### Table 1. Axial basis de nitions for models with xed-edge boundary conditions (2.6). 16

"... In PAGE 43: ... Note that in this and subsequent tables and gures, equal index limits are assumed and denoted by Nu = Nv = Nw = N. Speci c basis limits for the cubic splines are summarized in Table 10 (see also, Table1 ). Due to the nature of the forcing function, the Fourier limit M = 3 was su cient for resolving the circumferential behavior.... In PAGE 47: ...igure 12. Errors of transverse displacement with N = 4 cubic spline axial basis functions. Absolute errors with N = 8 and N = 16 are graphically indistinguishable from the x ? plane. (ii) Linear Spline Bases for uN; vN, Cubic Spline Basis for wN: To compare the performance of the fully cubic spline approximations with linear spline approximations of the longitudinal and circumferential displacements, the computations of (i) were repeated with the linear spline basis functions summarized in Table1 . The absolute errors obtained in this manner are reported in Table 12 while the ratios of these errors when the discretization levels are doubled are reported in Table 13.... In PAGE 51: ...13) in RN; N = 2N . As indicated by the large eigenvalue ratios summarized in Table1 4, this system is relatively sti and a variable-stepsize, variable-order sti ODE routine was used to numerically integrate the system. All subsequent solutions are reported at time T = 1:5 seconds.... In PAGE 56: ... Note that all computations were performed with double precision accuracy. In Table1 8, the natural frequencies obtained through this dynamic patch excitation are compared with those obtained for the undamped shell by solving the matrix eigenvalue prob- lem (4.14).... ..."

Cited by 1

### Table 2. Interior boundary and jump conditions for the minimax problem.

"... In PAGE 15: ...) = 0 [see Eq. (I 47)]. On forward integration, an additional trivial di erential equation for the unknown 0 is required. Moreover, in Table2 , the interior boundary conditions and the jump conditions are drawn up determining the seven major switching points|not those imposed by the nonsmooth approximations of model data|, and the auxiliary variables such as jump parameters and minimal altitude. Of course, from an engineering point of view it is not meaningful to com- pute a solution accurate to 10 digits, however this accuracy is necessary to perform the numerical integration.... ..."

### Table 5-6 Boundary Objects for Assurance GQIPSP System Model

"... In PAGE 37: ...1 Use case Model for Assurance GQIPSP System Model Actor Name Role Taken Resource User This actor represents either the VPN Provisioning BB or the Assurance Configuration BB, which rely on the GQIPS. Table5 -1 GQIPSP System Actors Request resource reservation GQIPSPS Modify reservation Cancel reservation Answer the resource reservation request accept alter reject Request resource activation Cancel activation Resource User... In PAGE 38: ...10, QA-II.19 Table5 -2 Use case description of Request Resource Reservation UsecaseName Answer the resource allocation request Summary An RAR has been requested of the GQIPS that spans more than the network domain that the GQIPS manages. Actors Resource User Pre-Conditions A QoS allocation has been requested.... In PAGE 38: ...equirements: QA-II.09, QA-II.11, QA-II.18, QA-II.19, QA-V.26 Table5... In PAGE 39: ...equirements: QA-II.08, QA-II.09, QA-II.19 Table5 -4 Use case description of Cancel Reservation UsecaseName Request Activation Reservation Summary Either the VPN Service or Assurance Configuration require activation of network resources from the GQIPS Management System. Actors Resource User Pre-Conditions An SLA has been defined and exists for the requested QoS allocation.... In PAGE 39: ...10, QA-II.19 Table5... In PAGE 40: ... Table5 -7 Entity Objects for Assurance GQIPSP System Model 5.2.... In PAGE 40: ... Policy Server Maintains policies Policy Decision Point Re-acts to requests based on policy information Policy Mediation Device Mediates requests between policy server and the underlying network. Table5... ..."

