### Table 2: Necessary conditions for events

2005

### Table 1. Necessary Conditions for Development. (Peterson amp; Hicks, 1999).

"... In PAGE 2: ... These are called the Necessary Conditions for Development by the authors of the PDI study (Peterson amp; Hicks, 1999). Those conditions include insight into development needs, motivation to change, opportunity to acquire and practice new skills and accountability for follow through (see Table1 .) A deficit in any of these conditions limits the ability of the individual or organization to develop.... ..."

### Table 1: The necessary conditions of the meta-functions (part)

1999

"... In PAGE 3: ... Note that the furna- ce which is a sub-component of a boiler is separated from the boiler as a heat exchanger for explanation. We have defined the nine types of meta-functions as shown in Figure 2c and Table1 . Table 1 shows the ne-... In PAGE 4: ... In general, the to drive is a role of an en- ergy function for an object function. To Enable (enabler role) This meta-function is used for representing a condition playing a crucial role in fo except to provide and to drive (see Table1 ). For example, because the steam of which phase is gas plays a crucial role in occurrence of the heat-expansion process in the turbine and the phase is neither material of rotation nor the consumed energy, the to vaporize function of the boiler is said to have the meta-function to enable (see mf5).... ..."

### Table 1: Test for necessary and sufficient conditions for various classes of codes for PCRC.

708

"... In PAGE 24: ...Discussion and Simulation Results The results of our necessary and sufficient conditions (16), (46) and (47) as well as the sufficient condition in [18], evaluated for various classes of codes for PCRC are shown in Table 1. As can be seen from the last column of Table1 , the sufficient condition in [18] identifies only COD2 (Alamouti) and CUW4 as SSDs for PCRC. However, our conditions (16, (46) and (47) identify CIOD4, RR8, and CODs from RODs, in addition to COD2 and CUW4, as SSDs for PCRC (4th column of Table 1).... In PAGE 24: ... As can be seen from the last column of Table 1, the sufficient condition in [18] identifies only COD2 (Alamouti) and CUW4 as SSDs for PCRC. However, our conditions (16, (46) and (47) identify CIOD4, RR8, and CODs from RODs, in addition to COD2 and CUW4, as SSDs for PCRC (4th column of Table1 ). It is noted that, CIOD4 being a construction by using G = COD2 in (50) and coordinate interleaving, it is SSD for PCRC from Lemma 2 and Theorem 4.... ..."

### Table 1: Necessary and su#0Ecientschedulability conditions.

1997

"... In PAGE 4: ... The conditions which determine if a set of connections is schedulable, called schedulability conditions, constitute the admission control test in bounded-delay services. Table1 shows necessary and su#0Ecientschedulability conditions for the EDF and SP packet schedulers that are derived in #5B18#5D. In the EDF condition we use s max j to denote the maximum transmission time of a packet from connection j.... In PAGE 7: ...1 #5B18#5D: t #15 X i2C 1 A #03 i #28t , d 1 #29+ P X p=2 X i2C p A #03 i #28t , d p +#01#29+ max d q #3Et,#01 s max q #283#29 A comparison of the condition for RPQ in equation #283#29 with the EDF condition in Table1 shows that RPQ can approximate EDF with arbitrary precision if #01 is selected su#0Eciently small. Note that the schedulability conditions guarantee that FIFO 0 is empty at queue rotations.... In PAGE 16: ...+ scheduler is designed to be a hybrid between SP and EDF in the sense that #281#29 RPQ + always achieves an e#0Eciency at least as good as SP, #282#29 the e#0Eciency of RPQ + is nondecreasing as the rotation interval #01 is reduced 2 , and #283#29 the e#0Eciency of RPQ + approaches that of EDF as #01 ! 0. The latter two claims are easy to show; the second holds since the right-hand-side of equation #289#29 increases with #01, while the #0Cnal claim follows from verifying that the RPQ + condition in equation #2810#29 and the EDF condition from Table1 are identical for #01 = 0. We conclude this section by arguing that any set of connections schedulable with SP are also schedulable with RPQ + .... In PAGE 17: ...n both experiments we use the most accurate, i.e., necessary and su#0Ecient, admission control tests for each packet scheduler to obtain a precise comparison of the e#0Eciency of the schedulers. We use the schedulability conditions from Theorem 1 for RPQ + , the conditions from Table1 for EDF and SP, and the condition in equation #283#29 for RPQ. 7.... ..."

