title: Loudspeaker

text: The wire in a voice coil is usually made of copper, though aluminum—and, rarely, silver—may be used. The advantage of aluminum is its light weight, which reduces the moving mass compared to copper. This raises the resonant frequency of the speaker and increases its efficiency. A disadvantage of aluminum is that it is not easily soldered, and so connections must be robustly crimped together and sealed. Voice-coil wire cross sections can be circular, rectangular, or hexagonal, giving varying amounts of wire volume coverage in the magnetic gap space. The coil is oriented co-axially inside the gap; it moves back and forth within a small circular volume (a hole, slot, or groove) in the magnetic structure. The gap establishes a concentrated magnetic field between the two poles of a permanent magnet; the outside ring of the gap is one pole, and the center post (called the pole piece) is the other. The pole piece and backplate are often made as a single piece, called the poleplate or yoke.


title: Loudspeaker

text: The size and type of magnet and details of the magnetic circuit differ, depending on design goals. For instance, the shape of the pole piece affects the magnetic interaction between the voice coil and the magnetic field, and is sometimes used to modify a driver's behavior. A "shorting ring", or "Faraday loop", may be included as a thin copper cap fitted over the pole tip or as a heavy ring situated within the magnet-pole cavity. The benefits of this complication is reduced impedance at high frequencies, providing extended treble output, reduced harmonic distortion, and a reduction in the inductance modulation that typically accompanies large voice coil excursions. On the other hand, the copper cap requires a wider voice-coil gap, with increased magnetic reluctance; this reduces available flux, requiring a larger magnet for equivalent performance.


title: Loudspeaker

text: Electromagnets were often used in musical instrument amplifiers cabinets well into the 1950s; there were economic savings in those using tube amplifiers as the field coil could, and usually did, do double duty as a power supply choke. Very few manufacturers still produce electrodynamic loudspeakers with electrically powered field coils, as was common in the earliest designs.


title: Loudspeaker

text: Alnico, an alloy of aluminum, nickel, and cobalt became popular after WWII, since it dispensed with the problems of field-coil drivers. Alnico was used almost exclusively until about 1980, despite the problem of alnico magnets being partially demagnetized by accidental pops or clicks caused by loose connections, especially if used with a high-power amplifier. After 1980, most driver manufacturers switched from alnico to ferrite magnets, which are made from a mix of ceramic clay and fine particles of barium or strontium ferrite. Although the energy per kilogram of these ceramic magnets is lower than alnico, it is substantially less expensive, allowing designers to use larger yet more economical magnets to achieve a given performance. Due to increases in transportation costs and a desire for smaller, lighter devices there is a trend toward the use of more compact rare-earth magnets made from materials such as neodymium and samarium cobalt.


title: Loudspeaker

text: Speaker system design is both an art, involving subjective perceptions of timbre and sound quality and a science, involving measurements and experiments. Adjusting a design to improve performance is done using a combination of magnetic, acoustic, mechanical, electrical, and materials science theory, and tracked with high-precision measurements and the observations of experienced listeners. A few of the issues speaker and driver designers must confront are distortion, acoustic lobing, phase effects, off-axis response, and crossover artifacts. Designers can use an anechoic chamber to ensure the speaker can be measured independently of room effects, or any of several electronic techniques that, to some extent, substitute for such chambers. Some developers eschew anechoic chambers in favor of specific standardized room setups intended to simulate real-life listening conditions.


title: Loudspeaker

text: Individual electrodynamic drivers provide their best performance within a limited frequency range. Multiple drivers (e.g., subwoofers, woofers, mid-range drivers, and tweeters) are generally combined into a complete loudspeaker system to provide performance beyond that constraint. The three most commonly used sound radiation systems are the cone, dome and horn type drivers.


title: Loudspeaker

text: A full- or wide-range driver is a speaker driver designed to be used alone to reproduce an audio channel without the help of other drivers and therefore must cover the audio frequency range required by the application. These drivers are small, typically in diameter to permit reasonable high-frequency response, and carefully designed to give low-distortion output at low frequencies, though with reduced maximum output level. Full-range drivers are found, for instance, in public address systems, in televisions, small radios, intercoms, and some computer speakers.


title: Loudspeaker

text: In hi-fi speaker systems, the use of wide-range drivers can avoid undesirable interactions between multiple drivers caused by non-coincident driver location or crossover network issues but also may limit frequency response and output abilities (most especially at low frequencies). Hi-fi speaker systems built with wide-range drivers may require large, elaborate or, expensive enclosures to approach optimum performance.


title: Loudspeaker

text: Full-range drivers often employ an additional cone called a "whizzer": a small, light cone attached to the joint between the voice coil and the primary cone. The whizzer cone extends the high-frequency response of the driver and broadens its high-frequency directivity, which would otherwise be greatly narrowed due to the outer diameter cone material failing to keep up with the central voice coil at higher frequencies. The main cone in a whizzer design is manufactured so as to flex more in the outer diameter than in the center. The result is that the main cone delivers low frequencies and the whizzer cone contributes most of the higher frequencies. Since the whizzer cone is smaller than the main diaphragm, output dispersion at high frequencies is improved relative to an equivalent single larger diaphragm.


title: Loudspeaker

text: Limited-range drivers, also used alone, are typically found in computers, toys, and clock radios. These drivers are less elaborate and less expensive than wide-range drivers, and they may be severely compromised to fit into very small mounting locations. In these applications, sound quality is a low priority.


title: Loudspeaker

text: A subwoofer is a woofer driver used only for the lowest-pitched part of the audio spectrum: typically below 200 Hz for consumer systems, below 100 Hz for professional live sound, and below 80 Hz in THX-approved systems. Because the intended range of frequencies is limited, subwoofer system design is usually simpler in many respects than for conventional loudspeakers, often consisting of a single driver enclosed in a suitable enclosure. Since sound in this frequency range can easily bend around corners by diffraction, the speaker aperture does not have to face the audience, and subwoofers can be mounted in the bottom of the enclosure, facing the floor. This is eased by the limitations of human hearing at low frequencies; Such sounds cannot be located in space, due to their large wavelengths compared to higher frequencies which produce differential effects in the ears due to shadowing by the head, and diffraction around it, both of which we rely upon for localization clues.


title: Loudspeaker

text: To accurately reproduce very low bass notes, subwoofer systems must be solidly constructed and properly braced to avoid unwanted sounds from cabinet vibrations. As a result, good subwoofers are typically quite heavy. Many subwoofer systems include integrated power amplifiers and electronic subsonic-filters, with additional controls relevant to low-frequency reproduction (e.g., a crossover knob and a phase switch). These variants are known as "active" or "powered" subwoofers. In contrast, "passive" subwoofers require external amplification.


title: Loudspeaker

text: In typical installations, subwoofers are physically separated from the rest of the speaker cabinets. Because of propagation delay and positioning, their output may be out of phase with the rest of the sound. Consequently, a subwoofer's power amp often has a phase-delay adjustment which may be used improve performance of the system as a whole. Subwoofers are widely used in large concert and mid-sized venue sound reinforcement systems. Subwoofer cabinets are often built with a bass reflex port, a design feature which if properly engineered improves bass performance and increases efficiency.


title: Loudspeaker

text: A woofer is a driver that reproduces low frequencies. The driver works with the characteristics of the speaker enclosure to produce suitable low frequencies. Some loudspeaker systems use a woofer for the lowest frequencies, sometimes well enough that a subwoofer is not needed. Additionally, some loudspeakers use the woofer to handle middle frequencies, eliminating the mid-range driver.


title: Loudspeaker

text: A mid-range speaker is a loudspeaker driver that reproduces a band of frequencies generally between 1–6 kHz, otherwise known as the 'mid' frequencies (between the woofer and tweeter). Mid-range driver diaphragms can be made of paper or composite materials, and can be direct radiation drivers (rather like smaller woofers) or they can be compression drivers (rather like some tweeter designs). If the mid-range driver is a direct radiator, it can be mounted on the front baffle of a loudspeaker enclosure, or, if a compression driver, mounted at the throat of a horn for added output level and control of radiation pattern.


title: Loudspeaker

text: A tweeter is a high-frequency driver that reproduces the highest frequencies in a speaker system. A major problem in tweeter design is achieving wide angular sound coverage (off-axis response), since high frequency sound tends to leave the speaker in narrow beams. Soft-dome tweeters are widely found in home stereo systems, and horn-loaded compression drivers are common in professional sound reinforcement. Ribbon tweeters have gained popularity in recent years, as the output power of some designs has been increased to levels useful for professional sound reinforcement, and their output pattern is wide in the horizontal plane, a pattern that has convenient applications in concert sound.


title: Loudspeaker

text: A coaxial driver is a loudspeaker driver with two or several combined concentric drivers. Coaxial drivers have been produced by many companies, such as Altec, Tannoy, Pioneer, KEF, SEAS, B&C Speakers, BMS, Cabasse and Genelec.


title: Loudspeaker

text: Used in multi-driver speaker systems, the crossover is an assembly of filters that separate the input signal into different frequency ranges (i.e. "bands"), according to the requirements of each driver. Hence the drivers receive power only at their operating frequency (the sound frequency range they were designed for), thereby reducing distortion in the drivers and interference between them. The ideal characteristics of a crossover may include perfect out-of-band attenuation at the output of each filter, no amplitude variation ("ripple") within each passband, no phase delay between overlapping frequency bands, to name just a few.


title: Loudspeaker

text: Crossovers can be "passive" or "active". A passive crossover is an electronic circuit that uses a combination of one or more resistors, inductors, or non-polar capacitors. These components are combined to form a filter network and are most often placed between the full frequency-range power amplifier and the loudspeaker drivers to divide the amplifier's signal into the necessary frequency bands before being delivered to the individual drivers. Passive crossover circuits need no external power beyond the audio signal itself, but have some disadvantages: they may require larger inductors and capacitors due to power handling requirements (being driven by the amplifier), limited component availability to optimize the crossover's characteristics at such power levels, etc. Unlike active crossovers which include a built-in amplifier, passive crossovers have an inherent attenuation within the passband, typically leading to a reduction in damping factor before the voice coil An active crossover is an electronic filter circuit that divides the signal into individual frequency bands "before" power amplification, thus requiring at least one power amplifier for each bandpass. Passive filtering may also be used in this way before power amplification, but it is an uncommon solution, being less flexible than active filtering. Any technique that uses crossover filtering followed by amplification is commonly known as bi-amping, tri-amping, quad-amping, and so on, depending on the minimum number of amplifier channels.


