Specifically, a left module over the ring R consists of an abelian group (M, +) and an operation R × M → M (called scalar multiplication, usually just written by juxtaposition, i.e. as rx for r in R and x in M) such that For all r,s in R, x,y in M, we have r(x+y) = rx+ry (r+s)x = rx+sx (rs)x = rSee also:

Module mathematics, Module mathematics - Motivation, Module mathematics - Definition, Module mathematics - Examples, Module mathematics - Submodules and homomorphisms, Module mathematics - Types of modules, Module mathematics - Relation to representation theory, Module mathematics - Generalizations

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The laboratory is a cylindrical module designed to fit in the cargo bay of the Space Shuttle, very similar in shape to the Multi-Purpose Logistics Module. Once launched with Flight 1E, it will subsequently be attached at the Node 2's starboard side, with the cylinder pointing outwards. The hatch is located in the port cone, most on-board computers in the starboard cone. The module contains 10 International Standard Payload Racks (ISPRs). 4 racks are located on the forward side, 4 on the aft side, 2 are in overhead locations. 3 deck ra ...

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Columbus ISS module, Columbus ISS module - Description, Columbus ISS module - History, Columbus ISS module - Specifications

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The Service Module was an unpressurized cylindrical structure, measuring 24 feet 7 inches (7.5 m) long and 12 feet 10 inches (3.9 m) in diameter. It housed the service propulsion system and its propellants, the fuel cell power system, four maneuvering thruster quads, the S-band antenna, and storage tanks for water and hydrogen. On Apollo 15, 16 and 17 it also carried a scientific instrument package. It was connected to the Command module using three tension ties and six compression pads. The tension t ...

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Apollo Command/Service Module, Apollo Command/Service Module - Command Module CM, Apollo Command/Service Module - Construction, Apollo Command/Service Module - Earth Landing System, Apollo Command/Service Module - Reaction Control System, Apollo Command/Service Module - Hatches, Apollo Command/Service Module - Docking Assembly, Apollo Command/Service Module - Cabin interior arrangement, Apollo Command/Service Module - Service Module SM, Apollo Command/Service Module - Service Module Sectors, Apollo Command/Service Module - CSMs produced, Apollo Command/Service Module - In fiction

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Suppose M is some R-module, and Mi is a submodule of M for every i in I. If every x in M can be written in one and only one way as a sum of finitely many elements of the Mi, then we say that M is the internal direct sum of the submodules Mi. In this case, M is naturally isomorphic to the (external) di ...

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Direct sum of modules, Direct sum of modules - Construction for vector spaces and abelian groups, Direct sum of modules - Construction for two vector spaces, Direct sum of modules - Construction for two abelian groups, Direct sum of modules - Construction for an arbitrary family of modules, Direct sum of modules - Properties, Direct sum of modules - Internal direct sum, Direct sum of modules - Categorical interpretation, Direct sum of modules - Direct sum of modules with additional structure, Direct sum of modules - Direct sum of Banach spaces, Direct sum of modules - Direct sum of Hilbert spaces

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In the language of category theory, the direct sum is a coproduct and hence a colimit in the category of left R-modules, which means that it is characterized by the following universal property. For every i in I, consider the natural embedding which sends the elements of Mi to those functions which are zero for all arguments but i. If fi : Mi → M are arbitrary R-linear maps for every i, then ...

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Direct sum of modules, Direct sum of modules - Construction for vector spaces and abelian groups, Direct sum of modules - Construction for two vector spaces, Direct sum of modules - Construction for two abelian groups, Direct sum of modules - Construction for an arbitrary family of modules, Direct sum of modules - Properties, Direct sum of modules - Internal direct sum, Direct sum of modules - Categorical interpretation, Direct sum of modules - Direct sum of modules with additional structure, Direct sum of modules - Direct sum of Banach spaces, Direct sum of modules - Direct sum of Hilbert spaces

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ESA's Board of Directors approved the Columbus program in 1985. From then on, numerous studies and proposals were made. Initially the Columbus program included 3 flight configurations: a Man-tended Free-Flyer (MTFF) element serviced by the Hermes shuttle and flying periodically to the station for maintenance and reconfiguration, an Attached Pressurized Module (APM), and a Polar Platform (PPF). For development cost saving and optimization of spares provisioning during the operational phase commonality was foreseen between ...

