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.

These can range from simple spelling changes and word forms to switching the entire writing system itself, as when Turkey switched from the Arabic alphabet to a Turkish alphabet of Latin origin.

These can be as simple as a searchlight for a police helicopter or as complicated as the tactical system for an airborne early warning platform.

These simple ciphers and examples are easy to crack, even without plaintext-ciphertext pairs.

These individuals are often capable of relatively simple forms of visual awareness ( like being able to spatially locate an x in a picture ) but do not report anything concerning what it is like to experience these visual stimuli.

These range from a simple dulling of awareness produced by sedatives, to increases in the intensity of sensory qualities produced by stimulants, cannabis, or most notably by the class of drugs known as psychedelics.

These atomic orbitals are known to have specific angular relationships between each other, and thus the valence bond model can successfully predict the bond angles observed in simple molecules.

These composite bows, made of several layers, are much stronger and more efficient in releasing energy than simple wooden bows.

These humble scenes deal with simple, everyday activities, yet they also have functioned as a source of documentary information about a level of French society not hitherto considered a worthy subject for painting.

: These have a region of operation showing negative resistance caused by quantum tunneling, allowing amplification of signals and very simple bistable circuits.

These simple resolvers ( called " stub resolvers ") rely on a recursive name server to perform the work of finding information for them.

These hypothetical forms of life range from simple bacteria-like organisms to beings far more complex than humans.

These simple earning rules work well for small or simple projects because generally each activity tends to be fairly short in duration.

These were the second family of finite simple groups, after the alternating groups.

These point systems are typically simple enough to be manually calculated by a " league commissioner.

These short ( often one small reel ) films were often simple visual aids and accompaniments to live lectures and speeches, and were carried from city to city, town to town, village to village ( along with the lecturers ) to indoctrinate the entire countryside, even reaching areas where film had not been previously seen.

" These summaries were usually simple concatenations of received replies with little to no quality checking.

These include alpha-amylase from bacteria, which converts starch to simple sugars, chymosin from bacteria or fungi that clots milk protein for cheese making, and pectinesterase from fungi which improves fruit juice clarity.

These aim to make it simple and seamless for researchers to use GÉANT to work together, wherever they are located.

These other metals and their alloys can be cold-worked, or melted in simple pottery kilns and cast in molds ; but smelted iron requires hot-working and can be melted only in specially designed furnaces.

These simple relationships hold true only when there is no mutual coupling of magnetic fields between individual inductors.

These types of lamps are still in use today in areas of the world without electricity, because they give a much better light than a simple wick-type lamp does ..

These functions were more complex than simple AND and OR gates.

These formulas can even serve as the definition of the trigonometric functions for complex arguments x.

These results, however, are very sensitive to the accuracy of the twiddle factors used in the FFT ( i. e. the trigonometric function values ), and it is not unusual for incautious FFT implementations to have much worse accuracy, e. g. if they use inaccurate trigonometric recurrence formulas.

These two researchers developed several formulas for mineral nutrient solutions, known as Hoagland solution.

These same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations.

These formulas provide the solution for the initial-value problem for the wave equation.

These changes can be represented in formulas by inserting appropriate electrons into each half-reaction:

These formulas however only provide the calculation for the τ = τ < sub > 0 </ sub > case.

These formulas may be used when h is much smaller than the radius of the Earth ( 6371 km ), including all views from any mountaintops, aeroplanes, or high-altitude balloons.

These formulas characterize the periapsis and apoapsis of an orbit:

These formulas are traditionally used in analog televisions and equipment ; digital equipment such as HDTV and digital video cameras use Y ' CbCr.

These formulas are connected to the Schubert decomposition of the Grassmannian, and are q-analogs of the Betti numbers of complex Grassmannians.

These formulas are the basis for comparing and investigating the nature of non-random patterns in the structure of food web networks among many different types of ecosystems.

These formulas are generalized by the Faà di Bruno's formula.

These formulas can also be written using Lagrange's notation.

These formulas contain the " slope " of the line connecting P and Q, hence involve divisions between residue classes modulo n, which can be performed using the extended Euclidean algorithm.

These operators are direct extensions of their complex analogs: if and are taken from the real subset of complex numbers, the appearance of the conjugate in the formulas has no effect, so the operators are the same as those for the complex numbers.

These ideas were regarded as dynamic forces that Herbart attempted to explain by means of mathematical formulas.

These formulas for denatured alcohol are found in 27 CFR part 21 of the Code of Federal Regulations.

These formulas are for single-frequency sine waves or narrowband signals.

These formulas only state in another form the assertions in the table of derivatives.

These formulas all provide a different view into the processes that generate longshore drift.

These five formulas are:

These formulas give the explicit numbers of rational curves of all degrees in a large class of Calabi – Yau manifolds, in terms of the Picard – Fuchs equations of the corresponding mirror manifolds.

These two formulas, added together, produce