title: Loudspeaker

text: Some loudspeaker designs use a combination of passive and active crossover filtering, such as a passive crossover between the mid- and high-frequency drivers and an active crossover between the low-frequency driver and the combined mid- and high frequencies.


title: Loudspeaker

text: Passive crossovers are commonly installed inside speaker boxes and are by far the most usual type of crossover for home and low-power use. In car audio systems, passive crossovers may be in a separate box, necessary to accommodate the size of the components used. Passive crossovers may be simple for low-order filtering, or complex to allow steep slopes such as 18 or 24 dB per octave. Passive crossovers can also be designed to compensate for undesired characteristics of driver, horn, or enclosure resonances, and can be tricky to implement, due to component interaction. Passive crossovers, like the driver units that they feed, have power handling limits, have insertion losses (10% is often claimed), and change the load seen by the amplifier. The changes are matters of concern for many in the hi-fi world. When high output levels are required, active crossovers may be preferable. Active crossovers may be simple circuits that emulate the response of a passive network, or may be more complex, allowing extensive audio adjustments. Some active crossovers, usually digital loudspeaker management systems, may include electronics and controls for precise alignment of phase and time between frequency bands, equalization, dynamic range compression and limiting control.


title: Loudspeaker

text: Most loudspeaker systems consist of drivers mounted in an enclosure, or cabinet. The role of the enclosure is to prevent sound waves emanating from the back of a driver from interfering destructively with those from the front. The sound waves emitted from the back are 180° out of phase with those emitted forward, so without an enclosure they typically cause cancellations which significantly degrade the level and quality of sound at low frequencies.


title: Loudspeaker

text: The simplest driver mount is a flat panel (i.e., baffle) with the drivers mounted in holes in it. However, in this approach, sound frequencies with a wavelength longer than the baffle dimensions are canceled out, because the antiphase radiation from the rear of the cone interferes with the radiation from the front. With an infinitely large panel, this interference could be entirely prevented. A sufficiently large sealed box can approach this behavior.


title: Loudspeaker

text: Since panels of infinite dimensions are impossible, most enclosures function by containing the rear radiation from the moving diaphragm. A sealed enclosure prevents transmission of the sound emitted from the rear of the loudspeaker by confining the sound in a rigid and airtight box. Techniques used to reduce transmission of sound through the walls of the cabinet include thicker cabinet walls, lossy wall material, internal bracing, curved cabinet walls—or more rarely, visco-elastic materials (e.g., mineral-loaded bitumen) or thin lead sheeting applied to the interior enclosure walls.


title: Loudspeaker

text: However, a rigid enclosure reflects sound internally, which can then be transmitted back through the loudspeaker diaphragm—again resulting in degradation of sound quality. This can be reduced by internal absorption using absorptive materials (often called "damping"), such as glass wool, wool, or synthetic fiber batting, within the enclosure. The internal shape of the enclosure can also be designed to reduce this by reflecting sounds away from the loudspeaker diaphragm, where they may then be absorbed.


title: Loudspeaker

text: Other enclosure types alter the rear sound radiation so it can add constructively to the output from the front of the cone. Designs that do this (including "bass reflex", "passive radiator", "transmission line", etc.) are often used to extend the effective low-frequency response and increase low-frequency output of the driver.


title: Loudspeaker

text: To make the transition between drivers as seamless as possible, system designers have attempted to time-align (or phase adjust) the drivers by moving one or more driver mounting locations forward or back so that the acoustic center of each driver is in the same vertical plane. This may also involve tilting the face speaker back, providing a separate enclosure mounting for each driver, or (less commonly) using electronic techniques to achieve the same effect. These attempts have resulted in some unusual cabinet designs.


title: Loudspeaker

text: The speaker mounting scheme (including cabinets) can also cause diffraction, resulting in peaks and dips in the frequency response. The problem is usually greatest at higher frequencies, where wavelengths are similar to, or smaller than, cabinet dimensions. The effect can be minimized by rounding the front edges of the cabinet, curving the cabinet itself, using a smaller or narrower enclosure, choosing a strategic driver arrangement, using absorptive material around a driver, or some combination of these and other schemes.


title: Loudspeaker

text: Horn loudspeakers are the oldest form of loudspeaker system. The use of horns as voice-amplifying megaphones dates at least to the 17th century, and horns were used in mechanical gramophones as early as 1877. Horn loudspeakers use a shaped waveguide in front of or behind the driver to increase the directivity of the loudspeaker and to transform a small diameter, high pressure condition at the driver cone surface to a large diameter, low pressure condition at the mouth of the horn. This improves the acoustic—electro/mechanical impedance match between the driver and ambient air, increasing efficiency, and focusing the sound over a narrower area.


title: Loudspeaker

text: The size of the throat, mouth, the length of the horn, as well as the area expansion rate along it must be carefully chosen to match the drive to properly provide this transforming function over a range of frequencies (every horn performs poorly outside its acoustic limits, at both high and low frequencies). The length and cross-sectional mouth area required to create a bass or sub-bass horn require a horn many feet long. 'Folded' horns can reduce the total size, but compel designers to make compromises and accept increased complication such as cost and construction. Some horn designs not only fold the low frequency horn, but use the walls in a room corner as an extension of the horn mouth. In the late 1940s, horns whose mouths took up much of a room wall were not unknown amongst hi-fi fans. Room sized installations became much less acceptable when two or more were required.


title: Loudspeaker

text: A horn loaded speaker can have a sensitivity as high as 110 dB at 2.83 volts (1 watt at 8 ohms) at 1 meter. This is a hundredfold increase in output compared to a speaker rated at 90 dB sensitivity, and is invaluable in applications where high sound levels are required or amplifier power is limited.


title: Loudspeaker

text: A transmission line loudspeaker is a loudspeaker enclosure design that uses an acoustic transmission line within the cabinet, compared to the simpler enclosures used by sealed (closed) or bass reflex designs. Instead of reverberating in a fairly simple damped enclosure, sound from the back of the bass speaker is directed into a long (generally folded) damped pathway within the speaker enclosure, which allows far greater control and use of speaker energy and the resulting sound.


title: Loudspeaker

text: Most home hi-fi loudspeakers use two wiring points to connect to the source of the signal (for example, to the audio amplifier or receiver). To accept the wire connection, the loudspeaker enclosure may have binding posts, spring clips, or a panel-mount jack. If the wires for a pair of speakers are not connected with respect to the proper electrical polarity (the + and − connections on the speaker and amplifier should be connected + to + and − to −; speaker cable is almost always marked so that one conductor of a pair can be distinguished from the other, even if it has run under or behind things in its run from amplifier to speaker location), the loudspeakers are said to be "out of phase" or more properly "out of polarity". Given identical signals, motion in one cone is in the opposite direction of the other. This typically causes monophonic material in a stereo recording to be canceled out, reduced in level, and made more difficult to localize, all due to destructive interference of the sound waves. The cancellation effect is most noticeable at frequencies where the loudspeakers are separated by a quarter wavelength or less; low frequencies are affected the most. This type of miswiring error does not damage speakers, but is not optimal for listening.


title: Loudspeaker

text: With sound reinforcement system, PA system and instrument amplifier speaker enclosures, cables and some type of jack or connector are typically used. Lower- and mid-priced sound system and instrument speaker cabinets often use 1/4" speaker cable jacks. Higher-priced and higher powered sound system cabinets and instrument speaker cabinets often use Speakon connectors. Speakon connectors are considered to be safer for high wattage amplifiers, because the connector is designed so that human users cannot touch the connectors.


title: Loudspeaker

text: Wireless speakers are very similar to traditional (wired) loudspeakers, but they receive audio signals using radio frequency (RF) waves rather than over audio cables. There is normally an amplifier integrated in the speaker's cabinet because the RF waves alone are not enough to drive the speaker. This integration of amplifier and loudspeaker is known as an active loudspeaker. Manufacturers of these loudspeakers design them to be as lightweight as possible while producing the maximum amount of audio output efficiency.


title: Loudspeaker

text: Wireless speakers still need power, so require a nearby AC power outlet, or possibly batteries. Only the wire to the amplifier is eliminated.


title: Loudspeaker

text: The load that a driver presents to an amplifier consists of a complex electrical impedance—a combination of resistance and both capacitive and inductive reactance, which combines properties of the driver, its mechanical motion, the effects of crossover components (if any are in the signal path between amplifier and driver), and the effects of air loading on the driver as modified by the enclosure and its environment. Most amplifiers' output specifications are given at a specific power into an ideal resistive load; however, a loudspeaker does not have a constant impedance across its frequency range. Instead, the voice coil is inductive, the driver has mechanical resonances, the enclosure changes the driver's electrical and mechanical characteristics, and a passive crossover between the drivers and the amplifier contributes its own variations. The result is a load impedance that varies widely with frequency, and usually a varying phase relationship between voltage and current as well, also changing with frequency. Some amplifiers can cope with the variation better than others can.


title: Loudspeaker

text: To make sound, a loudspeaker is driven by modulated electric current (produced by an amplifier) that passes through a "speaker coil" which then (through inductance) creates a magnetic field around the coil. The electric current variations that pass through the speaker are thus converted to a varying magnetic field, whose interaction with the driver's magnetic field moves the speaker diaphragm, which thus forces the driver to produce air motion that is similar to the original signal from the amplifier.


title: Loudspeaker

text: Examples of typical measurements are: amplitude and phase characteristics vs. frequency; impulse response under one or more conditions (e.g., square waves, sine wave bursts, etc.); directivity vs. frequency (e.g., horizontally, vertically, spherically, etc.); harmonic and intermodulation distortion vs. sound pressure level (SPL) output, using any of several test signals; stored energy (i.e., ringing) at various frequencies; impedance vs. frequency; and small-signal vs. large-signal performance. Most of these measurements require sophisticated and often expensive equipment to perform, and also good judgment by the operator, but the raw sound pressure level output is rather easier to report and so is often the only specified value—sometimes in misleadingly exact terms. The sound pressure level (SPL) a loudspeaker produces is measured in decibels (dB).


