Envelope

An envelope is a common packaging item, usually made of thin flat material. It is designed to contain a flat object, such as a letter or card.

Traditional envelopes are made from sheets of paper cut to one of three shapes: a rhombus, a short-arm cross, or a kite. These shapes allow for the creation of the envelope structure by folding the sheet sides around a central rectangular area. In this manner, a rectangle-faced enclosure is formed with an arrangement of four flaps on the reverse side.

Overview

When the folding sequence is such that the last flap to be closed is on a short side it is referred to in commercial envelope manufacture as a pocket - a format frequently employed in the packaging of small quantities of seeds. Although in principle the flaps can be held in place by securing the topmost flap at a single point (for example with a wax seal), generally they are pasted or gummed together at the overlaps. They are most commonly used for enclosing and sending mail (letters) through a prepaid-postage postal system.

Envelope (mathematics)

In geometry, an envelope of a family of curves in the plane is a curve that is tangent to each member of the family at some point. Classically, a point on the envelope can be thought of as the intersection of two "adjacent" curves, meaning the limit of intersections of nearby curves. This idea can be generalized to an envelope of surfaces in space, and so on to higher dimensions.

Envelope of a family of curves

Let each curve C_t in the family be given as the solution of an equation f_t(x, y)=0 (see implicit curve), where t is a parameter. Write F(t, x, y)=f_t(x, y) and assume F is differentiable.

The envelope of the family C_t is then defined as the set of points for which

for some value of t, where is the partial derivative of F with respect to t.

Note that if t and u, t≠u are two values of the parameter then the intersection of the curves C_t and C_u is given by

or equivalently

Letting u→t gives the definition above.

An important special case is when F(t, x, y) is a polynomial in t. This includes, by clearing denominators, the case where F(t, x, y) is a rational function in t. In this case, the definition amounts to t being a double root of F(t, x, y), so the equation of the envelope can be found by setting the discriminant of F to 0.

Synthesizer

A sound synthesizer (usually abbreviated as "synthesizer" or "synth", also spelled "synthesiser") is an electronic musical instrument that generates electric signals that are converted to sound through instrument amplifiers and loudspeakers or headphones. Synthesizers may either imitate the still existing sounds (instruments, vocal, natural sound, etc.), or generate new electronic timbres not existing before. They are often played with a musical keyboard, but they can be controlled via a variety of other input devices, including music sequencers, instrument controllers, fingerboards, guitar synthesizers, wind controllers, and electronic drums. Synthesizers without built-in controllers are often called sound modules, and are controlled via MIDI or CV/Gate using a controller device.

Synthesizers use various methods to generate signal. Among the most popular waveform synthesis techniques are subtractive synthesis, additive synthesis, wavetable synthesis, frequency modulation synthesis, phase distortion synthesis, physical modeling synthesis and sample-based synthesis. Other less common synthesis types (see #Types of synthesis) include subharmonic synthesis, a form of additive synthesis via subharmonics (used by mixture trautonium), and granular synthesis, sample-based synthesis based on grains of sound, generally resulting in soundscapes or clouds.

Mankind

Mankind may refer to:

See also

Mankind (video game)

Mankind is a massively multiplayer online real-time strategy (MMORTS) computer game.

History

Mankind was initially published in December 1998 by the French computer game developer Vibes Online Gaming. After the transfer of Vibes to its Asian partner, the game was bought by O2 Online Entertainment Ltd. and while still active today, is being primarily maintained by Quantex since 2008.

Estimates of the number of active players are hard to come by - while the official site claimed both 145,000 and "more than 200,000" players on the same page, these figures likely included inactive as well as trial accounts. According to an interview with an O2OE spokesman, just about 3,000 accounts were active anymore in May 2003.

During the game rework of Quantex in early 2009, the graphic engine of Mankind got fully ported to DirectX 9 and full support for Windows Vista got implemented. Further, dozens of small improvements got implemented.

In December 2015 the Mankind servers were shut down.