### Table 5.1: Width and amplitude of annular elements of the Bessel transducer obtained from the zeroth-order Bessel function.

### Table 1. A grammar to link RFC and HLCB descriptions ment is a straight line. In addition to be marked \rise quot;, \fall quot; or \connection quot;, each element has two scaling fac- tors. The rst number represents the duration of the ele- ment in seconds and the second the amplitude of the ele- ment in Hertz. The form of the equation using the scaling factors is given in equation 1, where f0 represents F0, t represents time, D is the duration of the element and A is the amplitude. is used to control the curvature of the rise and fall elements, and in principle this is variable. However, in practice a constant value of 2.0 was found to be adequate in all cases.

1993

"... In PAGE 3: ....3. HLCB Labeller The HLCB labeller takes the output from the RFC labeller and produces a description of the tune in terms of H, L, C and B elements using the grammar de ned in table 1. Table1 does not give concrete de nitions of notions such as \starts late in syllable quot;, \starts early in sylla- ble quot; as the theory underlying the model has not yet been su ciently developed to give formal de nitions for these concepts. However, for practical purposes it is possible to de ne some thresholds which can be used to subclassify the accent types.... ..."

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### Table 2: Spin density matrix elements for the elastic electroproduction of a1 mesons, expressed as a function of the helicity amplitudes a37 a38 a28 a38 a43 : second column: the single-flip a37 a5a13a9 and double-

in Bassler§

1999

"... In PAGE 21: ...Table2 , the expressions of the matrix elements are given in terms of the helicity am- plitudes for two specific sets of assumptions. In column 2, the double helicity flip amplitudes a37 a5 a17 a5 and a37 a17 a5a7a5 and the single flip amplitudes a37 a5a17a9 and a37 a17 a5a13a9 for the production of transversely polarised a1 mesons by longitudinal photons are neglected, and the NPE relations a37 a9 a17 a5 a25 a27 a37 a9a15a5 and a37 a17 a5 a17 a5 a25 a37 a5a7a5 are assumed (see the discussion in section 5.... In PAGE 28: ...3). A comparison of the forms of a18 a3a20a19 a3a21a3 in columns 2 and 3 of Table2 indicates that the effect of SCHC violation on the measurement of a22 is a21 a24a23 a4 a14 a12 a25a23 a4 a18 . This is neglected.... In PAGE 32: ...1, this effect is attributed to a violation of SCHC for the matrix element a7 a2 a9a7a9 . As can be deduced from the second column of Table2 , the a7 a2 a9a7a9 matrix element is approx- imately proportional to the amplitude a37 a9a15a5 for a transverse photon to produce a longitudinal a1 meson: a7 a2 a9a7a9 a25 a11 a42 a58 a31 a3 a17 a58 a0 a37 a9a15a5 a0 a0 a37 a5a7a5 a0 a10 (40) where the term a0 a37 a9a15a5 a0 a7 has been neglected with respect to a0 a37 a5a7a5 a0 a7 in the denominator and the amplitudes a37 a9a7a9 and a37 a9a15a5 are assumed to be in phase and purely imaginary [31]. With these approximations and with a17 a25 a31 , the measurement of a7 a2 a9a7a9 allows the determination of the ratio of the a37 a9a15a5 amplitude to the non-flip amplitudes a29 a0 a37 a9a7a9 a0 a7 a3 a0 a37 a5a7a5 a0 a7 for the present a0 a7 domain: a0 a37 a9a18a5 a0 a29 a0 a37 a9a7a9 a0 a7 a3 a0 a37 a5a7a5 a0 a7 a25 a0 a37 a9a15a5 a0 a0 a37 a5a7a5 a0 a11 a31 a3 a58 a25 a7 a2 a9a7a9a1a0 a31 a3 a58 a42 a58 (41) a25 a54 a0 a2 a8 a10 (42) using the results in Table 3 and eq.... ..."

