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Asymptote

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.

The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos) which means "not falling together", from ἀ priv. + σύν "together" + πτωτ-ός "fallen". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve.

There are three kinds of asymptotes: horizontal, vertical and oblique. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. Vertical asymptotes are vertical lines near which the function grows without bound. An oblique asymptote has a slope that is non-zero but finite, such that the graph of the function approaches it as x tends to +∞ or −∞.

More generally, one curve is a curvilinear asymptote of another (as opposed to a linear asymptote) if the distance between the two curves tends to zero as they tend to infinity, although the term asymptote by itself is usually reserved for linear asymptotes.

Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph. The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis.

Introduction
The idea that a curve may come arbitrarily close to a line without actually becoming the same may seem to counter everyday experience. The representations of a line and a curve as marks on a piece of paper or as pixels on a computer screen have a positive width. So if they were to be extended far enough they would seem to merge, at least as far as the eye could discern. But these are physical representations of the corresponding mathematical entities; the line and the curve are idealized concepts whose width is 0 (see Line). Therefore, the understanding of the idea of an asymptote requires an effort of reason rather than experience.

Consider the graph of the function $$f(x) = \frac{1}{x}$$ shown in this section. The coordinates of the points on the curve are of the form $$\left(x, \frac{1}{x}\right)$$ where x is a number other than 0. For example, the graph contains the points (1, 1), (2, 0.5), (5, 0.2), (10, 0.1), ... As the values of $$x$$ become larger and larger, say 100, 1,000, 10,000 ..., putting them far to the right of the illustration, the corresponding values of $$y$$, .01, .001, .0001, ..., become infinitesimal relative to the scale shown. But no matter how large $$x$$ becomes, its reciprocal $$\frac{1}{x}$$ is never 0, so the curve never actually touches the x-axis. Similarly, as the values of $$x$$ become smaller and smaller, say .01, .001, .0001, ..., making them infinitesimal relative to the scale shown, the corresponding values of $$y$$, 100, 1,000, 10,000 ..., become larger and larger. So the curve extends farther and farther upward as it comes closer and closer to the y-axis. Thus, both the x and y-axis are asymptotes of the curve. These ideas are part of the basis of concept of a limit in mathematics, and this connection is explained more fully below.

Asymptotes of functions
The asymptotes most commonly encountered in the study of calculus are of curves of the form y = ƒ(x). These can be computed using limits and classified into horizontal, vertical and oblique asymptotes depending on their orientation. Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. As the name indicates they are parallel to the x-axis. Vertical asymptotes are vertical lines (perpendicular to the x-axis) near which the function grows without bound. Oblique asymptotes are diagonal lines such that the difference between the curve and the line approaches 0 as x tends to +∞ or −∞.

Vertical asymptotes
The line x = a is a vertical asymptote of the graph of the function y = ƒ(x) if at least one of the following statements is true:

 * 1) $$\lim_{x \to a^{-}} f(x)=\pm\infty,$$
 * 2) $$\lim_{x \to a^{+}} f(x)=\pm\infty,$$

where $$\lim_{x\to a^-}$$ is the limit as x approaches the value a from the left (from lesser values), and $$\lim_{x\to a^+}$$ is the limit as x approaches a from the right.

For example, if ƒ(x) = x/(x–1), the numerator approaches 1 and the denominator approaches 0 as x approaches 1. So
 * $$\lim_{x\to 1^{+}}\frac{x}{x-1}=+\infty$$
 * $$\lim_{x\to 1^{-}}\frac{x}{x-1}=-\infty$$

and the curve has a vertical asymptote x = 1.

The function ƒ(x) may or may not be defined at a, and its precise value at the point x = a does not affect the asymptote. For example, for the function

 * $$f(x) = \begin{cases} \frac{1}{x} & \text{if } x > 0, \\ 5 & \text{if } x \le 0. \end{cases}$$

has a limit of +∞ as x → 0+, ƒ(x) has the vertical asymptote x = 0, even though ƒ(0) = 5. The graph of this function does intersect the vertical asymptote once, at (0, 5). It is impossible for the graph of a function to intersect a vertical asymptote (or a vertical line in general) in more than one point. Moreover, if a function is continuous at each point where it is defined, it is impossible that its graph does intersect any vertical asymptote.

A common example of a vertical asymptote is the case of a rational function at a point x such that the denominator is zero and the numerator is non-zero.

If a function has a vertical asymptote, then it isn't necessarily true that the derivative of the function has a vertical asymptote at the same place. An example is
 * $$f(x) = \tfrac 1x + \sin(\tfrac 1x)\quad$$ at $$\quad x=0$$.

This function has a vertical asymptote at $$x=0,$$ because
 * $$\lim_{x\to0^+} f(x) = \lim_{x\to0^+}\left(\tfrac 1x + \sin\left(\tfrac 1x\right)\right) = +\infty,$$

and

 * $$\lim_{x\to0^-} f(x) = \lim_{x\to0^-}\left(\tfrac 1x + \sin\left(\tfrac 1x\right)\right) = -\infty$$.

The derivative of $$f$$ is the function
 * $$f'(x)=\frac{-(\cos(\tfrac 1x) + 1)}{x^2}$$.

For the sequence of points
 * $$x_n=\frac{(-1)^n}{(2n+1)\pi},\quad$$ for $$\quad n=0,1,2,\ldots$$

that approaches $$x=0$$ both from the left and from the right, the values $$f'(x_n)$$ are constantly $$0$$. Therefore, both one-sided limits of $$f'$$ at $$0$$ can be neither $$+\infty$$ nor $$-\infty$$. Hence $$f'(x)$$ doesn't have a vertical asymptote at $$x=0$$.

Horizontal asymptotes

Horizontal asymptotes are horizontal lines that the graph of the function approaches as $x → ±∞$. The horizontal line y = c is a horizontal asymptote of the function y = ƒ(x) if
 * $$\lim_{x\rightarrow -\infty}f(x)=c$$ or $$\lim_{x\rightarrow +\infty}f(x)=c$$.

In the first case, ƒ(x) has y = c as asymptote when x tends to $−∞$, and in the second ƒ(x) has y = c as an asymptote as x tends to $+∞$.

For example, the arctangent function satisfies
 * $$\lim_{x\rightarrow -\infty}\arctan(x)=-\frac{\pi}{2}$$ and $$\lim_{x\rightarrow+\infty}\arctan(x)=\frac{\pi}{2}.$$

So the line $y = –\pi/2$ is a horizontal asymptote for the arctangent when x tends to $–∞$, and $y = \pi/2$ is a horizontal asymptote for the arctangent when x tends to $+∞$.

Functions may lack horizontal asymptotes on either or both sides, or may have one horizontal asymptote that is the same in both directions. For example, the function $ƒ(x) = 1/(x^{2}+1)$ has a horizontal asymptote at y = 0 when x tends both to $−∞$ and $+∞$ because, respectively,
 * $$\lim_{x\to -\infty}\frac{1}{x^2+1}=\lim_{x\to +\infty}\frac{1}{x^2+1}=0.$$

Other common functions that have one or two horizontal asymptotes include $x ↦ 1/x$ (that has an hyperbola as it graph), the Gaussian function $$x\mapsto \exp(-x^2),$$ the error function, and the logistic function.

Oblique asymptotes
When a linear asymptote is not parallel to the x- or y-axis, it is called an oblique asymptote or slant asymptote. A function ƒ(x) is asymptotic to the straight line y = mx + n (m ≠ 0) if

 * $$\lim_{x \to +\infty}\left[ f(x)-(mx+n)\right] = 0 \, \mbox{ or } \lim_{x \to -\infty}\left[ f(x)-(mx+n)\right] = 0.$$

In the first case the line y = mx + n is an oblique asymptote of ƒ(x) when x tends to +∞, and in the second case the line y = mx + n is an oblique asymptote of ƒ(x) when x tends to −∞.