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Columbus ISS module, Columbus ISS module - Description, Columbus ISS module - History, Columbus ISS module - Specifications

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The Command Module was a truncated cone measuring 10 feet 7 inches (3.2 m) tall and having a diameter of 12 feet 10 inches (3.9 m) across the base. The forward compartment contained two reaction control engines, the docking tunnel, and the components of the Earth Landing System. The inner pressure vessel housed the crew accommodations, equipment bays, controls and displays, and many spacecraft systems. The last section, the aft compartment, contained 10 reaction control engines and their related propellant tanks, fresh water tanks, and the CSM umbilical cables. ...

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Apollo Command/Service Module, Apollo Command/Service Module - Command Module CM, Apollo Command/Service Module - Construction, Apollo Command/Service Module - Earth Landing System, Apollo Command/Service Module - Reaction Control System, Apollo Command/Service Module - Hatches, Apollo Command/Service Module - Docking Assembly, Apollo Command/Service Module - Cabin interior arrangement, Apollo Command/Service Module - Service Module SM, Apollo Command/Service Module - Service Module Sectors, Apollo Command/Service Module - CSMs produced, Apollo Command/Service Module - In fiction

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The time module added a real-time clock. The clock allowed you to use the actual time in your programs. You could also define alarms that triggered calls to user programs. The alarms were able to switch the calculator on, so it was possible to create programs that executed at some point during the day, then switched the calculator off until the next alarm. As the HP-41 was often used as data-gathering device in labs, this allowed the calculator to read data from monitored devices at specific times every day, without having to run inbetween the readings (thus saving ba ...

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HP-41 extension module, HP-41 extension module - The Memory Modules HP-41C only, HP-41 extension module - The Application Pacs, HP-41 extension module - The 82104A Card Reader, HP-41 extension module - The 82182A Time Module, HP-41 extension module - The 82143A Thermal Printer/Plotter, HP-41 extension module - The 82153A Optical Wand, HP-41 extension module - The 82180A Extended Functions Module, HP-41 extension module - The 82181A Extended Memory Module, HP-41 extension module - The HP82160A HP Interface Loop HP-IL module

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Informally, modules are an abstraction of the concept of a number of directions, together with distances (or coefficients) in each direction. A generating set is a list which spans all the possible directions. A finitely-generated module is one for which there is a finite generating set. This image should nonetheless be used with care, because in a given module "distance" might not be interpreted as a continuous quantity (see examples 2 and 3 below of modules where "distance" is always a whole number). In some modules counter-intuitiv ...

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Finitely-generated module, Finitely-generated module - Intuitive introduction, Finitely-generated module - Formal definition, Finitely-generated module - Some facts, Finitely-generated module - Finitely-presented module

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Finitely generated modules over the ring of integers Z coincide with the finitely generated abelian groups; these are completely classified. The same is true for the finitely generated modules over any principal ideal domain. Every homomorphic image of a finitely generated module is finitely generated. In general, submodules of a finitely generated modules need not be finitely generated. (As an example, consider the ring R=Z[X1,X2,...] of all polynomials in countably many variab ...

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Finitely-generated module, Finitely-generated module - Intuitive introduction, Finitely-generated module - Formal definition, Finitely-generated module - Some facts, Finitely-generated module - Finitely-presented module

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The front end of an SSB receiver is the same as that of an AM or FM receiver, consisting of a superheterodyne RF front end that produces a frequency-shifted version of the radio frequency (RF) signal within a standard intermediate frequency (IF) band. To recover the original signal from the IF SSB signal, the single sideband must be frequency-shifted down to its original range of baseband frequencies, by using a product detector which mixes it with the output of a beat frequency oscillator (BFO).  In ot ...

