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FT

The (FT) is a international daily specializing in , , , and , founded on 9 January 1888 in by James Sheridan alongside his brother, with as its initial chairman. It is published in format on distinctive salmon-pink paper and emphasizes rigorous, data-driven financial journalism aimed at professional readers, including executives and investors. Owned since 2015 by the Japanese media conglomerate , the FT merged with the Financial News in 1945 under , consolidating its position amid competition from other titles, and has since expanded into digital platforms, specialist publications, and global printing in multiple continents. By 2022, it achieved a record 1.2 million paying subscribers, with over one million digital, reflecting successful adaptation to online models through premium content and paywalls, alongside an estimated global audience exceeding 21 million readers. The publication is noted for influential columns like Lex and for authoritative economic analysis, though its editorial perspective has drawn scrutiny for aligning with views on and markets, potentially underrepresenting dissenting empirical critiques of those paradigms.

Measurements and units

Foot (unit of length)

The foot (symbol: ft) is a unit of length in the US customary system and formerly in the British imperial system, defined as exactly 12 inches or 0.3048 meters. This precise value, termed the international foot, resulted from a 1959 international agreement among the United States, United Kingdom, Canada, Australia, New Zealand, and South Africa to express the yard (3 feet) as exactly 0.9144 meters, thereby facilitating compatibility with metric measurements while retaining customary units for practical applications. The unit subdivides into 12 inches, with each inch historically tied to smaller anthropometric measures but now exactly 2.54 centimeters under the same agreement. Historically, the foot emerged as an anthropometric unit approximating the length of an adult male foot, employed across ancient cultures for land measurement and before formal . In , the pes—equivalent to one foot—measured about 295.7 millimeters, comprising 12 unciae (precursors to inches) and serving as a basis for and . Variations persisted regionally; for instance, medieval English feet ranged from 9 to 13 inches due to local customs, until efforts like King Henry I's decree around 1100 attempted uniformity based on his own foot length, though inconsistencies endured until the . Empirical accelerated in the , with the British Parliament defining the imperial foot in 1824 as one-third of a yard derived from a bar, later refined metrologically. In the United States, the foot initially followed definitions but diverged for purposes. established the US survey foot in as exactly 1200/3937 meters (approximately 0.3048006096 meters), a value retained after the 1893 metric adoption to preserve legacy geodetic data. This survey foot exceeds the international foot by 2 parts per million, accumulating to noticeable discrepancies over long distances—e.g., about 3.3 feet difference per 1,000 miles—which prompted the Geodetic Survey to deprecate it for new measurements in 2016, mandating exclusive use of the international foot by 2022 to eliminate errors in modern geospatial work. Today, the international foot remains in use primarily in the United States for construction, real estate, and engineering, where it interfaces with the inch for precision tasks like framing and piping. Globally, metrication has supplanted it in most countries, though it persists in aviation (e.g., altitude in feet) and nautical contexts under international conventions. Legacy survey foot data requires conversion factors, such as multiplying by 0.999998 to yield international feet, to ensure accuracy in updated surveys.

Publications and media

Financial Times

The (FT) is a global business and financial newspaper headquartered in , , with a focus on international markets, , corporate news, and policy analysis. Founded on January 9, 1888, by James Sheridan and his brother, it initially targeted financial professionals amid competition from other specialist publications. The paper merged with its rival, the Financial News, in 1945 under , consolidating its position in financial journalism. A hallmark of the FT is its salmon-pink newsprint, introduced in 1893 to visually distinguish it from the white pages of competitors like the Financial News, a choice that persists in its print edition despite the shift toward digital dominance. The newspaper emphasizes data-driven reporting, in-depth analysis, and opinion pieces from economists and executives, covering topics from stock markets and mergers to geopolitical risks affecting trade. It publishes Monday through Saturday, with supplements on sectors like and . Pearson plc owned the FT until 2015, when it sold the FT Group to Japan's Nikkei, Inc. for £844 million (approximately $1.3 billion), allowing Nikkei to expand its global footprint while pledging editorial independence for the FT. Roula Khalaf has served as editor since January 2020, succeeding Lionel Barber and overseeing expansions in digital subscriptions and events like the FT Weekend Festival. The FT maintains a paywall model introduced in 2002, one of the earliest in journalism, which has driven growth amid declining print sales. As of , the FT reports a paying audience of 2.6 million, including over 1.3 million subscribers, with around 103,000 copies monthly; it aims for 3 million subscribers by 2028 through diversification into podcasts, newsletters, and AI-focused reporting. assessments rate the FT as highly reliable for factual reporting, with minimal partisan bias—center-leaning overall but economically pragmatic and skeptical of —though its editorial endorsements have favored centrist figures like in past elections. The publication sponsors the annual FT & Business Book of the Year Award, recognizing influential works.