An example is ƒ(x) = x + 1/x, which has the oblique asymptote y = x (that is m = 1, n = 0) as seen in the limits
 * $$\lim_{x\to\pm\infty}\left[f(x)-x\right]$$
 * $$=\lim_{x\to\pm\infty}\left[\left(x+\frac{1}{x}\right)-x\right]$$
 * $$=\lim_{x\to\pm\infty}\frac{1}{x}=0.$$

Elementary methods for identifying asymptotes
The asymptotes of many elementary functions can be found without the explicit use of limits (although the derivations of such methods typically use limits).

General computation of oblique asymptotes for functions
The oblique asymptote, for the function f(x), will be given by the equation y = mx + n. The value for m is computed first and is given by

 * $$m\;\stackrel{\text{def}}{=}\,\lim_{x\rightarrow a}f(x)/x$$

where a is either $$-\infty$$ or $$+\infty$$ depending on the case being studied. It is good practice to treat the two cases separately. If this limit doesn't exist then there is no oblique asymptote in that direction.

Having m then the value for n can be computed by

 * $$n\;\stackrel{\text{def}}{=}\,\lim_{x\rightarrow a}(f(x)-mx)$$

where a should be the same value used before. If this limit fails to exist then there is no oblique asymptote in that direction, even should the limit defining m exist. Otherwise y = mx + n is the oblique asymptote of ƒ(x) as x tends to a.

For example, the function ƒ(x) = (2x2 + 3x + 1)/x has

 * $$m=\lim_{x\rightarrow+\infty}f(x)/x=\lim_{x\rightarrow+\infty}\frac{2x^2+3x+1}{x^2}=2$$ and then
 * $$n=\lim_{x\rightarrow+\infty}(f(x)-mx)=\lim_{x\rightarrow+\infty}\left(\frac{2x^2+3x+1}{x}-2x\right)=3$$

so that y = 2x + 3 is the asymptote of ƒ(x) when x tends to +∞.

The function ƒ(x) = ln x has

 * $$m=\lim_{x\rightarrow+\infty}f(x)/x=\lim_{x\rightarrow+\infty}\frac{\ln x}{x}=0$$ and then

 * $$n=\lim_{x\rightarrow+\infty}(f(x)-mx)=\lim_{x\rightarrow+\infty}\ln x$$, which does not exist.

So y = ln x does not have an asymptote when x tends to +∞.

Asymptotes for rational functions
A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes.

The degree of the numerator and degree of the denominator determine whether or not there are any horizontal or oblique asymptotes. The cases are tabulated below, where deg(numerator) is the degree of the numerator, and deg(denominator) is the degree of the denominator.

The vertical asymptotes occur only when the denominator is zero (If both the numerator and denominator are zero, the multiplicities of the zero are compared). For example, the following function has vertical asymptotes at x = 0, and x = 1, but not at x = 2.
 * $$f(x)=\frac{x^2-5x+6}{x^3-3x^2+2x}=\frac{(x-2)(x-3)}{x(x-1)(x-2)}$$

Oblique asymptotes of rational functions

When the numerator of a rational function has degree exactly one greater than the denominator, the function has an oblique (slant) asymptote. The asymptote is the polynomial term after dividing the numerator and denominator. This phenomenon occurs because when dividing the fraction, there will be a linear term, and a remainder. For example, consider the function
 * $$f(x)=\frac{x^2+x+1}{x+1}=x+\frac{1}{x+1}$$

shown to the right. As the value of x increases, f approaches the asymptote y = x. This is because the other term, 1/(x+1), approaches 0.

If the degree of the numerator is more than 1 larger than the degree of the denominator, and the denominator does not divide the numerator, there will be a nonzero remainder that goes to zero as x increases, but the quotient will not be linear, and the function does not have an oblique asymptote.

Transformations of known functions
If a known function has an asymptote (such as y=0 for f(x)=ex), then the translations of it also have an asymptote.
 * If x=a is a vertical asymptote of f(x), then x=a+h is a vertical asymptote of f(x-h)
 * If y=c is a horizontal asymptote of f(x), then y=c+k is a horizontal asymptote of f(x)+k

If a known function has an asymptote, then the scaling of the function also have an asymptote.

For example, f(x)=ex-1+2 has horizontal asymptote y=0+2=2, and no vertical or oblique asymptotes.
 * If y=ax+b is an asymptote of f(x), then y=cax+cb is an asymptote of cf(x)

General definition

Let A : (a,b) → R2 be a parametric plane curve, in coordinates A(t) = (x(t),y(t)). Suppose that the curve tends to infinity, that is:
 * $$\lim_{t\rightarrow b}(x^2(t)+y^2(t))=\infty.$$

A line ℓ is an asymptote of A if the distance from the point A(t) to ℓ tends to zero as t → b. From the definition, only open  curves  that  have  some  infinite branch can have an asymptote. No closed curve can have an asymptote.

For example, the upper right branch of the curve y = 1/x can be defined parametrically as x = t, y = 1/t (where t > 0). First, x → ∞ as t → ∞ and the distance from the curve to the x-axis is 1/t which approaches 0 as t → ∞. Therefore, the x-axis is an asymptote of the curve. Also, y → ∞ as t → 0 from the right, and the distance between the curve and the y-axis is t which approaches 0 as t → 0. So the y-axis is also an asymptote. A similar argument shows that the lower left branch of the curve also has the same two lines as asymptotes.

Although the definition here uses a parameterization of the curve, the notion of asymptote does not depend on the parameterization. In fact, if the equation of the line is $$ax+by+c=0$$ then the distance from the point A(t) = (x(t),y(t)) to the line is given by
 * $$\frac{|ax(t)+by(t)+c|}{\sqrt{a^2+b^2}}$$

if γ(t) is a change of parameterization then the distance becomes
 * $$\frac{|ax(\gamma(t))+by(\gamma(t))+c|}{\sqrt{a^2+b^2}}$$

which tends to zero simultaneously as the previous expression.

An important case is when the curve is the graph of a real function (a function of one real variable and returning real values). The graph of the function y = ƒ(x) is the set of points of the plane with coordinates (x,ƒ(x)). For this, a parameterization is
 * $$t\mapsto (t,f(t)).$$

This parameterization is to be considered over the open intervals (a,b), where a can be −∞ and b can be +∞.

An asymptote can be either vertical or non-vertical (oblique or horizontal). In the first case its equation is x = c, for some real number c. The non-vertical case has equation y = mx + n, where m and $$n$$ are real numbers. All three types of asymptotes can be present at the same time in specific examples. Unlike asymptotes for curves that are graphs of functions, a general curve may have more than two non-vertical asymptotes, and may cross its vertical asymptotes more than once.

Curvilinear asymptotes
Let A : (a,b) → R2 be a parametric plane curve, in coordinates A(t) = (x(t),y(t)), and B be another (unparameterized) curve. Suppose, as before, that the curve A tends to infinity. The curve B is a curvilinear asymptote of A if the shortest distance from the point A(t) to a point on B tends to zero as t → b. Sometimes B is simply referred to as an asymptote of A, when there is no risk of confusion with linear asymptotes.

For example, the function
 * $$y = \frac{x^3+2x^2+3x+4}{x}$$

has a curvilinear asymptote y = x2 + 2x + 3, which is known as a parabolic asymptote because it is a parabola rather than a straight line.

Asymptotes and curve sketching
Asymptotes are used in procedures of curve sketching. An asymptote serves as a guide line to show the behavior of the curve towards infinity. In order to get better approximations of the curve, curvilinear asymptotes have also been used although the term asymptotic curve seems to be preferred.

Algebraic curves
The asymptotes of an algebraic curve in the affine plane are the lines that are tangent to the projectivized curve through a point at infinity. For example, one may identify the asymptotes to the unit hyperbola in this manner. Asymptotes are often considered only for real curves, although they also make sense when defined in this way for curves over an arbitrary field.

