### Table 4 Yield Envelope

"... In PAGE 9: ... The initial spot rate is 6%. The results are shown in Figure 9 and Table4... ..."

### Table 1: Lower and upper bounds of (n; m). (n) is the functional inverse of Ackermann apos;s function. m/ (n; m) Lower Bound Upper Bound O

1995

"... In PAGE 10: ...of its arcs and of its vertical segments. The complexity of the upper envelope of f is bounded by the length of a Davenport-Schinzel sequence on an alphabet of n letters with at most m + 2 repetitions, a so-called (n; m + 2)-Davenport-Schinzel sequences (see Table1 for tight bounds of (n; m) and [ASS89, Sha87, Sha88] for further information on such sequences). The number of arcs of CH(O+) is thus bounded by (n; m+2) and therefore jCH(O+)j 2 (n; m+2).... In PAGE 24: ... Note that we use the algorithm of section 6:2 to perform tests like p lt; h in the while-loop. Let c(n; h) be the cost of the algorithm, we obtain: c(n; h) = O(1) + O 0 @dlogloghe X i=0 n (22i; m) 22i 2i1 A + O n (he; m) he log he : Let (p; m) be an upper bound of the ratio (p;m) p that satis es (p2; m) = O( (p; m)) like (p; m) O(2 (p)cm ) with cm an integer depending on m (this upper- bound is deduced from the maximal length of (n; s)-Davenport-Schinzel sequences, see Table1 ). We bound c(n; h) as follows: c(n; h) O 0 @n (h; m) dlogloghe X i=0 2i1 A + O ?n (h2; m) log h2 ; c(n; h) = O(n (h; m) log h): This yields the desired upper-bound c(n; h) = O(n (h; m) log h).... ..."

Cited by 6

### Table 2. Examples of different envelopes.

"... In PAGE 6: ... Anyway, we are focusing on the envelope of one subphrase level, so the rst result is useful. Figures (a), (b) and (c) in Table2 shows examples of different envelopes obtained... ..."

### Table 1. Spatial envelope properties of

2001

"... In PAGE 4: ...in Table1 summarizes the different criteria. The two first criteria concerned the naturalness status of the en- vironment (man-made scenes, urban vs.... ..."

Cited by 80

### Table 5: Vehicle emulation envelope

2005

### Table 1: Notation

2000

Cited by 13

### Table 1. Entropies, temperatures, densities, and lepton numbers used in this paper. The entries are: entropy per baryon or temperature in the envelope, senv, Tenv; entropy per baryon or temperature in the core, score, Tcore; maximum baryon number density of the envelope correlated with the entropy per baryon or temperature in the envelope, n(senv, Tenv); minimum baryon number density of the core correlated with the entropy per baryon or temperature in the core, n(score, Tcore); baryon number density below which the neutrinos are not trapped, n(Yl;env); baryon number density above which the neutrinos are totally trapped, n(Yl;core); lepton fraction inside the core, Yl;core. Label

"... In PAGE 2: ...here the neutrinos are trapped (Burrows et al. 1995). Below this density, the neutrinos can freely escape and the chemical potential of the neutrinos vanishes, e = 0 (Cooperstein 1988). We refer to Table1 for the detailed parameters of the EPNS models studied here. 2.... In PAGE 3: ... 10?4, the second number gives the upper density boundary, i.e. 6 10?3. ?di 10 s, is by an order of magnitude larger than the PNS apos;s age. We model this late type protoneutron star (LPNS) with a neutrino transparent envelope with densi- ties n lt; nenv = 6 10?4 fm?3 and a neutrino opaque core with densities n gt; ncore and Yl = 0:4 (see Table1 ). The transition region between nenv and ncore is called neutrino sphere (Janka 1993).... In PAGE 5: ...ig. 3. Pressure versus baryon number density for densities n gt; 0:1 fm?3 for di erent EOS apos;s of our model of hot dense matter. The abbreviations are described in Table1 . The pres- sure of the HNSs2 EOS is nearly identical to the LPNSs1 YL04 case in this density region and is not shown for that reason.... In PAGE 8: ... The speed of sound vs in the density region around and above nuclear matter density for di erent EOS apos;s. The abbreviations are described in Table1 . The maximum value is reached in the CNS EOS: nmax c (CNS) = 1:246 fm?3 ! vs = 0:964 (in units of c).... In PAGE 9: ...ig. 13. The gravitational mass versus stellar radius (as mea- sured by an observer located at in nity) of non-rotating NS apos;s and PNS apos;s. The abbreviations for the di erent EOS apos;s are de- scribed in Table1 . The lower long dashed line corresponds to the HNSs1 EOS and the upper long dashed line to the HNSs2 EOS.... In PAGE 11: ... Properties of non-rotating and with Kepler frequency rotating PNS apos;s and NS apos;s, for a xed baryonic mass MB = 1:5 M . The EOS apos;s are summarized in Table1 . The entries are: gravitational mass, MG; baryonic mass, MB; circumferential radius (as measured in in nity), Rinf; central baryon number density, nc; central temperature, Tc; Kepler frequency, K; angular momentum, J (M km ^ =5:966 1048 g cm2 s?1).... ..."

### Table 1. Properties of envelope models Model

"... In PAGE 3: ...hey can be estimated from envelope models as, e.g., (@f=@Xs) apos; f= Xs, for di erences between two envelope models di ering in Xs but having the same . In order to test this hypothesis, three di erent envelope models were used; their properties are listed in Table1 . Models EN1 and EN2 have the same values of surface hydrogen abundance Xs while EN1 and EN3 have the same values of .... ..."