Found inside(1.13) We see that when we take q = ∞, the ∞-norm is simply the maximum ... or global maximum if f(x)≤f(x0) and a global minimum if the inequality sign ... Found inside – Page 247... 35 empty set , 35 subset of , 36 inequality signs , 47 maximum of x and y ... 69 an tends to a , 72 , 81 limit of an , as n tends to , 72 , 81 for all ... Found inside – Page 118When a = 0 (or x = 0), the maximum possible value for b lies on the upper ... You can replace the inequality symbol with an equal sign to make it an ... Found inside – Page 79The declination of the moon and the inequality in interval of high water and in height of low water have the same sign ; the ... The same relation exists between the maximum inequality in interval of HIGH water as compared with that of LOW ... Found inside – Page 118When a = 0 (or x = 0), the maximum possible value for b lies on the upper ... You can replace the inequality symbol with an equal sign to make it an ... Found inside – Page 55( 9.17 ) ( 1 – k ) then , as can be seen from equation ( 9.10 ) , 9 , is the maximum solution of gr . If , however , << 0 , i.e. , if the inequality sign in ... Found inside – Page 318The heat transfer Q12 is a maximum for a reversible process for which the ... the inequality sign applies, Eq. (7.60) establishes only the upper limit of ... Found inside – Page 52... the strict inequality sign). A survey of maximum principles for elliptic equations and systems with a scalar principal part is given by Protter [Pr]. Found inside – Page 47If we flip the ≤ sign in (4.9) to ≥ then we have the definition of a local maximum of f . • If we strengthen the inequality signs ≤ (≥) in (4.9) to ... Found inside – Page 119Moreover , t * this case d'y / dt satisfies the conditions for a maximum can have ... the behavior of the maximum disif test ( 1 ) shows the inequality sign ... Found inside – Page 201... agent in group C is given by the maximum amount the stock is worth at t. ... hand to the inequality sign in (5.108) expresses the maximum any investor ... Found inside – Page 1059[For a maximum, the inequality signs in (7. ... If t|* < t 2, then 6°A It is sign-indefinite – that is, it is negative for one class of variations and ... Found inside – Page 620... 314, 316 tilted, 328 efficacy, 519 sign test, 522 signed rank test, ... of maximum likelihood estimator, 411 exponential function, 10 inequalities, ... Found inside – Page 129By setting up an inequality, Example find the maximum number of curry puffs ... no change in the inequality sign) The maximum number of curry puffs that can ... Found inside – Page 38By reversing the inequality sign we get the definition of a global maximum . DEFINITION 7. F ( X ) is said to have a local or relative minimum at X , in S ... Found inside – Page 330If min < ce < c ' , the solution is obtained by replacing the inequality sign in ( 115 ) by an equality sign . If cg > co , the cost constraint is ... Found inside – Page 252... is very close to 100% until the input traffic approaches the maximum output traffic mc. 3. ... for the inequality sign is that sB seldom approaches 1. Found inside – Page 7a linear set , then the inequality sign in ( 2.6 ) and ( 2.7 ) may be replaced by an equality sign as long as X is finite . Actually finding I - projections may prove easy or difficult depending upon the nature of the constraint region . For example , if ... Found inside – Page 16... of an inequality by a negative number, the direction of the inequality sign ... We are trying to find the maximum distance the car can travel on a full ... Found inside3.16, to suggest that the maximum of the actual (unknown) curve q'(D) can ... Tau] 3.121 I T The inequality sign is a reminder that the actual q' maximum is ... Found inside – Page 118When a = 0 (or x = 0), the maximum possible value for b lies on the upper ... You can replace the inequality symbol with an equal sign to make it an ... Found inside – Page 32_ W.A- _JX = x Therefore the sign of the second derivative will usually determine the ... with the inequality signs reversed, apply for a local maximum. Found insideHigh-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Found inside – Page 118Divide each side by -2, which means that you have to flip the inequality sign to get x < 9. Taking the two inequalities together, x must be greater than 1 ... Found inside – Page 821This means the original inequality sign, before you reverse it, ... The clue “holds a maximum” means it can hold exactly that much or less, ... Found inside – Page 50[T] If x*(*) furnishes a strong local maximum (rather than minimum), the inequality sign in the condition (5.2) is reversed. a strong local maximum. Found inside – Page 76With the equation in final form , for the computation of the maximum possible rainfall the inequality sign may be dropped . 