### Table 1: Boundary conditions

in SUMMARY

"... In PAGE 5: ... The narrowness of the Gaussian pro#0Cle has a relevant in#0Duence on the calculated #0Dame length, so that its parameters have to be determined appropriately #5B19#5D. The boundary conditions are summarized in Table1 . Finally, we note that the use of the de#0Cnition of the vorticity #281#29 for the vorticity outlet boundary condition does not yield any relevantchanges in the computed solution.... In PAGE 5: ... 3. GENERAL SOLUTION ALGORITHM The partial di#0Berential equations #282#29 together with the boundary conditions #28see Table1 #29 are discretized on a two dimensional tensor product grid. A solution is #0Crst obtained on an initial coarse grid.... In PAGE 6: ...i#0Berence expressions. Di#0Busion and source terms are evaluated using centered di#0Berences. We adopt a monotonicity preserving upwind scheme for the convective terms #28see #5B20, p. 304#5D#29, for instance, v r @S @r = maxf#28v r #29 i, 1 2 ; 0g S i , S i,1 r i , r i,1 , maxf,#28v r #29 i+ 1 2 ; 0g S i+1 , S i r i+1 , r i : #283#29 The boundary conditions given in Table1 involve only zero or #0Crst order derivatives. For the latter terms, #0Crst order back or forward di#0Berences can be used, except for two boundary conditions which require a more accurate treatment.... In PAGE 7: ... By comparing our numerical solutions with a primitivevariable solution of the same problem #5B19#5D, we found that these two boundary conditions exerted a strong in#0Duence on the overall accuracy of the numerical solution. The discretization of the partial di#0Berential equations #282#29 together with the boundary conditions #28 Table1 #29 yields a set of algebraic equations of the form F #28U#29 = 0, which is solved using a damped Newton method J#28U n #29#01U n = ,#15 n F #28U n #29; n =0;1;:::; #285#29 with convergence tolerance k#01U n k S #3C 10 ,5 . The Jacobian matrix J#28U n #29 is computed numerically using vector function evaluations and the grid nodes are split into nine independent groups which are perturbed simultaneously #28see #5B2#5D for more details#29.... ..."

### Table 1. Axial basis de nitions for models with xed-edge boundary conditions (2.6).

"... In PAGE 27: ... When approximating the solutions to (5.1), both the linear and cubic axial basis functions summarized in Table1 were considered. For both cases, the maximum absolute errors over a uniform 25 25 grid in (x; ) are summarized in Table 8 while ratios of the errors are given in Table 9 (the absolute errors provide the same information as relative errors since the magnitudes of the solutions are on the order of one).... In PAGE 32: ... Note that all computations were performed with double precision accuracy. In Table1 3, the natural frequencies obtained through this dynamic patch excitation are compared with those obtained for the undamped shell by solving the matrix eigenvalue prob- lem (4.13).... ..."

### Table 4. Comparison of Measures of Accuracy

"... In PAGE 6: ... As justified in Harrell et al (1996), for the former we used the c index (approximate area under the ROC curve), and for the latter the Nagelkerke R2 (a monotonic transformation of the negative log likelihood to a 0-1 bounded statistic). As shown in Table4 , there were no clinically nor statistically meaningful differences in the numerical measures of discrimination or global fit. Table 4.... ..."

### Table 1. Boundary Conditions for the f

"... In PAGE 8: ... Note that since the linear form of the pressure-strain rate model is used here, the value for C L di ers from that used previously (C L =0:2, see Manceau and Hanjali c 2000) for the form of the elliptic relaxation equation given in (11). Boundary conditions are needed for the f ij and are determined, in the vicinity of the wall, by the balance of the redistributivetermby the viscous di usion of the Reynolds stresses resulting in Table1 . Only the 22- and 12-components of f have determinate solutions to the near-wall balance of the stress transport equations.... In PAGE 19: ... n Boundary Conditions The expressions for the n boundary conditions are derived from the basis tensors T (n) ij used in the representation of f ij f ij = 3 X n=1 n ^ T (n) ij ! 8 gt; gt; gt; gt; gt; lt; gt; gt; gt; gt; gt; : f 11 = 2 T (2) 11 + 3 T (3) 11 f 22 = 2 T (2) 22 + 3 T (3) 22 f 33 = 3 T (3) 33 f 12 = 1 T (1) 12 (A1) Table1 gives the corresponding boundary conditions for these f ij components. The boundary condition for 1 is directly proportional to the f 12 boundary condition and is given by 1;;w = f 12;;w T (1) 12 = p 2f 12;;w = ;20 p 2 2 12 quot; 2 w y 4 (1) (A2) The coe cient 3 appears in all three expansions of the diagonal terms of f ij .... ..."

