### Table 3: Axiomatization

"... In PAGE 21: ... 8S2 S2 gt;s1 ) 9A ideal(A; S2,circuit1) (Conclusion B: The circuit will always respect the idealization.) Table3 : Problem Statement The following inferences can now be demonstrated. Conclusion CA is a consequence of the theory consisting of axioms (1-15), constraints (P1-P7), and hypothesis HA, but conclusion CB is not.... ..."

### Table 3: Axiomatization of (N; 0; 1; +; )

"... In PAGE 35: ... By our completeness theorem for disjunctively closed algebras it follows that the full type hierarchy over this algebra is completely axiomatized by ( ), ( ), and the equational the- ory of this algebra. An axiomatization of this theory is shown in Table3 . The reader may recognize this as the equational theory of a commutative ring with unit.... ..."

### 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 MEAN FIELD THEORIES

1997

### Table 3: A Domain Theory For Promoters promoter :-contact, conformation.

1990

"... In PAGE 3: ... A pro- moter is a genetic region which initiates the rst step in the expression of an adjacent gene (transcription). Table3 contains the initial domain theory used in the promoter recognition task. The rst rule says that a promoter involves two subcategories: a contact and a conformation region.... ..."

Cited by 180

### Table 2: Predictions Computed from Decision Field Theory

2003

"... In PAGE 24: ... We assumed an equal probability of attending to each of the three dimensions, and the remaining parameters were the same as used to generate Figure 5. The asymptotic choice probability results, predicted the theory, are summarized in Table2 , below. ... ..."

### Table 2: CH bond-lengths of the various conformations in A.

"... In PAGE 97: ... The extrapolated values for the HCH angles are almost exactly the predicted ndings in [68]. Table2 lists the experimental CH bond length for the main conformations and the corresponding theoretical estimates [68]. The above consistency with theory stresses the peculiarity of the saddle point in the conformation density at C2V .... ..."

### Table 2. An imperfect domain theory for DNA promoters.

1994

"... In PAGE 15: ...ecognizing promoters in E. coli DNA (Towell et al., 1990); promoters are the sites where the process of quot;expressing quot; a gene to create a protein begins. Table2 contains the initial domain theory used in the promoter recognition task (underscore, _, indicates a position that can be filled by any DNA nucleotide). The first rule says that a promoter involves two subcategories: a contact and a conformation region.... ..."

Cited by 61

### Table 2. An imperfect domain theory for DNA promoters.

1994

"... In PAGE 15: ...ecognizing promoters in E. coli DNA (Towell et al., 1990); promoters are the sites where the process of quot;expressing quot; a gene to create a protein begins. Table2 contains the initial domain theory used in the promoter recognition task (underscore, _, indicates a position that can be filled by any DNA nucleotide). The first rule says that a promoter involves two subcategories: a contact and a conformation region.... ..."

Cited by 61

### Table 2. An imperfect domain theory for DNA promoters.

1994

"... In PAGE 15: ...ecognizing promoters in E. coli DNA (Towell et al., 1990); promoters are the sites where the process of quot;expressing quot; a gene to create a protein begins. Table2 contains the initial domain theory used in the promoter recognition task (underscore, _, indicates a position that can be filled by any DNA nucleotide). The first rule says that a promoter involves two subcategories: a contact and a conformation region.... ..."

Cited by 61