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Dipteronia

Dipteronia is a genus with two living and one extinct species in the soapberry family Sapindaceae. The living species are native to central and southern China, The fossil species has been found in Middle Paleocene to Early Oligocene sediments of North America and China.

Classification
Older classifications segregated the maples (Acer) and Dipteronia into the family Aceraceae, however work by the Angiosperm Phylogeny Group (APG I onward) and related investigations led to the subsuming of Acereae into Sapindaceae as the tribe Acereae. Dipteronia is considered to be the sister genus to Acer.

Description
They are deciduous flowering shrubs or small trees, reaching 10–15 m tall. The leaf arrangement is opposite and pinnate with between 7 - 15 leaflets on each leaf. The inflorescences are paniculate, terminal or axillary. The flowers have five sepals and petals; staminate flowers have eight stamens, and bisexual flowers have a two-celled ovary. The fruit is a rounded samara containing two compressed nutlets, flat, encircled by a broad wing which turns from light green to red with ripening.

The name Dipteronia stems from the Greek "di-" (two, both) & "pteron" (wings), from the winged fruits with wings on both sides of the seed.

There are only two living species, Dipteronia sinensis and Dipteronia dyeriana; both are endemic to mainland China. Dipteronia dyeriana is listed by the IUCN as being a "Red List" threatened species, and known from only five isolated populations in south-eastern Yunnan Province.

Fossil record
The extinct species Dipteronia brownii is known from Middle Paleocene to Early Oligocene sites across western North America. The oldest fossils are found in the Fort Union Formation of Wyoming and the Tsagayan Formation of Northeastern coastal Russia. In the Early Eocene the species expanded northward to the Eocene Okanagan Highlands sites such as the Klondike Mountain Formation of Washington, Driftwood Shales and Tranquille Formation of British Columbia as well as into the John Day Formation of central Oregon. During the middle to late Eocene the species spread east and south to the Ruby Basin Flora of Montana and the Florissant Formation of Colorado, while the last occurrences are in the Early Oligocene, Rupelian of the Bridge Creek Flora in the upper John Day Formation. Concurrently, several Dipteronia brownii fruits have also been collected from Rupelian lacustrine mudstones in Chuxiong Yi Autonomous Prefecture southwestern China.

title: Dipteronia


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Laser Interferometer Space Antenna

The Laser Interferometer Space Antenna (LISA) is a planned space probe to detect and accurately measure gravitational waves —tiny ripples in the fabric of spacetime—from astronomical sources. LISA will be the first dedicated space-based gravitational-wave observatory. It aims to measure gravitational waves directly by using laser interferometry. The LISA concept features three spacecraft arranged in an equilateral triangle with each side 2.5 million kilometers long, flying in an Earth-like heliocentric orbit. The distance between the satellites is precisely monitored to detect a passing gravitational wave.

The LISA project started out as a joint effort between NASA and the European Space Agency (ESA). However, in 2011, NASA announced that it would be unable to continue its LISA partnership with the European Space Agency due to funding limitations. The project is a recognized CERN experiment (RE8). A scaled-down design initially known as the New Gravitational-wave Observatory (NGO) was proposed as one of three large projects in ESA's long-term plans. In 2013, ESA selected 'The Gravitational Universe' as the theme for one of its three large projects in the 2030s whereby it committed to launch a space-based gravitational-wave observatory.

In January 2017, LISA was proposed as a candidate mission. On June 20, 2017, the suggested mission received its clearance goal for the 2030s, and was approved as one of the main research missions of ESA.

On 25 January 2024, the LISA Mission was formally adopted by ESA. This adoption recognises that the mission concept and technology are advanced enough that building the spacecraft and its instruments can commence.

The LISA mission is designed for direct observation of gravitational waves, which are distortions of spacetime travelling at the speed of light. Passing gravitational waves alternately squeeze and stretch space itself by a tiny amount. Gravitational waves are caused by energetic events in the universe and, unlike any other radiation, can pass unhindered by intervening mass. Launching LISA will add a new sense to scientists' perception of the universe and enable them to study phenomena that are invisible in normal light.

Potential sources for signals are merging massive black holes at the centre of galaxies, massive black holes orbited by small compact objects, known as extreme mass ratio inspirals, binaries of compact stars, and possibly other sources of cosmological origin, such as a cosmological phase transition shortly after the Big Bang, and speculative astrophysical objects like cosmic strings and domain boundaries.

Mission description
The LISA mission's primary objective is to detect and measure gravitational waves produced by compact binary systems and mergers of supermassive black holes. LISA will observe gravitational waves by measuring differential changes in the length of its arms, as sensed by laser interferometry. Each of the three LISA spacecraft contains two telescopes, two lasers and two test masses (each a 46 mm, roughly 2 kg, gold-coated cube of gold/platinum), arranged in two optical assemblies pointed at the other two spacecraft. These form Michelson-like interferometers, each centred on one of the spacecraft, with the test masses defining the ends of the arms. The entire arrangement, which is ten times larger than the orbit of the Moon, will be placed in solar orbit at the same distance from the Sun as the Earth, but trailing the Earth by 20 degrees, and with the orbital planes of the three spacecraft inclined relative to the ecliptic by about 0.33 degree, which results in the plane of the triangular spacecraft formation being tilted 60 degrees from the plane of the ecliptic. The mean linear distance between the formation and the Earth will be 50 million kilometres.

To eliminate non-gravitational forces such as light pressure and solar wind on the test masses, each spacecraft is constructed as a zero-drag satellite. The test mass floats free inside, effectively in free-fall, while the spacecraft around it absorbs all these local non-gravitational forces. Then, using capacitive sensing to determine the spacecraft's position relative to the mass, very precise thrusters adjust the spacecraft so that it follows, keeping itself centered around the mass.

Arm length
The longer the arms, the more sensitive the detector is to long-period gravitational waves, but its sensitivity to wavelengths shorter than the arms is reduced (2,500,000 km is lightseconds, or  Hz [compare to LIGO's peak sensitivity around 500 Hz]). As the satellites are free-flying, the spacing is easily adjusted before launch, with upper bounds being imposed by the sizes of the telescopes required at each end of the interferometer (which are constrained by the size of the launch vehicle's payload fairing) and the stability of the constellation orbit (larger constellations are more sensitive to the gravitational effects of other planets, limiting the mission lifetime). Another length-dependent factor which must be compensated for is the "point-ahead angle" between the incoming and outgoing laser beams; the telescope must receive its incoming beam from where its partner was a few seconds ago, but send its outgoing beam to where its partner will be a few seconds from now.

The original 2008 LISA proposal had arms 5 million kilometres (5 Gm) long. When downscoped to eLISA in 2013, arms of 1 million kilometres were proposed. The approved 2017 LISA proposal has arms 2.5 million kilometres (2.5 Gm) long.

Detection principle

Like most modern gravitational wave-observatories, LISA is based on laser interferometry. Its three satellites form a giant Michelson interferometer in which two "transponder" satellites play the role of reflectors and one "master" satellite the roles of source and observer. When a gravitational wave passes the interferometer, the lengths of the two LISA arms vary due to spacetime distortions caused by the wave. Practically, LISA measures a relative phase shift between one local laser and one distant laser by light interference. Comparison between the observed laser beam frequency (in return beam) and the local laser beam frequency (sent beam) encodes the wave parameters. The principle of laser-interferometric inter-satellite ranging measurements was successfully implemented in the Laser Ranging Interferometer onboard GRACE Follow-On.

