If one assumes that the average flux did not change between measurements, a mass-distribution curve is obtained which relates the flux of particles larger than a given radius to the inverse 7/2 power of the radius.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

In the following paper it is shown that in a certain definite sense, exactly an odd number of squares can be inscribed in every such curve which does not contain an infinite number of inscribed squares.

If the vertex is at Af, and if the interior of C is on the left as one moves in the direction of increasing t, then every such corner can be found from the curve obtained by rotating C clockwise through 90-degrees about the vertex.

But Af is just the curve Af translated without rotation through a small arc, for Af is always obtained by rotating C through exactly 90-degrees.

The arc is itself a segment of an analytic curve.

Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

The order of this congruence is Af, since Af secants of a curve of symbol ( B ) on a quadric surface pass through an arbitrary point.

For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.

Each generator, **yl, of Af is also exceptional, for each is transformed into the entire congruence of secants of the curve into which that generator is transformed by the point involution on Q.

Hence C' is a Af curve on Q.

By ( 1 ), the image of this pencil is a ruled surface of order Af which is met by the plane of the pencil in a curve, C, of order Af.

To avoid this contradiction it is necessary that C be composite, with the secant of **zg and a curve of order Af as components.

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.

This contradicts the preceding observations, and so, under the assumption of this paper, we must reject the possibility that **zg is a Af curve on a quadric surface.

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.

We assume that average total unit cost in the relevant region of operation is constant with respect to quantity produced ( the average cost curve is horizontal, and therefore is identical with the marginal cost curve ), and is the same for every firm ( and therefore for the industry ).

These are defined by a simple involutorial transformation of the points in which a general line meets a nonsingular quadric surface bearing a curve of symbol Af.

The curve has a shape similar to the numeral 8 and to the ∞ symbol.

A symbol of Schmitt trigger shown with a non-inverting hysteresis curve embedded in a buffer amplifier | buffer.

The symbol for Schmitt triggers in circuit diagrams is a triangle with a symbol inside representing its ideal hysteresis curve.

Other symbols show a hysteresis curve ( which may be inverting or non-inverting ) embedded in a buffer followed by a bubble, which is similar to the traditional symbol for a inverter ( logic gate ) | digital inverter that shows a buffer followed by a bubble.

Typical hysteresis curve ( Non-inverting ) ( which matches the curve shown on a # two thresholds | Schmitt trigger symbol )

For example, if the pilot had selected an airport to the left, then this symbol would curve off to the left and down.

Moreover, as the net impulse produced by rotating mass particles along a circle is zero ( in Dean drive ), he proposed the transformation of the aforementioned circle to a figure-eight-shaped curve ( symbol of infinity ) in which only the upper ( or lower ) 180 degrees are drawn thus causing anti-gravity effects.

The set of intersections of Af, the rotated curve, with the original curve C consists of just the set of forward corner points on C corresponding to the vertex at Af, plus the vertex itself.

A continuous change in T through an amount E results in a translation along an analytic arc of the curve Af.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

A conic, C, being a ( 1, 1 ) curve on Q, meets the image of any line of Af, which we have already found to be a Af curve on Q, in Af points.

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.

For Dunedin, George Smith Duncan further developed the Hallidie model, introducing the pull curve and the slot brake ; the former was a way to pull cars through a curve, since Dunedin's curves were too sharp to allow coasting, while the latter forced a wedge down into the cable slot to stop the car.

A plot of the first few factorials makes clear that such a curve can be drawn, but it would be preferable to have a formula that precisely describes the curve, in which the number of operations does not depend on the size of n. The simple formula for the factorial, n < nowiki >!</ nowiki > = 1 × 2 × … × n, cannot be used directly for fractional values of n since it is only valid when n is a natural number ( i. e., a positive integer ).

The relation between the tangent vectors defined earlier and derivations is as follows: if γ is a curve with tangent vector γ '( 0 ), then the corresponding derivation is D ( ƒ ) = ( ƒ ∘ γ )'( 0 ) ( where the derivative is taken in the ordinary sense, since ƒ ∘ γ is a function from (- 1, 1 ) to R ).

A titration curve is a curve in the plane whose x-coordinate is the volume of titrant added since the beginning of the titration, and whose y-coordinate is the concentration of the analyte at the corresponding stage of the titration ( in an acid-base titration, the y-coordinate is usually the pH of the solution ).

3 would have no effect on equilibrium quantities demanded, since the budget line would rotate around the corner of the indifference curve.

One can determine a value of current ( I ) for a given value of applied voltage ( V ) from the curve, but not from Ohm's law, since the value of " resistance " is not constant as a function of applied voltage.

It was also in 1960 that Patricia DeCoursey invented the phase response curve, one of the major tools used in the field since.

The resulting futures or forward curve would typically be downward sloping ( i. e. " inverted "), since contracts for further dates would typically trade at even lower prices.

The futures or forward curve would typically be upward sloping ( i. e. " normal "), since contracts for further dates would typically trade at even higher prices.

The steering wheel sensor also helps in the operation of Cornering Brake Control ( CBC ), since this will tell the ABS that wheels on the inside of the curve should brake more than wheels on the outside, and by how much.

The integral is usually around a closed curve, since electric currents can only flow around closed paths.

The " short-run Phillips curve " is also called the " expectations-augmented Phillips curve ", since it shifts up when inflationary expectations rise, Edmund Phelps and Milton Friedman argued.

* If we found at some stage ( the point at infinity on the elliptic curve ), then again we should start over with a new curve and starting point, since is the zero element for, so after this point we would be just repeating.

The most interesting cases for ECM are and, since they force the group orders of the curve modulo primes to be divisible by 12 and 16 respectively.

the two part tariff is another form of price discrimination where the producer charges an initial fee then a secondary fee for the use of the product, an example of this is razors, you pay an initial cost for the Gillette razor and then pay for the replacement blades, this pricing strategy works because it shifts the demand curve to the right since you have already paid for the initial blade holder you will buy the blades which are now cheaper than buying a disposable razor,

Any timelike curve admits a comoving observer whose " time axis " corresponds to that curve, and, since no observer is privileged, we can always find a local coordinate system in which lightcones are inclined at 45 degrees to the time axis.