### Table 1: Loss function using Gauss-Newton optimiza- tion and iterative identi cation and control

1995

"... In PAGE 3: ... In each iden- ti cation step the designed sensitivity function from the previous iteration is used as pre lter. The results of the simulations can be found in Table1 where the achieved cost J of (5) are shown. It can be seen that for low designed bandwidths the iterative identi ca- tion and control scheme performs very well.... ..."

Cited by 4

### Table 1. Membership values for planets in the set of big planets Most of the time we will deal with fuzzy sets over a continuous domain. In this case, mathematical functions and graphics describe the membership functions. Some functions with specific shapes are highly preferred, such as triangular, trapezoidal, s-shaped, and gauss functions.

in FUZZY LOGIC

"... In PAGE 3: ....2/1+0.5/2+0.8/3+1/4+0.8/5+0.5/6+0.2/7. A table, as in Table1 , relating each element with its degree of membership is the usual informal representation of discrete fuzzy sets. ... ..."

### Table 1: Validation of Gauss-Weierstrass kernel smoothing with test function Yl0m0.

2005

### Table 1: Comparison of Gauss quadrature accuracy for the integration of a rational function (24).

"... In PAGE 12: ... Consider the following rational function de ned on 2 [?1; 1]: f( ) = ( 0 for ? 1 lt; 0 3 2+2 3+ 2+1 for 0 1 (24) This function is C0 continuous in the interval ?1 1, but it is only non-zero on 2 [0; 1]. Table1 compares the accuracy of Gauss quadrature for two cases. In the rst case, one integration cell is used which covers the entire interval.... ..."

### Table 2. The table illustrate the decrease in loss function g and the gradient magnitude jrgj using the Gauss-Newton optimisation.

"... In PAGE 28: ... Comparing Figure 12c and i, we can also see that the iteration decreases the angle re- siduals, particularly the residual represented by the lowest lines. The e ectiveness of the optimisation routine is illustrated in Table2 . Notice the rapid reduction of the loss function and the norm of the gradient.... ..."

### Table 2. A su cient set of Reidemeister moves for Gauss diagrams.

"... In PAGE 6: ...Corollary 1. A function on Gauss diagrams de nes a knot invariant if and only if it is invariant under the transformations in Table2 , where the dotted segments indicate a part of the Gauss diagram that is unchanged. In Table 2, the positive direction of a move is from left to right.... In PAGE 6: ... A function on Gauss diagrams de nes a knot invariant if and only if it is invariant under the transformations in Table 2, where the dotted segments indicate a part of the Gauss diagram that is unchanged. In Table2 , the positive direction of a move is from left to right. 3.... In PAGE 9: ... an-, dn- and wn-subdiagrams contain no such arrows, so the set of such subdiagrams does not change. 2 Proof of 2-invariance: An 2-move introduces (or removes) two arrows in the Gauss diagram as in Table2 . The tails of these arrows are adjacent on the circle, and the heads are also adjacent on the circle.... In PAGE 10: ...OLOF-PETTER OSTLUND We see in Table2 that for an 3 +++-move, two a ected arrows that have a head and a tail next to each other are crossed if and only if the head comes before the tail. Hence no pair of arrows that are a ected by an 3 +++-move can belong to an an-subdiagram.... In PAGE 11: ... (Subdiagrams such that only one arrow belong to the changing part are unchanged by the move.) The changing part is depicted in Table2 . We see that there can be no subdiagrams of this kind after the positively directed move, when the changing part looks as on the right side in the Table.... ..."

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### Table 2 We now present the formal definition of multivalued (We give the definition in Beeri, Fagin, dependencies. and Howard1, which is slightly more general than the definition in Fagin7, in that the left- and right-hand sides of the multivalued dependency need not be disjoint.) Let R be a relation. the column names of R, and u is a tuple of R, then by u[X] we mean the projection of u onto X. When we say that x is an X-value of the relation R, we mean that x=u[X] for some tuple u of R. Let X and Y be subsets of the column names of R. Define

1977

"... In PAGE 4: ... this set is a function of x alone and does not depend on the z-values that appear with x. T(EMPLOYEE,CHILD,SALARY,YEAR) in Table2 . The multivalued dependency EMPLOYEE%HILD holds for T, since, for example, CHILDT(Gauss) equals both CHILDT(Gauss, $4OK, 1975) and CHILDT(Gauss, $5OK,1976), which all equal {Gwendolyn,Greta).... In PAGE 4: ... multivalued dependencies provide a necessary and sufficient condition for a relation to be decomposable into two of its projections without loss of information (in the usual sense that the original relation is guaranteed to be in the natural join of the two projections). EMPLOYEEWHILD holds for the relation T(EMPLOYEE,CHILD,SALARY,YEAR) in Table2 , it follows that this relation can be decomposed into the two relations T1(EMPLOYEE,CHILD) and Tq(EMPLOYEE,SALARY,YEAR) without loss of information (see Table 3). We note that T(EMPLOYEE,CHILD,SALARY,YEAR) cannot be decomposed on the basis of any functional dependencies, because there are none (except trivial functional dependencies, such as A+A).... ..."

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### Table 2: Running times in milliseconds for direct evaluation, fast Gauss transform and improved fast Gauss transform in three di- mensions.

2003

"... In PAGE 6: ...etween 0 and 1. The bandwidth of the Gaussian is h =0.2. We set the relative error bound to 2% which is reasonable for most kernel density estimation, because the estimated density function itself is an approximation. Table2 re- ports the CPU times using direct evaluation, the original fast Gauss transform (FGT) and the improved fast Gauss trans- form (IFGT). All the algorithms are programmed in C++ and were run on a 900MHz PIII PC.... ..."

Cited by 36

### Table 5: Example 4 with = 1, = :001 Gauss-Seidel Iteration.

1999

"... In PAGE 35: ... This running cost corresponds to the dynamics _ x1 = ?2 x1 + (sin x2 + u) _ x2 = ? x1: The \ quot; scaling above is convenient so that the set of interest can be taken to be the unit square. The associated PDE is given by infu [hu; DV (x)i + L(x; u)] = 0 for x 2 G V (x) = 0 for x 2 @G: Table5 includes the results for a Gauss-Seidel approximation with = 0:001 and = 1. In the table, we also record the successive di erences for the approximations as a function of n in the rightmost column.... ..."

Cited by 29

### Table 9: Average error rates for the lookahead selective sampling algorithm using the two alternative utility functions. Utility Pima Ionosphere Image Letters Two Two Multi Indians Segm. Spirals Gaussians Gauss

1999

"... In PAGE 31: ... We performed an experiment to compare this function to our standard utility function. The results are shown in Table9 . For most datasets the exploratory utility function yields the slight improvement over the accuracy-based utility function.... ..."

Cited by 31