Unlike terrestrial gravitational-wave observatories, LISA cannot keep its arms "locked" in position at a fixed length. Instead, the distances between satellites vary significantly over each year's orbit, and the detector must keep track of the constantly changing distance, counting the millions of wavelengths by which the distance changes each second. Then, the signals are separated in the frequency domain: changes with periods of less than a day are signals of interest, while changes with periods of a month or more are irrelevant.

This difference means that LISA cannot use high-finesse Fabry–Pérot resonant arm cavities and signal recycling systems like terrestrial detectors, limiting its length-measurement accuracy. But with arms almost a million times longer, the motions to be detected are correspondingly larger.

LISA Pathfinder
An ESA test mission called LISA Pathfinder (LPF) was launched in 2015 to test the technology necessary to put a test mass in (almost) perfect free fall conditions. LPF consists of a single spacecraft with one of the LISA interferometer arms shortened to about 38 cm, so that it fits inside a single spacecraft. The spacecraft reached its operational location in heliocentric orbit at the Lagrange point L1 on 22 January 2016, where it underwent payload commissioning. Scientific research started on March 8, 2016. The goal of LPF was to demonstrate a noise level 10 times worse than needed for LISA. However, LPF exceeded this goal by a large margin, approaching the LISA requirement noise levels.

Science goals

Gravitational-wave astronomy seeks to use direct measurements of gravitational waves to study astrophysical systems and to test Einstein's theory of gravity. Indirect evidence of gravitational waves was derived from observations of the decreasing orbital periods of several binary pulsars, such as the Hulse–Taylor pulsar. In February 2016, the Advanced LIGO project announced that it had directly detected gravitational waves from a black hole merger.

Observing gravitational waves requires two things: a strong source of gravitational waves—such as the merger of two black holes—and extremely high detection sensitivity. A LISA-like instrument should be able to measure relative displacements with a resolution of 20 picometres—less than the diameter of a helium atom—over a distance of a million kilometres, yielding a strain sensitivity of better than 1 part in 1020 in the low-frequency band about a millihertz.

A LISA-like detector is sensitive to the low-frequency band of the gravitational-wave spectrum, which contains many astrophysically interesting sources. Such a detector would observe signals from binary stars within our galaxy (the Milky Way); signals from binary supermassive black holes in other galaxies; and extreme-mass-ratio inspirals and bursts produced by a stellar-mass compact object orbiting a supermassive black hole. There are also more speculative signals such as signals from cosmological phase transitions, cosmic strings and primordial gravitational waves generated during cosmological inflation.

Galactic compact binaries
LISA will be able to detect the nearly monochromatic gravitational waves emanating of close binaries consisting of two compact stellar objects (white dwarfs, neutron stars, and black holes) in the Milky Way. At low frequencies these are actually expected to be so numerous that they form a source of (foreground) noise for LISA data analysis. At higher frequencies LISA is expected to detect and resolve around 25,000 galactic compact binaries. Studying the distribution of the masses, periods, and locations of this population, will teach us about the formation and evolution of binary systems in the galaxy. Furthermore, LISA will be able to resolve 10 binaries currently known from electromagnetic observations (and find ≈500 more with electromagnetic counterparts within one square degree). Joint study of these systems will allow inference on other dissipation mechanisms in these systems, e.g. through tidal interactions. One of the currently known binaries that LISA will be able to resolve is the white dwarf binary ZTF J1539+5027 with a period of 6.91 minutes, the second shortest period binary white dwarf pair discovered to date.

Massive black hole mergers
LISA will be able to detect the gravitational waves from the merger of a pair of massive black holes with a chirp mass between 104 and 107 solar masses all the way back to their earliest formation at redshift around z ≈ 10. The most conservative population models expect at least a few such events to happen each year. For mergers closer by (z < 3), it will be able to determine the spins of the components, which carry information about the past evolution of the components (e.g. whether they have grown primarily through accretion or mergers). For mergers around the peak of star formation (z ≈ 2) LISA will be able to locate mergers within 100 square degrees on the night sky at least 24 hours before the actual merger, allowing electromagnetic telescopes to search for counterparts, with the potential of witnessing the formation of a quasar after a merger.

Extreme mass ratio inspirals
Extreme mass ratio inspirals (EMRIs) consist of a stellar compact object (<60 solar masses) on a slowly decaying orbit around a massive black hole of around 105 solar masses. For the ideal case of a prograde orbit around a (nearly) maximally spinning black hole, LISA will be able to detect these events up to z=4. EMRIs are interesting because they are slowly evolving, spending around 105 orbits and between a few months and a few years in the LISA sensitivity band before merging. This allows very accurate (up to an error of 1 in 104) measurements of the properties of the system, including the mass and spin of the central object and the mass and orbital elements (eccentricity and inclination) of the smaller object. EMRIs are expected to occur regularly in the centers of most galaxies and in dense star clusters. Conservative population estimates predict at least one detectable event per year for LISA.

Intermediate mass black hole binaries
LISA will also be able to detect the gravitational waves emanating from black hole binary mergers where the lighter black hole is in the intermediate black hole range (between 102 and 104 solar masses). In the case of both components being intermediate black holes between 600 and 104 solar masses, LISA will be able to detect events up to redshifts around 1. In the case of an intermediate mass black hole spiralling into a massive black hole (between 104 and 106 solar masses) events will be detectable up to at least z=3. Since little is known about the population of intermediate mass black holes, there is no good estimate of the event rates for these events.

Multi-band gravitational wave astronomy
Following the announcement of the first gravitational wave detection, GW150914, it was realized that a similar event would be detectable by LISA well before the merger. Based on the LIGO estimated event rates, it is expected that LISA will detect and resolve about 100 binaries that would merge a few weeks to months later in the LIGO detection band. LISA will be able to accurately predict the time of merger ahead of time and locate the event with 1 square degree on the sky. This will greatly aid the possibilities for searches for electromagnetic counterpart events.

Fundamental black hole physics
Gravitational wave signals from black holes could provide hints at a more fundamental theory of gravity. LISA will be able to test possible modifications of Einstein's general theory of relativity, motivated by dark energy or dark matter. These could manifest, for example, through modifications of the propagation of gravitational waves, or through the possibility of hairy black holes.

Probe expansion of the universe
LISA will be able to independently measure the redshift and distance of events occurring relatively close by (z < 0.1) through the detection of massive black hole mergers and EMRIs. Consequently, it can make an independent measurement of the Hubble parameter H0 that does not depend on the use of the cosmic distance ladder. The accuracy of such a determination is limited by the sample size and therefore the mission duration. With a mission lifetime of 4 years one expects to be able to determine H0 with an absolute error of 0.01 (km/s)/Mpc. At larger ranges LISA events can (stochastically) be linked to electromagnetic counterparts, to further constrain the expansion curve of the universe.

Gravitational wave background
LISA will be sensitive to the stochastic gravitational wave background generated in the early universe through various channels, including inflation, first-order cosmological phase transitions related to spontaneous symmetry breaking, and cosmic strings.

Exotic sources
LISA will also search for currently unknown (and unmodelled) sources of gravitational waves. The history of astrophysics has shown that whenever a new frequency range/medium of detection is available new unexpected sources show up. This could for example include kinks and cusps in cosmic strings.

Memory effects
LISA will be sensitive to the permanent displacement induced on probe masses by gravitational waves, known as gravitational memory effect.