title: Loudspeaker

text: Loudspeaker efficiency is defined as the sound power output divided by the electrical power input. Most loudspeakers are inefficient transducers; only about 1% of the electrical energy sent by an amplifier to a typical home loudspeaker is converted to acoustic energy. The remainder is converted to heat, mostly in the voice coil and magnet assembly. The main reason for this is the difficulty of achieving proper impedance matching between the acoustic impedance of the drive unit and the air it radiates into. (At low frequencies, improving this match is the main purpose of speaker enclosure designs). The efficiency of loudspeaker drivers varies with frequency as well. For instance, the output of a woofer driver decreases as the input frequency decreases because of the increasingly poor match between air and the driver.


title: Loudspeaker

text: Driver ratings based on the SPL for a given input are called sensitivity ratings and are notionally similar to efficiency. Sensitivity is usually defined as so many decibels at 1 W electrical input, measured at 1 meter (except for headphones), often at a single frequency. The voltage used is often 2.83 V, which is 1 watt into an 8 Ω (nominal) speaker impedance (approximately true for many speaker systems). Measurements taken with this reference are quoted as dB with 2.83 V @ 1 m.


title: Loudspeaker

text: The sound pressure output is measured at (or mathematically scaled to be equivalent to a measurement taken at) one meter from the loudspeaker and on-axis (directly in front of it), under the condition that the loudspeaker is radiating into an infinitely large space and mounted on an infinite baffle. Clearly then, sensitivity does not correlate precisely with efficiency, as it also depends on the directivity of the driver being tested and the acoustic environment in front of the actual loudspeaker. For example, a cheerleader's horn produces more sound output in the direction it is pointed by concentrating sound waves from the cheerleader in one direction, thus "focusing" them. The horn also improves impedance matching between the voice and the air, which produces more acoustic power for a given speaker power. In some cases, improved impedance matching (via careful enclosure design) lets the speaker produce more acoustic power.


title: Loudspeaker

text: A driver with a higher maximum power rating cannot necessarily be driven to louder levels than a lower-rated one, since sensitivity and power handling are largely independent properties. In the examples that follow, assume (for simplicity) that the drivers being compared have the same electrical impedance, are operated at the same frequency within both driver's respective pass bands, and that power compression and distortion are low. For the first example, a speaker 3 dB more sensitive than another produces double the sound power (is 3 dB louder) for the same power input. Thus, a 100 W driver ("A") rated at 92 dB for 1 W @ 1 m sensitivity puts out twice as much acoustic power as a 200 W driver ("B") rated at 89 dB for 1 W @ 1 m when both are driven with 100 W of input power. In this particular example, when driven at 100 W, speaker A produces the same SPL, or loudness as speaker B would produce with 200 W input. Thus, a 3 dB increase in sensitivity of the speaker means that it needs half the amplifier power to achieve a given SPL. This translates into a smaller, less complex power amplifier—and often, to reduced overall system cost.


title: Loudspeaker

text: It is typically not possible to combine high efficiency (especially at low frequencies) with compact enclosure size and adequate low frequency response. One can, for the most part, choose only two of the three parameters when designing a speaker system. So, for example, if extended low-frequency performance and small box size are important, one must accept low efficiency. This rule of thumb is sometimes called Hofmann's Iron Law (after J.A. Hofmann, the "H" in KLH).


title: Loudspeaker

text: The interaction of a loudspeaker system with its environment is complex and is largely out of the loudspeaker designer's control. Most listening rooms present a more or less reflective environment, depending on size, shape, volume, and furnishings. This means the sound reaching a listener's ears consists not only of sound directly from the speaker system, but also the same sound delayed by traveling to and from (and being modified by) one or more surfaces. These reflected sound waves, when added to the direct sound, cause cancellation and addition at assorted frequencies (e.g., from resonant room modes), thus changing the timbre and character of the sound at the listener's ears. The human brain is very sensitive to small variations, including some of these, and this is part of the reason why a loudspeaker system sounds different at different listening positions or in different rooms.


title: Loudspeaker

text: A significant factor in the sound of a loudspeaker system is the amount of absorption and diffusion present in the environment. Clapping one's hands in a typical empty room, without draperies or carpet, produces a zippy, fluttery echo due both to a lack of absorption and to reverberation (that is, repeated echoes) from flat reflective walls, floor, and ceiling. The addition of hard surfaced furniture, wall hangings, shelving and even baroque plaster ceiling decoration changes the echoes, primarily because of diffusion caused by reflective objects with shapes and surfaces having sizes on the order of the sound wavelengths. This somewhat breaks up the simple reflections otherwise caused by bare flat surfaces, and spreads the reflected energy of an incident wave over a larger angle on reflection.


title: Loudspeaker

text: In a typical rectangular listening room, the hard, parallel surfaces of the walls, floor and ceiling cause primary acoustic resonance nodes in each of the three dimensions: left-right, up-down and forward-backward. Furthermore, there are more complex resonance modes involving three, four, five and even all six boundary surfaces combining to create standing waves. This is called speaker boundary interference response (SBIR). Low frequencies excite these modes the most, since long wavelengths are not much affected by furniture compositions or placement. The mode spacing is critical, especially in small and medium size rooms like recording studios, home theaters and broadcast studios. The proximity of the loudspeakers to room boundaries affects how strongly the resonances are excited as well as affecting the relative strength at each frequency. The location of the listener is critical, too, as a position near a boundary can have a great effect on the perceived balance of frequencies. This is because standing wave patterns are most easily heard in these locations and at lower frequencies, below the Schroeder frequency – typically around 200–300 Hz, depending on room size.


title: Loudspeaker

text: Acousticians, in studying the radiation of sound sources have developed some concepts important to understanding how loudspeakers are perceived. The simplest possible radiating source is a point source, sometimes called a simple source. An ideal point source is an infinitesimally small point radiating sound. It may be easier to imagine a tiny pulsating sphere, uniformly increasing and decreasing in diameter, sending out sound waves in all directions equally, independent of frequency.


title: Loudspeaker

text: Any object radiating sound, including a loudspeaker system, can be thought of as being composed of combinations of such simple point sources. The radiation pattern of a combination of point sources is not the same as for a single source, but depends on the distance and orientation between the sources, the position relative to them from which the listener hears the combination, and the frequency of the sound involved. Using geometry and calculus, some simple combinations of sources are easily solved; others are not.


title: Loudspeaker

text: One simple combination is two simple sources separated by a distance and vibrating out of phase, one miniature sphere expanding while the other is contracting. The pair is known as a doublet, or dipole, and the radiation of this combination is similar to that of a very small dynamic loudspeaker operating without a baffle. The directivity of a dipole is a figure 8 shape with maximum output along a vector that connects the two sources and minimums to the sides when the observing point is equidistant from the two sources, where the sum of the positive and negative waves cancel each other. While most drivers are dipoles, depending on the enclosure to which they are attached, they may radiate as monopoles, dipoles (or bipoles). If mounted on a finite baffle, and these out of phase waves are allowed to interact, dipole peaks and nulls in the frequency response result. When the rear radiation is absorbed or trapped in a box, the diaphragm becomes a monopole radiator. Bipolar speakers, made by mounting in-phase monopoles (both moving out of or into the box in unison) on opposite sides of a box, are a method of approaching omnidirectional radiation patterns.


title: Loudspeaker

text: In real life, individual drivers are complex 3D shapes such as cones and domes, and they are placed on a baffle for various reasons. A mathematical expression for the directivity of a complex shape, based on modeling combinations of point sources, is usually not possible, but in the far field, the directivity of a loudspeaker with a circular diaphragm is close to that of a flat circular piston, so it can be used as an illustrative simplification for discussion. As a simple example of the mathematical physics involved, consider the following:


title: Loudspeaker

text: where , is the pressure on axis, is the piston radius, is the wavelength (i.e. ) is the angle off axis and is the Bessel function of the first kind.


title: Loudspeaker

text: A planar source radiates sound uniformly for low frequencies' wavelengths longer than the dimensions of the planar source, and as frequency increases, the sound from such a source focuses into an increasingly narrower angle. The smaller the driver, the higher the frequency where this narrowing of directivity occurs. Even if the diaphragm is not perfectly circular, this effect occurs such that larger sources are more directive. Several loudspeaker designs approximate this behavior. Most are electrostatic or planar magnetic designs.


title: Loudspeaker

text: Various manufacturers use different driver mounting arrangements to create a specific type of sound field in the space for which they are designed. The resulting radiation patterns may be intended to more closely simulate the way sound is produced by real instruments, or simply create a controlled energy distribution from the input signal (some using this approach are called monitors, as they are useful in checking the signal just recorded in a studio). An example of the first is a room corner system with many small drivers on the surface of a 1/8 sphere. A system design of this type was patented and produced commercially by Professor Amar Bose—the 2201. Later Bose models have deliberately emphasized production of both direct and reflected sound by the loudspeaker itself, regardless of its environment. The designs are controversial in high fidelity circles, but have proven commercially successful. Several other manufacturers' designs follow similar principles.


title: Loudspeaker

text: Directivity is an important issue because it affects the frequency balance of sound a listener hears, and also the interaction of the speaker system with the room and its contents. A very directive (sometimes termed 'beamy') speaker (i.e., on an axis perpendicular to the speaker face) may result in a reverberant field lacking in high frequencies, giving the impression the speaker is deficient in treble even though it measures well on axis (e.g., "flat" across the entire frequency range). Speakers with very wide, or rapidly increasing directivity at high frequencies, can give the impression that there is too much treble (if the listener is on axis) or too little (if the listener is off axis). This is part of the reason why on-axis frequency response measurement is not a complete characterization of the sound of a given loudspeaker.


