### Table 1: Classical Gram-Schmidt orthogonalization procedure.

### Table 1: The rules of the classical system KE. The applications of the only branching rule can be restricted to subformulae and further controlled by sys- tematic procedures.

in A Generalization of Analytic Deduction via Labelled Deductive Systems I: Basic Substructural Logics

1994

"... In PAGE 4: ... In [DM94] these ideas lead to the formulation of a new system of analytic deduction for classical logic, the system KE, which is proved to be essentially more e cient than the tableau method3. The rules of the classical KE system are listed in Table1 . Notice that all the operational rules have a linear format and the only branching rule is a rule expressing the classical Principle of Bivalence.... ..."

Cited by 53

### Table 1 The main procedures of our heuristic algorithms are coded with FORTRAN-77 and compu- tations are done on an IBM PC compatible processor 486 DX. We use SITATION attached in Daskin [2] as external supporting procedure to deal with the classical standard p-median problem in the algorithm.

"... In PAGE 13: ... In our computational experiments the xed cost for each delivery base is c = 800; the unit transportation cost is = 5:2; the capacity limit in each delivery base is = 400; the total number of post sectors is n = 83; and the total beats in the system is B = 1643: All these data approximately simulate the magnitude of the practical problem. The function (t) is a concave piecewise linear function, see its data in Table1 . The curve... ..."

Cited by 1

### Table 1: The probability of making at least one statement with con dence for three multiple comparisons procedures|Bayesian, classical Honestly Signi - cant Di erence, and classical Wholly Signi cant Di erence|as a function of the number of studies and the between-study standard deviation. Computa- tions for each procedure and each value of = are based on 10000 simulations from the hierarchical normal model.

2000

"... In PAGE 12: ...Table 2: The computed experimentwise Type S error rate|that is, the num- ber of simulations in which at least at least one Type S error was made, divided by the number of simulations in which at least one comparison was made with con dence|for three multiple comparisons procedures. See cap- tion of Table1 for more information. 4.... In PAGE 12: ... Results appear in Tables 1{3. Table1 displays the probability that at least one statement with con dence is made among all possible pairwise comparisons. Table 2 shows the probability... In PAGE 13: ...001 Table 3: The computed comparisonwise Type S error rate|that is, the num- ber of comparisons in which a Type S error was made, divided by the number of comparisons made with con dence|for three multiple comparisons proce- dures. See caption of Table1 for more information. least one statement with con dence being made.... In PAGE 13: ...ures. See caption of Table 1 for more information. least one statement with con dence being made. (Thus, the denominator for the ratio computed in Table 2 is the numerator of the ratio for Table1 .) Table 3 summarizes the comparisonwise Type S error rates|that is, the proportion of con dent claims that have the wrong sign.... In PAGE 15: ...robabilities of making at least one statement with con dence are 0.008, 0.824 and 1.000 (see Table1 ). Thus in general, the uncertainty about makes the Bayesian testing procedure less likely to make a claim with con dence (except for small values of = ).... ..."

Cited by 2

### Table 1. Point-wise performance results, in terms of FAR, FRR and HTER (%), on the test set of the NIST database using classical ML training, MAP training and MAP plus T-normalization procedure. These results where obtained by selecting the threshold that minimized the EER on the development set.

"... In PAGE 3: ... This has already been demonstrated empirically. For instance, one can see in Table1 and in Figures 1 and 2 the comparative performance of three systems on the NIST database described in appendix A. One system is trained using the classical EM training approach (also called maximum likelihood approach, or ML), the second one is trained using the MAP adaptation technique, and the third one is trained using MAP and applying the T-norm normalization technique.... In PAGE 3: ... One system is trained using the classical EM training approach (also called maximum likelihood approach, or ML), the second one is trained using the MAP adaptation technique, and the third one is trained using MAP and applying the T-norm normalization technique. Table1 shows the a priori performance of all three systems on the test set in terms of FAR, FRR, and HTER, after selecting 4 Note that actually, generative approaches that effectively work usually implement... ..."

### Table 2: Situations where BFGS failed to converge.

2004

"... In PAGE 11: ... In every situation, the alternated algorithm achieved con- vergence, and the same did not hold for the BFGS algorithm. The percentage of situations for which BFGS did not con- verge is presented in Table2 . Again, the classical procedure is unreliable.... ..."