Other gravitational-wave experiments
Previous searches for gravitational waves in space were conducted for short periods by planetary missions that had other primary science objectives (such as Cassini–Huygens), using microwave Doppler tracking to monitor fluctuations in the Earth–spacecraft distance. By contrast, LISA is a dedicated mission that will use laser interferometry to achieve a much higher sensitivity. Other gravitational wave antennas, such as LIGO, Virgo, and GEO600, are already in operation on Earth, but their sensitivity at low frequencies is limited by the largest practical arm lengths, by seismic noise, and by interference from nearby moving masses. Conversely, NANOGrav measures frequencies too low for LISA. The different types of gravitational wave measurement systems — LISA, NANOGrav and ground-based detectors — are complementary rather than competitive, much like astronomical observatories in different electromagnetic bands (e.g., ultraviolet and infrared).

History
The first design studies for a gravitational-wave detector to be flown in space were performed in the 1980s under the name LAGOS (Laser Antena for Gravitational radiation Observation in Space). LISA was first proposed as a mission to ESA in the early 1990s. First as a candidate for the M3-cycle, and later as 'cornerstone mission' for the 'Horizon 2000 plus' program. As the decade progressed, the design was refined to a triangular configuration of three spacecraft with three 5-million-kilometre arms. This mission was pitched as a joint mission between ESA and NASA in 1997.

In the 2000s the joint ESA/NASA LISA mission was identified as a candidate for the 'L1' slot in ESA's Cosmic Vision 2015–2025 programme. However, due to budget cuts, NASA announced in early 2011 that it would not be contributing to any of ESA's L-class missions. ESA nonetheless decided to push the program forward, and instructed the L1 candidate missions to present reduced cost versions that could be flown within ESA's budget. A reduced version of LISA was designed with only two 1-million-kilometre arms under the name NGO (New/Next Gravitational wave Observatory). Despite NGO being ranked highest in terms of scientific potential, ESA decided to fly Jupiter Icy Moons Explorer (JUICE) as its L1 mission. One of the main concerns was that the LISA Pathfinder mission had been experiencing technical delays, making it uncertain if the technology would be ready for the projected L1 launch date.

Soon afterwards, ESA announced it would be selecting themes for its Large class L2 and L3 mission slots. A theme called "the Gravitational Universe" was formulated with the reduced NGO rechristened eLISA as a straw-man mission. In November 2013, ESA announced that it selected "the Gravitational Universe" for its L3 mission slot (expected launch in 2034). Following the successful detection of gravitational waves by the LIGO, ground-based detectors in September 2015, NASA expressed interest in rejoining the mission as a junior partner. In response to an ESA call for mission proposals for the `Gravitational Universe' themed L3 mission, a mission proposal for a detector with three 2.5-million-kilometre arms again called LISA was submitted in January 2017.

As of January 2024, LISA is expected to launch in 2035 on an Ariane 6, two years earlier than previously announced.

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

title: Laser Interferometer Space Antenna


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Telephone number portability

Telephone number portability can refer to:

 * Mobile number portability - telephone number portability for mobile phone users.
 * Local number portability - telephone number portability for landline users.
 * Toll-free number portability - telephone number portability for freephone subscribers.

title: Telephone number portability


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Gelfand representation

In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) is either of two things:

 * a way of representing commutative Banach algebras as algebras of continuous functions;
 * the fact that for commutative C*-algebras, this representation is an isometric isomorphism.

In the former case, one may regard the Gelfand representation as a far-reaching generalization of the Fourier transform of an integrable function. In the latter case, the Gelfand–Naimark representation theorem is one avenue in the development of spectral theory for normal operators, and generalizes the notion of diagonalizing a normal matrix.

Historical remarks
One of Gelfand's original applications (and one which historically motivated much of the study of Banach algebras) was to give a much shorter and more conceptual proof of a celebrated lemma of Norbert Wiener (see the citation below), characterizing the elements of the group algebras L1(R) and $$\ell^1({\mathbf Z})$$ whose translates span dense subspaces in the respective algebras.

The model algebra
For any locally compact Hausdorff topological space X, the space C0(X) of continuous complex-valued functions on X which vanish at infinity is in a natural way a commutative C*-algebra:
 * The algebra structure over the complex numbers is obtained by considering the pointwise operations of addition and multiplication.
 * The involution is pointwise complex conjugation.
 * The norm is the uniform norm on functions.

The importance of X being locally compact and Hausdorff is that this turns X into a completely regular space. In such a space every closed subset of X is the common zero set of a family of continuous complex-valued functions on X, allowing one to recover the topology of X from C0(X).

Note that C0(X)  is unital if and only if X is compact, in which  case C0(X) is equal to C(X), the algebra of all continuous complex-valued functions on X.

Gelfand representation of a commutative Banach algebra
Let $$ A $$ be a commutative Banach algebra, defined over the field $$ \mathbb{C} $$ of complex numbers. A non-zero algebra homomorphism (a multiplicative linear functional) $$ \Phi \colon A \to \mathbb{C} $$ is called a character of $$ A $$; the set of all characters of $$ A $$ is denoted by $$ \Phi_A $$.

It can be shown that every character on $$ A $$ is automatically continuous, and hence $$ \Phi_A $$ is a subset of the space $$ A^* $$ of continuous linear functionals on $$ A $$; moreover, when equipped with the relative weak-* topology, $$ \Phi_A $$ turns out to be locally compact and Hausdorff. (This follows from the Banach–Alaoglu theorem.) The space $$ \Phi_A $$ is compact (in the topology just defined) if and only if the algebra $$ A $$ has an identity element.

Given $$ a \in A $$, one defines the function $$\widehat{a}:\Phi_A\to{\mathbb C}$$ by $$\widehat{a}(\phi)=\phi(a)$$. The definition of $$ \Phi_A $$and the topology on it ensure that $$\widehat{a}$$ is continuous and vanishes at infinity, and that the map $$a\mapsto \widehat{a}$$ defines a norm-decreasing, unit-preserving algebra homomorphism from $$ A $$ to $$ C_0(\Phi_A)$$. This homomorphism is the Gelfand representation of $$ A $$, and $$\widehat{a}$$ is the Gelfand transform of the element $$a$$. In general, the representation is neither injective nor surjective.

In the case where $$ A $$ has an identity element, there is a bijection between $$ \Phi_A $$ and the set of maximal ideals in $$ A $$ (this relies on the Gelfand–Mazur theorem). As a consequence, the kernel of the Gelfand representation $$ A \to C_0 (\Phi_A) $$ may be identified with the Jacobson radical of $$ A $$. Thus the Gelfand representation is injective if and only if $$ A $$ is (Jacobson) semisimple.

Examples
In the case where $$ A=L^1(\mathbb{R}) $$, the group algebra of $$ \mathbb{R} $$, then $$ \Phi_A $$ is homeomorphic to $$ \mathbb{R} $$ and the Gelfand transform of $$ f \in L^1(\mathbb{R}) $$ is the Fourier transform $$\tilde{f}$$.

In the case where $$ A=L^1(\mathbb{R}_+) $$, $$\mathbb{R}_+$$ is not a group under addition, so the Gelfand transform is not applicable, and thus is not correct to say the Laplace transform is the Gelfand transform on this algebra. $$\mathbb{R}_+$$ is however, a group under multiplication in which the Gelfand transform is the Mellin transform.