### Table 2: Spin density matrix elements for the elastic electroproduction of AQ mesons, expressed as a function of the helicity amplitudes CCALAQ ALAD: second column: the single-flip CCBDBC and double- flip CCBDA0BD amplitudes are neglected and the NPE relations (31) are assumed for the other ampli- tudes; third column: the SCHC conditions and the NPE relation CCA0BDA0BD BP CCBDBD are assumed (i.e. the CCBCBD helicity flip amplitude is also neglected). CA is the ratio of cross sections for AQ production by longitudinal and transverse photons. The nucleon helicities are omitted for brevity.

"... In PAGE 21: ...Table2 , the expressions of the matrix elements are given in terms of the helicity am- plitudes for two specific sets of assumptions. In column 2, the double helicity flip amplitudes CCBDA0BD and CCA0BDBD and the single flip amplitudes CCBDBC and CCA0BDBC for the production of transversely polarised AQ mesons by longitudinal photons are neglected, and the NPE relations CCBCA0BD BP A0CCBCBD and CCA0BDA0BD BP CCBDBD are assumed (see the discussion in section 5.... In PAGE 28: ...3). A comparison of the forms of D6BCBG BCBC in columns 2 and 3 of Table2 indicates that the effect of SCHC violation on the measurement of CA is BEBMBH A6 BDBMBHB1. This is neglected.... In PAGE 32: ...1, this effect is attributed to a violation of SCHC for the matrix element D6BH BCBC. As can be deduced from the second column of Table2 , the D6BH BCBC matrix element is approx- imately proportional to the amplitude CCBCBD for a transverse photon to produce a longitudinal AQ meson: D6BH BCBC B3 D4BECA BD B7 AYCA CYCCBCBDCY CYCCBDBDCY BN (40) where the term CYCCBCBDCYBE has been neglected with respect to CYCCBDBDCYBE in the denominator and the amplitudes CCBCBC and CCBCBD are assumed to be in phase and purely imaginary [31]. With these approximations and with AY B3 BD, the measurement of D6BH BCBC allows the determination of the ratio of the CCBCBD amplitude to the non-flip amplitudes D4CYCCBCBCCYBE B7 CYCCBDBDCYBE for the present C9BE domain: CYCCBCBDCY D4CYCCBCBCCYBE B7 CYCCBDBDCYBE B3 CYCCBCBDCY CYCCBDBDCYD4BD B7 CA B3 D6BH BCBC D6BD B7 CA BECA (41) B3 BK A6 BFB1 BN (42) using the results in Table 3 and eq.... ..."

### Table 2: Spin density matrix elements for the elastic electroproduction of AQ mesons, expressed as a function of the helicity amplitudes CCALAQ ALAD: second column: the single-flip CCBDBC and double- flip CCBDA0BD amplitudes are neglected and the NPE relations (31) are assumed for the other ampli- tudes; third column: the SCHC conditions and the NPE relation CCA0BDA0BD BP CCBDBD are assumed (i.e. the CCBCBD helicity flip amplitude is also neglected). CA is the ratio of cross sections for AQ production by longitudinal and transverse photons. The nucleon helicities are omitted for brevity.

