### Table 2: A List of Laplace and Inverse Laplace Transforms Related to Fractional Order Calculus (Continued)

2001

### Table 2 Median Rank of the Output-order in WAS and LSA of Response Words to Given Cues for the 10 Strongest Responses in the Free Association Norms.

"... In PAGE 22: ...20 words in the corpus, Table2 gives for each of the first ten ranked responses in free association (the columns) the median rank in WAS. The median was used to avoid excessive skewing of the average by a few high ranks.... In PAGE 22: ... The median was used to avoid excessive skewing of the average by a few high ranks. An additional variable that was tabulated in Table2 is k, the number of dimensions of WAS. -------------------------------------------------------------------- Insert Table 2 about here -------------------------------------------------------------------- There are three trends to be discerned in Table 2.... In PAGE 22: ... An additional variable that was tabulated in Table 2 is k, the number of dimensions of WAS. -------------------------------------------------------------------- Insert Table2 about here -------------------------------------------------------------------- There are three trends to be discerned in Table 2. First, it can be observed that for 400 dimensions, the strongest responses to the cues in free association norms are predominantly the closest neighbors to the cues in WAS.... In PAGE 22: ... An additional variable that was tabulated in Table 2 is k, the number of dimensions of WAS. -------------------------------------------------------------------- Insert Table 2 about here -------------------------------------------------------------------- There are three trends to be discerned in Table2 . First, it can be observed that for 400 dimensions, the strongest responses to the cues in free association norms are predominantly the closest neighbors to the cues in WAS.... In PAGE 22: ... We also analyzed the correspondence between the similarities in the LSA space (Landauer amp; Dumais, 1997) based on the tasa corpus with the order of output in free association. As can be observed in Table2 , the rank of the response strength of the free association norms clearly has an effect on the ordering of similarities in LSA: strong associates are closer neighbors ... ..."

### Table 2. The Structural Rules for the Operational Semantics.

"... In PAGE 7: ... Clock Distribution Equations. The transition relation is given through a set of inference rules, listed in Table2 , defined in a structural inductive manner (apart from the rule for recursion). It is worthwhile observing that these rules are parametric w.... In PAGE 8: ... This new formulation is given because it will be helpful i) in order to prove that performance bisimulation is a congruence for all the operators of the language; ii) in the definition of the axiomatization of the semantic congruences we are going to investi- gate, and also iii) in comparing these performance-based semantics with other non interleaving ones. The rules of Table2 define essentially a tyft system [14] for which strong bisimulation equiva- lence (hence, in this case, also performance equivalence) is a congruence. The relevant exceptions are rules Act and Rec, which do not fit in the format because they do not only exploit the top level operator name.... In PAGE 8: ... Rules Act and Rec are replaced by the axiom and inference rules reported in Table 3, which presents an additional rule for the clock prefixing operator. The whole set of operational rules includes also rules Alt01, Alt02, Par0 1 and Par0 2 which are as their corresponding rules in Table2 where the transition relation ?! is substituted for ?!. UBLCS-95-1... In PAGE 10: ...Behavioural Semantics This observation should definitely clarify that the operational semantics on extended states, defined by ?!, is exactly the same we have proposed for states in Table2 , as all the states in the same congruence class have the same semantics. Now, a result by [14] ensures that strong bisimulation is a congruence on the set of extended states.... In PAGE 10: ... Now, a result by [14] ensures that strong bisimulation is a congruence on the set of extended states. In order to prove that this is a congruence also on the subalgebra of states, it is enough to observe that there is no transition from a state to an extended state in the transition system defined by the rules in Table2 , i.... ..."

### Table 2: Eigenvalues of Hamiltonian pencils

"... In PAGE 36: ... Nevertheless we will call our form Hamilto- nian Kronecker canonical form in order to avoid confusion when generalizing these results at a later stage to singular Hamiltonian pencils. As shown in Table2 for a regular Hamiltonian pencil Mh ? Lh we have similar sym- metries in the nite spectrum. So most of the analysis in this section has to be devoted to the part of the canonical form associated with in nite eigenvalues.... ..."