The C*-algebra case
As motivation, consider the special case A = C0(X). Given x in X, let $$\varphi_x \in A^*$$ be pointwise evaluation at x, i.e. $$\varphi_x(f) = f(x)$$. Then $$\varphi_x$$ is a character on A, and it can be shown that all characters of A are of this form; a more precise analysis shows that we may identify ΦA with X, not just as sets but as topological spaces. The Gelfand representation is then an isomorphism
 * $$C_0(X)\to C_0(\Phi_A).\ $$

The spectrum of a commutative C*-algebra
The spectrum or Gelfand space of a commutative C*-algebra A, denoted Â, consists of the set of non-zero *-homomorphisms from A to the complex numbers. Elements of the spectrum are called characters on A. (It can be shown that every algebra homomorphism from A to the complex numbers is automatically a *-homomorphism, so that this definition of the term 'character' agrees with the one above.)

In particular, the spectrum of a commutative C*-algebra is a locally compact Hausdorff space: In the unital case, i.e. where the C*-algebra has a multiplicative unit element 1, all characters f must be unital, i.e. f(1) is the complex number one. This excludes the zero homomorphism. So Â is closed under weak-* convergence and the spectrum is actually compact. In the non-unital case, the weak-* closure of Â is Â ∪ {0}, where 0 is the zero homomorphism, and the removal of a single point from a compact Hausdorff space yields a locally compact Hausdorff space.

Note that spectrum is an overloaded word. It also refers to the spectrum σ(x) of an element x of an algebra with unit 1, that is the set of complex numbers r for which x − r 1 is not invertible in A. For unital C*-algebras, the two notions are connected in the following way: σ(x) is the set of complex numbers f(x) where f ranges over Gelfand space of A. Together with the spectral radius formula, this shows that Â is a subset of the unit ball of A* and as such can be given the relative weak-* topology. This is the topology of pointwise convergence. A net {fk}k of elements of the spectrum of A converges to f if and only if for each x in A, the net of complex numbers {fk(x)}k converges to f(x).

If A is a separable C*-algebra, the weak-* topology is metrizable on bounded subsets. Thus the spectrum of a separable commutative C*-algebra A can be regarded as a metric space. So the topology can be characterized via convergence of sequences.

Equivalently, σ(x) is the range of γ(x), where γ is the Gelfand representation.

Statement of the commutative Gelfand–Naimark theorem
Let A be a commutative C*-algebra and let X be the spectrum of A. Let
 * $$\gamma:A \to C_0(X)$$

be the Gelfand representation defined above.

Theorem. The Gelfand map γ is an isometric *-isomorphism from A onto C0(X).

See the Arveson reference below.

The spectrum of a commutative C*-algebra can also be viewed as the set of all maximal ideals m of A, with the hull-kernel topology. (See the earlier remarks for the general, commutative Banach algebra case.) For any such m the quotient algebra A/m is one-dimensional (by the Gelfand-Mazur theorem), and therefore any a in A gives rise to a complex-valued function on Y.

In the case of C*-algebras with unit, the spectrum map gives rise to a contravariant functor from the category of commutative C*-algebras with unit and unit-preserving continuous *-homomorphisms, to the category of compact Hausdorff spaces and continuous maps. This functor is one half of a contravariant equivalence between these two categories (its adjoint being the functor that assigns to each compact Hausdorff space X the C*-algebra C0(X)). In particular, given compact Hausdorff spaces X and Y, then C(X) is isomorphic to C(Y) (as a C*-algebra) if and only if X is homeomorphic to Y.

The 'full' Gelfand–Naimark theorem is a result for arbitrary (abstract) noncommutative C*-algebras A, which though not quite analogous to the Gelfand representation, does provide a concrete representation of A as an algebra of operators.

Applications
One of the most significant applications is the existence of a continuous functional calculus for normal elements in C*-algebra A: An element x is normal if and only if x commutes with its adjoint x*, or equivalently if and only if it generates a commutative C*-algebra C*(x). By the Gelfand isomorphism applied to C*(x) this is *-isomorphic to an algebra of continuous functions on a locally compact space. This observation leads almost immediately to:

Theorem. Let A be a C*-algebra with identity and x a normal element of A. Then there is a *-morphism f → f(x) from the algebra of continuous functions on the spectrum σ(x) into A such that
 * It maps 1 to the multiplicative identity of A;
 * It maps the identity function on the spectrum to x.

This allows us to apply continuous functions to bounded normal operators on Hilbert space.

title: Gelfand representation


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Ross rifle

The Ross rifle is a straight-pull bolt action rifle chambered in .303 British that was produced in Canada from 1903 until 1918.

The Ross Mk.II (or "model 1905") rifle was highly successful in target shooting before World War I, but the close chamber tolerances, lack of primary extraction and length made the Mk.III (or "1910") Ross rifle unsuitable for the conditions of trench warfare, exacerbated by the often poor quality ammunition issued.

By 1916, the rifle had been withdrawn from front line service but continued to be used by many snipers of the Canadian Expeditionary Force until the end of the war due to its exceptional accuracy.

The Ross Rifle Co. made sporting rifles from early in its production, most notably chambered in .280 Ross, introduced in 1907. This cartridge is recorded as the first to achieve over 3000 ft/s muzzle velocity and the cartridge acquired a very considerable international reputation among target shooters and hunters.

History
During the Second Boer War (1899–1902), a minor diplomatic fight broke out between Canada and the United Kingdom, after the latter refused to license the Lee–Enfield SMLE design for production in Canada. Sir Charles Ross offered to finance the construction of a factory in Canada to produce his newly designed straight-pull rifle for Canadian service. This offer was accepted by the Liberal government of Sir Wilfrid Laurier and Ross was awarded his first contract in 1903 for 12,000 Mark I Ross rifles.

It is generally accepted that Ross' design was inspired by the straight-pull Austrian Mannlicher M1895 Rifle introduced into Austro-Hungarian service in the 1890s and used throughout World War I, and as secondary weapons into World War II. Ross' earliest rifles unmistakably borrowed a number of mechanical details directly from the Mannlicher which was a relatively new design at the time Ross was producing his first rifles in the late 1890s.

The operating principle of the straight-pull bolt action comprises a bolt "sleeve" to which the bolt lever or handle is attached. The sleeve is hollow and has spiral grooves or "teeth" cut into its inner surface in which slide corresponding projections or "teeth" on the outside of the bolt head or "body". As the bolt lever and sleeve are moved, the bolt head is forced to rotate through about 90°, locking or unlocking it in the receiver of the rifle. The bolt handle and sleeve thus need only be pushed backwards or forwards to open or close the action of the rifle.

In conventional bolt-action rifles such as the Mauser, Mosin–Nagant or Lee–Enfield, the bolt is unlocked or locked by the raising or lowering of the bolt handle, before the bolt is drawn back and after it is pushed forward. The single motion required to open or close the bolt of a straight-pull-action rifle is theoretically faster and easier for soldiers to learn, thus perhaps offering a higher rate of fire. Unlike the Lee–Enfield, the bolt of the Ross rifle could be taken apart without special tools, although this was not necessarily an advantage as it encouraged unauthorized disassembly by soldiers.

Service
The first 1,000 rifles were given to the Royal North-West Mounted Police (RNWMP) for testing. Routine inspection before operational testing found 113 defects bad enough to warrant rejection. One of these was a poorly designed bolt lock that enabled the bolt to fall right out of the rifle. Another was poorly tempered component springs that were described as being as "soft as copper". In 1906, the RNWMP reverted to their Model 1894 Winchesters and Lee–Metfords. The Ross rifle was modified to correct these faults and became the Mark II Ross (Model 05 (1905)). In 1907, the Mk II was modified to handle the higher pressure of newly designed .280 Ross, this variant was called Mk II**. The Model 10 (1910) was a completely new design, made to correct the shortcomings of the 1905. None of the major parts are interchangeable between the 1905 and the 1910 models. Although the British were now encouraging standardization across the Empire on the Lee–Enfield, Canada stayed with the Ross. The Model 10 was the standard infantry weapon of the First Canadian Contingent of the Canadian Expeditionary Force when it first arrived in France in February 1915.

