into a process expression by removing all type annotations of the form :t and substituting process names for type names.... In PAGE 8: ...Rules Description s1 = rename(s2) s1 s2 true t quot; s1 s2 v1:s1 v2:s2 (z1) (z2) z1 z2 primitive rules for t1 t0 1 t2 t0 2 d1 d0 1 : : : dn d0 n v:t1:m(d1; : : : ; dn) t2 v0:t0 1:m(d0 1; : : : ; d0 n) t0 2 message sending t2 t3 v:t1:m(d1; : : : ; dn) t2 t3 subtypes may specify additional message sendings t t0 s0 1 s1 : : : s0 n sn m(_ v1:s1; : : : ; _ vn:sn) t m(_ v1:s0 1; : : : ; _ vn:s0 n) t0 subtypes don apos;t specify additional message acceptings t1 t2 t3 t4 t5 t6 _ v:t1$t3 t5 _ v:t2$t4 t6 t3 t4 _ v:t1$t2 t3 t4 subtypes may specify additional Actor creations c c0 t t0 d1 d0 1 : : : dk d0 k s0 1 s1 : : : s0 l sl c(d1; : : : ; dk; _ v1:s1; : : : ; _ vl:sl) t c0(d0 1; : : : ; d0 k; _ v1:s0 1; : : : ; _ vl:s0 l) t0 subprocess application t1 t2 t3 t4 t1 + t3 t2 + t4 t1 t2 t3 t4 t1 jj t3 t2 jj t4 alternative and parallel type compositions t t0 s0 1 s1 : : : s0 k sk d1 d0 1 : : : dl d0 l (_ v1:s1; : : : ; _ vk:sk; d1; : : : ; dl) t (_ v0 1:s0 1; : : : ; _ v0 k:s0 k; d0 1; : : : ; d0 l) t0 named type speci cation Table 5 contains { compared with Table2 { an additional equation which states that quot; is the neutral element for +. The reason why this equation is not present in Table 2 is that a process p + quot; can either terminate immediately or execute p; this is obviously di erent from executing p as the only choice.... In PAGE 8: ...Rules Description s1 = rename(s2) s1 s2 true t quot; s1 s2 v1:s1 v2:s2 (z1) (z2) z1 z2 primitive rules for t1 t0 1 t2 t0 2 d1 d0 1 : : : dn d0 n v:t1:m(d1; : : : ; dn) t2 v0:t0 1:m(d0 1; : : : ; d0 n) t0 2 message sending t2 t3 v:t1:m(d1; : : : ; dn) t2 t3 subtypes may specify additional message sendings t t0 s0 1 s1 : : : s0 n sn m(_ v1:s1; : : : ; _ vn:sn) t m(_ v1:s0 1; : : : ; _ vn:s0 n) t0 subtypes don apos;t specify additional message acceptings t1 t2 t3 t4 t5 t6 _ v:t1$t3 t5 _ v:t2$t4 t6 t3 t4 _ v:t1$t2 t3 t4 subtypes may specify additional Actor creations c c0 t t0 d1 d0 1 : : : dk d0 k s0 1 s1 : : : s0 l sl c(d1; : : : ; dk; _ v1:s1; : : : ; _ vl:sl) t c0(d0 1; : : : ; d0 k; _ v1:s0 1; : : : ; _ vl:s0 l) t0 subprocess application t1 t2 t3 t4 t1 + t3 t2 + t4 t1 t2 t3 t4 t1 jj t3 t2 jj t4 alternative and parallel type compositions t t0 s0 1 s1 : : : s0 k sk d1 d0 1 : : : dl d0 l (_ v1:s1; : : : ; _ vk:sk; d1; : : : ; dl) t (_ v0 1:s0 1; : : : ; _ v0 k:s0 k; d0 1; : : : ; d0 l) t0 named type speci cation Table 5 contains { compared with Table 2 { an additional equation which states that quot; is the neutral element for +. The reason why this equation is not present in Table2 is that a process p + quot; can either terminate immediately or execute p; this is obviously di erent from executing p as the only choice. Since a type is only a partial speci cation there can always be alternatives not explicitly expressed in the type; t means that a process corresponding to t is able to execute a corresponding alternative.... ..."