A plane curve of degree n intersects its asymptote at most at n−2 other points, by Bézout's theorem, as the intersection at infinity is of multiplicity at least two. For a conic, there are a pair of lines that do not intersect the conic at any complex point: these are the two asymptotes of the conic.

A plane algebraic curve is defined by an equation of the form P(x,y) = 0 where P is a polynomial of degree n
 * $$P(x,y) = P_n(x,y) + P_{n-1}(x,y) + \cdots + P_1(x,y) + P_0$$

where Pk is homogeneous of degree k. Vanishing of the linear factors of the highest degree term Pn defines the asymptotes of the curve: setting $Q = P_{n}$, if $P_{n}(x, y) = (ax − by) Q_{n−1}(x, y)$, then the line
 * $$Q'_x(b,a)x+Q'_y(b,a)y + P_{n-1}(b,a)=0$$

is an asymptote if $$Q'_x(b,a)$$ and $$Q'_y(b,a)$$ are not both zero. If $$Q'_x(b,a)=Q'_y(b,a)=0$$ and $$P_{n-1}(b,a)\neq 0$$, there is no asymptote, but the curve has a branch that looks like a branch of parabola. Such a branch is called a parabolic branch, even when it does not have any parabola that is a curvilinear asymptote. If $$Q'_x(b,a)=Q'_y(b,a)=P_{n-1}(b,a)=0,$$ the curve has a singular point at infinity which may have several asymptotes or parabolic branches.

Over the complex numbers, Pn splits into linear factors, each of which defines an asymptote (or several for multiple factors). Over the reals, Pn splits in factors that are linear or quadratic factors. Only the linear factors correspond to infinite (real) branches of the curve, but if a linear factor has multiplicity greater than one, the curve may have several asymptotes or parabolic branches. It may also occur that such a multiple linear factor corresponds to two complex conjugate branches, and does not corresponds to any infinite branch of the real curve. For example, the curve x4 + y2 - 1 = 0 has no real points outside the square $$ |x|\leq 1, |y|\leq 1$$, but its highest order term gives the linear factor x with multiplicity 4, leading to the unique asymptote x=0.

Asymptotic cone
The hyperbola
 * $$\frac{x^2}{a^2}-\frac{y^2}{b^2}= 1$$

has the two asymptotes
 * $$y=\pm\frac{b}{a}x.$$

The equation for the union of these two lines is
 * $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=0.$$

Similarly, the hyperboloid
 * $$\frac{x^2}{a^2}-\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$$

is said to have the asymptotic cone

 * $$\frac{x^2}{a^2}-\frac{y^2}{b^2}-\frac{z^2}{c^2}=0.$$

The distance between the hyperboloid and cone approaches 0 as the distance from the origin approaches infinity.

More generally, consider a surface that has an implicit equation $$P_d(x,y,z)+P_{d-2}(x,y,z) + \cdots P_0=0,$$ where the $$P_i$$ are homogeneous polynomials of degree $$ i $$ and $$P_{d-1}=0$$. Then the equation $$P_d(x,y,z)=0$$ defines a cone which is centered at the origin. It is called an asymptotic cone, because the distance to the cone of a point of the surface tends to zero when the point on the surface tends to infinity.

title: Asymptote


text: Talk:Arbitration in the United States

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Arbitration in the United States


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Andrew S. Tanenbaum

Andrew Stuart Tanenbaum (born March 16, 1944), sometimes referred to by the handle ast, is an American computer scientist and professor emeritus of computer science at the Vrije Universiteit Amsterdam in the Netherlands.

He is the author of MINIX, a free Unix-like operating system for teaching purposes, and has written multiple computer science textbooks regarded as standard texts in the field. He regards his teaching job as his most important work. Since 2004 he has operated Electoral-vote.com, a website dedicated to analysis of polling data in federal elections in the United States.

Biography
Tanenbaum was born in New York City and grew up in suburban White Plains, New York, where he attended the White Plains High School. His paternal grandfather was born in Khorostkiv in the Austro-Hungarian empire.

He received his Bachelor of Science degree in physics from MIT in 1965 and his PhD degree in astrophysics from the University of California, Berkeley in 1971.

He moved to the Netherlands to live with his wife, who is Dutch, but he retains his United States citizenship. He taught courses on Computer Organization and Operating Systems and supervised the work of PhD candidates at the VU University Amsterdam. On July 9, 2014, he announced his retirement.

Books
Tanenbaum's textbooks on computer science include:
 * (1981, with David J. Wetherall and Nickolas Feamster)
 * Operating Systems: Design and Implementation, co-authored with Albert Woodhull
 * Modern Operating Systems (1992, 2001, 2007, 2014, 2022)
 * (with Maarten van Steen)
 * (with Maarten van Steen)
 * (with Maarten van Steen)

His book, Operating Systems: Design and Implementation and MINIX were Linus Torvalds' inspiration for the Linux kernel. In his autobiography Just for Fun, Torvalds describes it as "the book that launched me to new heights".

Doctoral students
Tanenbaum has had a number of PhD students who themselves have gone on to become widely known computer science researchers. These include:
 * Henri Bal, professor at the Vrije Universiteit in Amsterdam
 * Frans Kaashoek, professor at MIT
 * Werner Vogels, Chief Technology Officer at Amazon.com

Dean of the Advanced School for Computing and Imaging
In the early 1990s, the Dutch government began setting up a number of thematically oriented research schools that spanned multiple universities. These schools were intended to bring professors and PhD students from different Dutch (and later, foreign) universities together to help them cooperate and enhance their research.

Tanenbaum was one of the cofounders and first Dean of the Advanced School for Computing and Imaging (ASCI). This school initially consisted of nearly 200 faculty members and PhD students from the Vrije Universiteit, University of Amsterdam, Delft University of Technology, and Leiden University. They were especially working on problems in advanced computer systems such as parallel computing and image analysis and processing.

Tanenbaum remained dean for 12 years, until 2005, when he was awarded an Academy Professorship by the Royal Netherlands Academy of Arts and Sciences, at which time he became a full-time research professor.

Amsterdam Compiler Kit
The Amsterdam Compiler Kit is a toolkit for producing portable compilers. It was started sometime before 1981 and Andrew Tanenbaum was the architect from the start until version 5.5.

MINIX
In 1987, Tanenbaum wrote a clone of UNIX, called MINIX (MINi-unIX), for the IBM PC. It was targeted at students and others who wanted to learn how an operating system worked. Consequently, he wrote a book that listed the source code in an appendix and described it in detail in the text. The source code itself was available on a set of floppy disks. Within three months, a Usenet newsgroup, comp.os.minix, had sprung up with over 40,000 subscribers discussing and improving the system. One of these subscribers was Linus Torvalds, who began adding new features to MINIX and tailoring it to his own needs. On October 5, 1991, Torvalds announced his own (POSIX-like) kernel, called Linux, which originally used the MINIX file system but is not based on MINIX code.

Electoral-vote.com
In 2004, Tanenbaum created Electoral-vote.com, a web site analyzing opinion polls for the 2004 U.S. Presidential Election, using them to project the outcome in the Electoral College. He stated that he created the site as an American who "knows first hand what the world thinks of America and it is not a pretty picture at the moment. I want people to think of America as the land of freedom and democracy, not the land of arrogance and blind revenge. I want to be proud of America again." The site provided a color-coded map, updated each day with projections for each state's electoral votes. Through most of the campaign period Tanenbaum kept his identity secret, referring to himself as "the Votemaster" and acknowledging only that he personally preferred John Kerry. Mentioning that he supported the Democrats, he revealed his identity on November 1, 2004, the day before the election, and also stating his reasons and qualifications for running the website.

Through the site he also covered the 2006 midterm elections, correctly predicting the winner of all 33 Senate races that year.

For the 2008 elections, he got every state right except for Indiana, which he said McCain would win by 2% (Obama won by 1%) and Missouri, which he said was too close to call (McCain won by 0.1%). He correctly predicted all the winners in the Senate except for Minnesota, where he predicted a 1% win by Norm Coleman over Al Franken. After 7 months of legal battling and recounts, Franken won by 312 votes (0.01%).