The shortcomings of the rifle were made apparent before the Second Battle of Ypres in April 1915. Princess Patricia's Canadian Light Infantry was the first unit to voice its objections about the rifle, the regiment replaced the Ross rifle with the more familiar and rugged Lee-Enfield and later persuaded the 3rd Division to switch to the Lee-Enfield. The rifle showed poor tolerance of dirt when used in field conditions, particularly the screw threads operating the bolt lugs, jamming the weapon open or closed; it also had problems when British-made ammunition was used, which was produced with lower tolerances than Canadian-made ammunition. Another part of the jamming problem came from the bolt's outer face hitting the bolt stop, then deforming the thread shape. The bolt could also be disassembled for routine cleaning and inadvertently reassembled in a manner that would fail to lock but still allow a round to be fired, leading to serious injury or death of the operator as the bolt flew back into his face. However, reports of such incidents with regard to this specific failing were relatively minor. Still another deficiency was the tendency for an affixed bayonet to become dislodged and fall off during discharge of the rifle. Many Canadians of the First Contingent (now renamed the 1st Canadian Division) at Ypres purposefully retrieved Lee–Enfield rifles from fallen British soldiers to replace their own inferior Ross rifles. Lieutenant Chris Scriven of the 10th Battalion, CEF, commented that it sometimes took five men just to keep one rifle firing. Major T.V. Scudamore of the British Columbia Regiment, having been captured at Ypres after being wounded, wrote of the "contemptible" Ross rifle, "Those in the front line with that rifle will never forget... what it is like to be charged by the flower of the German army... and be unable to fire a shot in return."

Complaints rapidly reached the rifle's chief sponsor, the Canadian Minister of Militia and Defence Sam Hughes. He nevertheless continued to believe in its strengths despite the professional opinion of Sir Edwin Alderson, the British Army officer who was commander of the First Canadian Division. The rifle became an element in political issues within Canada and between Canada and the British. Hughes responded to Alderson's criticism by accusing Alderson of ignorance and copied the letter to many officers in the corps. The effect was to undermine confidence in Alderson and the rifle. Hughes also made accusations that Canadian officers were induced to produce adverse reports on the rifle. After negative reports regarding the rifle were published through the Ottawa Citizen, it became increasingly clear that his own claims before the House of Commons that all the faults of the rifle had been cured were patently false, and Hughes' defence of the rifle could no longer be supported by the Prime Minister.

In particular, the Ross was more accurate at long range than the SMLE, and this potentially overcame the serious problem British and Canadian troops had faced during the Boer War, with the accurate long-range fire from the 7×57mm Mauser chambered Mauser Model 1895 rifle. In all, approximately 420,000 Ross service rifles were produced, 342,040 of which were purchased by the British.

Replacement
Canadians retained the Ross even as additional contingents arrived in France. On 12 June 1915, the 1st Canadian Division replaced all its Ross rifles with Enfields. By the time of the Somme battles of July 1916, Sir Douglas Haig, the new Commander-in-Chief of the British Expeditionary Force, had ordered the replacement of all Ross rifles in the three Canadian Divisions by the Pattern 1914 Enfield, which was finally available in quantity. Hughes refused to accept that there were problems with the Ross, and it took the intervention of many influential people to persuade him otherwise. In November 1916, Hughes resigned after Sir Robert Borden's decision to appoint a Minister of Overseas Forces. Ross rifles were then used in training roles, both in Canada and the UK, to free up more Lee–Enfields for the front. After the United States entered the war in 1917, Ross rifles were shipped to the U.S. for the same reasons, freeing up supplies of the M1903 Springfield rifle. Hughes' reputation was inevitably tarnished, but Sir Charles Ross had already made a considerable fortune from his rifle design and manufacturing contracts despite its reputation. At around the same time, the Dominion Rifle Factory (Quebec City) converted a number of Rosses into the Huot automatic rifle, under the guidance of designer Joseph Alphonse Huot. It was an effective design, feeding from a drum magazine, and cheaper than a Lewis Gun. Despite successful trials, it was never adopted for service.

Military variants
This was the first production military model Ross Rifle. The first few hundred were fitted with the full-length folding Sight, Ross Mk I. Before any were delivered, the sight was replaced with a shorter version graduated to 2,200 yards rather than 2,500 yards. Years later, this sight would be designated Sight, Ross Mk I*. Many weapons would have this replaced with the Sight, Ross Mk II, a curved sliding "Lange Vizier" type. The barrel was 28 inch long, and the fore-stock ended 4 inches short of the muzzle. The front band had a bayonet lug. The safety was a sliding flat plate on the back of the bolt handle operated by pushing a square button on the plate. The magazine cut-off was on the lower right of the magazine protruding through the stock, and pressing it down engaged the cut-off. The magazine cut-off release was inside the front of the trigger guard, and depressing it would disengage the cut-off. A large lever was on the right side which was used to depress the magazine follower for "dump loading" all five rounds at once. The weapon was a straight-pull cock-on-close design. There was a sliding trap in the butt-stock for cleaning tools. A total of 10,500 were manufactured. A number of the original 500 were re-purposed as training rifles and fitted with longer front barrel bands as used on later production Rifle, Ross Mk II. This was done so they could more easily endure the stress of constant bayonet practice.
 * Rifle, Ross Mk I

The RNWMP purchased 1,000 shorter versions of the Ross Mk I. The main difference was the barrel length of 26 inches. The full stock of the rifle was retained, and the barrel projected only 2 inches past the forestock. As presented for inspection, the carbines used the shorter version of the Sight, Ross Mk I. However, at the inspector's request, the weapons were delivered fitted with the Sight, Ross Mk II.
 * Carbine, Ross Mk I

This designation was a 1909 re-designation of those Mk I rifles that had been fitted with the Sight, Ross Mk II.
 * Rifle, Ross Mk II

After various complaints had been received, the weapon was re-designed to address the issues. The 28 inch barrel length was retained, and the Sight, Ross Mk II was used. The most noticeable change was the replacement of the side-mounted magazine cut-off control and trigger-guard mounted cut-off release with a single hook shaped control inside the front trigger guard that performed both functions. The action was also changed to cock-on-open. The safety was similar to the earlier model's, but the slider was more solid and inside the bolt handle, moved by pushing a round button on the back of the bolt handle. Changes were introduced in production without change in designation until the introduction of the Sight, Ross Mk III when the nomenclature of the earlier rifles was expanded to Rifle, Ross Mk II with Sight, Ross Mk II.
 * Rifle, Ross Mk II / Rifle, Ross Mk II with Sight, Ross Mk II

The "Sight, Ross Mk II" proved more fragile than desired, and it was replaced with a simpler version, the "Sight, Ross Mk III". Instead of a curved bend to the slider, they employed a straight slider with curve-cut sides bent down. The official nomenclature for this model was "Rifle, Ross Mk II with Sight, Ross Mk III". The 28 inch barrel was retained, the sight change being the difference. Further improvements would be introduced to production without changing the designation.
 * Rifle, Ross Mk II with Sight, Ross Mk III