Cited by 11

### Table 1: Clebsch-Gordan coe cients In Table 1 we list the ve measured process amplitudes in terms of the two in- dependent isospin amplitudes A32( N) and A10( N). From the measured process amplitude moduli a unique value of A10 and A32 can be found up to an overall sign. 2

### Table 1: The inverted list for the example triple base. a1 c1 p1 p2 p3

"... In PAGE 3: ... The keywords are ordered in alphabetic order, and the instances are ordered by their identifiers. Table1 shows the inverted list for our example... In PAGE 4: ... Another option is to specify the attribute name in the cells of the inverted list. For example, the cell ( tian , p1) in Table1 could be modified to record name:1 . However, this method would considerably complicate query answering.... In PAGE 11: ...08GB. As shown in Table1 1, our indexing technique scales well: on average it took 123.8 milliseconds to look up the index for predicate queries, only 4.... ..."

### Table 1 Index terms list

2005

"... In PAGE 13: ... The results are shown in Table 11. In Table1 0, the results indicate that the proposed algorithm outperforms the other two algorithms in all situations. Among these three algorithms, ANN outper- forms SW, and SW outperforms GM.... ..."

### Table 1: Steps in the Pipelined Striped Partitioning Algorithm. step(l) P[0] P[1] P[2] P[3] P[4] P[5] P[6]

1998

"... In PAGE 6: ...2). The processor index (i) in Relation (2) is always greater or equal to 1 (see Table1 ). In this case, from Relation (2), it follows: i 1 =) l ? 3 k 1 =) 3 k l ? 1 =) k (l ? 1) div 3 (4) By carefully analyzing Table 1, one can observe that the above relations for communications apply for the elimination as well, but for l ? 2 instead of l.... In PAGE 6: ...ariant of the algorithm (Subsection 3.2). The processor index (i) in Relation (2) is always greater or equal to 1 (see Table 1). In this case, from Relation (2), it follows: i 1 =) l ? 3 k 1 =) 3 k l ? 1 =) k (l ? 1) div 3 (4) By carefully analyzing Table1 , one can observe that the above relations for communications apply for the elimination as well, but for l ? 2 instead of l. Coordination Based on the above considerations, it is possible to present the 2sp coordination of this algorithm (Figures 4 and 5).... In PAGE 8: ... (3) Otherwise, the processor waits to receive data to be used for one of the above actions. Table1 shows the algorithm apos;s steps. Let l be the current step.... In PAGE 8: ... To solve these problems is not easy. We have chosen to present the activ- ities of 7 processors in Table1 ; a smaller number is not enough for a clear presentation. The solutions of the above problems are presented in detail by... ..."

Cited by 6

### Table 1: Different applications of P2P

2004

"... In PAGE 4: ... For example, a user can send the SIP INVITE message to many potentially nomadic users to invite them in a conference by creating one-to-many binding. Table1 summarizes the similarity and differences among these types. In Table 1: Different applications of P2P... ..."

Cited by 15

### 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.... ..."

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### Table 1: Bolivian Terms of Trade Index ..

"... In PAGE 34: ...STATISTICAL APPENDIX Table1 : Bolivian Terms of Trade Index, 1980-92 (1987=100) Year Export price index hbport price index Ternn oftrade index 1980 181.0 91.... ..."

### Table 4: Measures of index term complexity

"... In PAGE 5: ...3%. Why did the subjects demonstrate such a strong preference for the human terms? Table4 illustrates some important differences between the human terms and the automatically identified terms. The terms selected on are longer, as measured in number of words, and more complex, as measured by number of prepositions per index terms and by number of con- tent-bearing words.... ..."

### Table 1. Various P2P Perspectives Illustrating What is and What is Not New in P2P.

2002

"... In PAGE 4: ...erent vertical markets. Section 2.3 provides a more thorough evaluation of P2P markets and Section 5 de- scribes the horizontal technologies in more detail. The following three lists, which are summarized in Table1 , are an attempt to define the nature of P2P, what is and is not new in P2P. P2P is concerned with: The historical evolution of computing in general and the Internet in particular; computing at the edge of the Internet.... In PAGE 46: ... In this section, we evaluate the implications that P2P has for users, develop- ers, and IT departments. In Table1 0, we compare P2P with its alternatives. P2P has the following implications for the users of P2P systems and applications: pervasive- ness, complexity of use, state of the art, and trust and rep- utation.... ..."

Cited by 110