### Table 1: (Un)decidability of the equational theories of classes of cylindric algebras.

1999

"... In PAGE 6: ... In fact, the expansion Crs+ 3 of Crs3 with a single operation k1 1 has an undecidable equational theory. We summarized these results in Table1 . We note that, similarly to the relation algebra case, the unde- cidable equational theories are in fact r.... ..."

Cited by 4

### Table 1 Quantitative information on the proofs. Book Lines Definitions Theorems Hints

2002

"... In PAGE 22: ... The proof of the critical pair theorem is in the book critical-pairs and decid- ability of the equational theory of a complete TRS is proved in kb-decidability. Table1 gives some quantitative information on the proof. The first column contains the name of the book.... ..."

Cited by 6

### Table 2. Exampleof matchingrecords detectedby our equational theory rule base.

"... In PAGE 8: ... Otherwise, in the third stage, more precise \edit-distance quot; functions are used over some elds as a last attempt for merging a pair of records. Table2 demonstrates a number of actual records the rule-program correctly deems equivalent. It is important to note that the essence of the approach proposed here permits a wide range of equational theories on various data types.... In PAGE 8: ... We could equally as well demonstrate the concepts using alternative databases of di erent typed objects and correspondingly di erent rule sets. Table2 displays records with such errors that may commonly be found in mailing lists, for example. (Indeed, poor implementations of the merge/purge task by commercial organizations typically lead to several pieces of the same mail being mailed at obviously greater expense to the same household, as nearly everyone has experienced.... ..."

### Table 4{2: Rules of inference in the equational theory

"... In PAGE 61: ...2.1 Constructing subtableaux A tableau consists of a number of eliminating subtableaux constructed using the rules REC, SUM, and PREFIX of Table4 {1. Each of these rules is forwards sound in the sense that if the antecedent is true (the equation relates bisimilar processes) then one can nd a set of true consequents.... In PAGE 62: ... If instead jY j lt; jXj similar remarks would apply except that the residual then has the form = . The next step is to apply one of the SUB rules of Table4 {1 to each leaf other than residuals of an eliminating subtableau. If the residual is = we apply SUBL, and if it is = we apply SUBR.... In PAGE 70: ... Deciding bisimilarity for normed BPA Thus, the special case ; j= E = F states that E F (relative to the system of process equations ). The proof system is given in Table4 {2. Equivalence and congruence rules are R1-5.... In PAGE 77: ... Thus we see that REWRITE will only be used between updatings of R, as desired. The rules in Table4 {3 are sound w.... In PAGE 78: ...4.2 An auxiliary tableau for R `T ? is a maximal sequence of se- quents R0 `T ?0; R1 `T ?1; : : : ; Rn?1 `T ?n?1; Rn `T ?n where R `T ? = R0 `T ?0 and for all i 0 Ri+1 `T ?i+1 is the consequent of using a rule in Table4 {3 with Ri `T ?i as premise. An auxiliary tableau is nite if for some n all equations in ?n are identities (i.... In PAGE 80: ...Chapter 4. Deciding bisimilarity for normed BPA Rules within subtableaux REC X = Y E = F where X def= E and Y def= F PREFIX a = a = SUM (Pm i=1 ai i) = (Pn j=1 bj j) fai i = bf(i) f(i) gm i=1 fag(j) g(j) = bj j gn j=1 where f : f1; : : : ; mg ! f1; : : : ; ng g : f1; : : : ; ng ! f1; : : : ; mg with m; n 1 Rules for new subtableaux SUBL i = i i = i where = is the residual SUBR i = i i = i where = is the residual Table4... In PAGE 82: ...Chapter 4. Deciding bisimilarity for normed BPA EXTEND R `T X = Y ; ? R; Y = X `T = ; ? if = is the residual of X = Y and R; Y = X is fundamental COMPARE R `T X = Y ; ? R `T X1 1 = X ; = ; ? if Y 2 Dom(R) and = is the residual for X = Y but (Y; X1 1) 2 R UPDATE R `T X = Y ; ? R; Y = (X ) # R `T ( ) # R = ( ) # R; ? if Y 62 Dom(R) and = is the residual for X = Y but some variable Z 2 Dom(R) occurs in X REWRITE R `T X = Y ; ? R `T (X ) # R = (Y ) # R; ? if (X ) # R 6 = X or (Y ) # R 6 = Y CONGL R `T 1 = 2; ? R `T 1 = 2; ? CONGR R `T 1 = 2 ; ? R `T 1 = 2; ? Table4... ..."