In 2010, he correctly projected 35 out of 37 Senate races in the Midterm elections on the website. The exceptions were Colorado and Nevada.

Electoral-vote.com incorrectly predicted Hillary Clinton would win the 2016 United States presidential election. The website incorrectly predicted Clinton would win Wisconsin, Michigan, Pennsylvania, North Carolina, and Florida. Electoral-vote.com did not predict a winner for Nevada, which Clinton would win. The website predicted the winners of the remaining 44 states and the District of Columbia correctly.

Tanenbaum–Torvalds debate
The Tanenbaum–Torvalds debate was a famous debate between Tanenbaum and Linus Torvalds regarding kernel design on Usenet in 1992.

Awards

 * Fellow of the ACM
 * Fellow of the IEEE for outstanding contributions to research and education in computer networks and operating systems.
 * Member of the Royal Netherlands Academy of Arts and Sciences
 * Winner of the TAA McGuffey award for classic textbooks for Modern Operating Systems, 2010
 * Winner of the 2007 IEEE James H. Mulligan, Jr. Education Medal

Honorary doctorates

 * On May 12, 2008, Tanenbaum received an honorary doctorate from Universitatea Politehnica din București.
 * On October 7, 2011, Universitatea Petru Maior din Târgu Mureș (Petru Maior University of Târgu Mureș) granted Tanenbaum the Doctor Honoris Causa (honorary doctorate) title for his work in the field of computer science and achievements in education.

title: Andrew S. Tanenbaum


text:
Ariane 5

Ariane 5 is a retired European heavy-lift space launch vehicle developed and operated by Arianespace for the European Space Agency (ESA). It was launched from the Guiana Space Centre (CSG) in French Guiana. It was used to deliver payloads into geostationary transfer orbit (GTO), low Earth orbit (LEO) or further into space. The launch vehicle had a streak of 82 consecutive successful launches between 9 April 2003 and 12 December 2017. Since 2014, Ariane 6, a direct successor system, is in development.

The system was designed as an expendable launch system by the Centre national d'études spatiales (CNES), the French government's space agency, in cooperation with various European partners. Despite not being a direct derivative of its predecessor launch vehicle program, it was classified as part of the Ariane rocket family. ArianeGroup was the prime contractor for the manufacturing of the vehicles, leading a multi-country consortium of other European contractors. Ariane 5 was originally intended to launch the Hermes spacecraft, and thus it was rated for human space launches.

Since its first launch, Ariane 5 was refined in successive versions: "G", "G+", "GS", "ECA", and finally, "ES". The system had a commonly used dual-launch capability, where up to two large geostationary belt communication satellites can be mounted using a SYLDA (Système de Lancement Double Ariane, meaning "Ariane Double-Launch System") carrier system. Up to three, somewhat smaller, main satellites are possible depending on size using a SPELTRA (Structure Porteuse Externe Lancement Triple Ariane, which translates to "Ariane Triple-Launch External Carrier Structure"). Up to eight secondary payloads, usually small experiment packages or minisatellites, could be carried with an ASAP (Ariane Structure for Auxiliary Payloads) platform.

Following the launch of 15 August 2020, Arianespace signed the contracts for the last eight Ariane 5 launches, before it was succeeded by the new Ariane 6 launcher, according to Daniel Neuenschwander, director of space transportation at the ESA. Ariane 5 flew its final mission on 5 July 2023.

Cryogenic main stage

Ariane 5's cryogenic H173 main stage (H158 for Ariane 5G, G+, and GS) was called the EPC (Étage Principal Cryotechnique — Cryotechnic Main Stage). It consisted of a 5.4 m diameter by 30.5 m high tank with two compartments, one for liquid oxygen and one for liquid hydrogen, and a Vulcain 2 engine at the base with a vacuum thrust of 1390 kN. The H173 EPC weighed about 189 t, including 175 t of propellant. After the main cryogenic stage runs out of fuel, it re-entered the atmosphere for an ocean splashdown.

Solid boosters
Attached to the sides were two P241 (P238 for Ariane 5G and G+) solid rocket boosters (SRBs or EAPs from the French Étages d'Accélération à Poudre), each weighing about 277 t full and delivering a thrust of about 7080 kN. They were fueled by a mix of ammonium perchlorate (68%) and aluminium fuel (18%) and HTPB (14%). They each burned for 130 seconds before being dropped into the ocean. The SRBs were usually allowed to sink to the bottom of the ocean, but, like the Space Shuttle Solid Rocket Boosters, they could be recovered with parachutes, and this was occasionally done for post-flight analysis. Unlike Space Shuttle SRBs, Ariane 5 boosters were not reused. The most recent attempt was for the first Ariane 5 ECA mission in 2009. One of the two boosters was successfully recovered and returned to the Guiana Space Center for analysis. Prior to that mission, the last such recovery and testing was done in 2003.

The French M51 submarine-launched ballistic missile (SLBM) shared a substantial amount of technology with these boosters.

In February 2000, the suspected nose cone of an Ariane 5 booster washed ashore on the South Texas coast, and was recovered by beachcombers before the government could get to it.

Second stage

The second stage was on top of the main stage and below the payload. The original Ariane — Ariane 5G — used the EPS (Étage à Propergols Stockables — Storable Propellant Stage), which was fueled by monomethylhydrazine (MMH) and nitrogen tetroxide, containing 10000 kg of storable propellant. The EPS was subsequently improved for use on the Ariane 5G+, GS, and ES.

The EPS upper stage was capable of repeated ignition, first demonstrated during flight V26 which was launched on 5 October 2007. This was purely to test the engine, and occurred after the payloads had been deployed. The first operational use of restart capability as part of a mission came on 9 March 2008, when two burns were made to deploy the first Automated Transfer Vehicle (ATV) into a circular parking orbit, followed by a third burn after ATV deployment to de-orbit the stage. This procedure was repeated for all subsequent ATV flights.

Ariane 5ECA used the ESC (Étage Supérieur Cryotechnique — Cryogenic Upper Stage), which was fueled by liquid hydrogen and liquid oxygen. The ESC used the HM7B engine previously used in the Ariane 4 third stage. The propellent load of 14.7 tonne allowed the engine to burn for 945 seconds while providing 6.5 tonne of thrust. The ESC provided roll control during powered flight and full attitude control during payload separation using hydrogen gas thrusters. Oxygen gas thrusters allowed longitudinal acceleration after engine cutoff. The flight assembly included the Vehicle Equipment Bay, with flight electronics for the entire rocket, and the payload interface and structural support.

Fairing
The payload and all upper stages were covered at launch by a fairing for aerodynamic stability and protection from heating during supersonic flight and acoustic loads. It was jettisoned once sufficient altitude has been reached, typically above 100 km. It was made by Ruag Space and since flight VA-238 it was composed of 4 panels.

Launch pricing and market competition
, the Ariane 5 commercial launch price for launching a "midsize satellite in the lower position" was approximately €50 million, competing for commercial launches in an increasingly competitive market.

The heavier satellite was launched in the upper position on a typical dual-satellite Ariane 5 launch and was priced higher than the lower satellite, on the order of €90 million.

Total launch price of an Ariane 5 – which could transport up to two satellites to space, one in the "upper" and one in the "lower" positions – was around €150 million.

Ariane 5 ME
The Ariane 5 ME (Mid-life Evolution) was in development into early 2015, and was seen as a stopgap between Ariane 5ECA/Ariane 5ES and the new Ariane 6. With first flight planned for 2018, it would have become ESA's principal launcher until the arrival of the new Ariane 6 version. ESA halted funding for the development of Ariane 5ME in late 2014 to prioritize development of Ariane 6.