1999

"... In PAGE 21: ...Table2 , the expressions of the matrix elements are given in terms of the helicity am- plitudes for two specific sets of assumptions. In column 2, the double helicity flip amplitudes CCBDA0BD and CCA0BDBD and the single flip amplitudes CCBDBC and CCA0BDBC for the production of transversely polarised AQ mesons by longitudinal photons are neglected, and the NPE relations CCBCA0BD BP A0CCBCBD and CCA0BDA0BD BP CCBDBD are assumed (see the discussion in section 5.... In PAGE 28: ...3). A comparison of the forms of D6BCBG BCBC in columns 2 and 3 of Table2 indicates that the effect of SCHC violation on the measurement of CA is BEBMBH A6 BDBMBHB1. This is neglected.... In PAGE 32: ...1, this effect is attributed to a violation of SCHC for the matrix element D6BH BCBC. As can be deduced from the second column of Table2 , the D6BH BCBC matrix element is approx- imately proportional to the amplitude CCBCBD for a transverse photon to produce a longitudinal AQ meson: D6BH BCBC B3 D4BECA BD B7 AYCA CYCCBCBDCY CYCCBDBDCY BN (40) where the term CYCCBCBDCYBE has been neglected with respect to CYCCBDBDCYBE in the denominator and the amplitudes CCBCBC and CCBCBD are assumed to be in phase and purely imaginary [31]. With these approximations and with AY B3 BD, the measurement of D6BH BCBC allows the determination of the ratio of the CCBCBD amplitude to the non-flip amplitudes D4CYCCBCBCCYBE B7 CYCCBDBDCYBE for the present C9BE domain: CYCCBCBDCY D4CYCCBCBCCYBE B7 CYCCBDBDCYBE B3 CYCCBCBDCY CYCCBDBDCYD4BD B7 CA B3 D6BH BCBC D6BD B7 CA BECA (41) B3 BK A6 BFB1 BN (42) using the results in Table 3 and eq.... ..."

### Table 1 S-wave and P-wave amplitudes for the nonleptonic decay of octet baryons S-wave P-wave

"... In PAGE 1: ... P T does poorly in describing the P-wave amplitudes of B ! B at leading order. Table1 shows the experimental and theoretical amplitudes both at loop and tree-level. The nonleptonic weak couplings are t to the experimentally measured S-wave amplitudes in B ! B , and together with the experimentally measured axial matrix elements give rise to theoretical predictions for the P-wave amplitudes[1].... ..."

### Table 5.1 Observe the length of each interval that appears in the rst column of Table 5.1. How is the quantization interval length related to the number of quantization levels of a uniform quantizer? The entries in the 2nd column are referred to as quantization levels; only these values appear at the quantizer output. A.3 Generate the 8 element sampled sequence x where each element of x represents the analog pulse amplitude at that sampling instant: x = [ 0.8, 0.6, 0.2, -0.4, 0.1, -0.9, -0.3, 0.7 ]; Apply quantization rule described in Table 5.1 to sequence x: Element x

### Table 1: Critical Reynolds numbers Rn and ratios n for the period doubling cascade. The rst one, two, four and eight periodic states are sketched in Figure 2, where we have represented the amplitude z versus the amplitude v. 3.2 Liapunov exponents. Liapunov exponents give us information about the stability of the orbits and the long-term behaviour of the volume elements in phase space (i.e., contraction and expansion). For our problem we consider again the rst order variational dynamical system _ x = f(x; R) ;

"... In PAGE 9: ... The transversality to is ensured by moving x0 along the orbit to a point p where the angle between the orbit and the Poincar e Map is maximum: f(x; R) kf(x; R)kk k f(p ; R) kf(p ; R)kk k 8x 2 (27) By gradually varying the Reynolds number R we can determine with a high degree of accuracy (by succesive linear interpolation, for example) the bifurcating values of R. We have found a period doubling cascade, whose rst nine period doubling bifurcation values can be seen in Table1 . The table also shows the ratios between the successive bifurcation intervals, de ned by: n = Rn+1 ? Rn Rn+2 ? Rn+1 (28) We can observe that these ratios approach Feigenbaum apos;s universal con- stant F = 4:66920160 : : :.... ..."

### Table 3. Orbital elements of the tted orbit.

"... In PAGE 2: ... The derived orbital parameters (best least-square t) show the planet orbits its parent star in an almost circular orbit, with a period of 24.13 days, inducing a velocity semi-amplitude of 62 m s?1 - Table3 . Given the orbital pe- riod and the mass of the parent star (0.... ..."

### Table 1: Comparison of tactile displays (n.s. = not stated)

2003

"... In PAGE 5: ... Newer servo technology, such as digital servos, will also improve display performance. We compare the current implementation of our design with the state of the art in tactile displays utilizing different actuator technologies ( Table1 ), as done in [25]. The comparison focuses on array style tactile displays that display forces normal to the skin.... ..."

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