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Single-sideband modulation, Single-sideband modulation - Signal generation, Single-sideband modulation - Mathematical Highlights, Single-sideband modulation - Demodulation, Single-sideband modulation - Suppressed carrier SSB and VSB, Single-sideband modulation - Vestigial sideband

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The left R-module M is finitely-generated if and only if there exist a1, a2, ..., an in M such that for all x in M, there exist r1, r2, ..., rn in R with x = r1a1 + r2a2 + ... + rnan. The set {a1, a2, ..., an} is re ...

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Finitely-generated module, Finitely-generated module - Intuitive introduction, Finitely-generated module - Formal definition, Finitely-generated module - Some facts, Finitely-generated module - Finitely-presented module

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Main article on quantization Quantization error e can be treated as white noise as we can assume that a signal can be in the range of one step with an equal distribution. Its mean square value is Oversampling ratio, where fs is the sampling frequence and 2f0 is Nyquist rate The noise power within the band ...

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Delta-sigma modulation, Delta-sigma modulation - Principle, Delta-sigma modulation - Quantization theory formulas, Delta-sigma modulation - Oversampling, Delta-sigma modulation - Example of decimation, Delta-sigma modulation - Changes from Δ-modulation, Delta-sigma modulation - Naming

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Extended memory modules added more extended memory to the HP-41C. They required an extended functions module to be present, or the HP-41CX version of the calculator. Each module added 238 registers of extended memory. Up to two extended memory modules could be inserted, for a grand total of 124 + 2*238 = 600 registers. Added to the 319 registers of main memory, this covered practically all of the machin ...

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HP-41 extension module, HP-41 extension module - The Memory Modules HP-41C only, HP-41 extension module - The Application Pacs, HP-41 extension module - The 82104A Card Reader, HP-41 extension module - The 82182A Time Module, HP-41 extension module - The 82143A Thermal Printer/Plotter, HP-41 extension module - The 82153A Optical Wand, HP-41 extension module - The 82180A Extended Functions Module, HP-41 extension module - The 82181A Extended Memory Module, HP-41 extension module - The HP82160A HP Interface Loop HP-IL module

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Gumdrop Charlie Brown Columbia Yankee Clipper Odyssey Kitty Hawk Endeavour Casper America ...

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Apollo Command/Service Module, Apollo Command/Service Module - Command Module CM, Apollo Command/Service Module - Construction, Apollo Command/Service Module - Earth Landing System, Apollo Command/Service Module - Reaction Control System, Apollo Command/Service Module - Hatches, Apollo Command/Service Module - Docking Assembly, Apollo Command/Service Module - Cabin interior arrangement, Apollo Command/Service Module - Service Module SM, Apollo Command/Service Module - Service Module Sectors, Apollo Command/Service Module - CSMs produced, Apollo Command/Service Module - In fiction

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The ROM-based application 'pac' modules added up to 4 kilobytes of read-only memory (some up to 8 kilobytes, but these were simply two independent 4K modules in the same box). Most modules held a dozen of programs written in the HP-41C programming language, Focal. Programs in the ROM modules could be called from a user program, using the ubiquitous XEQ function. In the program code, XEQ appe ...

See also:

HP-41 extension module, HP-41 extension module - The Memory Modules HP-41C only, HP-41 extension module - The Application Pacs, HP-41 extension module - The 82104A Card Reader, HP-41 extension module - The 82182A Time Module, HP-41 extension module - The 82143A Thermal Printer/Plotter, HP-41 extension module - The 82153A Optical Wand, HP-41 extension module - The 82180A Extended Functions Module, HP-41 extension module - The 82181A Extended Memory Module, HP-41 extension module - The HP82160A HP Interface Loop HP-IL module

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The Extended Functions module added many functionalities the uses had wanted for ages, as the ability to programmatically assign functions to keys, repartition memory, etc. But the most important new function was the management of extended memory: while the HP-41C could theoretically access up to 1024 registers, the early design limited main memory to 319 registers only. The Extended Functions module added instructions to manage a bank of additional memory in the available addressing space of the machine. As this memory was not direct ...

