### Table I. Structures for 160 Geometry Theorems

2000

Cited by 6

### Table 6, where each rule is proven as a theorem from the structural operational semantics.

2003

"... In PAGE 12: ... Table6 : Programming Language Axiomatic Semantics The most interesting of these proofs were those of the Rule of Adaptation... ..."

Cited by 2

### Table 1: VCS for strong access structures on at most four participants. The next theorem proves that for the strong access structure 12, a VCS with m = 4 does not exist. Theorem 9.2 Let (?Qual; ?Forb) be the strong access structure on participant set P = f1; 2; 3; 4g having basis ?0 = f123; 14; 34g. Then there is no (?Qual; ?Forb; 4)-VCS. Proof. Suppose by contradiction that there exists a (?Qual; ?Forb; 4)-VCS. From Lemma 3.4 and Theorem 5.13 any matrix M 2 C1 and any matrix M0 2 C0 are equal, up to a column permutation, respectively, to M =

### Table 1 : O-Minimal Structures

2000

"... In PAGE 21: ... To illustrate the continuous behavior that can be captured, we apply Theorem 5.4 for each o-minimal structure of Table1... ..."

Cited by 121

### Table 4: Axioms for interworking sequencing The structured operational semantics of the interworking sequencing and of the auxiliary opera- tors is given in Table 5. The term deduction system T(IWD quot;(A; EID; E)) consists of the deduction rules of T(BPA ; quot;(A)) and the deduction rules of Table 5. Next, we will formulate some interesting theorems concerning this process algebra. These theorems relate the process algebra IWD quot;(A; EID; E) to the process algebra BPA ; quot;(A) and to the structured operational semantics as given by the term deduction systems. Theorem 2.2.1 (Congruence) Bisimulation equivalence is a congruence for the function sym- bols in the signature of IWD quot;(A; EID; E). Proof It is straightforward to verify that the deduction rules of the term deduction system which 5

1995

"... In PAGE 5: ... L iw y = . Consequently, we also de ne x R iw quot; = . If we apply this in the de nition of the sequencing operator as given in [MvWW93] we get quot; iw quot; = quot; L iw quot; + quot; R iw quot; = + = . This is not what we want and therefore we need the additional operator p as given in Table4 . This operator has also been used by Baeten and Weijland [BW90] in axiomatizing the free merge in... ..."

Cited by 1

### Table 1: Classi cation and characterization of structurally stable phase portraits of the second order replication mutation equation for three species in the limit of small mutation rates. The diagrams are obtained by application of the RPM theorem to the 35 robust phase portraits of the error free systems [40].

### Table 1 : O-Minimal Structures Structure Sample De nable Sets Sample De nable Trajectories (R; lt;; +; ?; 0; 1) Polyhedral sets Linear trajectories

2000

"... In PAGE 21: ... To illustrate the continuous behavior that can be captured, we apply Theorem 5.4 for each o-minimal structure of Table1... ..."

Cited by 121

### Table 1: VCS for strong access structures on at most four participants. Theorem 9.1 Let (?Qual; ?Forb) be a strong access structure on participant set P = f1; 2; 3; 4g such that f1; 2; 4g; f1; 3; 4g 2 ?0. If there exists a (?Qual; ?Forb; 4)-VCS, then there is no X 2 ?0 such that f2; 3g X. Proof. From Lemma 3.4 any (?Qual; ?Forb; 4)-VCS contains (induced) a VCS for the strong access structures ?0 and ?00 having basis ?0 0 = ff1; 2; 4gg and ?00 0 = ff1; 3; 4gg, respectively. Therefore, from Theorem 5.13 any matrix M 2 C1 and any matrix M0 2 C0 are equal, up to a column permutation, respectively, to

1996

Cited by 27