title: Loudspeaker

text: The moving iron speaker was the first type of speaker that was invented. Unlike the newer dynamic (moving coil) design, a moving-iron speaker uses a stationary coil to vibrate a magnetized piece of metal (called the iron, reed, or armature). The metal is either attached to the diaphragm or is the diaphragm itself. This design was the original loudspeaker design, dating back to the early telephone. Moving iron drivers are inefficient and can only produce a small band of sound. They require large magnets and coils to increase force.


title: Loudspeaker

text: Balanced armature drivers (a type of moving iron driver) use an armature that moves like a see-saw or diving board. Since they are not damped, they are highly efficient, but they also produce strong resonances. They are still used today for high-end earphones and hearing aids, where small size and high efficiency are important.


title: Loudspeaker

text: Piezoelectric speakers are frequently used as beepers in watches and other electronic devices, and are sometimes used as tweeters in less-expensive speaker systems, such as computer speakers and portable radios. Piezoelectric speakers have several advantages over conventional loudspeakers: they are resistant to overloads that would normally destroy most high frequency drivers, and they can be used without a crossover due to their electrical properties. There are also disadvantages: some amplifiers can oscillate when driving capacitive loads like most piezoelectrics, which results in distortion or damage to the amplifier. Additionally, their frequency response, in most cases, is inferior to that of other technologies. This is why they are generally used in single frequency (beeper) or non-critical applications.


title: Loudspeaker

text: Piezoelectric speakers can have extended high frequency output, and this is useful in some specialized circumstances; for instance, sonar applications in which piezoelectric variants are used as both output devices (generating underwater sound) and as input devices (acting as the sensing components of underwater microphones). They have advantages in these applications, not the least of which is simple and solid state construction that resists seawater better than a ribbon or cone based device would.


title: Loudspeaker

text: In 2013, Kyocera introduced piezoelectric ultra-thin medium-size film speakers with only 1 millimeter of thickness and 7 grams of weight for their 55" OLED televisions and they hope the speakers will also be used in PCs and tablets. Besides medium-size, there are also large and small sizes which can all produce relatively the same quality of sound and volume within 180 degrees. The highly responsive speaker material provides better clarity than traditional TV speakers.


title: Loudspeaker

text: Instead of a voice coil driving a speaker cone, a magnetostatic speaker uses an array of metal strips bonded to a large film membrane. The magnetic field produced by signal current flowing through the strips interacts with the field of permanent bar magnets mounted behind them. The force produced moves the membrane and so the air in front of it. Typically, these designs are less efficient than conventional moving-coil speakers.


title: Loudspeaker

text: Magnetostrictive transducers, based on magnetostriction, have been predominantly used as sonar ultrasonic sound wave radiators, but their use has spread also to audio speaker systems. Magnetostrictive speaker drivers have some special advantages: they can provide greater force (with smaller excursions) than other technologies; low excursion can avoid distortions from large excursion as in other designs; the magnetizing coil is stationary and therefore more easily cooled; they are robust because delicate suspensions and voice coils are not required. Magnetostrictive speaker modules have been produced by Fostex and FeONIC and subwoofer drivers have also been produced.


title: Loudspeaker

text: Electrostatic loudspeakers use a high voltage electric field (rather than a magnetic field) to drive a thin statically charged membrane. Because they are driven over the entire membrane surface rather than from a small voice coil, they ordinarily provide a more linear and lower-distortion motion than dynamic drivers. They also have a relatively narrow dispersion pattern that can make for precise sound-field positioning. However, their optimum listening area is small and they are not very efficient speakers. They have the disadvantage that the diaphragm excursion is severely limited because of practical construction limitations—the further apart the stators are positioned, the higher the voltage must be to achieve acceptable efficiency. This increases the tendency for electrical arcs as well as increasing the speaker's attraction of dust particles. Arcing remains a potential problem with current technologies, especially when the panels are allowed to collect dust or dirt and are driven with high signal levels.


title: Loudspeaker

text: Electrostatics are inherently dipole radiators and due to the thin flexible membrane are less suited for use in enclosures to reduce low frequency cancellation as with common cone drivers. Due to this and the low excursion capability, full range electrostatic loudspeakers are large by nature, and the bass rolls off at a frequency corresponding to a quarter wavelength of the narrowest panel dimension. To reduce the size of commercial products, they are sometimes used as a high frequency driver in combination with a conventional dynamic driver that handles the bass frequencies effectively.


title: Loudspeaker

text: Electrostatics are usually driven through a step-up transformer that multiplies the voltage swings produced by the power amplifier. This transformer also multiplies the capacitive load that is inherent in electrostatic transducers, which means the effective impedance presented to the power amplifiers varies widely by frequency. A speaker that is nominally 8 ohms may actually present a load of 1 ohm at higher frequencies, which is challenging to some amplifier designs.


title: Loudspeaker

text: A ribbon speaker consists of a thin metal-film ribbon suspended in a magnetic field. The electrical signal is applied to the ribbon, which moves with it to create the sound. The advantage of a ribbon driver is that the ribbon has very little mass; thus, it can accelerate very quickly, yielding very good high-frequency response. Ribbon loudspeakers are often very fragile—some can be torn by a strong gust of air. Most ribbon tweeters emit sound in a dipole pattern. A few have backings that limit the dipole radiation pattern. Above and below the ends of the more or less rectangular ribbon, there is less audible output due to phase cancellation, but the precise amount of directivity depends on ribbon length. Ribbon designs generally require exceptionally powerful magnets, which makes them costly to manufacture. Ribbons have a very low resistance that most amplifiers cannot drive directly. As a result, a step down transformer is typically used to increase the current through the ribbon. The amplifier "sees" a load that is the ribbon's resistance times the transformer turns ratio squared. The transformer must be carefully designed so that its frequency response and parasitic losses do not degrade the sound, further increasing cost and complication relative to conventional designs.


title: Loudspeaker

text: Planar magnetic speakers (having printed or embedded conductors on a flat diaphragm) are sometimes described as ribbons, but are not truly ribbon speakers. The term planar is generally reserved for speakers with roughly rectangular flat surfaces that radiate in a bipolar (i.e., front and back) manner. Planar magnetic speakers consist of a flexible membrane with a voice coil printed or mounted on it. The current flowing through the coil interacts with the magnetic field of carefully placed magnets on either side of the diaphragm, causing the membrane to vibrate more or less uniformly and without much bending or wrinkling. The driving force covers a large percentage of the membrane surface and reduces resonance problems inherent in coil-driven flat diaphragms.


title: Loudspeaker

text: Bending wave transducers use a diaphragm that is intentionally flexible. The rigidity of the material increases from the center to the outside. Short wavelengths radiate primarily from the inner area, while longer waves reach the edge of the speaker. To prevent reflections from the outside back into the center, long waves are absorbed by a surrounding damper. Such transducers can cover a wide frequency range (80 Hz to 35,000 Hz) and have been promoted as being close to an ideal point sound source. This uncommon approach is being taken by only a very few manufacturers, in very different arrangements.


title: Loudspeaker

text: The Ohm Walsh loudspeakers use a unique driver designed by Lincoln Walsh, who had been a radar development engineer in WWII. He became interested in audio equipment design and his last project was a unique, one-way speaker using a single driver. The cone faced down into a sealed, airtight enclosure. Rather than move back-and-forth as conventional speakers do, the cone rippled and created sound in a manner known in RF electronics as a "transmission line". The new speaker created a cylindrical sound field. Lincoln Walsh died before his speaker was released to the public. The Ohm Acoustics firm has produced several loudspeaker models using the Walsh driver design since then. German Physiks, an audio equipment firm in Germany, also produces speakers using this approach.


title: Loudspeaker

text: The German firm Manger has designed and produced a bending wave driver that at first glance appears conventional. In fact, the round panel attached to the voice coil bends in a carefully controlled way to produce full range sound. Josef W. Manger was awarded with the Rudolf-Diesel-Medaille for extraordinary developments and inventions by the German institute of inventions.


title: Loudspeaker

text: There have been many attempts to reduce the size of speaker systems, or alternatively to make them less obvious. One such attempt was the development of "exciter" transducer coils mounted to flat panels to act as sound sources, most accurately called exciter/panel drivers. These can then be made in a neutral color and hung on walls where they are less noticeable than many speakers, or can be deliberately painted with patterns, in which case they can function decoratively. There are two related problems with flat panel techniques: first, a flat panel is necessarily more flexible than a cone shape in the same material, and therefore moves as a single unit even less, and second, resonances in the panel are difficult to control, leading to considerable distortions. Some progress has been made using such lightweight, rigid, materials such as Styrofoam, and there have been several flat panel systems commercially produced in recent years.


title: Loudspeaker

text: Oskar Heil invented the air motion transducer in the 1960s. In this approach, a pleated diaphragm is mounted in a magnetic field and forced to close and open under control of a music signal. Air is forced from between the pleats in accordance with the imposed signal, generating sound. The drivers are less fragile than ribbons and considerably more efficient (and able to produce higher absolute output levels) than ribbon, electrostatic, or planar magnetic tweeter designs. ESS, a California manufacturer, licensed the design, employed Heil, and produced a range of speaker systems using his tweeters during the 1970s and 1980s. Lafayette Radio, a large US retail store chain, also sold speaker systems using such tweeters for a time. There are several manufacturers of these drivers (at least two in Germany—one of which produces a range of high-end professional speakers using tweeters and mid-range drivers based on the technology) and the drivers are increasingly used in professional audio. Martin Logan produces several AMT speakers in the US and GoldenEar Technologies incorporates them in its entire speaker line.


title: Loudspeaker

text: In 2013, a research team introduced Transparent ionic conduction speaker which a 2 layers transparent conductive gel and a layer of transparent rubber in between to make high voltage and high actuation work to reproduce good sound quality. The speaker is suitable for robotics, mobile computing and adaptive optics fields.