### Table4-13BoundaryObjectsforAssuranceIESPSystemModel

"... In PAGE 16: ... Assurance is to this point only. Table4... In PAGE 17: ...equirements: [EC-II.28] [EC-II.29][IA-II.10] Table4... In PAGE 18: ...equirements: [EC-II.27][IA-II.07][IA-II.09][IA-V.16] Table4 -3 Use case description of Produce Assurance Event UsecaseName Request Service Report Summary Allows a report on the performance of a service that is monitored by the Assurance system. Actors Application Service Manager Pre-Conditions The service specified must be one for which the system is monitoring for SLA conformance.... In PAGE 18: ...28][IA-II.10] Table4... In PAGE 19: ...27] [IA-II.08] Table4 -5 Use case description of Register Server/Proxy Event UsecaseName Register Network Events Summary When errors in the network occurs it is not always sufficient for these errors to be reported at the next poll. It is possible therefore for asynchronous notification of problems to be produced.... In PAGE 19: ...27][IA-II.08] Table4... In PAGE 20: ... Traceability Requirements: [IA-V.15] Table4 -7 Use case description of Set Management Policy UsecaseName Terminate Assurance Support for SLA Summary When a customer no longer wishes to use a particular service then he can request that the SLA be terminated. Actors Order Handling, IES Manager Pre-Conditions The SLA must be registered with the system Begins When A request to terminate the SLA is made.... In PAGE 20: ...equirements: [EC-II.26][IA-I.05][IA-II.06][IA-I.02][IA-I.03][IA-V.17] Table4... In PAGE 21: ...equirements: [EC-II.26][IA-I.05][IA-II.06][IA-I.02][IA-I.03] [IA-V.17] Table4 -9Usecasedescriptionof AgreeAssuranceSupportforSLA UsecaseName Register Service Summary To support an SLA for a particular service then it is necessary to know the structure of the service. This use case allows this structure to be registered with theassurancesystem.... In PAGE 21: ... Traceability Requirements: [IA-I.04] Table4... In PAGE 22: ...equirements: [EC-II.28][EC-II.29][IA-II.10] Table4 -11 Use case description of Request Custom Report UsecaseName Access Service Information Summary When SLAs are introduced/removed from the system then the underlying network needs to be reconfigured to monitor them. Actors Application Service Manager Pre-Conditions At least one service is registered with the system Begins When Access to the service information is requested.... In PAGE 22: ... Traceability Requirements: [IA-I.04] Table4... In PAGE 23: ... Table4 -14EntityObjectsforAssuranceIESPSystemModel 4.2.... In PAGE 23: ... SLA Monitoring Monitors the components of the different services to ensure that the supported SLAs are conformed to. Table4... In PAGE 36: ... CustomerReportingService This contract offers a Web-based service which enable a customer to login as service user and use the web service to request selected data to be displayed on his browser or saved in a file. Table4... ..."

### Table 1. Test models

2005

"... In PAGE 3: ... The bifurcation diagram shows hysteresis. 3 EXAMPLES We have tested the discovery tool on a variety of example models that are listed in Table1 . Figure 1 shows the progress of the fitness in a typical optimization run for locating a Hopf bifurcation.... ..."

### Table 6-4 Boundary Objects for Assurance ASP System Model

"... In PAGE 45: ... Actor Name Role Taken IESP Represents the IESP systems when they are shown interacting with system in other domains. Table6 -1 ASP System Actors ASP Domain (from Domains) Get Server Statistics Configure Servers IESP (f rom Ac to rs)... In PAGE 46: ...10][IA-II.07] Table6 -2 Use case description of Configure Servers UsecaseName Get Server Statistics Summary Statistics generated by servers are necessary to monitor how an SLA is being conformed to. This use case allows server statistics to be polled as necessary.... In PAGE 46: ... Post-Conditions None Exceptions None Traceability Requirements: [EC-II.28] Table6... In PAGE 47: ... Server Components Represents the components of the assurance system locally managing the servers/proxy involved in providing the service. Table6 -5 Control Objects for Assurance ASP System Model : SLA Monitoring : Application Se rver(s ) : Instrument ation Int erface GetStatistics GetStatistics Statistics Statistics... In PAGE 50: ... These objects perform a number of different tasks such as initialising and managing downloadable extensions to the module. Table6... ..."