If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

If modernization programs are imposed from above, without the understanding and cooperation of the people, they will encounter grave difficulties.

If the bottom name in each column did not have a responsible executive identified, the next name above which identified such a responsible executive was substituted.

If the above issue is settled by requiring public education for all citizens, Issue No. 6 may be moot.

If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.

If she chose, and in that final decision discarded, what, above all, all of us value, life itself, must she not have risen to her fullest height, and transcending her murky self, felt at last the passion of a great moral decision??

If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture — there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e. g. in photography.

If the ratio a '/ a be sufficiently constant, as is often the case, the above relation reduces to the condition of Airy, i. e. tan w '/ tan w = a constant.

If we look at this situation from far above, so that we cannot see the supporters, we see the large balloon as a small object animated by erratic movement.

If we wish to implement this filter as a digital filter, we can apply the bilinear transform by substituting for the formula above ; after some reworking, we get the following filter representation:

If in the above we relax Banach space to normed space the analogous structure is called a normed algebra.

If a house or car is above a certain value, the bankrupt can buy the interest back from the estate in order to keep the asset.

If the first theory is correct ( see above ), then the absence of cavalry removed the main Athenian tactical disadvantage, and the threat of being outflanked made it imperative to attack.

If the character encoding for a web page is chosen appropriately then HTML character references are usually only required for a markup delimiting characters mentioned above, and for a few special characters ( or not at all if a native Unicode encoding like UTF-8 is used ).

If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).

If f is a function of as above, then the second derivative of is:

If the above condition is instead satisfied for

If the ball hits the upright above the cross-bar before going through, it is not considered a dead ball, and the points are scored.

If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.

If the density of the chain is variable then the analysis above can be adapted to produce equations for the curve given the density, or given the curve to find the density.

If a stitch in a finished crocheted item breaks, the stitches above and below remain intact, and because of the complex looping of each stitch, the stitches on either side are unlikely to come loose unless heavily stressed.

If enough magma is ejected, the emptied chamber is unable to support the weight of the volcanic edifice above it.

If the third layer is placed so that its atoms are directly above those of the first layer, the stacking will be ABA — this is the hcp structure, and it continues ABABABAB.

#: If, replace in above rules with some new variable and add rule.

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If the German people favor such a settlement we should not oppose Germany following the example of Austria.

If the railroads, for example, regularly slaughtered 25,000 passengers each year, the high priests of the cult would have cause to tremble for their personal safety, for such a holocaust would excite demands for the hanging of every railroad president in the United States.

For example: If your bodily injury claims start payment after the first $250, a 25% premium saving is often made.

If you plan to sell fresh vegetables or whole milk, for example, you should be close to a town or city.

Statements such as the Banach – Tarski paradox can be rephrased as conditional statements, for example, " If AC holds, the decomposition in the Banach – Tarski paradox exists.

If the original word was capitalised, then the first letter of its abbreviation should retain the capital, for example Lev.

If, for example, a string sounds the note C when plucked, a string twice as long will sound the same note an octave lower.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

Litigation for the purpose of profit is referred to as “ Ambulance chasing ”: If for the purpose of harassment, for example to silence critics, it is known as a strategic lawsuit against public participation ( SLAPP ).

If the defense makes no attempt to put the baserunner out ( for example, if the catcher doesn't even look his way ), the play is scored as defensive indifference ( also called fielder's indifference ), and no stolen base is credited to the runner.

If rotation is arrested, the energy stored in fashioning the concave surface must be dissipated, for example through friction, before an equilibrium flat surface is restored.

If organized as a division then the top manager is often known as an Executive Vice President ( for example, Todd Bradley who heads the Personal Systems Group in Hewlett Packard ).

If that business is a subsidiary which has considerably more independence then the title might be known as Chairman and CEO ( for example, Philip I. Kent of Turner Broadcasting System in Time Warner ).

If a new player feels that he or she needs assistance in learning the rules of craps, it is recommended to approach an empty craps table at a slow time of day ( for example, between 9 a. m. and 11 a. m .).

If dynamic re-routing is established, even if one or more nodes depart and abandon a downloading file, for example, the remaining nodes should still have the data needed to complete the download.

( If one string runs out of letters to compare, then it is deemed to come first ; for example, " cart " comes before " carthorse ".

If integration via the bus is achieved, the data warehouse, through its two data marts, will not only be able to deliver the specific information that the individual data marts are designed to do, in this example either " Sales " or " Production " information, but can deliver integrated Sales-Production information, which, often, is of critical business value.

If there is a change in the potential energy of a system ; for example μ < sub > 1 </ sub >> μ < sub > 2 </ sub > ( μ is Chemical potential ) an energy flow will occur from S < sub > 1 </ sub > to S < sub > 2 </ sub >, because nature always prefers low energy and maximum entropy.

If it is generally by temporary uninhabitability, for example a nuclear winter, then n < sub > r </ sub > may be relatively high.

The best known example is the ring of quaternions H. If we allow only rational instead of real coefficients in the constructions of the quaternions, we obtain another division ring.

Since mathematics is related to logic, he cites an example from mathematics: If we have a formula like ( a + b )( a-b )= a²-b² it does not tell us how to think mathematically.

If the electrode has a positive potential with respect to the SHE, then that means it is a strongly reducing electrode which forces the SHE to be the anode ( an example is Cu in aqueous CuSO < sub > 4 </ sub > with a standard electrode potential of 0. 337 V ).

If they have been damaged ( from rheumatic fever, for example ) the risk of bacteria attachment is increased.