### Table 2: Mapping of Boolean Algebra onto Relational Algebra

1993

"... In PAGE 19: ... quot; The empty set ; serves as the element \0 quot; in the relational algebra, but \1 quot; depends on the particular schema. Table2 shows the translation for each property of the Boolean algebra into the corresponding property of the relational algebra. The symbol \1 quot; denotes the natural join, and R denotes the completion of R, the cartesian product of all of R apos;s attribute domains.... ..."

Cited by 24

### Table 7. Normalised trial completion time for each target position in the two display modes. Times have been normalised by divid- ing by the overall mean trial completion time for the stereo condi- tion.

1997

"... In PAGE 5: ... The rever- sal for trial completion time from being slowest in the monoscopic condition to being comparable to the X axis in the stereoscopic condition is a bit surprising in light of work by Zhai [18], how- ever, his studies did not consider the direction along each axis separately. Table7 shows the normalised performance for each target position in the stereoscopic and monoscopic conditions.... ..."

Cited by 19

### Table 7. Normalised trial completion time for each target position in the two display modes. Times have been normalised by divid- ing by the overall mean trial completion time for the stereo condi- tion.

"... In PAGE 5: ... The rever- sal for trial completion time from being slowest in the monoscopic condition to being comparable to the X axis in the stereoscopic condition is a bit surprising in light of work by Zhai [18], how- ever, his studies did not consider the direction along each axis separately. Table7 shows the normalised performance for each target position in the stereoscopic and monoscopic conditions.... ..."

### Table 1: Informal relationships to Notions in Process Algebra

1998

"... In PAGE 30: ... This enables us to handle open expressions, but the proof technique fails to be complete (for example, it cannot prove that any pair of weak head normal forms are equivalent). We summarise some informal correspondences between the notions in process calculus and the relations defined in this article in Table1 . Our attempts to complete this picture find a more exact correspondence between the proof techniques relating to bisimulation up to improvement and contexthave so far been unsuccessful.... ..."

Cited by 10

### Table 1: Informal relationships to Notions in Process Algebra

"... In PAGE 30: ... This enables us to handle open expressions, but the proof technique fails to be complete (for example, it cannot prove that any pair of weak head normal forms are equivalent). We summarise some informal correspondences between the notions in process calculus and the relations defined in this article in Table1 . Our attempts to complete this picture find a more exact correspondence between the proof techniques relating to bisimulation up to improvement and contexthave so far been unsuccessful.... ..."

### Table 8. Evaluation of the proposed complete temporal relational algebra based on the criteria of McKenzie and Snodgrass (1991b)

1996

"... In PAGE 12: ...6 It is also compared to five other existing algebras: (1) the time relational model by Ben-Zvi (1982), (2) the homogeneous model by Gadia (1988), (3) the temporal relational model by Navathe and Ahmed (1989), (4) the historical relational algebra by Sarda (1990) and (5) the historical relational al- gebra by McKenzie and Snodgrass (1991a). This evaluation and comparison is summarized in Table8 . From this table, it can be seen that the proposed algebra satisfies the maximum number of criteria.... ..."

Cited by 6

### Table 1. A* versus relational Algebra.

"... In PAGE 17: ...onsequently the elaboration of any language based on A* (i.e.: ERA* Language) depends on the object/relational queries space to be expressed. From a purely relational point of view, A* is complete in the sense where it offers the possibility of expressing any relational query (see comparison in the Table1 .).... In PAGE 17: ... Compared to the Codd apos;s relational algebra, A*-algebra contains five basic operators and two derived operators. We give in Table1 the algorithmic structure to translate A* into relational algebra. The set of basic operators of A* contains operators based on the first order logic (e.... In PAGE 17: ... The derived operators Tclose* and Compose* are based on the composition and transitive closure operations, defined by Codd. We notice that the A* operators are a more simply way to express queries that necessitate many Codd relational operators (see Table1 ). Extensions operators in A*.... ..."

### Table 2. Frequency of usability errors by subject, and probable causes. The raw data has not been normalised for the number of sessions completed by the subjects.

2003

Cited by 8

### Table 4 Lie algebras of contact transformations in C 2

"... In PAGE 3: ... The groups of point transformations naturally fall into three classes | the primitive groups, for which there is no invariant foliation, the imprimitive, transitive groups, and, nally, the intransitive groups. In addition, there are just three nite-dimensional groups of contact transforma- tions not contact-equivalent to any point transformation group; in Table4 , I have listed the characteristics Q(x; u; ux) of the in nitesimal generators, the rst order generators themselves being recovered by the standard formula v(1) = ? @Q @p @ @x + Q ? p @Q @p @ @u + @Q @x + p @Q @u @ @p : (3) The complete classi cation allows us to determine the stabilization order for every possible transformation group in the plane, and, in addition, the complete system of di erential invariants. One remarkable consequence is that, in the scalar case, Example 4 provides the only examples of transformation groups that pseudo-stabilize.... ..."

### Table 1: Examples of important features of the algebra. Description Format Examples

"... In PAGE 4: ... This compaction mechanism can also be used when some portion of the entire state is symmetric, since superposition is associative. The definitions for the two types of symmetric entanglement are presented in Table1 . Formally, we de- fine these states to be the result of a function a7 a1a0 , which is derived from the EPR function, but we use the a1 operator as semantic sugar to des- ignate symmetric entanglement.... In PAGE 4: ... The algebra is also complete and expressive, as it is capable of de- scribing any legal quantum state or operation. The a4 , a19a21a20a23a22a25a24 , and a21 gates have been declared in Table1 and form a universal set, so the algebra can express any quantum state or algorithm [8]. We need not restrict ourselves to the primitive gates, however.... ..."