The Ariane 5ME was to use a new upper stage, with increased propellant volume, powered by the new Vinci engine. Unlike the HM-7B engine, it was to be able to restart several times, allowing for complex orbital maneuvers such as insertion of two satellites into different orbits, direct insertion into geosynchronous orbit, planetary exploration missions, and guaranteed upper stage deorbiting or insertion into graveyard orbit. The launcher was also to include a lengthened fairing up to 20 m and a new dual launch system to accommodate larger satellites. Compared to an Ariane 5ECA model, the payload to GTO was to increase by 15% to 11500 kg and the cost-per-kilogram of each launch was projected to decline by 20%.

Development
Originally known as the Ariane 5ECB, Ariane 5ME was to have its first flight in 2006. However, the failure of the first ECA flight in 2002, combined with a deteriorating satellite industry, caused ESA to cancel development in 2003. Development of the Vinci engine continued, though at a lower pace. The ESA Council of Ministers agreed to fund development of the new upper stage in November 2008.

In 2009, EADS Astrium was awarded a €200 million contract, and on 10 April 2012 received another €112 million contract to continue development of the Ariane 5ME with total development effort expected to cost €1 billion.

On 21 November 2012, ESA agreed to continue with the Ariane 5ME to meet the challenge of lower priced competitors. It was agreed the Vinci upper stage would also be used as the second stage of a new Ariane 6, and further commonality would be sought. Ariane 5ME qualification flight was scheduled for mid-2018, followed by gradual introduction into service.

On 2 December 2014, ESA decided to stop funding the development of Ariane 5ME and instead focus on Ariane 6, which was expected to have a lower cost per launch and allow more flexibility in the payloads (using two or four P120C solid boosters depending on total payload mass).

Solid propellant stage
Work on the Ariane 5 EAP motors was continued in the Vega programme. The Vega 1st stage engine – the P80 engine – was a shorter derivation of the EAP. The P80 booster casing was made of filament wound graphite epoxy, much lighter than the current stainless steel casing. A new composite steerable nozzle was developed while new thermal insulation material and a narrower throat improved the expansion ratio and subsequently the overall performance. Additionally, the nozzle had electromechanical actuators which replaced the heavier hydraulic ones used for thrust vector control.

These developments could maybe have made their way back into the Ariane programme, but this was most likely an inference based on early blueprints of the Ariane 6 having a central P80 booster and 2-4 around the main one. The incorporation of the ESC-B with the improvements to the solid motor casing and an uprated Vulcain engine would have delivered 27000 kg to LEO. This would have been developed for any lunar missions but the performance of such a design might not have been possible if the higher Max-Q for the launch of this launch vehicle would have posed a constraint on the mass delivered to orbit.

Ariane 6
The design brief of the next generation launch vehicle Ariane 6 called for a lower-cost and smaller launch vehicle capable of launching a single satellite of up to 6500 kg to GTO. However, after several permutations the finalized design was nearly identical in performance to the Ariane 5, focusing instead on lowering fabrication costs and launch prices. , Ariane 6 was projected to be launched for about €70 million per flight, about half of the Ariane 5 price.

Initially development of Ariane 6 was projected to cost €3.6 billion. In 2017, the ESA set 16 July 2020 as the deadline for the first flight. As of May 2024, Arianespace expects the maiden flight to occur as early as June 2024. On 9 July 2024 the Ariane 6 successfully completed it's maiden flight.

Notable launches

Ariane 5's first test flight (Ariane 5 Flight 501) on 4 June 1996 failed, with the rocket self-destructing 37 seconds after launch because of a malfunction in the control software. A data conversion from 64-bit floating-point value to 16-bit signed integer value to be stored in a variable representing horizontal bias caused a processor trap (operand error) because the floating-point value was too large to be represented by a 16-bit signed integer. The software had been written for the Ariane 4 where efficiency considerations (the computer running the software had an 80% maximum workload requirement ) led to four variables being protected with a handler while three others, including the horizontal bias variable, were left unprotected because it was thought that they were "physically limited or that there was a large margin of safety". The software, written in Ada, was included in the Ariane 5 through the reuse of an entire Ariane 4 subsystem despite the fact that the particular software containing the bug, which was just a part of the subsystem, was not required by the Ariane 5 because it has a different preparation sequence than the Ariane 4.

The second test flight (L502, on 30 October 1997) was a partial failure. The Vulcain nozzle caused a roll problem, leading to premature shutdown of the core stage. The upper stage operated successfully, but it could not reach the intended orbit. A subsequent test flight (L503, on 21 October 1998) proved successful and the first commercial launch (L504) occurred on 10 December 1999 with the launch of the XMM-Newton X-ray observatory satellite.

Another partial failure occurred on 12 July 2001, with the delivery of two satellites into an incorrect orbit, at only half the height of the intended GTO. The ESA Artemis telecommunications satellite was able to reach its intended orbit on 31 January 2003, through the use of its experimental ion propulsion system.

The next launch did not occur until 1 March 2002, when the Envisat environmental satellite successfully reached an orbit of 800 km above the Earth in the 11th launch. At 8111 kg, it was the heaviest single payload until the launch of the first ATV on 9 March 2008, at 19360 kg.

The first launch of the ECA variant on 11 December 2002 ended in failure when a main booster problem caused the rocket to veer off-course, forcing its self-destruction three minutes into the flight. Its payload of two communications satellites (STENTOR and Hot Bird 7), valued at about €630 million, was lost in the Atlantic Ocean. The fault was determined to have been caused by a leak in coolant pipes allowing the nozzle to overheat. After this failure, Arianespace SA delayed the expected January 2003 launch for the Rosetta mission to 26 February 2004, but this was again delayed to early March 2004 due to a minor fault in the foam that protects the cryogenic tanks on the Ariane 5. The failure of the first ECA launch was the last failure of an Ariane 5 until flight 240 in January 2018.

On 27 September 2003, the last Ariane 5G boosted three satellites (including the first European lunar probe, SMART-1), in Flight 162. On 18 July 2004, an Ariane 5G+ boosted what was at the time the heaviest telecommunication satellite ever, Anik F2, weighing almost 6000 kg.

The first successful launch of the Ariane 5ECA took place on 12 February 2005. The payload consisted of the XTAR-EUR military communications satellite, a 'SLOSHSAT' small scientific satellite and a MaqSat B2 payload simulator. The launch had been scheduled for October 2004, but additional testing and a military launch (of a Helios 2A observation satellite) delayed the attempt.

On 11 August 2005, the first Ariane 5GS (featuring the Ariane 5ECA's improved solid motors) boosted Thaicom 4, the heaviest telecommunications satellite to date at 6505 kg, into orbit.

On 16 November 2005, the third Ariane 5ECA launch (the second successful ECA launch) took place. It carried a dual payload consisting of Spaceway F2 for DirecTV and Telkom-2 for PT Telekomunikasi of Indonesia. This was the launch vehicle's heaviest dual payload to date, at more than 8000 kg.

On 27 May 2006, an Ariane 5ECA launch vehicle set a new commercial payload lifting record of 8200 kg. The dual-payload consisted of the Thaicom 5 and Satmex 6 satellites.

On 4 May 2007, the Ariane 5ECA set another new commercial record, lifting into transfer orbit the Astra 1L and Galaxy 17 communication satellites with a combined weight of 8600 kg, and a total payload weight of 9400 kg. This record was again broken by another Ariane 5ECA, launching the Skynet 5B and Star One C1 satellites, on 11 November 2007. The total payload weight for this launch was of 9535 kg.

On 9 March 2008, the first Ariane 5ES-ATV was launched to deliver the first ATV called Jules Verne to the International Space Station (ISS). The ATV was the heaviest payload ever launched by a European launch vehicle, providing supplies to the space station with necessary propellant, water, air and dry cargo. This was the first operational Ariane mission which involved an engine restart in the upper stage. The ES-ATV Aestus EPS upper stage was restartable while the ECA HM7-B engine was not.

