### TABLE 2. Normalizing Narrowing vs. SLD-Resolution: Permutation Sort

### Table 3: Rate Constants for Reduction of Thiopyridinyl-Cysteine Derivatives by DTTa

1999

"... In PAGE 4: ... In the case of R69C (Figure 4c), P71C, L68C, and L72C (Figure 4a), the grouping was primarily based on the reactivity in the light (see below). Table3 gives the rate constants divided by the DTT concentrations used in the measurement. The rate constants of the mutants in the highly reactive group (0.... ..."

Cited by 1

### Table 1 shows the relevance of our work in declarative and procedural semantics with the work done by others. The xpoint semantics based on the operator TI P extends the theory based on the operator TP of van Em- den and Kowalski (1976) for Horn programs. The model-state semantics extends the least model semantics of Horn programs. It also characterizes the minimal model semantics developed by Minker (1982) for disjunctive databases. SLO-resolution is an extension of SLD-resolution of Horn pro- grams. Theorem 2.12. reduces to Theorem 2.11. when dealing with Horn programs.

"... In PAGE 13: ...Positive Consequences Semantics Horn Disjunctive Theory Reference Theory Reference Fixpoint TP quot; ! (1) TI P quot; ! (2) Semantics Model Least Model (1) Minimal Model (3) Theory Model-State (4) Procedure SLD (5) SLO (4) (1) van Emden amp; Kowalski (1976) (4) Lobo, Minker amp; Rajasekar (1989) (2) Minker and Rajasekar (1990) (5) Hill (1974) (3) Minker (1982) Table1 : Positive Consequence Semantics for Logic Programs comparing the two de nitions. The two resolutions, SLO and SLD, are sim- ilar in their structure too.... ..."

### Table 2: Truth Table for Second-Order Modified Booth Encoding [35]

"... In PAGE 23: ...Table2... In PAGE 24: ...) Modified Booth Selector [35] The modified Booth Selector requires 10 transistors per bit as compared to the regular Booth Selector which requires 18 transistors per bit for its implementation. The modification shown in Table2 . yields 44% reduction in the transistor count for the Booth Selector of the 54X54-bit multiplier.... ..."

### Table 2: Truth Table for Second-Order Modified Booth Encoding [35]

"... In PAGE 23: ...) A modified equations (b.) obtained from the Table2 . yield simpler Booth Selector implementation than the regular case.... In PAGE 24: ...ig. 19. (a.) Regular Booth Selector (b.) Modified Booth Selector [35] The modified Booth Selector requires 10 transistors per bit as compared to the regular Booth Selector which requires 18 transistors per bit for its implementation. The modification shown in Table2 . yields 44% reduction in the transistor count for the Booth Selector of the 54X54-bit multiplier.... ..."

### Table 1. Lie apos;s classi cation of invariant second-order ordinary di erential equations No. Equation Symmetry algebra

"... In PAGE 13: ... Surprisingly, it is possible to implement this approach to classifying second-order PDEs (1) by their second-order conditional symmetries in full generality. In Table1 we present the complete list of invariant real second-order ordinary di erential equations together with their maximal invariance algebras, obtained by Lie ([21, 22]). Note that a; k are arbitrary real parameters and f is an arbitrary function.... In PAGE 13: ... Note that a; k are arbitrary real parameters and f is an arbitrary function. As classi cation has been done to within an arbitrary reversible transformation of the variables x; y, the equations given in Table1 are representatives of the conjugacy classes of invariant ordinary di erential equations. Table 1.... In PAGE 14: ...Table1 , since the corresponding ordinary di erential equation is not integrable by quadratures. Next, since our nal aim is to exploit conditional symmetries for the description and reduction of initial value problems, it make no sense to consider case 4.... In PAGE 14: ... Next, since our nal aim is to exploit conditional symmetries for the description and reduction of initial value problems, it make no sense to consider case 4. This is because the symmetry group admitted by the corresponding ordinary di erential equation within the class (18) is the same as that of the more general equation given in case 3 of Table1 . The same argument applies to case 8.... In PAGE 14: ...quation given in case 3 of Table 1. The same argument applies to case 8. Consequently, we will deal only with the remaining cases 2, 3, 5{7, 9. We take as the function in operator (3) the expressions y00 ? f(x; y; y0), where f is one of the right-hand sides of equations listed in the second column of Table1 and make the replacements y ! u, y0 ! ux and y00 ! uxx. We classify PDEs of the form ut = uxx + F (t; x; u; ux) (27) admitting the corresponding Lie-Backlund vector elds.... ..."

### Table 1. Pointwise bias (up to O(h2)) and variance of bivariate Nadaraya-Watson and locally linear kernel estimators using second-order kernels.

"... In PAGE 4: ... Given standard conditions regarding the kernel, bandwidth, and data generating process, these estimators are consistent, and one is referred to Hardle (1990, pg 29) and Fan (1992) for details. Table1... In PAGE 5: ... Finally, this approach does not correct for boundary bias and is bias-reducing rather than bias-removing since it ignores all but the leading terms in the bias expansion. Higher order kernels can be used for curvature-based bias-reduction of Nadaraya-Watson estimators in this context since the leading terms in the bias expansion given in Table1... ..."