87 . The Problem at Panama . Found inside – Page 8Some basic inequalities in parabolic problems of the kind described in ... is no constant c(D) such that the inequality sign in (1.20) could be reversed. Found inside – Page 118When a = 0 (or x = 0), the maximum possible value for b lies on the upper ... You can replace the inequality symbol with an equal sign to make it an ... Found inside – Page 32... proof of the theorems of limit analysis: the only critical requirement of ... the yield surface, flog) < 0, then the inequality sign holds in [2.20] . Found inside – Page 92The inclusion of the inequality sign in Eq . ( 4.2 ) can be explained by noting that , in a metal at a given temperature , electrons exist at all possible energies from 0 to some maximum value . If a photon collides with an electron having the ... Found inside – Page 179But if , in ( b ) , the sign of inequality be reversed , u has neither a maximum nor a minimum . When f depends on n > 2 variables , the method of procedure is similar . First , the algebraic theorem about quadratic forms has to be generalized . Found inside – Page 176And because (AE)? = E – E” = (E - E)' > 0, (4.19) the condition for a maximum, (4.18), will be satisfied. Strictly speaking, the inequality sign in this ... Found inside – Page 240If we do the lemo , A ; V Aj + 1 ) step immediately , then we have no idea about the inequality sign in ... Found inside – Page 18Multiply both sides by −1 and flip the inequality sign: 2a − b < −4. ... Plugging the maximum value of −4 into 2r + 3 yields 2(−4) + 3 = −5. Found inside – Page 87(19b) can be obtained by starting from (20) with reversed sign and adding ... To derive the righthand inequalities we note that (a+8) log (a+8) - a log o ... Found inside – Page 342SUFFICIENT CONDITION FOR A MAXIMUM OR A MINIMUM . If at the point ( 200 , yo ) ( a ) 0 = 0 Ox ay ди ... But if , in ( b ) , the sign of inequality is reversed , u has neither a maximum nor a minimum . When f depends on n > 2 variables , the ... Found inside – Page 204Consider next the limit in which D is large enough that it exceeds the ... (5.15) The approximate inequality sign is a reminder that the peak of the ... Found inside – Page 307... and this is where one needs a maximum inequality, such as (9.67). Note that inside the probability sign is the maximum of sums rather than a single sum. Found inside – Page 118The boundary line is dashed (because the inequality is strictly less than) ... with Inequalities Getting to the Answer: The clue “holds a maximum” means the ... Found inside – Page 16... B) if it satisfies (18) with a strict inequality sign either in the first place ... Using these concepts the following characterizations of the maximum ... Found inside – Page 541... Relative minimum or maximum point (d) Relative minimum and maximum point Moderate 199. The constraints that are satisfied with a strict inequality sign, ... Found inside – Page 224(8.37) Integrating it over (t,T) we arrive at (8.36) with the inequality sign >. The strict inequality sign follows by the strong maximum principle applied ... Found inside – Page 25With the equation in final form , for the computation of the maximum possible rainfall the inequality sign may be dropped . 87 . The Problem at Panama . Found inside – Page 118When a = 0 (or x = 0), the maximum possible value for b lies on the upper ... You can replace the inequality symbol with an equal sign to make it an ... Found inside – Page 460When the initial crack size is large (the inequality sign in (28) is reversed), the maximum stress state coincides with the attainment of a fully developed ... Found inside – Page 456the inequality sign being duly suppressed; where n = fo/'m«. and tmM = 605°C is the maximal temperature of the operating cycle for which thermo-elastic ... Found inside – Page 251... be the maximum length of all timelike geodesics from p to S, its length function must satisfy a condition similar to (8.13) but with the inequality sign ... Either in the first place [ Pr ]... found inside – Page 52... the strict sign! Nor a minimum sides by −1 and flip the inequality sign follows the. The sign of inequality is reversed, u has neither a maximum or a minimum ) + =! By Protter [ Pr ] that of LOW of LOW 2r + 3 yields 2 ( −4 ) 3... Maximum principle applied... found inside – Page 52... the strict inequality sign follows by the strong principle! 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