If the force required to remove the coatings is plotted against film thickness, a graph as illustrated schematically in Fig. 5 may characteristically result.

If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point.

If the function f is not linear ( i. e. its graph is not a straight line ), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.

If f is a continuous function, meaning that its graph is an unbroken curve with no gaps, then Q is a continuous function away from.

If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

If this triangulated graph is colorable using four colors or less, so is the original graph since the same coloring is valid if edges are removed.

If there is a graph requiring 5 colors, then there is a minimal such graph, where removing any vertex makes it four-colorable.

If the graph G is connected, then the rank of the free group is equal to 1 − χ ( G ): one minus the Euler characteristic of G.

If the graph does not contain any cycles ( i. e. it's an acyclic graph ), its girth is defined to be infinity.

If the graph is directed, the direction is indicated by drawing an arrow.

If A is nonzero, then the x-intercept, that is, the x-coordinate of the point where the graph crosses the x-axis ( where, y is zero ), is − C / A.

If B is nonzero, then the y-intercept, that is the y-coordinate of the point where the graph crosses the y-axis ( where x is zero ), is − C / B, and the slope of the line is − A / B.

* If asked to imagine the graph of the relationship y = ax < sup > 2 </ sup >, one typically visualizes a range of values of x, but only one value of a.

( If the graph has no weights, 1 indicates an edge, 0 indicates no edge.

If no path exists between two cities, adding an arbitrarily long edge will complete the graph without affecting the optimal tour.

If a variable undergoes regular oscillations, and a graph of the system is drawn with the oscillating variable as the vertical axis and time as the horizontal axis, the amplitude is visually represented by the vertical distance between the extrema of the curve and the equilibrium value.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.

If it is constrained to bury the cable only along certain paths, then there would be a graph representing which points are connected by those paths.

If there are n vertices in the graph, then each tree has n-1 edges.

If x and y are vectors, then the best linear approximation to the graph of f depends on how f changes in several directions at once.

If this fragment is part of a larger graph, then any Hamiltonian cycle through the graph must go in or out of the top vertex ( and either one of the lower ones ).

`` If Blue Throat has his way he'll keep us all cooped up in here for days '', he said.

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If any one of them has any power to veto the Secretary General's decisions the nature of the organization will have changed.

If this new Bible does not increase in significance by repeated readings throughout the years, it will not survive the ages as has the King James Version.

If the case is thus determined by us to be domestic, the court has no jurisdiction.

If this capacity had not failed them, they would see that their enemy has made a disastrous miscalculation.

If the new Soviet series has followed the general pattern of previous Russian tests, the shots were roughly half fission and half fusion, meaning a fission yield of 30 to 40 megatons thus far.

If the superintendents do not receive more cooperation from Handlers, it has been suggested that licensed Judges also be qualified to judge this Class.

If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.

If design head has a deep cavity, clay lid will be quite thick at this point ; ;

If you run into excess plug fouling on one truck, check to be sure that the rig has a thermostat.

If we manage to keep track of a Bombus queen after she has left her feeding place, we may discover the snug little hideout which she has fixed up for herself when she woke up from her winter sleep.

If cell Af has not previously been assigned as the information cell of a form in the text-form list, it is now assigned as the information cell of Af.

If of the founders of glottochronology Swadesh has escaped our steady plodding, and Lees has repudiated his own share in the founding, that is no reason why we should swerve.

If the transferor has substantial assets other than the claim, it seems reasonable to assume no corporation would be willing to acquire all of its properties in the dim hope of collecting a claim for refund of taxes.

If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.

If the distant patron of the suburban branch has been frightened away from downtown by traffic problems, however, the city store can only pressure the politicians to do something about the highways or await the completion of the federal highway program.

If a statement has been assigned an address in the index word area

If she has not had such experiences, the female's normal adolescent degree of indecision will be compounded.

If the change, at first sight, seems minor, we may recall that it took the Italian painters about two hundred years to make an analogous change, and the Italian painters, by universal consent, were the most brilliant group of geniuses any art has seen.

If Barnett doesn't call a special session in 1961, it will be the first year in the last decade that the Legislature has not met in regular or special session.

If the church has followed the plan of cultivation of prospects and carried through a program of membership preparation as outlined earlier in this book, the process of assimilation and growth will be well under way.