On 1 July 2009, an Ariane 5ECA launched TerreStar-1 (now EchoStar T1), which was then, at 6910 kg, the largest and most massive commercial telecommunication satellite ever built at that time until being overtaken by Telstar 19 Vantage, at 7080 kg, launched aboard Falcon 9. The satellite was launched into a lower-energy orbit than a usual GTO, with its initial apogee at roughly 17900 km.

On 28 October 2010, an Ariane 5ECA launched Eutelsat's W3B (part of its W Series of satellites) and Broadcasting Satellite System Corporation (B-SAT)'s BSAT-3b satellites into orbit. But the W3B satellite failed to operate shortly after the successful launch and was written off as a total loss due to an oxidizer leak in the satellite's main propulsion system. The BSAT-3b satellite, however, is operating normally.

The VA253 launch on 15 August 2020 introduced two small changes that increased lift capacity by about 85 kg; these were a lighter avionics and guidance-equipment bay, and modified pressure vents on the payload fairing, which were required for the subsequent launch of the James Webb Space Telescope. It also debuted a location system using Galileo navigation satellites.

On 25 December 2021, VA256 launched the James Webb Space Telescope towards a Sun–Earth L2 halo orbit. The precision of trajectory following launch led to fuel savings credited with potentially doubling the lifetime of the telescope by leaving more hydrazine propellant on board for station-keeping than was expected. According to Rudiger Albat, the program manager for Ariane 5, efforts had been made to select components for this flight that had performed especially well during pre-flight testing, including "one of the best Vulcain engines that we've ever built."

GTO payload weight records
On 22 April 2011, the Ariane 5ECA flight VA-201 broke a commercial record, lifting Yahsat 1A and Intelsat New Dawn with a total payload weight of 10064 kg to transfer orbit. This record was later broken again during the launch of Ariane 5ECA flight VA-208 on 2 August 2012, lifting a total of 10182 kg into the planned geosynchronous transfer orbit, which was broken again 6 months later on flight VA-212 with 10317 kg sent towards geosynchronous transfer orbit. In June 2016, the GTO record was raised to 10730 kg, on the first rocket in history that carried a satellite dedicated to financial institutions. The payload record was pushed a further 5 kg, up to 10735 kg on 24 August 2016 with the launch of Intelsat 33e and Intelsat 36. On 1 June 2017, the payload record was broken again to 10865 kg carrying ViaSat-2 and Eutelsat-172B. In 2021 VA-255 put 11,210 kg into GTO.

VA241 anomaly
On 25 January 2018, an Ariane 5ECA launched SES-14 and Al Yah 3 satellites. About 9 minutes and 28 seconds after launch, a telemetry loss occurred between the launch vehicle and the ground controllers. It was later confirmed, about 1 hour and 20 minutes after launch, that both satellites were successfully separated from the upper stage and were in contact with their respective ground controllers, but that their orbital inclinations were incorrect as the guidance systems might have been compromised. Therefore, both satellites conducted orbital procedures, extending commissioning time. SES-14 needed about 8 weeks longer than planned commissioning time, meaning that entry into service was reported early September instead of July. Nevertheless, SES-14 is still expected to be able to meet the designed lifetime. This satellite was originally to be launched with more propellant reserve on a Falcon 9 launch vehicle since the Falcon 9, in this specific case, was intended to deploy this satellite into a high inclination orbit that would require more work from the satellite to reach its final geostationary orbit. The Al Yah 3 was also confirmed healthy after more than 12 hours without further statement, and like SES-14, Al Yah 3's maneuvering plan was also revised to still fulfill the original mission. As of 16 February 2018, Al Yah 3 was approaching the intended geostationary orbit, after series of recovery maneuvers had been performed. The investigation showed that invalid inertial units' azimuth value had sent the vehicle 17° off course but to the intended altitude, they had been programmed for the standard geostationary transfer orbit of 90° when the payloads were intended to be 70° for this supersynchronous transfer orbit mission, 20° off norme. This mission anomaly marked the end of 82nd consecutive success streak since 2003.

Launch statistics
Ariane 5 launch vehicles had accumulated 117 launches, 112 of which were successful, yielding a success rate. Between April 2003 and December 2017, Ariane 5 flew 83 consecutive missions without failure, but the launch vehicle suffered a partial failure in January 2018.

List of launches
All launches are from Guiana Space Centre, ELA-3.

title: Ariane 5


text:
Arianespace

Arianespace SA is a French company founded in 1980 as the world's first commercial launch service provider. It is the operator of two different launch vehicles: Vega, a small-lift rocket and Ariane 6, a medium or heavy-lift rocket, depending on configuration.

European space launches are conducted by several private companies and government agencies working together. The role of Arianespace is to market the launch services, prepare the missions and handle all relations with customers. At the Guiana Space Centre (CSG) the company oversees the team that integrates and prepares vehicles for launch.

The rockets themselves are designed and produced by other companies, its parent company, ArianeGroup for the Ariane 6 or Avio for the Vega. Launch infrastructure at the CSG is owned by the European Space Agency and the land itself is owned and operated by CNES, the French national space agency.

, Arianespace had launched more than 850 satellites in 287 launches over 41 years. The first commercial flight managed by the new entity was Spacenet F1 launched on 23 May 1984. Arianespace uses the Guiana Space Centre in French Guiana as its main launch site. It has its headquarters in the Paris suburb of Évry-Courcouronnes.

History
The formation of Arianespace SA is closely associated with the desire of several European nations to pursue joint collaboration in the field of space exploration and the formation of a pan-national organisation, the European Space Agency (ESA), to oversee such undertaking during 1973. Prior to the ESA's formation, France had been lobbying for the development of a new European expendable launch system to serve as a replacement for the Europa rocket. Accordingly, one of the first programmes launched by the ESA was the Ariane heavy launcher. The express purpose of this launcher was to facilitate the delivery of commercial satellites into geosynchronous orbit.

France was the largest stakeholder in the Ariane development programme. French aerospace manufacturer Aérospatiale served as the prime contractor and held responsibility for performing the integration of all sections of the vehicle, while French engine manufacturer Société Européenne de Propulsion (SEP) provided the first, second and third stage engines (the third stage engines were produced in partnership with German aerospace manufacturer MBB). Other major companies involved included the French firms Air Liquide and Matra, Swedish manufacturer Volvo, and German aircraft producer Dornier Flugzeugwerke. Development of the third stage was a major focus point for the project - prior to Ariane, only the United States had ever flown a launcher that utilised hydrogen-powered upper stages.

Immediately following the successful first test launch of an Ariane 1 on 24 December 1979, the French space agency Centre national d'études spatiales (CNES) and the ESA created a new company, Arianespace, for the purpose of promoting, marketing, and managing Ariane operations. According to Arianespace, at the time of its establishment, it was the world's first launch services company. Following a further three test launches, the first commercial launch took place on 10 September 1982, which ended in failure as a result of a turbopump having failed in the third stage. The six remaining flights of the Ariane 1 were successful, with the final flight occurring during February 1986. As a result of these repeated successes, orders for the Ariane launcher quickly mounted up; by early 1984, a total of 27 satellites had been booked to use Ariane, which was estimated to be half of the world's market at that time. As a result of the commercial success, after the tenth Ariane mission was flown, the ESA formally transferred responsibility for Ariane over to Arianespace.

By early 1986, the Ariane 1, along with its Ariane 2 and Ariane 3 derivates, were the dominant launcher on the world market. The Ariane 2 and Ariane 3 were short-lived platforms while the more extensive Ariane 4 was being developed; it was a considerably larger and more flexible launcher that the earlier members of its family, having been intended from the onset to compete with the upper end of launchers worldwide. In comparison, while the Ariane 1 had a typical weight of 207 tonnes and could launch payloads of up to 1.7 tonnes into orbit; the larger Ariane 4 had a typical weight of 470 tonnes and could orbit payloads of up to 4.2 tonnes. Despite this, the Ariane 4 was actually 15 per cent smaller than the Ariane 3.