title: Loudspeaker

text: Plasma arc loudspeakers use electrical plasma as a radiating element. Since plasma has minimal mass, but is charged and therefore can be manipulated by an electric field, the result is a very linear output at frequencies far higher than the audible range. Problems of maintenance and reliability for this approach tend to make it unsuitable for mass market use. In 1978 Alan E. Hill of the Air Force Weapons Laboratory in Albuquerque, NM, designed the Plasmatronics Hill Type I, a tweeter whose plasma was generated from helium gas. This avoided the ozone and NOx produced by RF decomposition of air in an earlier generation of plasma tweeters made by the pioneering DuKane Corporation, who produced the Ionovac (marketed as the Ionofane in the UK) during the 1950s. Currently, there remain a few manufacturers in Germany who use this design, and a do-it-yourself design has been published and has been available on the Internet.


title: Loudspeaker

text: A less expensive variation on this theme is the use of a flame for the driver, as flames contain ionized (electrically charged) gases.


title: Loudspeaker

text: In 2008, researchers of Tsinghua University demonstrated a thermoacoustic loudspeaker of carbon nanotube thin film, whose working mechanism is a thermoacoustic effect. Sound frequency electric currents are used to periodically heat the CNT and thus result in sound generation in the surrounding air. The CNT thin film loudspeaker is transparent, stretchable and flexible.


title: Loudspeaker

text: In 2013, researchers of Tsinghua University further present a thermoacoustic earphone of carbon nanotube thin yarn and a thermoacoustic surface-mounted device. They are both fully integrated devices and compatible with Si-based semiconducting technology.


title: Loudspeaker

text: A rotary woofer is essentially a fan with blades that constantly change their pitch, allowing them to easily push the air back and forth. Rotary woofers are able to efficiently reproduce subsonic frequencies, which are difficult to impossible to achieve on a traditional speaker with a diaphragm. They are often employed in movie theaters to recreate rumbling bass effects, such as explosions.


title: Loudspeaker

text: Digital speakers have been the subject of experiments performed by Bell Labs as far back as the 1920s. The design is simple; each bit controls a driver, which is either fully 'on' or 'off'. Problems with this design have led manufacturers to abandon it as impractical for the present. First, for a reasonable number of bits (required for adequate sound reproduction quality), the physical size of a speaker system becomes very large. Secondly, due to inherent analog-to-digital conversion problems, the effect of aliasing is unavoidable, so that the audio output is "reflected" at equal amplitude in the frequency domain, on the other side of the Nyquist limit (half the sampling frequency), causing an unacceptably high level of ultrasonics to accompany the desired output. No workable scheme has been found to adequately deal with this.


title: Loudspeaker

text: The term "digital" or "digital-ready" is often used for marketing purposes on speakers or headphones, but these systems are not digital in the sense described above. Rather, they are conventional speakers that can be used with digital sound sources (e.g., optical media, MP3 players, etc.), as can any conventional speaker.


title: Actuarial science

text: Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, pension, finance, investment and other industries and professions. More generally, actuaries apply rigorous mathematics to model matters of uncertainty.


title: Actuarial science

text: Actuaries are professionals trained in this discipline. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations.


title: Actuarial science

text: Actuarial science includes a number of interrelated subjects, including mathematics, probability theory, statistics, finance, economics, financial accounting and computer science. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes since the 1980s due to the proliferation of high speed computers and the union of stochastic actuarial models with modern financial theory.


title: Actuarial science

text: Many universities have undergraduate and graduate degree programs in actuarial science. In 2010, a study published by job search website CareerCast ranked actuary as the #1 job in the United States. The study used five key criteria to rank jobs: environment, income, employment outlook, physical demands, and stress. A similar study by "U.S. News & World Report" in 2006 included actuaries among the 25 Best Professions that it expects will be in great demand in the future.


title: Actuarial science

text: Actuarial science became a formal mathematical discipline in the late 17th century with the increased demand for long-term insurance coverage such as burial, life insurance, and annuities. These long term coverages required that money be set aside to pay future benefits, such as annuity and death benefits many years into the future. This requires estimating future contingent events, such as the rates of mortality by age, as well as the development of mathematical techniques for discounting the value of funds set aside and invested. This led to the development of an important actuarial concept, referred to as the present value of a future sum. Certain aspects of the actuarial methods for discounting pension funds have come under criticism from modern financial economics.


title: Actuarial science

text: Actuarial science is also applied to property, casualty, liability, and general insurance. In these forms of insurance, coverage is generally provided on a renewable period, (such as a yearly). Coverage can be cancelled at the end of the period by either party.


title: Actuarial science

text: Property and casualty insurance companies tend to specialize because of the complexity and diversity of risks. One division is to organize around personal and commercial lines of insurance. Personal lines of insurance are for individuals and include fire, auto, homeowners, theft and umbrella coverages. Commercial lines address the insurance needs of businesses and include property, business continuation, product liability, fleet/commercial vehicle, workers compensation, fidelity & surety, and D&O insurance. The insurance industry also provides coverage for exposures such as catastrophe, weather-related risks, earthquakes, patent infringement and other forms of corporate espionage, terrorism, and "one-of-a-kind" (e.g., satellite launch). Actuarial science provides data collection, measurement, estimating, forecasting, and valuation tools to provide financial and underwriting data for management to assess marketing opportunities and the nature of the risks. Actuarial science often helps to assess the overall risk from catastrophic events in relation to its underwriting capacity or surplus.


title: Actuarial science

text: In the reinsurance fields, actuarial science can be used to design and price reinsurance and retrocession arrangements, and to establish reserve funds for known claims and future claims and catastrophes.


title: Actuarial science

text: There is an increasing trend to recognize that actuarial skills can be applied to a range of applications outside the traditional fields of insurance, pensions, etc. One notable example is the use in some US states of actuarial models to set criminal sentencing guidelines. These models attempt to predict the chance of re-offending according to rating factors which include the type of crime, age, educational background and ethnicity of the offender. However, these models have been open to criticism as providing justification for discrimination against specific ethnic groups by law enforcement personnel. Whether this is statistically correct or a self-fulfilling correlation remains under debate.


title: Actuarial science

text: Another example is the use of actuarial models to assess the risk of sex offense recidivism. Actuarial models and associated tables, such as the MnSOST-R, Static-99, and SORAG, have been used since the late 1990s to determine the likelihood that a sex offender will re-offend and thus whether he or she should be institutionalized or set free.


title: Actuarial science

text: Traditional actuarial science and modern financial economics in the US have different practices, which is caused by different ways of calculating funding and investment strategies, and by different regulations.


title: Actuarial science

text: Regulations are from the Armstrong investigation of 1905, the Glass–Steagall Act of 1932, the adoption of the Mandatory Security Valuation Reserve by the National Association of Insurance Commissioners, which cushioned market fluctuations, and the Financial Accounting Standards Board, (FASB) in the US and Canada, which regulates pensions valuations and funding.


title: Actuarial science

text: Historically, much of the foundation of actuarial theory predated modern financial theory. In the early twentieth century, actuaries were developing many techniques that can be found in modern financial theory, but for various historical reasons, these developments did not achieve much recognition.


title: Actuarial science

text: As a result, actuarial science developed along a different path, becoming more reliant on assumptions, as opposed to the arbitrage-free risk-neutral valuation concepts used in modern finance. The divergence is not related to the use of historical data and statistical projections of liability cash flows, but is instead caused by the manner in which traditional actuarial methods apply market data with those numbers. For example, one traditional actuarial method suggests that changing the asset allocation mix of investments can change the value of liabilities and assets (by changing the discount rate assumption). This concept is inconsistent with financial economics.


title: Actuarial science

text: The potential of modern financial economics theory to complement existing actuarial science was recognized by actuaries in the mid-twentieth century. In the late 1980s and early 1990s, there was a distinct effort for actuaries to combine financial theory and stochastic methods into their established models. Ideas from financial economics became increasingly influential in actuarial thinking, and actuarial science has started to embrace more sophisticated mathematical modelling of finance. Today, the profession, both in practice and in the educational syllabi of many actuarial organizations, is cognizant of the need to reflect the combined approach of tables, loss models, stochastic methods, and financial theory. However, assumption-dependent concepts are still widely used (such as the setting of the discount rate assumption as mentioned earlier), particularly in North America.


title: Actuarial science

text: Product design adds another dimension to the debate. Financial economists argue that pension benefits are bond-like and should not be funded with equity investments without reflecting the risks of not achieving expected returns. But some pension products do reflect the risks of unexpected returns. In some cases, the pension beneficiary assumes the risk, or the employer assumes the risk. The current debate now seems to be focusing on four principles:


title: Actuarial science

text: Essentially, financial economics state that pension assets should not be invested in equities for a variety of theoretical and practical reasons.


title: Actuarial science

text: Elementary mutual aid agreements and pensions arose in antiquity. Early in the Roman empire, associations were formed to meet the expenses of burial, cremation, and monuments—precursors to burial insurance and friendly societies. A small sum was paid into a communal fund on a weekly basis, and upon the death of a member, the fund would cover the expenses of rites and burial. These societies sometimes sold shares in the building of columbāria, or burial vaults, owned by the fund—the precursor to mutual insurance companies. Other early examples of mutual surety and assurance pacts can be traced back to various forms of fellowship within the Saxon clans of England and their Germanic forebears, and to Celtic society. However, many of these earlier forms of surety and aid would often fail due to lack of understanding and knowledge.


title: Actuarial science

text: The 17th century was a period of advances in mathematics in Germany, France and England. At the same time there was a rapidly growing desire and need to place the valuation of personal risk on a more scientific basis. Independently of each other, compound interest was studied and probability theory emerged as a well-understood mathematical discipline. Another important advance came in 1662 from a London draper, the father of demography, John Graunt, who showed that there were predictable patterns of longevity and death in a group, or cohort, of people of the same age, despite the uncertainty of the date of death of any one individual. This study became the basis for the original life table. One could now set up an insurance scheme to provide life insurance or pensions for a group of people, and to calculate with some degree of accuracy how much each person in the group should contribute to a common fund assumed to earn a fixed rate of interest. The first person to demonstrate publicly how this could be done was Edmond Halley (of Halley's comet fame). Halley constructed his own life table, and showed how it could be used to calculate the premium amount someone of a given age should pay to purchase a life annuity.


