In New Jersey, for example, the Administrative Office of the Court has promulgated a form of notice of appeal for use by appellants, though using this exact form is not mandatory and the failure to use it is not a jurisdictional defect provided that all pertinent information is set forth in whatever form of notice of appeal is used.

In the second example CH < sub > 3 </ sub > COOH undergoes the same transformation, in this case donating a proton to ammonia ( NH < sub > 3 </ sub >), but cannot be described using the Arrhenius definition of an acid because the reaction does not produce hydronium.

A graphical expression on Euclid's algorithm using example with 1599 and 650.

One example is the Banach – Tarski paradox which says that it is possible to decompose (" carve up ") the 3-dimensional solid unit ball into finitely many pieces and, using only rotations and translations, reassemble the pieces into two solid balls each with the same volume as the original.

However, the various preconditions for the development at Ford stretched far back into the 19th century, from the gradual realization of the dream of interchangeability, to the concept of reinventing workflow and job descriptions using analytical methods ( the most famous example being scientific management ).

John Hick also raises some questions regarding personal identity in his book, Death and Eternal Life using an interesting example of a person ceasing to exist in one place while an exact replica appears in another.

For example, if two characters are wrestling the relevant attribute is Strength ; a character could reveal a weapon, changing it to Warfare ; they could try to overcome the other character's mind using a power, changing it to Psyche ; or they could concentrate their strength on defense, changing it to Endurance.

Artists might work in both styles at different times or even mix the styles, creating an intellectually Romantic work using a Neoclassical visual style, for example.

Typically, young children will make an ASL sign in the correct location and use the correct hand motion, but may be able only to approximate the hand shape, for example, using one finger instead of three in signing water.

An anagram is a type of word play, the result of rearranging the letters of a word or phrase to produce a new word or phrase, using all the original letters exactly once ; for example orchestra can be rearranged into carthorse.

The Victorian love of anagramming as recreation is alluded to by Augustus De Morgan using his own name as example ; " Great Gun, do us a sum!

He adopted Ubu's ridiculous and pedantic figures of speech ; for example, he referred to himself using the royal we, and called the wind " that which blows " and the bicycle he rode everywhere " that which rolls ".

For example, using Cartesian coordinates on the plane, the distance between two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >) is defined by the formula

Take as an example a program that looks up a specific entry in a sorted list of size n. Suppose this program were implemented on Computer A, a state-of-the-art machine, using a linear search algorithm, and on Computer B, a much slower machine, using a binary search algorithm.

For example, if 95 % of the program can be parallelized, the theoretical maximum speedup using parallel computing would be 20 × as shown in the diagram, no matter how many processors are used.

For example, if a program needs 20 hours using a single processor core, and a particular portion of 1 hour cannot be parallelized, while the remaining promising portion of 19 hours ( 95 %) can be parallelized, then regardless of how many processors we devote to a parallelized execution of this program, the minimum execution time cannot be less than that critical 1 hour.

An example is methylacetylene ( propyne using IUPAC nomenclature ).

The Non-Commissioned Officer insignia are the same up until Warrant Officer ranks, where they are stylised for Australia ( for example, using the Australian, rather than the British coat of arms ).

In rural areas the grid's cost and impacts can be reduced by using single wire earth return systems ( for example, the MALT-system ).

An example of such a state within the common law jurisdiction, and using the black letter legal doctrine is Canada.

Many other BBS networks followed the example of FidoNet, using the same standards and the same software.

A notable example was Phil Katz's PKARC ( and later PKZIP, using the same ". zip " algorithm that WinZip and other popular archivers now use ); also other concepts of software distribution like freeware, postcardware like JPEGview and donationware like Red Ryder for the Macintosh first appeared on BBS sites.

The symphony was the first example of a major composer using voices in a symphony ( thus making it a choral symphony ).

A prototypical example of an algorithm is Euclid's algorithm to determine the maximum common divisor of two integers ; an example ( there are others ) is described by the flow chart above and as an example in a later section.

For example, the subprogram in Euclid's algorithm to compute the remainder would execute much faster if the programmer had a " modulus " ( division ) instruction available rather than just subtraction ( or worse: just Minsky's " decrement ").

In classical geometry, a proposition may be a construction that satisfies given requirements ; for example, Proposition 1 in Book I of Euclid's elements is the construction of an equilateral triangle.

Regardless of the form of the postulate, however, it consistently appears to be more complicated than Euclid's other postulates ( which include, for example, " Between any two points a straight line may be drawn ").

For example, in Book I of Euclid's Elements, a line is defined as a " breadthless length " ( Def.

For example, the first and fourth of Euclid's postulates, that there is a unique line between any two points and that all right angles are equal, hold in elliptic geometry.

For an example of homogeneity, note that Euclid's proposition I. 1 implies that the same equilateral triangle can be constructed at any location, not just in locations that are special in some way.

However, Euclid's original proof of this proposition is general, valid, and does not depend on the figure used as an example to illustrate one given configuration.

See, for example, Euclid's algorithm for finding the greatest common divisor of two numbers.

A formal system need not be mathematical as such, Spinoza's Ethics for example imitates the form of Euclid's Elements.

Take the historical development of geometry as an example ; the first steps in the abstraction of geometry were made by the ancient Greeks, with Euclid's Elements being the earliest extant documentation of the axioms of plane geometry — though Proclus tells of an earlier axiomatisation by Hippocrates of Chios.

E. T. Bell in his book Men of Mathematics wrote about Lobachevsky's influence on the following development of mathematics: The boldness of his challenge and its successful outcome have inspired mathematicians and scientists in general to challenge other ' axioms ' or accepted ' truths ', for example the ' law ' of causality which, for centuries, have seemed as necessary to straight thinking as Euclid's postulate appeared till Lobatchewsky discarded it.

The classic example is that of Euclid's ( see Euclid's Elements ) geometry ; its hundreds of propositions can be deduced from a set of definitions, postulates, and common notions: all three of which constitute first principles.

: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.

An example of the online algorithm for kurtosis implemented as described is:

For example, if for a given problem size a parallelized implementation of an algorithm can run 12 % of the algorithm's operations arbitrarily quickly ( while the remaining 88 % of the operations are not parallelizable ), Amdahl's law states that the maximum speedup of the parallelized version is times as fast as the non-parallelized implementation.

For example, algorithms are known for factoring an n-bit integer using just over 2n qubits ( Shor's algorithm ).

In contrast, randomized algorithms like the PPSZ algorithm by Paturi, Pudlak, Saks, and Zani set variables in a random order according to some heuristics, for example bounded-width resolution.

For example, the security available with a 1024-bit key using asymmetric RSA is considered approximately equal in security to an 80-bit key in a symmetric algorithm ( Source: RSA Security ).

Computation is a process following a well-defined model understood and expressed as, for example, an algorithm, or a protocol.

An Earley parser is an example of such an algorithm, while the widely used LR and LL parsers are simpler algorithms that deal only with more restrictive subsets of context-free grammars.

Since the invention of the MIDI system in the early 1980s, for example, some people have worked on programs which map MIDI notes to an algorithm and then can either output sounds or music through the computer's sound card or write an audio file for other programs to play.

This is done for example in the Jenkins-Traub algorithm.

) The inherent latency of the coding algorithm can be critical ; for example, when there is two-way transmission of data, such as with a telephone conversation, significant delays may seriously degrade the perceived quality.

A decision problem which can be solved by an algorithm, such as this example, is called decidable.

As an example, if we have a color depth of 12bits / pixel and an algorithm that compresses at 40x, then BPP equals 0. 3 ( 12 / 40 ).