On 15 June 1988, the first successful launch of the Ariane 4 was conducted. This maiden flight was considered a success, having placed multiple satellites into orbit. For the V50 launch onwards, an improved third stage, known as the H10+, was adopted for the Ariane 4, which raised the rocket's overall payload capacity by 110 kg and increased its burn time by 20 seconds.

Even prior to the first flight of the Ariane 4 in 1988, development of a successor, designated as the Ariane 5, had already commenced. In January 1985, the Ariane 5 was officially adopted as an ESA programme, and began an eleven-year development and test program to the first launch in 1996. It lacked the high levels of commonality that the Ariane 4 had with its predecessors, and had been designed not only for launching heavier payloads of up to 5.2 tonnes and at a 20 per cent cost reduction over the Ariane 4, but for a higher margin of safety due to the fact that the Ariane 5 was designed to conduct crewed space launches as well, being intended to transport astronauts using the proposed Hermes space vehicle. Development of the Ariane 5 was not without controversy as some ESA members considered the mature Ariane 4 platform to be more suited for meeting established needs for such launchers; it was reportedly for this reason that Britain chose not to participate in the Ariane 5 programme. For several years, Ariane 4 and Ariane 5 launchers were operated interchangeably; however, it was eventually decided to terminate all Ariane 4 operations in favour of concentrating on the newer Ariane 5.

During the mid-1990s, French firms Aérospatiale and SEP, along with Italian firm Bombrini-Parodi-Delfino (BPD), held discussions on the development of a proposed Ariane Complementary Launcher (ACL). Simultaneously, Italy championed the concept of a new solid-propellant satellite launcher, referred to as Vega. During March 2003, contracts for Vega's development were signed by the ESA and CNES; Italy provided 65 per cent of funding while six additional nations contributed the remainder. In May 2004, it was reported that a contract was signed between commercial operator Arianespace and prime contractor ELV to perform vehicle integration at Kourou, French Guiana. On 13 February 2012, the first launch of the Vega took place; it was reported as being an "apparently perfect flight". Since entering commercial service, Arianespace markets Vega as a launch system tailored for missions to polar and Sun-synchronous orbits.

During 2002, the ESA announced the Arianespace Soyuz programme in cooperation with Russia; a launch site for Soyuz was constructed as the Guiana Space Centre, while the Soyuz launch vehicle was modified for use at the site. On 4 February 2005, both funding and final approval for the initiative were granted. Arianespace had offered launch services on the modified Soyuz ST-B to its clients. On 21 October 2011, Arianespace launched the first Soyuz rocket ever from outside former Soviet territory. The payload consisted of two Galileo navigation satellites. Since 2011, Arianespace has ordered a total of 23 Soyuz rockets, enough to cover its needs until 2019 at a pace of three to four launches per year.

On 21 January 2019, ArianeGroup and Arianespace announced that it had signed a one-year contract with the ESA to study and prepare for a mission to the Moon to mine regolith.

In 2020, Arianespace suspended operations for nearly two months due to the COVID-19 pandemic. Operations were suspended on 18 March and are, as of 29 April, expected to resume on 11 May. The return to operations will observe a number of new health and safety guidelines including social distancing in the workplace.

In 2023, Ariane 5 was retired with the introduction of new Ariane 6, that comducted its maiden flight on 9 July 2024.

Company and infrastructure
Arianespace "is the marketing and sales organization for the European space industry and various component suppliers."

The primary shareholders of Arianespace are its suppliers, in various European nations. Arianespace had 24 shareholders in 2008, 21 in 2014, and just 17.

In 2015, Arianespace shareholding was restructured due to the creation of Airbus Safran Launchers (later renamed ArianeGroup), which is tasked with developing and manufacturing the Ariane 6 carrier rocket. Industrial groups Airbus and Safran pooled their shares along with the French government's CNES stake to form a partnership company holding just under 74% of Arianespace shares, while the remaining 26% is spread across suppliers in nine countries including further Airbus subsidiaries.

Corporate management
, the Arianespace management team was:

Subsidiaries

 * Arianespace inc. (U.S. Subsidiary)
 * Arianespace Singapore PTE LTD. (Asian Subsidiary)
 * Starsem S.A. (European-Russian Soyuz commercialization)

Competition and pricing
By 2004, Arianespace reportedly held more than 50% of the world market for boosting satellites to geostationary transfer orbit (GTO).

During the 2010s, the disruptive force represented by the new sector entrant SpaceX forced Arianespace to cut back on its workforce and focus on cost-cutting to decrease costs to remain competitive against the new low-cost entrant in the launch sector. In the midst of pricing pressure from such companies, during November 2013, Arianespace announced that it was enacting pricing flexibility for the "lighter satellites" that it carries to Geostationary orbits aboard its Ariane 5. According to Arianespace's managing director: "It's quite clear there's a very significant challenge coming from SpaceX (...) therefore things have to change (...) and the whole European industry is being restructured, consolidated, rationalised and streamlined."

During early 2014, Arianespace was considering requesting additional subsidies from European governments to face competition from SpaceX and unfavorable changes in the Euro-Dollar exchange rate. The company had halved subsidy support by €100m per year since 2002 but the fall in the value of the US Dollar meant Arianespace was losing €60m per year due to currency fluctuations on launch contracts. SpaceX had reportedly begun to take market share from Arianespace, Eutelsat CEO Michel de Rosen, a major customer of Arianespace, stated that: "Each year that passes will see SpaceX advance, gain market share and further reduce its costs through economies of scale."

By September 2014, Arianespace had reportedly to sign four additional contracts for lower slots on an Ariane 5 SYLDA dispenser for satellites that otherwise could be flown on a SpaceX launch vehicle; this was claimed to have been allowed via cost reductions; it had signed a total of 11 contracts by that point, while two additional ones that were under advanced negotiations. At the time, Arianespace has a backlog of launches worth €4.5 billion with 38 satellites to be launched on Ariane 5, 7 on Soyuz and 9 on Vega, claiming 60% of the global satellite launch market. However, since 2017, Arianespace's market share has been passed by SpaceX in commercial launches.

Launch vehicles
Currently, Arianespace operates 1 launch vehicle:

Additionally, Arianespace offers optional back-up launch service on H-IIA through Launch Services Alliance.

Ariane launch vehicles
Since the first launch in 1979, there have been several versions of the Ariane launch vehicle:

 * Ariane 1, first successful launch on December 24, 1979
 * Ariane 2, first successful launch on November 20, 1987 (the first launch on May 30, 1986, failed)
 * Ariane 3, first successful launch on August 4, 1984
 * Ariane 4, first successful launch on June 15, 1988
 * Ariane 5, first successful launch on October 30, 1997 (the first launch on June 4, 1996, failed).
 * Ariane 6, It has a similar payload capacity to that of Ariane 5 but considerably lower costs. Its first flight took place on July 9, 2024.
 * Ariane Next, in early development. It will be a partially reusable launcher that should succeed Ariane 6 from the 2030s. The objective of this reusable launcher is to halve the launch costs.

Other launch service providers

 * United Launch Alliance
 * International Launch Services
 * SpaceX
 * Antrix Corporation

title: Arianespace


text:
Talk:Alphanumeric keyboard

Image
That keyboard is extremely dirty, and seems to have globs of some mystery substance stuck all over it. Can someone get a better picture? --Edlin2 05:50, 29 October 2006 (UTC)

Computer architectures have their own keyboards, like the ibm pc XT keyboard, the Amiga keyboard, etc. We need to find a place for this keyboard classification. Tuxisuau
 * It's already in the article - the bullet list. See IBM_PC_keyboard; you may add Amiga keyboard.