title: Actuarial science

text: James Dodson's pioneering work on the long term insurance contracts under which the same premium is charged each year led to the formation of the Society for Equitable Assurances on Lives and Survivorship (now commonly known as Equitable Life) in London in 1762. William Morgan is often considered the father of modern actuarial science for his work in the field in the 1780s and 90s. Many other life insurance companies and pension funds were created over the following 200 years. Equitable Life was the first to use the word "actuary" for its chief executive officer in 1762. Previously, "actuary" meant an official who recorded the decisions, or "acts", of ecclesiastical courts. Other companies that did not use such mathematical and scientific methods most often failed or were forced to adopt the methods pioneered by Equitable.


title: Actuarial science

text: In the 18th and 19th centuries, calculations were performed without computers. The computations of life insurance premiums and reserving requirements are rather complex, and actuaries developed techniques to make the calculations as easy as possible, for example "commutation functions" (essentially precalculated columns of summations over time of discounted values of survival and death probabilities). Actuarial organizations were founded to support and further both actuaries and actuarial science, and to protect the public interest by promoting competency and ethical standards. However, calculations remained cumbersome, and actuarial shortcuts were commonplace. Non-life actuaries followed in the footsteps of their life insurance colleagues during the 20th century. The 1920 revision for the New-York based National Council on Workmen's Compensation Insurance rates took over two months of around-the-clock work by day and night teams of actuaries. In the 1930s and 1940s, the mathematical foundations for stochastic processes were developed. Actuaries could now begin to estimate losses using models of random events, instead of the deterministic methods they had used in the past. The introduction and development of the computer further revolutionized the actuarial profession. From pencil-and-paper to punchcards to current high-speed devices, the modeling and forecasting ability of the actuary has rapidly improved, while still being heavily dependent on the assumptions input into the models, and actuaries needed to adjust to this new world .


title: Soft Cell

text: Soft Cell are an English synthpop duo who came to prominence in the early 1980s. The duo consists of vocalist Marc Almond and instrumentalist David Ball. The band are primarily known for their 1981 hit version of "Tainted Love" and their platinum-selling debut album "Non-Stop Erotic Cabaret".


title: Soft Cell

text: In the United Kingdom, Soft Cell had twelve top 40 hits, including "Tainted Love" (number 1), "Torch" (number 2), "Say Hello, Wave Goodbye", "What" (both number 3), and "Bedsitter" (number 4). They also had four top 20 albums between 1981 and 1984. In 1984, the duo split; however, they reformed in 2001 to tour and release a new album. They held a reunion concert in London on 30 September 2018, stating it would be their last live UK performance as a duo but that they may still perform abroad and record together.


title: Soft Cell

text: Soft Cell's songs have been covered by several artists, including David Gray, Coil and Nine Inch Nails. Their track "Memorabilia" earned recognition for the band as pioneers of the synth-oriented techno genre. The duo have sold in excess of ten million records world-wide.


title: Soft Cell

text: Soft Cell were formed in 1978, after Almond and Ball had met at Leeds Polytechnic in the previous year. Their initial efforts at recording resulted in an EP titled "Mutant Moments", released in 1980 and which was funded by a loan of £2,000 from Dave Ball's mother and made with a simple two-track recorder.


title: Soft Cell

text: Soft Cell's next recording, "The Girl with the Patent Leather Face", appeared as a contribution to the "Some Bizzare Album", which featured bands such as Depeche Mode, The The, and Blancmange. The duo ultimately signed to the Some Bizzare label, backed by Phonogram Records. Their first single, "A Man Could Get Lost" b/w "Memorabilia" on 7" and "Memorabilia" b/w "Persuasion" on 12", was produced by Daniel Miller who founded Mute Records, "Memorabilia" was a success in nightclubs, but did not enter the UK singles chart.


title: Soft Cell

text: After the chart failure of "Memorabilia", Phonogram Records allowed Soft Cell to record a second and final single in an attempt to score a chart success. The band opted to record a cover version of "Tainted Love", an obscure 1965 northern soul track originally released by Gloria Jones (the girlfriend of Marc Bolan at the time of his death) and written by Ed Cobb of The Four Preps.


title: Soft Cell

text: Released in 1981, Soft Cell's "Tainted Love" was a No. 1 hit in 17 countries, including the United Kingdom, where it was the second best selling single of 1981 after selling 1.05 million copies (a total which increased to 1.35 million copies by of August 2017).


title: Soft Cell

text: In 1982, "Tainted Love" became a No. 8 single in the United States and went on to set a Guinness World Record at the time for the longest consecutive stay (43 weeks) on the US "Billboard" Hot 100 chart. The song's popularity developed slowly, needing 19 weeks to enter the US Top 40. The A-side of the 12-inch single of "Tainted Love" actually featured a two-song medley, with "Tainted Love" blending into the Motown classic "Where Did Our Love Go" (originally recorded by the Supremes in 1964).


title: Soft Cell

text: The duo's first album, "Non-Stop Erotic Cabaret", hit UK No. 5 and further explored the now-trademark Soft Cell themes of squalor and sleaze. "Seedy Films" talks of long nights in porno cinemas, while "Frustration" and "Secret Life" deal with the boredom and hypocrisy associated with suburban life. A companion video titled "Non-Stop Exotic Video Show" was released in 1982 and featured videos directed by Tim Pope. The video generated some controversy in Britain, mainly due to a scandal involved with the "Sex Dwarf" clip.


title: Soft Cell

text: "Non-Stop Erotic Cabaret" garnered two additional hits: "Bedsitter" dealt with the loneliness and lifestyle of a young man having recently left home to live in a bedsit while partying hard. "Bedsitter" reached No. 4 in the UK Singles Chart in November 1981. The song was highly acclaimed in a retrospective review by AllMusic journalist Ned Raggett who wrote that it "ranks as one of the best, most realistic portrayals of urban life recorded." The final single on the album, the ballad "Say Hello, Wave Goodbye", peaked at No. 3 in February 1982.


title: Soft Cell

text: During 1982, the duo spent most of their time recording and relaxing in New York City, where they met a woman named Cindy Ecstasy whom Almond would later confirm was his drug supplier (it was Cindy Ecstasy who introduced them to the new nightclub drug of the same name). Soon after "Say Hello Wave Goodbye" dropped out of the chart, Soft Cell released a brand new song: "Torch", a love song which was to prove the closest the band ever got to having a No. 1 hit with one of their own songs. The song entered straight into the Top 20 and peaked at No. 2.


title: Soft Cell

text: In June 1982, as was the trend at the time, the duo released a mini album titled "Non Stop Ecstatic Dancing", containing remixes of older material along with their new single, "What!". This was a cover of the 1965 song by Melinda Marx. It was later covered in 1968 by Judy Street, whose version became extremely popular on the Northern Soul scene."What!" was a major hit in the UK and reached No. 3 on the UK Singles Chart in August of that year.


title: Soft Cell

text: By 1983, fame and nearly constant drug use were having a bad effect on the duo. Marc Almond also formed the group Marc and the Mambas, featuring collaborations with The The's Matt Johnson and future Almond collaborator Annie Hogan, as an offshoot to experiment out of the glare of the Soft Cell spotlight. Soft Cell's third album release, appropriately titled "The Art of Falling Apart", was a Top 5 hit in the UK but the singles were only modest successes. The first single "Where The Heart Is" only reached 21, while the double A-side "Numbers"/"Barriers" peaked at 25. "Numbers" also generated controversy due to references in the song to the drug speed.


title: Soft Cell

text: In September 1983, the duo released a new single "Soul Inside", which returned them to the UK Top 20, but by early 1984 the duo had amicably decided to end Soft Cell. They played farewell concerts at Hammersmith Palais in January, and released one final album called "This Last Night in Sodom" (UK No. 12) in March. The album's second and final single "Down in the Subway" (UK No. 24), had already been released in February 1984.


title: Soft Cell

text: Almond and Ball reunited as Soft Cell in 2000 with a series of live dates. They performed at the opening of the Ocean nightclub in London during March 2001. A mini-tour followed later in the year. The track "God Shaped Hole" featured on the Some Bizzare compilation titled "I'd Rather Shout at a Returning Echo than Kid Someone's Listening", released during 2001. A new Soft Cell album, "Cruelty Without Beauty", was released during late 2002, followed by a European tour and a small US tour during early 2003. The second single from the album, a cover of The Four Seasons "The Night", reached No. 39 in the UK. Soft Cell had considered recording "The Night" in place of "Tainted Love" during 1981, though keyboardist David Ball stated in a 2003 interview with the BBC, "I think history has kind of shown that we did make the right choice [in 1981]".


title: Soft Cell

text: In 2005 they released an album compiling some of their early demo recordings called The Bedsit Tapes. Another similar compilation entitled Demo Non Stop was also released around this time.


title: Soft Cell

text: In November 2008, the band released a remix album entitled "Heat". The album included Soft Cell tracks remixed by such acts as Paul Dakeyne, The Grid, Manhattan Clique, Cicada, Richard X, Ladytron, MHC, Atomizer, Mark Moore, Spektrum, The Dark Poets and many more.


title: Soft Cell

text: In February 2018, Soft Cell announced that they would reunite for one last UK reunion concert. On 21 August 2018, Almond revealed on the Chris Evans Breakfast Show on BBC Radio 2 that Soft Cell were releasing two new tracks ahead of the concert: "Northern Lights" and "Guilty (Cos I Say You Are)". Entitled "Say Hello, Wave Goodbye", the reunion concert took place at the O2 Arena in London on 30 September 2018. It was stated this was their final live UK show as a duo, but that they may still perform abroad and record material together.


title: Soft Cell

text: In 2019 Ball said a new Soft Cell album was in the works. In May 2019, the "To Show You, I've Been There" book was released, which came with a vinyl copy of the "Magick Mutants" EP, a sequel to their debut "Mutant Moments" EP.


title: Soft Cell

text: In June 2020, the "Mutant Moments" EP received its first official release. Originally to be part of the UK June Record Store Day 2020, the 10 inch EP was sold directly through the band's website, as the event was cancelled due to the ongoing COVID-19 pandemic.