### Table 1 Theories, systems and models discussed in this paper Classical decision theory

2002

"... In PAGE 3: ... However, this comparison gives some interesting insights into the relation among the areas, and these insights are a good starting point for further and more complete comparisons. A summary of the comparison is given in Table1 . In our comparison, some concepts can be mapped easily onto concepts of other theories and systems.... ..."

### Table 1. Mean Field Theories

"... In PAGE 5: ...solated atoms. We rst present the results of the Iben et al. model. Table1 gives the calculated ground state ionization potentials, , and the probability densities, 2, at the nucleus for a screened Coulomb potential with Z taking on values from 1 to 6 and Debye radius RD = 0:45 , which is the solar value at R=R = 0:06. For Z = 1, Debye-H... In PAGE 6: ...the rate reduction factors, FIKS, by which the bound state capture rate is reduced due to screening, FIKS = 2e = 2 0e 0; (3) where the subscript 0 indicates unscreened values. Thus, we see from Table1 that bound state screening reduces the total capture rate by a factor R = (wc + FIKSwb1)=(wc + wb) = 0:85; (4) or by 15% . Screening e ects on continuum electrons were studied by Bahcall amp; Moeller (1969), who integrated numerically the Schroedinger equation for continuum electrons.... In PAGE 6: ... For 7Be under solar conditions, screening corrections are small but larger than our calculational accuracy. Let the screening corrections for continuum electrons be represented by FBM = lt; 2 gt; = lt; 2 0 gt; : (5) Table1 gives values of FIKS and FBM for di erent nuclear charges Z; solar values at R=R = 0:06 were used for and RD. The total electron capture rate should be calculated using a density enhancement factor wIKSBM = FBMwc + FIKSwb1; (6) where we make the excellent approximation that screened excited bound states give a negligible contribution.... In PAGE 7: ... The rst order expansion of the potential gives = Zr e?r=RD Zr ? Z RD : (7) Thus the potential near the nucleus is a Coulomb potential plus an approximately constant correction. In statistical equilibrium, the constant change in the potential reduces the electron density at the nucleus by a Boltzmann factor, FS = exp(? Z=RD), and the density enhancement factor is given by wS = FS(wc + wb): (8) Table1 compares, in the last two rows, our numerical values obtained from the detailed quantum mechanical calculations summarized by Eq. (6), and the simple Salpeter-like formula, Eq.... ..."

### Table 1, it is evident which KOD theories and practices have been extracted to complete this project.

"... In PAGE 6: ... Hence, the proposed model includes a framework that provides both a theoretical underpinning and a practicum for designing and assessing New Media products that follow usability guidelines. THE KNOWLEDGE-OPERATORS-AND-DOMAINS MODEL The authors propose a three-by-three model, referred to as Knowledge-Operators-and- Domains (KOD) (see Table1 ). In this model, the Knowledge Domains (ethnography, design, and media) and the Knowledge Operators (theory, application, and management) extend the boundaries of New Media theory and practice to include a more integrated approach to knowledge management that is far more centered on user interaction design theory and methods.... In PAGE 7: ... Table1 . The KOD Framework with three knowledge domains and operators.... ..."

### Table 1: A successful completion sequence for a fragment of group theory. 37

1990

Cited by 53