The bulleted list is rather... odd. I can't exactly understand what it's trying to say... I think there needs to be some explanation of what the list is regarding. Oracleoftruth 03:38, 15 May 2005 (UTC)

shouldnt dvorak be in this article somewhere

Merge
Presumably typewriter keyboards are "alphanumeric", so the merge may have been inappropriate. Claritas § 18:25, 20 June 2010 (UTC)
 * This article was redundant anyway; once you have a keyboard, the symbols that you can put on it are arbitrary. It's not like a telephone dial where there's a physical one-to-one correlation with the digit represented and the number of pulses made. How would an article on "alphanumeric keyboard" differ from an article on "alphabetic keyboard" or "numeric keyboard" ? --Wtshymanski (talk) 03:17, 21 June 2010 (UTC)

title: Talk:Alphanumeric keyboard


text:
Accumulator (computing)

In a computer's central processing unit (CPU), the accumulator is a register in which intermediate arithmetic logic unit results are stored.

Without a register like an accumulator, it would be necessary to write the result of each calculation (addition, multiplication, shift, etc.) to cache or main memory, perhaps only to be read right back again for use in the next operation.

Accessing memory is slower than accessing a register like an accumulator because the technology used for the large main memory is slower (but cheaper) than that used for a register. Early electronic computer systems were often split into two groups, those with accumulators and those without.

Modern computer systems often have multiple general-purpose registers that can operate as accumulators, and the term is no longer as common as it once was. However, to simplify their design, a number of special-purpose processors still use a single accumulator.

Basic concept
Mathematical operations often take place in a stepwise fashion, using the results from one operation as the input to the next. For instance, a manual calculation of a worker's weekly payroll might look something like:

 * 1) look up the number of hours worked from the employee's time card
 * 2) look up the pay rate for that employee from a table
 * 3) multiply the hours by the pay rate to get their basic weekly pay
 * 4) multiply their basic pay by a fixed percentage to account for income tax
 * 5) subtract that number from their basic pay to get their weekly pay after tax
 * 6) multiply that result by another fixed percentage to account for retirement plans
 * 7) subtract that number from their basic pay to get their weekly pay after all deductions

A computer program carrying out the same task would follow the same basic sequence of operations, although the values being looked up would all be stored in computer memory. In early computers, the number of hours would likely be held on a punch card and the pay rate in some other form of memory, perhaps a magnetic drum. Once the multiplication is complete, the result needs to be placed somewhere. On a "drum machine" this would likely be back to the drum, an operation that takes considerable time. Then the very next operation has to read that value back in, which introduces another considerable delay.

Accumulators dramatically improve performance in systems like these by providing a scratchpad area where the results of one operation can be fed to the next one for little or no performance penalty. In the example above, the basic weekly pay would be calculated and placed in the accumulator, which could then immediately be used by the income tax calculation. This removes one save and one read operation from the sequence, operations that generally took tens to hundreds of times as long as the multiplication itself.

Accumulator machines
An accumulator machine, also called a 1-operand machine, or a CPU with accumulator-based architecture, is a kind of CPU where, although it may have several registers, the CPU mostly stores the results of calculations in one special register, typically called "the accumulator". Almost all computers were accumulator machines with only the high-performance "supercomputers" having multiple registers. Then as mainframe systems gave way to microcomputers, accumulator architectures were again popular with the MOS 6502 being a notable example. Many 8-bit microcontrollers that are still popular, such as the PICmicro and 8051, are accumulator-based machines.

Modern CPUs are typically 2-operand or 3-operand machines. The additional operands specify which one of many general-purpose registers (also called "general-purpose accumulators" ) are used as the source and destination for calculations. These CPUs are not considered "accumulator machines".

The characteristic that distinguishes one register as being the accumulator of a computer architecture is that the accumulator (if the architecture were to have one) would be used as an implicit operand for arithmetic instructions. For instance, a CPU might have an instruction like:  that adds the value read from memory location memaddress to the value in the accumulator, placing the result back in the accumulator. The accumulator is not identified in the instruction by a register number; it is implicit in the instruction and no other register can be specified in the instruction. Some architectures use a particular register as an accumulator in some instructions, but other instructions use register numbers for explicit operand specification.

History of the computer accumulator
Any system that uses a single "memory" to store the result of multiple operations can be considered an accumulator. J. Presper Eckert refers to even the earliest adding machines of Gottfried Leibniz and Blaise Pascal as accumulator-based systems. Percy Ludgate was the first to conceive a multiplier-accumulator (MAC) in his Analytical Machine of 1909.

Historical convention dedicates a register to "the accumulator", an "arithmetic organ" that literally accumulates its number during a sequence of arithmetic operations:

 * "The first part of our arithmetic organ ... should be a parallel storage organ which can receive a number and add it to the one already in it, which is also able to clear its contents and which can store what it contains. We will call such an organ an Accumulator. It is quite conventional in principle in past and present computing machines of the most varied types, e.g. desk multipliers, standard IBM counters, more modern relay machines, the ENIAC" (Goldstine and von Neumann, 1946; p. 98 in Bell and Newell 1971).

Just a few of the instructions are, for example (with some modern interpretation):
 * Clear accumulator and add number from memory location X
 * Clear accumulator and subtract number from memory location X
 * Add number copied from memory location X to the contents of the accumulator
 * Subtract number copied from memory location X from the contents of the accumulator
 * Clear accumulator and shift contents of register into accumulator

No convention exists regarding the names for operations from registers to accumulator and from accumulator to registers. Tradition (e.g. Donald Knuth's (1973) hypothetical MIX computer), for example, uses two instructions called load accumulator from register/memory (e.g. "LDA r") and store accumulator to register/memory (e.g. "STA r"). Knuth's model has many other instructions as well.

Notable accumulator-based computers
The 1945 configuration of ENIAC had 20 accumulators, which could operate in parallel. Each one could store an eight decimal digit number and add to it (or subtract from it) a number it received. Most of IBM's early binary "scientific" computers, beginning with the vacuum tube IBM 701 in 1952, used a single 36-bit accumulator, along with a separate multiplier/quotient register to handle operations with longer results. The IBM 650, a decimal machine, had one 10 digit distributor and two ten-digit accumulators; the IBM 7070, a later, transistorized decimal machine had three accumulators. The IBM System/360, and Digital Equipment Corporation's PDP-6, had 16 general-purpose registers, although the PDP-6 and its successor, the PDP-10, call them accumulators.

The 12-bit PDP-8 was one of the first minicomputers to use accumulators, and inspired many later machines. The PDP-8 had but one accumulator. The HP 2100 and Data General Nova had 2 and 4 accumulators. The Nova was created when this follow-on to the PDP-8 was rejected in favor of what would become the PDP-11. The Nova provided four accumulators, AC0-AC3, although AC2 and AC3 could also be used to provide offset addresses, tending towards more generality of usage for the registers. The PDP-11 had 8 general-purpose registers, along the lines of the System/360 and PDP-10; most later CISC and RISC machines provided multiple general-purpose registers. Early 4-bit and 8-bit microprocessors such as the 4004, 8008 and numerous others, typically had single accumulators. The 8051 microcontroller has two, a primary accumulator and a secondary accumulator, where the second is used by instructions only when multiplying (MUL AB) or dividing (DIV AB); the former splits the 16-bit result between the two 8-bit accumulators, whereas the latter stores the quotient on the primary accumulator A and the remainder in the secondary accumulator B. As a direct descendant of the 8008, the 8080, and the 8086, the modern ubiquitous Intel x86 processors still uses the primary accumulator EAX and the secondary accumulator EDX for multiplication and division of large numbers. For instance, MUL ECX will multiply the 32-bit registers ECX and EAX and split the 64-bit result between EAX and EDX. However, MUL and DIV are special cases; other arithmetic-logical instructions (ADD, SUB, CMP, AND, OR, XOR, TEST) may specify any of the eight registers EAX, ECX, EDX, EBX, ESP, EBP, ESI, EDI as the accumulator (i.e. left operand and destination). This is also supported for multiply if the upper half of the result is not required. x86 is thus a fairly general register architecture, despite being based on an accumulator model. The 64-bit extension of x86, x86-64, has been further generalized to 16 instead of 8 general registers.

title: Accumulator (computing)