title: Soft Cell

text: In July 2021, the duo announced that their new album would be called "Happiness Not Included" and would feature tracks such as "Heart Like Chernobyl",


title: Soft Cell

text: "Light Sleepers" and "Nostalgia Machine". The album is due to be released in Spring 2022, 20 years after their last studio album release, with Dave Ball revealing Pet Shop Boys are working on a remix for a forthcoming single.


title: Soft Cell

text: Despite previously claiming their 2018 reunion show would be the last in the UK, Soft Cell reunited again for 5 performances in 2021. The short tour was to mark 40 years of the "Non Stop Erotic Cabaret" album, with the band performing the album in full, as well as some hits and new material. The run began at the 02 Academy in Glasgow, Scotland on 10 November and ended at the London Hammersmith Apollo on 16 November.


title: Soft Cell

text: The group cited David Bowie, Marc Bolan and Suicide as primary influences. Almond also named Siouxsie Sioux as a major influence for his early performance style.


title: Antonio Valencia

text: Luis Antonio Valencia Mosquera, known as Antonio Valencia (; born 4 August 1985), is an Ecuadorian former professional footballer who played primarily as a right-sided player throughout his career, initially as a right winger, before developing into a right-back.


title: Antonio Valencia

text: After progressing through the youth system at El Nacional, Valencia became a first team regular and made over 80 appearances for the club. He won the Ecuadorian Serie A with them before signing for La Liga side Villarreal in 2005. He only made two league appearances for the Spanish side in between loan spells at Recreativo for the 2005–06 season and later English Premier League club Wigan Athletic from 2006 to 2008. Wigan Athletic later signed Valencia on a three-year deal for an undisclosed fee in January 2008. His performances for Wigan Athletic soon attracted attention from several high-profile clubs, eventually signing for Manchester United in June 2009. His stint there established him as one of the greatest Ecuadorian players of all time, as Valencia was voted into the PFA Team of the Year in his debut season, spent time as club captain, and went on to win two Premier League titles, an FA Cup, two League Cups, three FA Community Shields and the UEFA Europa League. In July 2019 Valencia returned to Ecuador, signing with LDU Quito, with whom he won the inaugural Copa Ecuador in his first season. He announced his retirement in May 2021.


title: Antonio Valencia

text: Valencia made his Ecuador debut in 2004 and has represented his country at the 2006 FIFA World Cup, the 2007 Copa América, the 2011 Copa América, the 2014 FIFA World Cup, the Copa América Centenario and the 2019 Copa América. Valencia won 99 caps and scored 11 goals for his country.


title: Antonio Valencia

text: Valencia was born on 4 August 1985 in Lago Agrio, near the city of Nueva Loja, Ecuador, which is located in the Amazon rainforest. Valencia helped his mother sell drinks outside the stadium of his local club at Lago Agrio and would then search for empty bottles for his father to sell to a bottle-deposit in the capital, Quito. Valencia used to play barefoot on the pitch next to the bungalow he shared with his parents, five brothers and sister.


title: Antonio Valencia

text: When Valencia was aged 11, scout Pedro Perlaza spotted him playing on a dusty field near his home, and signed him to the local FA-run sports academy in Sucumbíos. At the age of 16, Valencia did not tell his father he left home to take up an offer to play for El Nacional, the military-backed club in Quito. Nobody knew about Valencia's decision, except his mother and his elder brother, Carlos Alfredo, who paid the fare for his eight-hour bus journey. Valencia began in central midfield and on a salary of 50 dollars a month.


title: Antonio Valencia

text: Valencia started his career at El Nacional and within a year he was fast-tracked into the under-20s, where he played alongside striker Christian "Chucho"’ Benítez. Valencia made his debut for El Nacional alongside his idol Édison Méndez. Valencia won his first club title as part of the El Nacional team that won the 2005 Clausura Tournament, earning him the attention of both the national team's manager and Spanish clubs.


title: Antonio Valencia

text: Valencia moved to Spanish club Villarreal in 2005. After failing to break into the first-team, however, he was loaned to Recreativo to gain experience. Valencia helped Recreativo gain promotion to La Liga as they finished the season top of the table.


title: Antonio Valencia

text: On 3 August 2006, Valencia joined English Premier League club Wigan Athletic, initially on a year-long loan deal. He made his debut for Wigan on 19 August 2006, in a 2–1 loss away to Newcastle United. His first goal for Wigan came in a 4–0 home win over Manchester City on 21 October 2006. Valencia returned after a three-month absence as he played 78 minutes of a 2–0 home loss to Everton on 21 January 2007. Valencia was sent off for the first time for Wigan on 9 April 2007, receiving a straight red card for a two-footed challenge on Wilfred Bouma during a 1–1 away draw against Aston Villa.


title: Antonio Valencia

text: The loan was extended into the following season, and on 18 January 2008, he transferred for an undisclosed fee, signing a three-and-a-half-year contract. The deal was said to be worth around £5 million. Valencia scored his first goal of the 2007–08 season in a 2–0 win over Derby County on 23 February 2008, before netting his first Wigan brace in a 2–0 away victory over Aston Villa on 3 May 2008.


title: Antonio Valencia

text: Valencia's first goal of the following season came in Wigan's 5–0 away victory over Hull City on 30 August 2008. He then grabbed a goal in the 2–1 home win over Manchester City on 28 September 2008, but followed it up by receiving a red card in the 3–2 loss at Liverpool on 18 October 2008. Valencia scored his final goal for Wigan on 13 December 2008, as he inspired them to a 3–0 victory over Blackburn Rovers. Wigan boss Steve Bruce confirmed that Valencia turned down the chance to join Real Madrid in January 2009. On 9 February 2009, Valencia was ruled out of action for three weeks after suffering a recurrence of a hamstring injury. In early June 2009, Wigan chairman Dave Whelan announced that he would not force Valencia to stay at the club.


title: Antonio Valencia

text: On 30 June 2009, Valencia became Manchester United's first summer signing, having cut his holiday short to have a medical with the club. He signed a four-year contract for an undisclosed fee, rumoured to be in the region of £16 million.


title: Antonio Valencia

text: On 29 July 2009, he made his debut for United and scored his first goal in the process, netting United's second in a 2–1 pre-season victory over Boca Juniors in the Audi Cup. He made his competitive debut for Manchester United in the 2009 FA Community Shield, when he came on for the injured Nani in the 62nd minute. On 17 October 2009, he scored his first competitive goal for the club, scoring United's second in a 2–1 league victory against Bolton Wanderers. His first UEFA Champions League goal followed four days later in a 1–0 away victory against CSKA Moscow.


title: Antonio Valencia

text: Valencia provided the assist for Wayne Rooney's winning goal in the 2010 League Cup Final against Aston Villa on 28 February 2010 and was named player of the match as United won 2–1. On 25 April 2010, Valencia was included in the PFA Premier League Team of the Year in his debut season for the club alongside teammates Patrice Evra, Darren Fletcher, and Wayne Rooney.


title: Antonio Valencia

text: On 8 August 2010, Valencia scored United's first goal in their 3–1 win over Chelsea in the 2010 Community Shield. During a Champions League game against Rangers on 14 September 2010, Valencia suffered a break to his left ankle. An operation the morning after the match showed that his left ankle was fractured and dislocated, and that his ankle ligaments were damaged. On 28 February 2011, Valencia returned to training with Manchester United's first team.


title: Antonio Valencia

text: He played his first game back from injury against Arsenal in the FA Cup sixth round on 12 March 2011. On 9 April 2011, he scored his first league goal of the season as he netted the second of a 2–0 home win over Fulham. Days later, he scored the first goal in United's 4–1 victory against the German team Schalke 04 in the second leg of the semi-final of the 2010–11 UEFA Champions League, game in which he was selected as player of the match. He became the first Ecuadorian player to win a Premier League medal, in the 2010–11 season. Valencia was a starter in United's 3–1 defeat to Barcelona in the 2011 Champions League Final at Wembley Stadium.


title: Antonio Valencia

text: On 1 August 2011, Valencia agreed a new four-year deal with Manchester United, keeping him at the club until the summer of 2015. Prior to the start of the 2011–12 season, Valencia picked up an ankle injury on international duty with Ecuador at the Copa América during the summer. He missed United's entire pre-season tour of the United States because of the injury. He also missed the first month of the season because of a lack of match fitness. Valencia made his first start of the season away at Benfica in the first group stage match of the UEFA Champions League. On 18 September 2011, he returned to Premier League action, replacing the injured Chris Smalling at right-back in the 3–1 win against Chelsea. He then continued to play right-back in the next three games against Leeds United in the League Cup, away at Stoke City, and home against Norwich City in the Premier League. Valencia scored his first goal of the season, in a fourth round League Cup tie against Aldershot Town, receiving the ball in the middle of the park and then turning and firing in from 25-yards to seal a 3–0 victory.


title: Antonio Valencia

text: Valencia scored his second goal of the season, the opening goal in Manchester United's Champions League fixture against Oțelul Galați. The game finished 2–0. On 26 December 2011, Valencia scored the fourth goal for Manchester United in a 5–0 home win against Wigan Athletic. He received the ball on the right hand edge of the penalty area and rifled a shot across goal and into the far corner. On 22 January 2012, Valencia scored the first goal against Arsenal with a header, before later setting up Danny Welbeck to win the game 2–1. On 2 April 2012, in his 100th appearance for the club in all competitions, Valencia scored the first goal in a 2–0 win against Blackburn Rovers, powerfully curling the ball around Paul Robinson and inside the far corner. Five minutes later, Valencia set up the second goal for Ashley Young.


title: Antonio Valencia

text: Valencia received the Sir Matt Busby Player of the Year and the Manchester United Players' Player of the Year awards for his contributions in the 2011–12 season. He also won the Manchester United Goal of the Season award for his goal against Blackburn Rovers on 2 April 2012.


title: Antonio Valencia

text: On 3 July 2012, it was confirmed that Valencia would wear the number 7 shirt, worn by past players such as Johnny Berry, Steve Coppell, Bryan Robson, Eric Cantona, David Beckham and Cristiano Ronaldo, after Sir Alex Ferguson offered the number upon Michael Owen's departure from the club. The number 25 shirt was given to Valencia's new teammate Nick Powell.


