### Table 3 Cohomologies for Lie algebras of vector fields

1994

"... In PAGE 10: ... 2]. Table3 describes the cohomology spaces H1(h; C1=M) for each of the Lie algebras and corresponding modules. The rst column indicates the dimension of the cohomology space, and the second column gives a representa- tive cocycle of each nontrivial cohomology class.... ..."

Cited by 6

### Table 1: 8 dimensional Cohomological Yang-Mills Theories

"... In PAGE 8: ... The reduction of the holomony group to Spin(7) or SU(4) allows an invariant closed four from , which we have used for both topological action and covariant gauge xing condition. A comparison of two cases is made in the Table1 . We expect that a model on the eight dimensional hyperKahler manifold with Sp(2) apos; Spin(5) holonomy is also interesting.... ..."

### Table 6 Cohomology for Lie Algebras of Vector Fields in R2

1996

### Table 3 Cohomologies for Lie algebras of vector fields Dimension Representatives 1. 0

1994

"... In PAGE 10: ... 2]. Table3 describes the cohomology spaces H1(h; C1=M) for each of the Lie algebras and corresponding modules. The rst column indicates the dimension of the cohomology space, and the second column gives a representa- tive cocycle of each nontrivial cohomology class.... ..."

Cited by 6

### Table 6 Cohomology for Lie Algebras of Vector Fields in R2 Dimension Representatives

1995

### 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 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 1. The table of cohomology groups for M

"... In PAGE 7: ... Note that the homology for Case I is computed incorrectly in [17]. The correct values are given in Table1 , with the computations given in Appendix 4. From Theorem 1.... In PAGE 7: ... Proof. For the spatial problem weseein Table1 that, in all parameter ranges, (M R (c;; h)) 6 = 0.... In PAGE 17: ... Then A apos; S 2 , each of the three components of B is contractible, and each of the three components of A \ B is homotopic to a circle. The Mayer-Vietoris sequence is then 0 ! Z ! H 2 (M R ) ! Z 3 ! 0 ! H 1 (M) ! Z 3 ! Z 4 ! H 0 (M R );; from which the values for Case I in Table1 follow. In fact, for lt; 0, it is not hard to identify the homotopy type of M R (c;; h) apos; K R (c;; h).... ..."

Cited by 4