For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.

For each of these lines meets Q in three points, namely two points on **zg and one point on one of the multiple secants.

Algorithm versus function computable by an algorithm: For a given function multiple algorithms may exist.

Many who side with this view disagree that Luke portrays Christianity or the Roman Empire as harmless and thus reject the apologetic view because “ Acts does not present Christians as politically harmless or law abiding for there are a large number of public controversies concerning Christianity, particularly featuring Paul .” For example, to support this view Cassidy references how Paul is accused of going against the Emperor because he is “ saying that there is another king named Jesus .” ( Acts 17: 7 ) Furthermore, there are multiple examples of Paul ’ s preaching causing uprisings in various cities ( Acts 14: 2 ; 14: 19 ; 16: 19-23 ; 17: 5 ; 17: 13-14 ; 19: 28-40 ; 21: 27 ).

For example, raw uncompressed PCM audio ( 44. 1 kHz, 16 bit stereo, as represented on an audio CD or in a. wav or. aiff file ) has long been a standard across multiple platforms, but its transmission over networks is slow and expensive compared with more modern compressed formats, such as MP3.

For example, each record in an " Employees ' Skills " table might contain an Employee ID, Employee Address, and Skill ; thus a change of address for a particular employee will potentially need to be applied to multiple records ( one for each of his skills ).

For a decision which generates multiple cash flows in multiple time periods, all the cash flows must be discounted and then summed into a single net present value.

For example, the skills, rules, and knowledge taxonomy of human behavior has been used by designers to develop systems that are compatible with multiple " ways of knowing ": abstract analytic reasoning, experience-based ' gut feelings ', and ' craft ' sensorimotor skills.

The GCD of two numbers a and b is the product of the prime factors shared by the two numbers, where a same prime factor can be used multiple times, but only as long as the product of these factors divides both a and b. For example, since 1386 can be factored into 2 × 3 × 3 × 7 × 11, and 3213 can be factored into 3 × 3 × 3 × 7 × 17, the greatest common divisor of 1386 and 3213 equals 63 = 3 × 3 × 7, the product of their shared prime factors.

For example, the Survey of Professional Forecasters contains forecasts for many forecasters ( cross-sectional observations ), at many points in time ( time series observations ), and at multiple forecast horizons ( a third dimension ).

For example, one of IBM's FORTRAN compilers ( H Extended IUP ) had a level of optimization which reordered the machine code instructions to keep multiple internal arithmetic units busy simultaneously.

For example, the cyclic group of addition modulo n can be obtained from the integers by identifying elements that differ by a multiple of n and defining a group structure that operates on each such class ( known as a congruence class ) as a single entity.

For example, introns are extremely common within the nuclear genome of higher vertebrates ( e. g. humans and mice ), where protein-coding genes almost always contain multiple introns, while introns are rare within the nuclear genes of some eukaryotic microorganisms, for example baker's / brewer's yeast ( Saccharomyces cerevisiae ).

For easier distribution of large programs, multiple class files may be packaged together in a. jar file ( short for Java archive ).

For example, 10 is a multiple of 5 because, so 10 is divisible by 5 and 2.

For each computer built, all of these had to be placed and soldered onto printed circuit boards, and often multiple boards would have to be interconnected in a chassis.

For example, when Rooster Teeth produced The Strangerhood using The Sims 2, a game that encourages the use of its AI, the group had to create multiple instances of each character to accommodate different moods.

For example, an operation on a character string could be done as a single machine instruction, thus avoiding multiple instruction fetches.

For example, 15 is the product of 3 and 5, and is both a multiple of 3 and a multiple of 5.

For fixed-wing aircraft, single syllable words denoted piston-prop and turboprop, while multiple syllables denoted jets.

For example, in a real nucleus, each nucleon is in multiple locations at once, spread throughout the nucleus.

For some, the underlying mechanism influencing the bone metabolism is straightforward, whereas for others the causes are multiple or unknown.

For example, Java is both an object-oriented language ( because it encourages object-oriented organization ) and a concurrent language ( because it contains built-in constructs for running multiple threads in parallel ).

For example, methods to locate a gene within a sequence, predict protein structure and / or function, and cluster protein sequences into families of related sequences.

For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1. 2 × 10 < sup > 12 </ sup > ( over a trillion ).

For the preceding property of unions of non-decreasing sequences of convex sets, the restriction to nested sets is important: The union of two convex sets need not be convex.

The completion of M can be constructed as a set of equivalence classes of Cauchy sequences in M. For any two Cauchy sequences ( x < sub > n </ sub >)< sub > n </ sub > and ( y < sub > n </ sub >)< sub > n </ sub > in M, we may define their distance as

For example, the most common hemoglobin sequences in humans and chimpanzees are nearly identical, differing by only one amino acid in both the alpha and the beta globin protein chains.

For a discussion of other sequences taught elsewhere, see here.

For example, more than a million copies of the Alu sequence are present in the human genome, and these sequences have now been recruited to perform functions such as regulating gene expression.

For more details on the sequences of operations used for various quantum algorithms, see universal quantum computer, Shor's algorithm, Grover's algorithm, Deutsch-Jozsa algorithm, amplitude amplification, quantum Fourier transform, quantum gate, quantum adiabatic algorithm and quantum error correction.

For many sequences of nonrandom operations, splay trees perform better than other search trees, even when the specific pattern of the sequence is unknown.

For a given alphabet an escape character's purpose is to start character sequences ( so named escape sequences ) which have to be interpreted differently from the same characters occurring alone.

For example, in the genomes of humans and mice, which diverged from a common ancestor 65 – 75 million years ago, protein-coding DNA sequences account for only about 20 % of conserved DNA, with the remaining 80 % of conserved DNA represented in noncoding regions.

For finite random sequences, Kolmogorov defined the " randomness " as the entropy, i. e. Kolmogorov complexity, of a string of length K of zeros and ones as the closeness of its entropy to K, i. e. if the complexity of the string is close to K it is very random and if the complexity is far below K, it is not so random.

For many of the pivotal action sequences, such as the " Burly Brawl ", he collaborated with Juno Reactor.

For example, many songs on the official DVD had their soundtracks altered, mainly in sequences where there were originally microphone problems.

For sequences x < sub > 1 </ sub >, ..., x < sub > n </ sub > and y < sub > 1 </ sub >, ..., y < sub > m </ sub > of random variables, we have

For the zero gravity sequences, the ILM team matched Visual Concepts Engineering's phaser blasts by hand-painting the effect in Photoshop.

For this film, the Rafferty brothers and Loader formed the production company " Archives Project Inc ." The filmmakers opted not to use narration, and instead they deployed carefully constructed sequences of film clips to make their points.

For a formation to be recognised as evaporitic it may simply require recognition of halite pseudomorphs, sequences composed of some proportion of evaporite minerals, and recognition of mud crack textures or other textures.

For Bach especially, the suite form was a base on which to spin more elaborate sequences.

The Oswald cartoons which Harman and Ising produced in 1928 and 1929 already show their distinctive style, which would later characterize their work on the Looney Tunes and Merrie Melodies cartoon series for Warner Bros. For example, in Sick Cylinders ( 1929 ) there are sequences which were later remade very closely in such Harman and Ising Warner Bros. efforts as Sinkin ' in the Bathtub ( 1930 ) and Bosko's Holiday ( 1931 ).

For the reissue, the original front-and-end title sequences were altered.