We now observe that the case in which **zg is a Af curve on a quadric is impossible if the complex of singular lines consists exclusively of the lines which meet Aj.

Continuing with the case in which **zg is a Af curve on a quadric Q, we first observe that the second regulus of Q consists precisely of the lines which join the two free intersections of **zg and the planes through any one of the multiple secants.

However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori.

When the rode is slack, the catenary curve presents a lower angle of pull on the anchor or mooring device than would be the case if it were nearly straight.

In this case, the curve has vertical asymptotes and this limits the span to πc.

* Dynamic as well as static cetenary curve equations derived – The equations governing the shape ( static case ) as well as dynamics ( dynamic case ) of a centenary is derived.

In that case, the curve would be at " y " =

This is because while the upward sloping aggregate labor supply would remain unchanged, instead of using the downward labor demand curve shown in the diagram above, monopsonistic employers would use a steeper downward sloping curve corresponding to marginal expenditures to yield the intersection with the supply curve resulting in a wage rate lower than would be the case under competition.

For a line, the secant between any two points is the line itself, but this is not the case for any other type of curve.

The money supply may be a vertical supply curve, if the central bank of a country chooses to use monetary policy to fix its value regardless of the interest rate ; in this case the money supply is totally inelastic.

On the other hand, the money supply curve is a horizontal line if the central bank is targeting a fixed interest rate and ignoring the value of the money supply ; in this case the money supply curve is perfectly elastic.

File: BitwiseTreesScaling. png | Behavior of Fredkin-style tries as a function of size ( in this case, nedtries, which is an in-place implementation, and therefore has a much steeper curve than a dynamic memory based trie implementation )

In this case the head keeps the same level at all times, whereas the hip follows a sine curve.

When two forces are present and thus enter in conflict, as this is the case with the curve or the zigzag line, we are in domain of drama ".

On the other hand some algorithms like hash tables have very poor worst case behaviours, but a well written hash table of sufficient size will statistically never give the worst case ; the average number of operations performed follows an exponential decay curve, and so the run time of an operation is statistically bounded.

* The Laffer Curve: Past, Present and Future: A detailed examination of the theory behind the Laffer curve, and many case studies of tax cuts on government revenue in the United States

The consumer surplus ( individual or aggregated ) is the area under the ( individual or aggregated ) demand curve and above a horizontal line at the actual price ( in the aggregated case: the equilibrium price ).

Note that in this special case where the consumer demand curve is linear, consumer surplus is the area of a triangle.

On the other hand, an upward shift in the IS curve along a vertical LM curve will lead to higher interest rates, but no change in output ( this case represents the Treasury View ).

More general type of asymptotes can be defined in this case.

In this special case, the rectangle joining the four points on the asymptotes directly above and below the vertices is a square, since the lengths of its sides 2a 2b.

But in our case -- and neither my wife nor I have extreme views on integration, nor are we given to emotional outbursts -- the situation has ruined one or two valued friendships and come close to wrecking several more.

( There are two receivers in case one should be dropped and damaged.

Some years ago Julian Huxley proposed to an audience made up of members of the British Association for the Advancement of Science that `` man's supernormal or extra-sensory faculties are ( now ) in the same case as were his mathematical faculties during the ice age ''.

But, here again, comparative benchmarks are lacking, and we do not know, in any case, what measure of profoundity and intensity to expect from healthy, young, secure and relatively inexperienced persons ; ;

The novels and stories like Pohl's Drunkard's Walk ( 1960 ), with the focus on adventure and with the dystopian elements only a dim background -- in this case an uneasy, overpopulated world in which the mass of people do uninteresting routine jobs while a carefully selected, university-trained elite runs everything -- are in all likelihood as numerous as dystopias.

That fact is very clearly illustrated in the case of the many present-day intellectuals who were Communists or near-Communists in their youth and are now so extremely conservative ( or reactionary, as many would say ) that they can define no important political conviction that does not seem so far from even a centrist position as to make the distinction between Mr. Nixon and Mr. Khrushchev for them hardly worth noting.

The very rules and regulations in every city are the primary case of slum conditions.

Our litterbug ordinances are not enforced and I have yet to read of a conviction in a littering case.

The replies from each individual town are not given in detail because the questions asked the personal opinion of the several assessors and are not necessarily the established policy of the town in each case.

All payments authorized under Section 7 of this Title shall be disbursed from the proper fund, as the case may be, and all amounts covered into the Treasury to the credit of the aforesaid funds are hereby permanently appropriated for the making of the payments authorized by Section 7 of this Title.

As is the case with the allotment provisions for support of vocational rehabilitation services, the matching requirements are also based on a statutory formula.

The District Courts, in the framing of equitable decrees, are clothed ' with large discretion to model their judgements to fit the exigencies of the particular case.

The same restrictions apply after local sunset in the case of class 3, stations operating on regional channels, which after that time are required to operate under nighttime restrictions in order to protect each other.

This conformational entropy is, in this case, equal to the usual entropy, for there are no other changes or other energies involved.

As is the case with the surface-active agent, the requirements for builders to be used in detergent compositions for washing textiles are also high.

The reader will find it helpful to think of the special case when the primes are of degree 1, and even more particularly, to think of the proof of Theorem 10, a special case of this theorem.

In each case, lines of the bundles are transformed by involutions within the pencils they determine with the multiple secant.

In the first case the fixed elements within each pencil are the multiple secant and the line joining the vertex, P, to the intersection of **zg and the plane of the pencil which does not lie on the multiple secant.

The multiple secants, of course, are exceptional and in each case are transformed into cones of order Af.

Thus, in the example cited above Fromm rests his whole case on the premise that the workers are being deprived unconsciously, unknowingly, of fulfillment, and then supports this with survey data reporting conscious, experienced frustrations.

Presumably the interfacial bond strength and gross cohesive properties are identical in each case.

Merchant has found that the same basic relationships which describe the geometry and force systems in the case of the cutting mechanism can also be applied to the discontinuous chip formation provided the proper values of instantaneous shear angle and instantaneous chip thickness or cross-sectional area are used.