### Table 1. The results of grouping the motion categories and varying the dimension of the projected space. In the second column, the number of unique integers indicates the number of motion categories, and the position of the integer indicates which motions belong to that category.

2005

Cited by 1

### Tableaux (SSYT), T, of shape by replacing each dot by a positive integer so that rows weakly increase and columns strictly increase. For example, if = (4; 2; 1) then its shape and a possible tableau are

### TablePosition = IntegerValue(Accumulator); /* nd nearest free slot to TablePosition */ Success = ReserveSlot(TablePosition,MaxBound); Accumulator = Accumulator + Unit; /* increment pointer */ od

### Table 1: Rules for rewriting symbolic expressions containing low and up functions. x and y are symbolic integer- valued expressions. x? and x+ respectively refer to the set of negative and positive integer values (neither contains 0) of x. x+ 0 is de ned by x+ including also 0. c is an integer constant. Continuing Example 1.1, we can simplify (5) as follows: low(J1 (J1 ? 1) 2

1998

"... In PAGE 5: ...f1g; UBJ3 = fJ1g; LBJ4 = f1g; UBJ4 = fJ2 ? 1g; LBN = fJ1g; UBN = f1g; B = LBN [ UBN [ S 1 i 4?LBJi [ UBJi Initially all lower and upper bounds in Q are set to ?1 and 1, respectively. The algorithm traverses E and replaces all -expressions of E using bound expressions in B and Q, and rewrite- rules of Table1 until E is a constant, ?1, or 1. During a single iteration of the REPEAT loop, the bounds in Q may become tighter as compared to the previous loop iteration.... In PAGE 5: ... The set of constraints I for this problem is given by (1). In order to prove the absence of a true dependence we have to show that low(J1 (J1?1) 2 + J2 ? J3 (J3?1) 2 ? J4) 0: low(J1 (J1 ? 1) 2 + J2 ? J3 (J3 ? 1) 2 ? J4) ! low(J1 (J1 ? 1) 2 ) + low(J2) ? up(J3 (J3 ? 1) 2 ) ? up(J4) (2) which is based on rewrite rules (7) and (8) of Table1 . Note that Table 1 displays primarily rewrite rules for low functions.... ..."

Cited by 27

### Table 1. Rules for rewriting symbolic expressions containing low and up functions. x and y are symbolic integer-valued expressions. x? and x+ respectively refer to the set of negative and positive integer values (neither contains 0) of x. x+ 0 is de ned by x+ including also 0. c is an integer constant.

"... In PAGE 6: ... A Demand driven algorithm to compute the lower and/or upper bound of a symbolic expression de ned in V [ P. The algorithm traverses E and replaces all -expressions of E using bound ex- pressions in B and Q, and rewrite-rules of Table1 until E is a constant, ?1, or 1. During a single iteration of the REPEAT loop, the bounds in Q may become tighter as compared to the previous loop iteration.... In PAGE 7: ...2. Rewrite -Expressions Rewriting (E) { where E is a symbolic expression { describes the process of apply- ing a rewrite rule (see Table1 ) to (E). For instance, a -expression low(E1 + E2) is rewritten as low(E1) + low(E2) according to rule 7 of Table 1: low(E1 + E2) !... In PAGE 7: ....2. Rewrite -Expressions Rewriting (E) { where E is a symbolic expression { describes the process of apply- ing a rewrite rule (see Table 1) to (E). For instance, a -expression low(E1 + E2) is rewritten as low(E1) + low(E2) according to rule 7 of Table1 : low(E1 + E2) !... In PAGE 8: ... The set of constraints I for this problem is given by (1). In order to prove the absence of a true dependence we have to show that low(J1 (J1?1) 2 + J2 ? J3 (J3?1) 2 ? J4) 0: low(J1 (J1 ? 1) 2 + J2 ? J3 (J3 ? 1) 2 ? J4) ! low(J1 (J1 ? 1) 2 ) + low(J2) ? up(J3 (J3 ? 1) 2 ) ? up(J4) (2) which is based on rewrite rules (7) and (8) of Table1 . Note that Table 1 displays primarily rewrite rules for low functions.... In PAGE 22: ... Therefore, our implementation can prove in 5 steps of a single iteration of EXPR BOUND that N N J2 under the constraints of I. A step corresponds to the application of a single rewrite rule of Table1 to a symbolic expression. 7.... ..."

### Table 4. Fields in FLORA, FAUNA and LANDSCAPES files of LMN database, showing length (max. no. of positions) and type of data (I = integer, A = alphanumeric, C = alphanumeric or integer).

"... In PAGE 9: ...ourth (and last) . . . etc. 6 2 3 3 2 3 2 1 3 2 3 3 3 3 I A I I I I I I I I I I I I Table4 lists the characteristics stored in the files FLORA (= species groups), FAUNA and LAND- SCAPES. With the exception of LANDSCAPES (see above) these components contain either origi- nal data or generalized data, i.... ..."

### Table 1. NAF, FAN, Booth encoding representations of some integers

"... In PAGE 3: ... Note that FAN can have successive nonzero bits unlike NAF. Table1 shows NAF, FAN, Booth, and non-signed binary representations of some positive integers.... ..."

### Table 1. NAF, FAN, Booth encoding representations of some integers

"... In PAGE 3: ... Note that FAN can have successive nonzero bits unlike NAF. Table1 shows NAF, FAN, Booth, and non-signed binary representations of some positive integers.... ..."

### Table I. A Subset of the Action Signature of DCNP. Notation: Agent, Agent2, C, E range over {c1,e1,...,en} Perf ranges over {cfp,bid,award,reject,inform,pay} Content, Content2 range over a finite set of task descriptions Round ranges over Z+, the set of positive integers

2007

Cited by 6

### Table 4: The values of aj(s). s increases from 1 to 16 horizontally and j increases from 1 to 7 vertically. 1. For any positive integer satisfying s = 2blog2(s)c, aj(s) can be represented as aj(s) = ( s; if j log2(s) + 1

1997

Cited by 1