In early 1909 it was decided to adapt the Rifle Ross Mk II with Sight, Ross Mk II for cadet use, doing full maintenance and upgrading components to later production changes. The Sight, Ross Mk II was retained, however. 5,800 weapons were so converted from late 1909 to mid 1910. The weapons were designated Rifle, Ross Mk II*. This designation identified specific conversions of older weapons and did not reflect any changes to new production.
 * Rifle, Ross Mk II*

Development of this weapon began in the spring of 1908, and the planned designation was Rifle, Ross Mk III. This model was intended as a major improvement over the previous Rifle, Ross Mark II with Sight, Ross Mk III. The barrel length was extended to 30.5 inches, the rear hand-guard was simplified, the safety was replaced by a completely new flag-type safety, and the rear sight was changed to the third-party Sight, Sutherland Mk I. The magazine cut-off was dispensed with entirely. By the time it was ready to be produced in numbers, an even more radical design change was in the works to become the Mk III, and this model was designated Rifle, Ross Mk II** instead. In May 1909, it was decided to convert some 500 of the Rifle, Ross Mk II, with Sight, Ross Mk III to the new design for field trials. This was increased to 700. While these weapons were being trialed, production of the shorter "Mk II" continued, with some of the "Mk II**" changes being introduced. In 1911, the Rifle, Ross Mk II** became the standard Canadian issue, and production began. Some 13,000 were newly manufactured before this model was superseded by the Rifle, Ross Mk III in 1912.
 * Rifle, Ross Mk II**

This rifle was an adaptation of the Rifle, Ross Mk II to use the Sight, Sutherland Mk II. Some internal improvements were made as well. The original sliding button safety and the magazine cut-off were retained, along with the 28 inch barrel and the stylish older rear hand-guard. None of this model were newly manufactured. All were converted from Rifle, Ross Mk II with Sight, Ross Mk III or the later Rifle, Ross Mk II4*. Some 26,000 were converted from 1910 to 1912. 20,000 were sold to the United States in Nov, 1917. In 1911, the shorter variants were replaced by the longer Rifle, Ross Mk II** as standard Canadian issue.
 * Rifle, Ross Mk II3*

This rifle was a simple upgrade of the last 4,000 manufactured Rifle, Ross Mk II with Sight, Ross Mk III to include the new larger extractor introduced with the Mk II**. The 28 inch barrel, stylish rear hand-guard, sliding button safety, and magazine cut-off were retained. They were completed in the early summer of 1910, then all 4,000 were immediately converted into the Rifle, Ross Mk II3*.
 * Rifle, Ross Mk II4*

The last of the shorter (28 inch barrel) Mk II line would be produced using the "Sight, Sutherland Mk I" and simplified rear hand-guard of the Mk II**. The 28 inch barrel, sliding button safety, and magazine cut-off were retained. Starting in 1910, some 15,000 were manufactured. In 1911, the shorter variants were replaced by the longer Mk II** as standard Canadian issue.
 * Rifle, Ross Mk II5*

For all practical purposes, the Mk III was an entirely new design. It incorporated the 30.5 inch barrel and flag safety of the Mk II**, taking that re-design much further. The internal double-stack magazine was replaced with an exposed single-stack magazine. The "dump loading" lever was gone, and a charger guide was added for loading with stripper clips. A magazine cut-off was employed, but the design that lowered the magazine shell was discarded and replaced by one that restricted the rearward travel of the bolt. The bolt-stop plunger was replaced by a flag lever with three positions (cut-off enabled, bolt release, cut-off disabled). The bolt was far sturdier and had multi-thread locking lugs. A new rear sight designated the "Ross Battle Aperture" was installed on the bridge of the receiver rather than on top of the barrel. World War I increased demand, and at least 235,540 were produced for Canadian forces.
 * Rifle, Ross Mk III

The British government chose to purchase a version of the Mk III with a far simpler rear sight known as the "War Office Pattern Sight". The stock was also strengthened. Some 66,590 were produced.
 * Rifle, Ross Mk IIIB

A "Rifle, Ross Mk III*" may have existed, employing a strengthened action, new front barrel band, and different front sight. The one source mentioning it considers the designation dubious.

Military name changes
In 1907, Rifle, Ross Mk II became Rifle, Ross Mk II with Sight, Ross Mk II and Rifle, Ross Mk II with Sight, Ross Mk III.

In 1912, all military variants were redesignated as follows: In 1918, Rifle, G.P. Ross, Rifle, Cadet, Ross, Rifle, Short, Ross Mk I, and Rifle, Short, Ross Mk II became Rifle, Ross, .303", Cadet D.P. (D.P. meaning Drill Purpose).
 * Rifle, Ross Mk I and Rifle, Ross Mk I* became Rifle, G.P. Ross (G.P. meaning general purpose).
 * Rifle, Ross Mk II with Sight, Ross Mk II and Rifle, Ross Mk II* became Rifle, Cadet, Ross.
 * Rifle, Ross Mk II with Sight, Ross Mk III became Rifle, Short, Ross Mk I.
 * Rifle, Ross Mk II3* and Rifle, Ross Mk II5* became Rifle, Short, Ross Mk II.
 * Rifle, Ross Mk II** became Rifle, Long, Ross Mk II.
 * Rifle, Ross Mk III became Rifle, Long, Ross Mk III.

Sniper rifles
Because of its long range accuracy, the Ross rifle continued in use among Allied snipers after it was withdrawn from normal front-line use in Europe. British snipers found the rifle accurate out to 600 yards and more, with only one inherent disadvantage: the Ross accepted only perfectly clean ammunition, totally free of mud and grit, or else it invariably jammed.

Two types of Mark III sniper rifles are identified by different telescopic sights. Five hundred rifles were fitted with 5.2× Warner & Swasey Company Model 1913 prismatic telescopic sights manufactured in Cleveland, Ohio. Serial numbers for rifles manufactured in 1915 have a FK prefix; while those manufactured in 1917 have a LU prefix. Another 907 rifles were fitted with Winchester Repeating Arms Company A5 telescopic sights. Both telescopic sights were mounted offset so the iron sights were usable and the rifle could still be loaded from charging strips.

Sporting variant
Ross settled a gun factory in Hartford, Connecticut, with machinist J. A. Bennett, to produce a sporting rifle called Model 1897 Magazine Sporting Rifle a hinged hammer type rifle. By the same time, he made a commercial agreement with the famous gunmaker firm Charles William Lancaster, inventor of the oval bore, to be his exclusive UK agent.

Early 1900, he brought out the Model 1900 Sporter, still made in Bennett's factory. This action used a coil spring to activate the firing pin, instead of the hinged-hammer of the M1897. Very few of these sporting rifles are known to exist. The militarized Pattern 1900 was also the first to be offered for trial to Canada.

Following was Model 1903 Sporter some of these rifles were made in Hartford, Connecticut, but most (200 units, made from spare parts) were assembled at the brand new fabricating plant in Quebec City. Some of the Pattern 1903 Sporting Rifles were made in the .370 Express calibre, while some prototype chambered for .450/.500 Nitro is known to exist. Models .303 Brit. are common, .256 Mannlicher rare, and .370 Express are rare.

Some sporterised M1905 (Mk II) military rifles were made available to general public in 1906. This model was called Model M. In 1907, Ross brought out the Model E, his first entirely Canadian-made rifle, based on the 1905 military action, chambered for .303 British and .35 WCF. Following was Model R, which was a plain looking rifle, no checkering, in .303 British only. In November 1906, Ross while in the process of developing a new and very powerful .280 caliber sporting cartridge, made some experimental tests with a necked-down version of the new .30-06 Springfield case which he called the .28-1906 (one rifle is known to exist). This led to the design of the .280 Ross. The new high-pressure round required some strengthening of the bolt and action receiver, but the rifle was otherwise only slightly different from the .303 Mark II. This design, called MK II**, was a transitional step between Mk II and Mk III actions.