### Table 1: uniform lower bounds for the modality of Borel subgroups in classical groups.

"... In PAGE 3: ...roup of G. Let r = rank G. There exists a quadratic polynomial f 2 Q[t] such that mod B f(r): That is, the modality of B grows quadratically with the rank of G. More speci cally, depending on the type of G the polynomial f may be taken as in Table1 below.... In PAGE 4: ...Table1 the one for type Ar is minimal (for r 4). Thus, we may formulate a uniform lower bound for mod B independent of the type of G: Corollary 3.... In PAGE 4: ... Then (a) is a quadratic polynomial in r. Moreover, (a) f(r), where f(r) may be taken as in Table1 above. Proof.... In PAGE 4: ... For a xed classical type we choose for f(r) the polynomial (a) which is minimal for that type. This yields the lower bounds of Table1 . Whence, Proposition 3.... In PAGE 4: ...uadratically with the rank of G. Thus the polynomial bounds in Theorem 3.1 are optimal in terms of their degrees. Considering the ratio of mod B by dim Bu as r grows for a xed classical type, we infer from Table1 that for all classical groups 1 6 lim r!1 mod B dim Bu 1: The same lower bound can be derived for type Ar from [7] (second part of the proof of Theorem 3.... In PAGE 4: ...or mod B. Thus we have mod B = (a) in these instances. We list these cases in Table 3 below together with the ideals a from Table 2. For G of type Ar, for r 7, B3, B4, and C3, the modality of Borel subgroups can also be determined from the information in Table1 in [4]. At present is not known whether mod B is a polynomial in r as suggested by these results.... In PAGE 6: ... [6]. For G2 this information can also be read o from Table1 in [4]. Type of G a dim a mod B = (a) A5 1; 3; 5 13 1 A6 1; 3; 5 18 1 A7 1; 4; 7 22 2 A8 1; 4; 7 29 3 A9 1; 4; 8 35 4 B3 2 7 1 B4 1; 3 14 2 B5 1; 4 21 3 B6 1; 4 29 5 C3 1; 3 8 1 C4 1; 4 13 2 C5 1; 5 19 3 D4 2 9 1 D5 3 15 2 D6 1; 4 25 4 Table 3: the modality of Borel subgroups in classical groups of small rank.... In PAGE 7: ...roup of G. Let r = rank G and s = rankss P . There exists a quadratic polynomial f 2 Q[t] such that mod P f(r ? s): That is, the modality of P grows at least quadratically with r ? s, the di erence of the semisimple ranks of G and P . Moreover, the polynomial f may be taken from Table1 above. Proof.... In PAGE 8: ...1 and Theorem 3.1, we infer that mod P mod Q f(r ? s) for some f 2 Q[t] from Table1 according to the type of H. We illustrate the procedure in the proof of Theorem 4.... ..."

### Table 2: Mean and Standard Deviation (STD) of the estimates of the Misclassi cation Error at four di erent sampling schemes of mixtures of normal distributions without contamination (u) and with contamination (c) for the Biweight S-estimator, the restricted most B-robust S-estimator and the classical estimator.

"... In PAGE 14: ... This yields a sequence of m estimates of the classi cation error, of which we computed the average and the standard deviation. In Table2 , results are shown for sampling schemes B, C, D, and E of He amp; Fung (2000, p. 158), with and without contamination, and for discriminant rules based on the Biweight S-estimator, the Most Robust S-estimator (with breakdown point equal to 0.... In PAGE 14: ...reakdown point equal to 0.5), and the classical estimator. Note that we did not report the results for Case A, since they coincide with Case B-uncontaminated. It is clearly seen from Table2 that there is a need to robustify discriminant analysis, since the misclassi cation probabilities under contamination of the classical procedures are always the biggest. If there is no contamination then the three procedures give quite similar results, the clas- sical estimator being marginally better.... ..."

### Table 1: Results of the fundamental matrix estimation in the left camera. The cameras intrinsic parameters are then computed from the fundamental matrices. We show table 2 the intrinsic parameters obtained by the standard calibration method using each of the three images, and the results of our method, with the polynomial method, and the iterative method used to compute all the parameters, or just the scale factors, starting from the previous value. It can be noted that no initial guess is required at all for the general method. The scale factors are determined with a good accuracy, however, this is not the case for the coordinates of the principal point. Thus the best is to assume that it is at the center of the image. We have then compared in the table 3 the camera motion obtained directly from the projection matrices given by the classic calibration procedure, and the estimation by performing the decomposition of the fundamental matrices already obtained, and using the camera parameters obtained by the self-calibraion method. As the table shows the relative error on the rotation anglem and the angular error on the rotation axis and translation direction, it is easy to see that the estimation is accurate.

1993

### Table 2-9 The Predefined Internal Procedures

"... In PAGE 28: ... IDLscript August 2000 2 The description of IDLscript grammar uses a syntax notation that is similar to Extended Backus-Naur Format (EBNF). Table2 -1 lists the symbols used in this format and their meaning. 2.... In PAGE 29: ...2.4 Keywords The identifiers listed in Table2 -3 are reserved for use as keywords and may not be used otherwise. Keywords obey the rules for identifiers (see quot;Identifiers quot; on page 2-21) and must be written exactly as shown in the above list.... In PAGE 29: ... For example, quot;class quot; is correct ; quot;Class quot; refers to an identifier and can produce an interpretation error. IDLscript scripts use the characters shown in Table2 -3 as punctuation. 2.... In PAGE 30: ...able 3-5 on page 3-6 in the CORBA 2.3 specification). The meaning of all other characters is implementation-dependent. Nongraphic characters must be represented using escape sequences as defined below in Table2 -4. Note that escape sequences must be used to represent single quote and backslash characters in character literals.... In PAGE 41: ... It allows programmers to check typing information for instance to check argument types of a procedure. Table2 -5 enumerates the set of functionalities which are supported by all IDLscript objects and types. 2.... In PAGE 43: ... Strings support a set of attributes, methods and operators. All these functionalities are enumerated in Table2 -6 and they never modify the target string. When indexes are out of the string bounds, an exception BadIndex is raised (see Section 2.... In PAGE 45: ... Moreover, array objects provide a set of operators, attributes and methods. All these functionalities are enumerated in Table2 -7. When indexes are out of the array bounds, an IDLscript internal exception BadIndex is raised.... In PAGE 48: ...7.6 Predefined Internal Procedures IDLscript provides some predefined internal procedures, see Table2 -9, respectively named by the following identifiers: eval, exec, getline, print, and println. The eval function provides the classical powerful evaluation function: it takes a stringified script, executes it, and returns the result of this evaluation.... ..."