title: Antonio Valencia

text: On 17 April 2013, Valencia scored his first league goal of the season, against West Ham United. On 22 April 2013, Valencia won his second Premier League title after Manchester United defeated Aston Villa in a 3–0 home win.


title: Antonio Valencia

text: After an indifferent 2012–13 season wearing the number 7 shirt, Valencia returned to his former number 25 shirt. Valencia started the season with a goal against Sevilla in Rio Ferdinand's testimonial at Old Trafford in a 3–1 defeat on 9 August 2013. Valencia subsequently appeared in the Community Shield against Wigan coming on as a substitute for Wilfried Zaha in the 62nd minute. Valencia started the Champions League campaign with a goal against Bayer Leverkusen the fourth in a 4–2 home victory as well as giving Robin van Persie an assist for the first on that night on 18 September 2013. He got his first goal of the Premier League season against Fulham on 2 November 2013, the first in a 3–1 away win. Valencia scored the first goal in the 5–0 away victory to Manchester United against Bayer Leverkusen in the group stage of Champions League on 27 November 2013. On 11 January 2014, Valencia scored in the 47th minute against Swansea City in a 2–0 home win. On 21 June 2014, he signed a three-year contract extension, which included an option to extend the deal until June 2018.


title: Antonio Valencia

text: The arrival of new manager Louis van Gaal led to Valencia being deployed in both the right-back and right-wing back positions, where he had occasionally played under both Sir Alex Ferguson and David Moyes. He made his first start of the season in this position, assisting Juan Mata in a 1–1 draw against Sunderland on 24 August 2014.


title: Antonio Valencia

text: On 25 October 2015, Valencia suffered a foot injury in a 0–0 draw with Manchester City, which required surgery and ruled him out for at least four months. He made his return on 17 March 2016 in the Europa League Round of 16 second leg against Liverpool, ending in a 1–1 draw. Valencia played the full 120 minutes at right-back in the 2016 FA Cup Final against Crystal Palace on 21 May 2016, in which United won 2–1 after extra-time.


title: Antonio Valencia

text: Manchester United triggered a one-year extension in Valencia's contract on 17 January 2017, keeping him at the club until 2018. On 19 March 2017, Valencia made his 200th league appearance for United and scored in injury time, after goalkeeper Víctor Valdés slipped, to complete a 3–1 victory over Middlesbrough. On 26 May 2017, two days after captaining United in the 2017 UEFA Europa League Final, his contract at the club was extended until June 2019, with an option to extend for a further year. On 17 September 2017, Valencia scored his first goal of the season in a 4–0 win against Everton with a 20-yard half-volley. Later on 14 October, Valencia captained the team in his 300th appearance as Manchester United drew 0–0 at Liverpool. After being ruled out for four weeks with a hamstring injury, Valencia returned to action as he scored the opening goal in a 3–0 home victory against Stoke City in January 2018.


title: Antonio Valencia

text: At the beginning of the 2018–19 season, and after the retirement of Michael Carrick, Manchester United manager José Mourinho announced Valencia would be the club's first captain. In March 2019, Manchester United declined to take up the option to extend Valencia's contract by an extra year, bringing to an end his 10-year spell with the club when his contract expired in June. Valencia left Manchester United having registered 325 Premier League appearances, which remains a record for a South American player.


title: Antonio Valencia

text: After being released by Manchester United, LDU Quito signed Valencia on a free transfer. He made his debut for the club in a 1–0 victory over América de Quito in the Ecuadorian Serie A on 18 July 2019.


title: Antonio Valencia

text: On 27 March 2005, he scored his first two international goals, coming in a 5–2 World Cup qualifying win against Paraguay. Three days later he scored again in a qualifying match, this time netting in 2–2 draw away to Peru. Valencia played in all of Ecuador's 2006 FIFA World Cup matches, and was chosen as a nominee for FIFA's ideal 11 team, which recognises the top stars for every position in the World Cup. He was also shortlisted as one of the six potential candidates for the Gillette Best Young Player award. An email broadly circulated in England encouraged votes for Valencia, in an attempt to prevent Cristiano Ronaldo from winning. Valencia ended up receiving the greatest number of votes in the online poll, but since the award's winner is determined by a combination of the fan vote and a judging panel, the award was eventually given to Lukas Podolski.


title: Antonio Valencia

text: On 27 June 2007, Valencia netted Ecuador's first goal of their 2007 Copa América campaign, however they eventually lost the match 3–2 to Chile and finished the tournament bottom of their group. Valencia received hs first red card for Ecuador on 12 October 2008, during a 1–0 victory over Chile in a World Cup qualifier. On 9 September 2009, Valencia scored his first 2010 World Cup qualification goal, netting in a 3–1 away victory over Bolivia. On 10 October 2009, he netted for the second qualifier in a row, this time netting Ecuador's single goal in a 2–1 defeat to the hands of Uruguay.


title: Antonio Valencia

text: On 3 July 2011, in a match against Paraguay at the 2011 Copa América, he suffered a sprained left ankle and was forced off at half-time.


title: Antonio Valencia

text: In June 2014, Valencia was named in Ecuador's squad for the 2014 FIFA World Cup. In a preparation match, he captained the team to a 2–2 draw with England at the Sun Life Stadium in Miami. During the match, he was fouled by Raheem Sterling and responded by shoving Sterling and grabbing him by the throat. Referee Jair Marrufo decided to send off both Valencia and Sterling. Valencia later apologized for his reaction. Valencia captained "La Tri" during all three of their matches at the World Cup and was sent off for a foul on Lucas Digne during their final game against France, a goalless draw at the Maracanã which saw his team eliminated.


title: Antonio Valencia

text: Valencia missed the 2015 Copa América in Chile due to urgent ankle surgery. He was selected in the Ecuador squad for the 2016 Copa América Centenario and on 12 June 2016, he scored in Ecuador's 4–0 victory over Haiti at MetLife Stadium.


title: Antonio Valencia

text: Valencia and his wife, Zoila, have a daughter named Domenica, who was born during the 2006 World Cup. Along with former Wigan Athletic teammates Maynor Figueroa and Wilson Palacios, Valencia began taking English lessons. Whilst at Wigan his English lessons would be once a week, however since his move to Manchester United they were sometimes every day. Former Manchester United manager Sir Alex Ferguson described Valencia as a quiet and shy boy. His older brother, Éder, was also a professional footballer who played for Independiente José Terán in Ecuador.


title: Seiðr

text: In Old Norse, (sometimes anglicized as "seidhr", "seidh", "seidr", "seithr", "seith", or "seid") was a type of magic which was practised in Norse society during the Late Scandinavian Iron Age. The practice of is believed to be a form of magic which is related to both the telling and the shaping of the future. Connected to the Old Norse religion, its origins are largely unknown, and the practice of it gradually declined after the Christianization of Scandinavia. Accounts of later made it into sagas and other literary sources, while further evidence of it has been unearthed by archaeologists. Various scholars have debated the nature of , some of them have argued that it was shamanic in context, involving visionary journeys by its practitioners.


title: Seiðr

text: In pre-Christian Norse mythology, was associated with both the god Óðinn, a deity who was simultaneously responsible for war, poetry and sorcery, and the goddess Freyja, a member of the Vanir who was believed to have taught the practice to the Æsir.


title: Seiðr

text: In the 20th century, adherents of various modern Pagan new religious movements adopted forms of magico-religious practice which include . The practices of these contemporary -workers have since been investigated by various academic researchers who are operating in the field of pagan studies.


title: Seiðr

text: is believed to come from Proto-Germanic "*", cognate with Lithuanian , 'tie, tether' and Proto-Celtic "*" 'sorcery' (giving Welsh , Breton 'magic'), all derived from Proto-Indo-European "*" 'string, rope', ultimately from the Proto-Indo-European root "*" 'to bind'.


title: Seiðr

text: Related words in Old High German (see German , used both in string instruments and in bows) and Old English refer to 'cord, string,' or 'snare, cord, halter' and there is a line in verse 15 of the skaldic poem Ragnarsdrápa that uses in that sense. However, it is not clear how this derivation relates to the practice of . It has been suggested that the use of a cord in attraction may be related to , where attraction is one element of the practice of magic described in Norse literature and with witchcraft in Scandinavian folklore. However, if involved "spinning charms", that would explain the distaff, a tool used in spinning flax or sometimes wool, that appears to be associated with practice. In any case, the string relates to the "threads of fate", that the Nornir spin, measure, and cut.


title: Seiðr

text: Old English terms cognate with are and , both of which are attested only in contexts that suggest that they were used by elves (); these seem likely to have meant something similar to . Among the Old English words for practitioners of magic are (m.) or (f.), the etymons of Modern English 'witch'.


title: Seiðr

text: In the Viking Age, the practice of by men had connotations of unmanliness or effeminacy, known as "ergi", as its manipulative aspects ran counter to masculine ideal of forthright, open behavior. Freyja and perhaps some of the other goddesses of Norse mythology were practitioners, as was Óðinn, a fact for which he is taunted by Loki in the "Lokasenna".


title: Seiðr

text: In the 13th century "Saga of Erik the Red", there was a or in Greenland named Þórbjǫrg ('protected by Thor'). She wore a blue cloak and a headpiece of black lamb trimmed with white ermine, carried the symbolic distaff (), which was buried with her, and would sit on a high platform. As related in the saga:


title: Seiðr

text: As described by Snorri Sturluson in his "Ynglinga saga", includes both divination and manipulative magic. It seems likely that the type of divination of -practitioners was generally distinct, by dint of an altogether more metaphysical nature, from the day-to-day auguries performed by the seers (, ).


title: Seiðr

text: However, in chapter 44 of the Icelandic saga "Vatnsdæla saga", Þórdís Spákona loans someone her black cloak and stick () for magic. The stick is used to strike a man three times on his left cheek to make him forget and three times on his right cheek to make him remember.


title: Seiðr

text: Price noted that, because of its connection with "ergi", was undoubtedly located on 'one of society's moral and psychological borders'. involved the incantation of spells ("galdrar", sing. ).