 * Model M (1905 Mk II action); .303 Brit
 * Model R (1905 Mk II action); .303 Brit.
 * Model E (1907 Mk II** action heavy barrel); .303 Brit., 35 WCF
 * Model 1907 'Scotch Deer Stalking Pattern'; .280 Ross

Model 1910 (Mk III) was made with a totally different bolt head; instead of having the solid bolt lugs travel in a vertical position and lock in a horizontal position, like for the Mk II and Mk II** (see illustration), Ross turned it 90 degrees so it travels in a horizontal position and locks vertically. Then, he used screw threads on the lugs outside which are locking into the matching threaded receiver. Some very scarce Mk II** with the same threaded lugs and receiver are known to exist. He also used the same shape of heavy barrel as used on the Mk II**. The M-10, in .280 Ross, is considered by many as being the finest rifle ever made by the Ross Rifle Co.

 * Model R-10; .303 Brit.

Model E-10; .303 Brit and .35 WCF

Model M-10; .280 Ross

1912 saw the introduction of the .22 rimfire sporting rifle. While using a simpler mechanism, it was still a straight-pull action. This model was very popular in Canada.
 * Model 1912 Cadet Commercial.
 * Model 1912 Cadet "Leftover" (no serial numbers or any other markings)

The problems with the Ross in combat were that it was really a sporting design of rifle asked to do the work of a military rifle under trench warfare conditions. However, as a sporting rifle, the Ross became quite popular after the war. The new .280 Ross cartridge gained it a fine reputation for medium-sized game, and for a time after 1918 it was a fairly common rifle on safari. It also proved itself as being an outstanding Match Rifle, building a strong reputation for accuracy.

Ross Mark II** Commercial Target Model in .303 British, with a 30+1/2 in heavy barrel, was a real success in the Match Ranges from 1908 to 1913. This rifle was looking like the military Mk II**, using the same bolt, except having the sight bridge mounted on the receiver. A scarce Presentation Target Rifle was also available. Unlike its military counterpart, it had the serial number stamped on the barrel.
 * Match rifles

Model 1907 and 1905/1910 Match Target Rifle These very important single-shot rifles (two rifles are known to exist) are bearing special feature that would make the M1910 so different; the threaded locking lugs and receiver.

Military Match Target Rifle unlike the military Mk III this rifle was using a box type magazine with flat floorplate. It was using the Ross Mk III military sight modified to fit the .280 Ross ammunitions. Barrel was 26 inches long.

Developments
After the rejection of the Ross as a battlefield rifle, the Dominion Rifle Factory adapted the action to a light machinegun, the Huot, using surplus rifles. These were cheaper than the Lewis guns then in use. They were subjected to extensive trials, but the war ended before they entered service.

Other users
British Coast guard units in Ireland were armed with Ross rifles during 1920 to 1921.

After the First World War, the British Empire supplied several models of .303 cal rifles, including Rosses to Estonia, Latvia and White Russian anti-communist forces. In the course of gaining control of the country, the Soviets captured large numbers of non Soviet origin rifles. In the 1930s Stalin approved aid shipments to the Spanish Civil War Republicans, disposals actually, of American Winchester Muskets, German Mauser 98s, British Lee Enfields, Austrian Mannlichers, and several French types. One shipment from the Baltic Sea port of Memel on 6 Nov 1936, included 18,000-odd Pattern '14s and 2310 Canadian .303 M10 Rosses. Reports suggest few of donated rifles were militarily effective due to insufficient ammunition supplies.

Ross rifles were issued once again in the Second World War. The Mark 3 Ross rifle was supplied to the Royal Canadian Navy, the Veteran's Guard of Canada, coastal defence units, training depots, the British Home Guard, Metropolitan Police, London Fire Brigade, Port of London Authority Police and the Soviets.

Ross Rifles were collected hurriedly from stocks held in the Shetland Islands in May 1942 to re-equip the survivors of Operation Fritham in Spitsbergen who had lost everything when their ship was sunk. The Ross rifles and equipment being delivered by Catalina 210/P captained by Flying Officer Tim Healy.

In the 1950s straight-pull Rosses were well known in European sport shooting for biathlon and running deer disciplines. During the World Shooting Championships in Moscow, visiting shooters were allowed to sign for Ross rifles converted to 7.62x54R to try out the competitions. Before biathlon switched to .22LR rifles, it was fired with full-bore cartridge rifles. While various models of Swedish Carl-Gustav rifle were popular, Soviet biathletes had success with Ross rifles outfitted with slings, target sights and 3-position stocks.

Users

 * 🇨🇦 Canada – Standard issue rifle of the CEF from 1905 to 1916, where it was replaced with the SMLE MK. III and MK. III*. Still used by snipers throughout the war for its accuracy.
 * 🇨🇱 chile – In 1920, Britain finally delivered the CHILEAN BATTLESHIP Almirante Latorre (HMS Canada (1913)), which had been sold to Chile, but snapped up by the Royal Navy when World War I broke out. Aboard the ship were 200 Mk III Ross rifles which became property of the Chilean Navy.
 * Republic of China (1912–1949) – British born Morris Cohen, a General for Sun Yat-sen, acquired 500 Ross rifles (probably Mark I) for the Chinese in 1911, described as "weren't up to much, but good enough for training". He made a second trip to Canada in 1925 to buy more Ross rifles, but it is unknown if any were acquired.
 * 🇪🇪 estonia – The British supplied Mk III Rosses to the Baltic states after World War I which wound up in the hands of the Soviet Union after their occupation in 1940.
 * 🇫🇷 france – An off-hand comment by Sir Charles Ross, stating that the French "never complained" about his rifles, leads some to believe that some Ross rifles may have been supplied to the French during World War I.
 * undefined – Some were captured and used by the Germans during World War I.
 * undefined - Ross rifles captured from Canadian soldiers designated the Gewehr 280(e). Ross rifles captured from Soviet soldiers designated the Gewehr 280(r).
 * 🇮🇱 Haganah – The Haganah (Jewish paramilitary organization in the British Mandate of Palestine) purchased and used the Ross Rifles during the 1947–1949 Palestine war. The rifles were called "Canadian Rifles" by the Haganah soldiers.
 * undefined – Around 8,000 Mk III Rosses were supplied to India in 1942 for "police duty", but were withdrawn in 1943.
 * 🇮🇩 indonesia – The Mk III Rosses supplied to the Netherlands are believed to have remained in Indonesia.
 * 🇱🇻 Latvia – MkIIIB Ross rifles were used by newly formed Latvian army during the Latvian War of Independence. They were delivered, together with ammunition and other war materials, by British warships. After the war, Ross rifles became the standard-issue service rifle of Latvian army, since the decision was taken to standardize rifle calibers to British .303. The rifles were also issued to members of the Aizsargi paramilitary guard and, since 1928, the Latvian police.
 * 🇱🇹 lithuania – The British supplied Mk III Rosses to the Baltic states after World War I which wound up in the hands of the Soviet Union after their occupation in 1940. The Lithuanian Army had bought 55,000 rifles with about 50-60 million rounds for a low price in Italy in 1924, after the Lithuanian Wars of Independence. They were mainly distributed among infantry regiments, although they were disliked, as they weren't as accurate as the Mauser rifles. At the first opportunity, the rifles were sold, gaining good profit, with the resulting money being used to order Mauser rifles at the Belgian Fabrique Nationale d'Armes de Guerre and the Czechoslovakian Brno weapons factory.
 * 🇱🇺 Luxembourg – Issued to the Grand Ducal Guard in 1945, replaced by Lee–Enfield in the same year.
 * 🇳🇱 netherlands – Britain is believed to have supplied Mk III Rosses to Netherlands forces bound for Indonesian "police actions", issued from stores at Woerden.
 * undefined – The British shipped some 300 Mk III Rosses to the New Zealand division of the Royal Navy, and these weapons transferred the Royal New Zealand Navy in 1941 to see active duty during World War II.
 * 🇳🇴 norway – In May 1942, some Free Norwegian troops were re-supplied at Spitzbergen with Ross Mk III rifles after their original weapons were lost at sea.
 * undefined – The British supplied Mk III Rosses to the Baltic states after World War I which wound up in the hands of the Soviet Union after their occupation in 1940.Some of these were supplied to Republican forces for the Spanish Civil War. Some additional weapons are thought to have been supplied under a lend-lease arrangement during World War II, though this has never been verified. In 1954, Ross Mk IIIs converted to Russian 7.62mm ammunition were used successfully in the World Shooting Championships in Caracas.
 * undefined – The Soviets are believed to have supplied Ross Mk III rifles to Spanish Republican forces during the Spanish Civil War. These weapons were used by Canadian and American volunteer units and were originally believed to have been supplied by Canada, which the Canadian government denied.
 * 🇬🇧 United Kingdom – issued to the Royal Navy to free up Lee–Enfields for land use. Used on minesweepers to detonate floating mines with rifle fire. The home guard had a number of Ross Mark IIIB rifles that were previously purchased in World War I. These were supplemented with 75,000 Ross Mark III rifles supplied by the Canadian government.
 * 🇺🇸 united states – The US purchased 20,000 Mk II3* for use as training rifles for World War I.
 * 🇷🇺 White Movement – The British supplied arms (probably including Mk III Rosses) to the White Movement after World War I which most likely fell into the hands of the Soviet Union after the end of the Russian Civil War. Around 1,000 rifles were issued with little proof of them being used or even working. Most of the shipments sent were captured by the Red Army.