Cited by 33

### Table 4 expresses the su#0Ecient and necessary conditions for a timed automata

1995

"... In PAGE 14: ... Let D be a declaration. The symbolic satisfaction relation ` D between symbolic states and formulas of L s is de#0Cned as the largest relation satisfying the implications in Table4 . We call a relation satisfying the implications in Table 4 a symbolic D = ; #29 #5Bl;D#5D ` apos; #5Bl;D#5D ` c #29 D #12 c #5Bl;D#5D ` p #29 p 2 V #28s#29 #5Bl;D#5D ` c _ apos; #29 #5Bl;D#5D ` #5Bl;D ^:c#5D ` apos; #5Bl;D#5D ` p _ apos; #29 #5Bl;D#5D ` p or #5Bl;D#5D ` apos; #5Bl;D#5D ` apos; 1 ^ apos; 2 #29 #5Bl;D#5D ` apos; 1 and #5Bl;D#5D ` apos; 2 #5Bl;D#5D ` #5Ba#5D apos; #29 #5Bl 0 ;r#28D ^ g#29#5D ` apos; whenever l g;a;r ,! l 0 #5Bl;D#5D `88 apos; #29 #5Bl;D#5D ` apos; and #5Bl;#28D ^ I#28n#29#29 quot; ^ I#28l#29#5D ` apos; #5Bl;D#5D ` x in apos; #29 #5Bl;fxgD#5D ` apos; #5Bl;D#5D ` Z #29 #5Bl;D#5D `D#28Z#29 Table 4.... In PAGE 14: ... The symbolic satisfaction relation ` D between symbolic states and formulas of L s is de#0Cned as the largest relation satisfying the implications in Table 4. We call a relation satisfying the implications in Table 4 a symbolic D = ; #29 #5Bl;D#5D ` apos; #5Bl;D#5D ` c #29 D #12 c #5Bl;D#5D ` p #29 p 2 V #28s#29 #5Bl;D#5D ` c _ apos; #29 #5Bl;D#5D ` #5Bl;D ^:c#5D ` apos; #5Bl;D#5D ` p _ apos; #29 #5Bl;D#5D ` p or #5Bl;D#5D ` apos; #5Bl;D#5D ` apos; 1 ^ apos; 2 #29 #5Bl;D#5D ` apos; 1 and #5Bl;D#5D ` apos; 2 #5Bl;D#5D ` #5Ba#5D apos; #29 #5Bl 0 ;r#28D ^ g#29#5D ` apos; whenever l g;a;r ,! l 0 #5Bl;D#5D `88 apos; #29 #5Bl;D#5D ` apos; and #5Bl;#28D ^ I#28n#29#29 quot; ^ I#28l#29#5D ` apos; #5Bl;D#5D ` x in apos; #29 #5Bl;fxgD#5D ` apos; #5Bl;D#5D ` Z #29 #5Bl;D#5D `D#28Z#29 Table4 . De#0Cnition of symbolic satis#0Cability.... In PAGE 15: ... Then the following holds: A j= apos; if and only if #5Bl 0 ;D 0 #5D ` apos; where l 0 is the initial node of A and D 0 is the linear constraint system fx = 0 j x 2 C #5B Kg. u t Given a symbolic satisfaction problem #5Bl;D#5D ` apos; wemay determine its validityby using the implications of Table4 as rewrite rules. Due to the maximal #0Cxed point propertyof`, rewriting may be terminated successfully in case cycles are encountered.... In PAGE 16: ...e. a problem#29 is related to its sons by application of the appropriate rewrite rule of Table4 : i.e.... In PAGE 16: ... The leaf-problem labeled #28b#29 is valid as #28D 3 ^ y #15 n#29=; holds under the assumption that n + m #15 i.Thus #28b#29 is an instance of the #0Crst rule of Table4 . The problem labeled #28a#29 is a reoccurrence of the earlier problem #5Bl 1 ;D 0 quot; #5D as it can be shown that D 0 quot; = D 1 quot; .... ..."

Cited by 85

### Table 6.1: The necessary conditions for inclusion in a region based on the distances along seven plane normal vectors (a-g).

### Table 1 describes the parameters involved. The necessary condition is a so- called under-subscribed scenario which is de ned as p1 = 0 and p2 gt; 0.

"... In PAGE 3: ... The necessary condition is a so- called under-subscribed scenario which is de ned as p1 = 0 and p2 gt; 0. Parameter Meaning Unit A token bucket rate packet/s Z token bucket size packet R requested rate packet/s p1 packet drop probability for in-pro le packets - p2 packet drop probability for out-pro le packets - T round-trip-time (RTT) s Table1 . Token bucket parameters The results of [4] make the TBM model a promising candidate for a PMM implementation.... ..."

### Table 1: This table summarizes the necessary condition on the ow to avoid self-intersection, where is the speed, 1 is the higher magnitude curvature, 2 is the lower magnitude curvature, and ~ N

1994

Cited by 11

### Table 4.5 contains the necessary conditions imposed at the gate input in order to be an element of the set CG. GateTypenGateOutput 000 010

1994

Cited by 4