### Table 1: Comparison of convergence results for the energy and other crucial quantities for di erent nite element methods. See the text for explanation of the notation.

1998

"... In PAGE 3: ... However, for the present problem of a non-convex energy density, the results are rather sobering: In general, it can only be shown that a minimizing deformation uh 2 Ah satis es E(uh) Ch1=2; (10) where C denotes a generic constant that may depend on the topology of the quasiuniform triangulation Th and the domain but not on the mesh-size h, see [8, 21, 22], and [7] for a de nition of quasiuniformity. For a complete list of results for important quantities, see Table1 . Moreover, it turns out that the quality of the approximation depends strongly on the degree of alignment of the numerical mesh with the physical laminates.... In PAGE 4: ... To this end, we present a new algorithm based on discontinuous nite elements. It will be shown that this algorithm allows much improved convergence rate estimates for the energy, namely O(h2), and other quantities of interest as they are given in Table1 . In particular, the resolution of laminate microstructure on general meshes is much better than by the classical (non-)conforming discussed above.... In PAGE 7: ... In the case (d), it additionally depends on the choice of the value of . Again, we stress the fact that these convergence results are much better than those derived for the conforming (using (bi-, tri-)linear ansatz functions, see [21]) or classical non-conforming (using piecewise rotated (bi-,tri)linear ansatz functions, see [20, 21]) nite element methods, see also Table1 . This re ects the increased accuracy of the ansatz for non-aligned meshes: The misaligned triangulation does not lead to a dramatic pollution of the computed solution anymore.... ..."

Cited by 5

### Table 1.1 Comparison of convergence results for the energy and other crucial quantities for di erent nite element methods. See the text for explanation of the notation.

1998

Cited by 5

### Table 1: Comparison of convergence results for the energy and other crucial quantities for

1998

"... In PAGE 3: ... However, for the present problem of a non-convex energy density, the results are rather sobering: In general, it can only be shown that a minimizing deformation u h 2A h satisn0ces En28u h n29 n14 Ch 1=2 ; n2810n29 where C denotes a generic constant that may depend on the topology of the quasiuniform triangulation T h and the domain n0a but not on the mesh-size h, see n5b8, 18, 17n5d, and n5b7n5d for a den0cnition of quasiuniformity.For a complete list of results for important quantities, see Table1 above. Moreover, it turns out that the quality of the approximation depends strongly... In PAGE 4: ... To this end, we present a new algorithm based on discontinuous n0cnite elements. It will be shown that this algorithm allows much improved convergence rate estimates for the energy, namely On28h 2 n29, and other quantities of interest as they are given in Table1 . In particular, the resolution of laminate microstructure on general meshes is much better than by the classical n28non-n29conforming discussed above.... In PAGE 7: ... The earlier case cancels out the contribution from the n28scaled, squaredn29 L 2 -norm of the deformation on the interior n0cnite elements and gives rise to an energy functional that is rotationally invariant, whereas the latter case is not rotationally invariant anymore, but allows for better approximation of the volume fractions. Again, we stress the fact that these convergence results are much better than those derived for the conforming n28using n28bi-, tri-n29linear ansatz functions, see n5b18n5dn29 or classical nonconforming n28using piecewise rotated n28bi-,trin29linear ansatz functions, see n5b18, 16n5dn29 n0cnite element methods, see also Table1 . This ren0dects the increased accuracy of the ansatz for non-aligned meshes: The misaligned triangulation does not lead to a dramatic pollution of the computed solution anymore.... ..."

Cited by 5

### Table 1: Summary of convergence results for the energy and other crucial quantities for

1999

"... In PAGE 1: ... The improved performance of this method is tested in computational experiments as well as supported through a rigorous convergence analysis, giving drastically improved orders of convergence, if compared to results for clas- sical conforming and nonconforming ansatzes. We refer to Table1 for a comparison of the distinct methods. The goal of the present paper is to propose a new adaptive method to resolve laminated microstructure, with the main focus on the verin0ccation of improved convergence statements 1 Mathematisches Seminar, Christian-Albrechts-Universitn7fat Kiel, Ludewig-Meyn-Str.... In PAGE 2: ...iscontinuity of a computed solution, i.e., the heightofinter-element jumps. We will outline the strategy in section 3, and propose the new adaptive algorithm there. | The application of such an adaptivity strategy allows for convergence results that are superior to those of previous methods collected in Table1 , even for the method that is based on discontinuous ansatz functions. We refer to Theorem 3.... ..."

Cited by 5

### Table 7 Persistently vacant industrial premises in Stoke-on-Trent: condition

"... In PAGE 9: ... Indeed, the dynamic of deterioration is evident from the survey results. As revealed in Table7 , there were some important transitions. Some 57 of the 81 buildings classified as good in 1994 had deteriorated to a degree, although most were still viewed as sound in structural terms and requiring only limited refurbishment to return them to some level of use (although without making any judgements on whether that use would be sustainable!).... In PAGE 9: ... Over 20 of the buildings classified as sound in 1994, were poor or very poor by the time of the 1997 survey. Only a few buildings had improved their status through repair and refurbishment in anticipation of letting or sale ( Table7 ). Looking... ..."

### Table 1: List of Shot-type and their important HLFs Shot-type Categories of related HLF

2006

"... In PAGE 2: ... For example, the place and scene HLFs are the crucial elements to disaster-type news. Table1 illustrates the association of various shot-types and the categories of HLFs. Only HLFs relevant to the particular type of news story will be considered.... ..."

Cited by 1

### Table 2. DC Element Usage (Average number of elements per record)

"... In PAGE 3: ... This would be important for parametric inferential statistical analysis, but is les crucial here, as both measures of central tendency give roughly the same ordering of DC elements. Table2 lists the average number of times that each element was used per record, per repository. For example, the mean average number of date elements per item acros the 19 repositories was 3.... In PAGE 3: ....1846. On average, records had 18.281 tags, with 9.4139 unique elements (non-zero elements) defined. Table2 sugests that most non-zero elements ocur about once per record. Several elements, however, tended to ocur more frequently.... ..."

### Table 1. The List of Crucial Information

"... In PAGE 4: ....2.1 Data Requirements The following data are needed for the main study: (a) the crucial information and functions for users to make a choice decision between the car and public transport; (b) user perceptions and the likely use of FTISs; (c) individual behavioural changes for various journeys as a result of using FTISs; and (d) profiles of respondents. A list of crucial information contents and a list of the system functions that will be provided by FTISs are developed (see Table1 and 2). The lists include not just travel time and costs, but also information and knowledge regarding comfort, convenience, flexibility, independence, environmental impacts and ways to offset car emissions.... ..."

### Table 12: Some Crucial Informations

### Table 2.1 Relationship between di erential forms and vector elds in 3D di erential forms spawns the familiar di erential operators of vector analysis (see table 2.2). The appropriate transformation of di erential forms under a smooth change of variables is described by the pullback operator, whose meaning for the vector proxies is listed in table 2.2. A crucial feature of the pullback is that it commutes both with integration and the exterior derivative. Given a triangulation Th (in the sense of [14]) of some domain 2 Rn, we choose some polytope as a reference element for each type of element occurring in Th. We demand that for each element we can nd a smooth, regular, maybe a ne, mapping

1999

Cited by 2