### Table 2. Nodal approximation on criss-cross mesh

2000

"... In PAGE 13: ... In the other two elements spurious modes appear, which neither converge to any continuous eigenvalue nor tend to zero or to in nity. We describe this behavior more precisely in Table2 for the P1 element. We can observe that the fourth numerical eigenvalue seems to converge to 6, which does not belong to the spectrum of the continuous problem.... ..."

Cited by 10

### Table 1 A criss-cross path.

"... In PAGE 26: ...Table 2 Allowed reordering of the variables. The generated basis sequence and the associated sequence of the indicator vectors u is presented in Table1 . This way seven pivot steps were needed to solve the problem.... ..."

### Table 3(a). Function Value Superconvergent Points for the Criss-Cross Pattern (in T1, n = 2, . . . , 4)

"... In PAGE 33: ... Superconvergence in T2 are obtained by symmetry. Table3 demonstrates function value superconvergent points in T1 for n = 2, .... In PAGE 34: ...Table3 (b). Function Value Superconvergent Points for the Criss-Cross Pattern (in T1, n = 5, .... ..."

### Table 3(b). Function Value Superconvergent Points for the Criss-Cross Pattern (in T1, n = 5, . . . , 8)

"... In PAGE 33: ... Superconvergence in T2 are obtained by symmetry. Table3 demonstrates function value superconvergent points in T1 for n = 2, .... In PAGE 33: ... Thus, the y-derivative superconvergent points can be obtained by symmetry. Table3 (a). Function Value Superconvergent Points for the Criss-Cross Pattern (in T1, n = 2, .... ..."

### Table 5. x-Derivative Superconvergent Points for the Criss-Cross Pattern (in T2, n = 1, . . . , 8)

### TABLE 3. Parallel multigrid performance for Mortar finite elements

### Table 4-7: Finite Element. Delaunay triangulation. Gridding effect. 83 control points.

1996

"... In PAGE 30: ... RMSE for 83 control points and 27 check points for polynomials or orders one to ten. Table4 -1 shows the RMSE for the control points. Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model.... In PAGE 30: ... Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model. This is not merely conjecture as shown by Table4 -2. The excursions which characterize polynomials are minimal with low order polynomials, but increase in magnitude as the polynomial order increases.... In PAGE 31: ...0 0.299 1.554 1.582 Table4 -1: Polynomial registration. 83 control points Polynomial RMSE -- Check Points Degree x y total 1 22.... In PAGE 31: ...0 10.323 68.148 68.925 Table4 -2: Polynomial registration. 27 check points.... In PAGE 32: ....3.2.1 Greedy Triangulation Table4 -3 shows the results from using the Greedy triangulation and three different grid resolutions. The most obvious result is surprising.... In PAGE 32: ... Another interesting observation is with respect to the gridding effect. It is quite evident if the grid is not dense enough as shown in Table4 -4. The transformed image will appear even less smooth than a standard piecewise linear model over triangles.... In PAGE 32: ...788 5.434 Table4 -3: Finite element.... In PAGE 32: ...139 1.177 Table4... In PAGE 33: ....236 0.992 1.019 Table4 -5: Finite element.... In PAGE 33: ....681 1.787 5.010 Table4 -6: Finite element Delaunay triangulation. 83 control points and 27 check points.... In PAGE 33: ... An unexpected outcome from the gridding process is its potential usefulness for distortion diagnostics. The gridding effect, see Table4 -7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table 4-8 lists the RMSEs using all of the... In PAGE 33: ... The gridding effect, see Table 4-7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table4 -8 lists the RMSEs using all of the... In PAGE 34: ....135 0.628 0.643 Table4 -8: Finite Element.... In PAGE 34: ...222 2.773 Table4 -9: Multiquadric method.... In PAGE 35: ...089 2.806 Table4 -10: MQ (no polynomial precision), MQ (linear precision) and TPS (linear precision by default). 83 control points and 27 check points.... ..."

Cited by 1

### 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 1 Subset of the Finite State Processes (FSP) notation

"... In PAGE 10: ... Finite State Processes (FSP) [12] is an algebraic notation for describing La- beled Transitions Systems. The main elements of the notation are summarized in Table1 . A Labeled Transitions System (LTS) is a form of state machine for the modeling of concurrent systems in which transitions are labeled with action names.... ..."