### Table 3. Translation functions.

"... In PAGE 13: ...by: S[msc M; lt;i gt;1; ; lt;i gt;n; endmsc]msc = ;(S[ lt;i gt;1]inst jj jj S[ lt;i gt;n]inst) S[instance i; lt;e gt;1; ; lt;e gt;n; endinstance]inst = [ lt;e gt;1]i event; ; [ lt;e gt;n]i event The function S[:]inst translates a single instance i into a process term which consists of the strong sequential composition of the events performed by i. As before, the events are translated by the function [:]i event given in Table3 . The function S[:]msc translates an MSC into a parallel composition (free merge) of the terms resulting from the translation of the instances.... In PAGE 16: ... The idea is that in a guarded process environ- ment, the rst transition of (X) does not depend on X itself in any way. In order for the MSC semantics de ned in Table3 to give rise to a guarded process environment, it is su cient (but not necessary) for any MSC within the document to contain at least one action on every instance. More generally, there should be no empty loop within the MSC document; that is, it should be impossible to glue together single MSCs in such a way that the initial and nal conditions of the combined chart coincide, while at the same time there is an instance without any action.... In PAGE 16: ... Now we consider the following alternative translation function, which features a global message pool rather than local ones for each MSC. The function is de ned by replacing [:]doc and [:]msc of Table3 by the following: G[mscdocument D; lt;m gt;1; ; lt;m gt;n; endmscdocument]doc = f? jjPool G[ lt;m gt;k]msc j 1 k ng G[msc M; lt;i gt;1; ; lt;i gt;n; endmsc]msc = ([[ lt;i gt;1]inst jj; jj; [ lt;i gt;n]inst) n(M) interpreted in the process environment G D : Cond ! LMSC (where Cond = Names) de ned by G D : c 7! X init(M)=c G[M] : As a consequence of Propositions 4 and 5, we can prove that [:] and G[:] are actually equivalent, in the following sense:... ..."

### Table 2. The Structural Rules for the Operational Semantics.

1997

"... In PAGE 6: ...3 The set of labels for the transition system is = Act N+. The transition relation is given through a set of inference rules, listed in Table2 , defined in a structural inductive manner.... In PAGE 7: ... This new formulation is given because it will be helpful i) in order to prove that performance bisimulation is a congruence for all the operators of the language; ii) in the definition of the axiomatization of the semantic congruences we are going to investigate, and also iii) in comparing these performance-based semantics with other non interleaving ones. The rules of Table2 define essentially an infinitary (i.e.... In PAGE 7: ... Rules Act and Rec are replaced by the axiom and inference rules reported in Table 3, which presents an additional rule for the clock prefixing operator. The whole set of operational rules includes also rules Alt0 1, Alt02, Par0 1 and Par0 2 which are as their corresponding rules in Table2 where the transition relation ?! is substituted for ?!. Act0 a:E lt;a;f(a) gt; ?! f(a) ) E Rec0 E[rec x: E=x] lt;a;n gt;?! t rec x: E lt;a;n gt;?! t Clock t lt;a;k gt; ?! t0 n ) t lt;a;n+k gt; ?! n ) t0 Table 3.... In PAGE 8: ...roposition 4.2 Let t1, t2 be extended states. Then, t1 lt;a;k gt; ?! t2 if and only if t1 lt;a;k gt; ?! t2. This observation should definitely clarify that the operational semantics on extended states, defined by ?!, is exactly the same we have proposed for states in Table2 , as all the states in the same congruence class have the same semantics. Now, a result by [15] ensures that strong bisimulation is a congruence on the set of extended states.... In PAGE 8: ... Now, a result by [15] ensures that strong bisimulation is a congruence on the set of extended states. In order to prove that this is a congruence also on the subalgebra of states, it is enough to observe that there is no transition from a state to an extended state in the transition system defined by the rules in Table2 , i.e.... ..."

Cited by 9

### TABLE I Curve-fitting analysis of human gelatinase B Results of simultaneous EXAFS curve-fitting analysis of pro (a) and activated human gelatinase B (b). The uncertainties are given. The symbols F and V stand for fixed and varied and indicate how the respective parameter was treated in the fit model. R is distance of atoms from the zinc atom (in Angstroms). s2 is the Debye-Waller factor.

### Table 2: Operational semantics for basic combinators.

1998

Cited by 114

### Table 2: Operational semantics for basic combinators.

1998

Cited by 114