title: Ross rifle


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Doppelmayr/Garaventa Group

Doppelmayr/Garaventa Group is an international manufacturer of ropeways and people movers for ski areas, urban transport, amusement parks, and material handling systems. As of 2023, the group had produced over 15,400 installations in 96 countries. Their annual revenue in 2022/2023 was 946 million euros. The Doppelmayr/Garaventa Group was formed in 2002 when Doppelmayr of Wolfurt, Austria merged with Garaventa AG of Switzerland to form the world's largest ropeway manufacturer.

History
Doppelmayr was founded in Wolfurt, Austria in 1893 (originally as Konrad Doppelmayr & Sohn), and started manufacturing ropeways in 1937. Garaventa was founded in 1928.

In 1967, Artur Doppelmayr, grandson of the founder Konrad and son of Emil, who was a businessman, became managing director of the company. As alpine recreation rapidly expanded around the world during the last half of the 20th century, Artur led and established the Vorarlberg cable car company as the world leader. In 1996, Doppelmayr Holding AG acquired Von Roll Seilbahnen AG, a Swiss manufacturer of gondola lifts, chairlifts, and cable cars. In 2002, Doppelmayr acquired CWA, a Swiss maker of gondola and cable car cabins. The merger of Doppelmayr and Garaventa was announced in 2001 and completed in 2002. In 2016 they broke two world records in Vietnam: Called the Ha Long Queen Cable Car, the largest cable car cabins (produced by Swiss company CWA) travel on the tallest ropeway support of the world. In 2017, produced by Garaventa and CWA, the steepest funicular railway came into effect in Stoos, Switzerland.

Divisions
Doppelmayr Garaventa Group operates subsidiaries in 50 countries manufacturing ropeways under the Doppelmayr and Garaventa brands. Seven of these are responsible for manufacturing parts, namely Doppelmayr Seilbahnen GmbH (Austria), Garaventa AG (Switzerland), Doppelmayr Canada Ltd., Sanhe Doppelmayr Transport Systems Co., Ltd. (China), Doppelmayr France SAS, Doppelmayr Italia Srl, and Doppelmayr USA, Inc.

The company's core ropeway products include cable cars, funiculars, gondola lifts, detachable chairlifts, fixed grip chairlifts, and surface lifts. The company developed the "3S" tricable gondola lift, having acquired the technology from Von Roll Seilbahnen, and built lifts including those located in Kitzbühel (Austria), Koblenz (Germany) and Whistler-Blackcomb (Canada).

Doppelmayr Cable Car
Doppelmayr Cable Car GmbH manufactures automated people movers. Their main product is the rope-propelled Cable Liner system, used in airports, city centres, intermodal passenger transport connections, park and ride facilities, campuses, resorts, and amusement parks. The company is a wholly owned subsidiary of the Doppelmayr Garaventa Group, having been established by Doppelmayr in 1996. Up until 2019, the subsidiary was referred to as DCC Doppelmayr Cable Car.

The first installation was completed at Mandalay Bay in Las Vegas in 1999. In 2003, after the world's first maglev transport system (opened in 1984 at Birmingham International Airport) fell into disrepair, DCC installed the "AirRail Link" to replace the maglev and temporary replacement bus-service that had been operating since 1995. The company is contracted to operate some of the systems it builds. A newer system is Luton DART, opened in March 2023.

Doppelmayr Transport Technology
Doppelmayr Transport Technology GmbH develops and sells material-handling ropeway systems. Initially, these systems were similar to cable cars and chairlifts designed for people, but fitted with specially designed carriers. In the early 2000s, Doppelmayr developed a cable-driven material-handling ropeway called RopeCon. RopeCon is a conveyor system that can transport materials over long distances with little ground disturbance. Such installations can be found in Papua New Guinea, Jamaica, Sudan, Switzerland, and Austria.

CWA Constructions
CWA Constructions SA of Olten, Switzerland, was acquired by Doppelmayr in 2001. The subsidiary manufactures cabins, such as gondola and people mover cabins, for most Doppelmayr Garaventa Group installations as well as for systems built by other manufacturers.

Frey AG Stans
Frey AG Stans was founded in 1966 and was acquired by Doppelmayr Garaventa Group in April 2017. The subsidiary manufactures various electrical components and control systems for ropeways.

Gassner Stahlbau
Gassner Stahlbau GmbH is a subsidiary based in Bürs, Austria, that manufactures steel for pylons, chairs, and suspension, as well as various plastic parts. Gassner Stahlbau has manufactured parts for Doppelmayr since 1969, and was later acquired by Doppelmayr.

Input Projektentwicklungs GmbH
The Input Projektentwicklungs GmbH division produces mountain systems and amusement rides, such as the experimental Mountain Glider roller coaster in Walibi, Belgium. This project was plagued with problems and the ride was eventually removed.

Liftbyggarna
In December 2013, the company's Swedish division, Doppelmayr Scandinavia AB, acquired Swedish lift manufacturer Liftbyggarna AB, which has retained its own separate branding. The company was originally founded in 1952.

LTW Intralogistics
LTW Intralogistics produces automated warehouse technology.

title: Doppelmayr/Garaventa Group