### Table 1 Iteration counts for unpreconditioned solution via GMRES of the nonlinear convection-di usion prob- lem, and the discrete two-norm of the overall error between the algebraic and exact solution for the nest grid case, without preconditioning.

"... In PAGE 7: ... Table1 shows the iteration count for a 10?5 reduction in residual of the unprecon- ditioned Newton correction equation, in both explicit (superscript ex) and matrix-free... ..."

### Table 1: Bounds for the in uence of small perturbations on the solution of ODE apos;s and di erential-algebraic systems (1)

"... In PAGE 17: ... The same qualitative behaviour can be observed for the discretiza- tion by backward Euler method. We summarize these results in Table1 , for simplicity we omitted the perturbations in the initial values. We used the simplifying notations R = max k R (s)dsk , R P = max k R P(s) (s)dsk , k k = max k ( )k , D = D(x) = k k + k 0k and so on and R h = h Pm k m+1k , R h P = h Pm kPm m+1k + h .... In PAGE 18: ...Table 1: Bounds for the in uence of small perturbations on the solution of ODE apos;s and di erential-algebraic systems (1) bounds of Table1 can not be improved. Note, that the results that are summarized in Table 1 can be proven only if the perturbed solution remains in a small neighbourhood of the exact solution.... ..."

### Table 2 Finite-dimensional modules for Lie algebras of vector fields

1994

"... In PAGE 10: ... OLVER systems than Lie.) Table2 describes the di erent nite-dimensional modules for each of these Lie algebras. The rst column tells whether the module is necessarily spanned by monomials, i.... In PAGE 10: ... Finally, Table 4 describes the quantization condition resulting from the quasi- exactly solvability assumption that, assuming M = f1g, the Lie algebra admit a nite-dimensional module N. If the cohomol- ogy is trivial, so g is spanned by vector elds and the constant functions, then it automatically satis es the quasi-exactly solvable condition, with the associated nite-dimensional modules being explicitly described in Table2 . The maximal al- gebras, namely Case 11, sl(2) sl(2), Case 15, sl(3), and Case 24, gl(2) n Rr, play an important role in Turbiner apos;s theory of di erential equations in two dimensions with orthogonal polynomial solutions, [33].... ..."

Cited by 6

### Table 4 Quasi-exactly solvable Lie algebras of differential operators

1994

"... In PAGE 10: ...ctually modi ed are indicated, i.e., those for which a = hF ; vai 6 0, cf. (17). In Case 4, Div M = ffx + gy j f; g 2 Mg. Finally, Table4 describes the quantization condition resulting from the quasi- exactly solvability assumption that, assuming M = f1g, the Lie algebra admit a nite-dimensional module N. If the cohomol- ogy is trivial, so g is spanned by vector elds and the constant functions, then it automatically satis es the quasi-exactly solvable condition, with the associated nite-dimensional modules being explicitly described in Table 2.... ..."

Cited by 6

### Table 2: Geometric estimation with initial data of algebraic ellipse # ops/1000, minimum is underlined ` apos; if non-convergence

"... In PAGE 20: ... If the algorithm didn apos;t terminate after 100 steps, it was assumed non-convergent and a ` apos; is shown instead. Table2 contains the results if the initial parameters were obtained from the Bookstein algorithm.... In PAGE 20: ...Table 2: Geometric estimation with initial data of algebraic ellipse # ops/1000, minimum is underlined ` apos; if non-convergence Table2 shows that all algorithms converge quickly with the more accurate initial data for exact conics. For the perturbed ellipse data, it apos;s primarily the newton algorithm which pro ts from the starting values close to the solution.... ..."

### Table: exactly once transaction solutions

2006

### TABLE II X Present solution Exact solution

2004

### Table 3: Commutative division algebras.

"... In PAGE 32: ... Proposition 2.2 [1, Theorem 3] An algebra given by Table3 is a division algebra if and only if d2 lt; 4b a b c d . First, we consider the case when A has exactly one idempotent.... In PAGE 33: ... Lemma 2.4 An algebra determined by Table3 has exactly one idempotent if and only if either (2a d)2 lt; 4c(1 2b) or d = 2a; b = 1 2. Taking into account Proposition 2.... ..."