See also:

HP-41 extension module, HP-41 extension module - The Memory Modules HP-41C only, HP-41 extension module - The Application Pacs, HP-41 extension module - The 82104A Card Reader, HP-41 extension module - The 82182A Time Module, HP-41 extension module - The 82143A Thermal Printer/Plotter, HP-41 extension module - The 82153A Optical Wand, HP-41 extension module - The 82180A Extended Functions Module, HP-41 extension module - The 82181A Extended Memory Module, HP-41 extension module - The HP82160A HP Interface Loop HP-IL module

Read more here: » HP-41 extension module: Encyclopedia II - HP-41 extension module - The 82180A Extended Functions Module

PWM can be used to reduce the total amount of power delivered to a load without losses normally incurred when a power source is limited by resistive means. This is due to the average power delivered is proportional to the modulation duty cycle. With a sufficiently high modulation rate, passive Electronic filters can be used to smooth the pulse train and recover an average analogue waveform. High frequency PWM power control systems are easily realisable with semiconductor switches. The discrete on/off states of the modulation are used ...

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Pulse-width modulation, Pulse-width modulation - Telecommunications, Pulse-width modulation - Power delivery, Pulse-width modulation - Voltage regulation, Pulse-width modulation - Audio effects and amplifcation

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The best way of thinking of SSB modulation is to first consider an amplitude-modulated signal. This will have two frequency-shifted copies of the modulating signal (the lower one is frequency-inverted) on either side of the remaining carrier wave. These are known as sidebands: either upper sideband (USB) or less commonly lower sideband (LSB). To produce an SSB signal, a filter removes one of the sidebands. Most often, the carrier is reduced (suppressed) or removed entirely. Assuming both sidebands are symme ...

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Single-sideband modulation, Single-sideband modulation - Signal generation, Single-sideband modulation - Mathematical Highlights, Single-sideband modulation - Demodulation, Single-sideband modulation - Suppressed carrier SSB and VSB, Single-sideband modulation - Vestigial sideband

Read more here: » Single-sideband modulation: Encyclopedia II - Single-sideband modulation - Signal generation

The best way of thinking of SSB modulation is to first consider an amplitude-modulated signal. This will have two frequency-shifted copies of the modulating signal (the lower one is frequency-inverted) on either side of the remaining carrier wave. These are known as sidebands. To produce an SSB signal, a filter removes one of the sidebands, leaving only either the upper sideband (USB) or less commonly the lower sideband (LSB). Most often, the carrier is reduced (suppressed) or removed entirely. Assuming bot ...

See also:

Single-sideband modulation, Single-sideband modulation - Signal generation, Single-sideband modulation - Mathematical Highlights, Single-sideband modulation - Demodulation, Single-sideband modulation - Suppressed carrier SSB and VSB, Single-sideband modulation - Vestigial sideband

Read more here: » Single-sideband modulation: Encyclopedia II - Single-sideband modulation - Signal generation

(main article: switched-mode power supply) PWM is also used in efficient voltage regulators. By switching voltage to the load with the appropriate duty cycle, the output will approximate a voltage at the desired level. The switching noise is usually filtered with an inductor and a capacitor. One method measures the output voltage. When it is lower than the desired voltage, it turns on the switch. When the output v ...

See also:

Pulse-width modulation, Pulse-width modulation - Telecommunications, Pulse-width modulation - Power delivery, Pulse-width modulation - Voltage regulation, Pulse-width modulation - Audio effects and amplifcation

Read more here: » Pulse-width modulation: Encyclopedia II - Pulse-width modulation - Voltage regulation

PWM is sometimes used in sound synthesis, in particular subtractive synthesis, as it gives a nice effect similar to chorus or slightly detuned oscillators played together. The ratio between the high and low level is typically modulated with a low frequency oscillator, or LFO. A new class of audio amplifiers based on the PWM principle is becoming popular. Called "Class-D amplifiers", these amplifiers produce a PWM equivalent of the analogue input signal which is fed to the loudspeaker via a suitable filter network to block the carrier ...

See also:

Pulse-width modulation, Pulse-width modulation - Telecommunications, Pulse-width modulation - Power delivery, Pulse-width modulation - Voltage regulation, Pulse-width modulation - Audio effects and amplifcation

Read more here: » Pulse-width modulation: Encyclopedia II - Pulse-width modulation - Audio effects and amplifcation