Military and vehicles

Renault FT tank

The Renault FT was a French light tank developed during World War I, recognized as the first production vehicle to feature a fully rotating turret and the modern layout of front-mounted crew compartment and rear-mounted engine, which became the standard configuration for subsequent tank designs. Weighing approximately 6.5 tons, it was armed with either an 8 mm Hotchkiss M1914 machine gun or a 37 mm Puteaux SA 18 cannon, operated by a crew of two: a driver and a commander/gunner. Powered by a 39 horsepower Renault four-cylinder gasoline engine, it achieved a maximum speed of about 7.5 km/h on rough terrain and had an operational range of 60 km. Development began in mid-1916 following a meeting between General Jean-Baptiste Estienne, an early advocate for armored warfare, and , who proposed a compact, mass-producible design contrasting with heavier British and French tanks like the Schneider CA1. A wooden mock-up was completed by October 1916, with the first prototype demonstrated on 30 December 1916; despite initial resistance from military leaders favoring larger tanks, production orders escalated from 100 units in February 1917 to over 3,000 by the on 11 November 1918. The design emphasized mobility and ease of manufacture, using riveted steel armor and a for transport by standard trucks, enabling swarm tactics to overwhelm defenses rather than direct tank-to-tank engagements. The FT entered combat on 31 May 1918 near Ploissy-Chazelle during a counter-attack in the Forest of Retz, where 31 tanks supported Moroccan against positions; it proved effective in subsequent offensives, including the , , and Meuse-Argonne, contributing to Allied breakthroughs by providing close support and suppressing machine-gun nests. Approximately two-thirds of production featured the mitrailleur variant with machine-gun armament, while one-third mounted the canon version with the 37 mm gun for anti-fortification roles; other adaptations included cast-steel turrets on early models and experimental radio-equipped command versions. Over 5,000 units were ultimately produced into the , with exports influencing designs in the United States (M1917), , , and . Post-World War I, the FT saw extensive service in conflicts such as the , Polish-Soviet War (1919–1921), , and , often in secondary roles due to its obsolescence against newer armor; remnants were used by French forces in 1940 and even in the Soviet-Afghan War. Its enduring legacy lies in establishing key principles of tank evolution, including turret-mounted main armament for all-around fire and compartmentalized layout for crew efficiency, directly shaping interwar and light tanks while highlighting the shift toward lighter, more versatile armored vehicles over cumbersome heavies.

Mathematics and physics

Fourier transform

The Fourier transform is an integral transform that decomposes a mathematical function, typically representing a signal in time or space, into its constituent frequencies, expressing it as a superposition of complex exponentials or sines and cosines. This decomposition facilitates analysis in the frequency domain, where operations like filtering become more straightforward than in the original domain. The transform was introduced by French mathematician Jean-Baptiste Joseph Fourier in his 1822 book Théorie analytique de la chaleur, where it solved the heat equation by representing temperature distributions as infinite sums of trigonometric functions, challenging prevailing views that analytic solutions required power series. The continuous of a complex-valued integrable f(t) is given by the formula \hat{f}(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i \omega t} \, [dt](/page/DT), where \omega denotes in radians per time and i = \sqrt{-1}. The inverse transform recovers the original via f(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} \hat{f}(\omega) e^{i \omega t} \, d\omega, with the $2\pi factor arising from the convention that ensures unitarity under the L² inner product. This pair assumes f is square-integrable over the real line; for non-integrable cases, the transform extends via distributions or tempered distributions. Key properties include : the transform of a f(t) + b g(t) equals a \hat{f}(\omega) + b \hat{g}(\omega); time-shifting: the transform of f(t - t_0) is e^{-i \omega t_0} \hat{f}(\omega); and via similar phase factors. The states that the transform of the (f * g)(t) = \int_{-\infty}^{\infty} f(\tau) g(t - \tau) \, d\tau is the product \hat{f}(\omega) \hat{g}(\omega), enabling efficient computation of convolutions in the , as exploited in algorithms like the for . Parseval's theorem preserves energy: \int_{-\infty}^{\infty} |f(t)|^2 \, dt = \frac{1}{2\pi} \int_{-\infty}^{\infty} |\hat{f}(\omega)|^2 \, d\omega, confirming the transform's on L² spaces and linking time-domain power to frequency-domain . In physics, the underpins solutions to wave equations, partial differential equations, and , where it relates position-space wavefunctions to momentum-space representations via the , as position and momentum operators are Fourier duals. In , it decomposes waveforms into spectra for tasks such as removal, , and data compression; for instance, it identifies dominant frequencies in audio or electromagnetic signals, allowing targeted or . Applications extend to , where two-dimensional variants reconstruct scans from projections, and to , modeling patterns as transforms of functions. These uses rely on the transform's ability to reveal causal structures in oscillatory phenomena, grounded in the empirical of many physical systems.

Sports and games

Full time

In , governed by the Laws of the Game established by the (IFAB), full time marks the conclusion of the standard regulation period, consisting of two halves of 45 minutes each, totaling 90 minutes before allowances for time lost due to substitutions, injuries, or other stoppages. The , acting as the official timekeeper, adds stoppage time (also called injury time) at the end of each half and signals full time by , typically once the ball goes out of play after the second half's allocated time expires. This distinguishes full time from , which provides a 15-minute for teams to regroup, during which no play occurs. If the score is tied at full time in competitions, matches may proceed to extra time—two additional 15-minute periods—or, if still unresolved, a to determine the winner, as outlined in Law 10. The term "full time" is also abbreviated as "FT" in reports, scorelines, and betting contexts to denote the result at the end of regulation play, excluding any extra time (AET) or penalties. The usage extends to , where full time ends the standard 80-minute match divided into two 40-minute halves, with the referee allowing play to continue beyond the clock until the next natural stoppage, such as the ball going dead, to ensure fairness. In , as in , tied scores at full time in certain tournaments trigger extra time periods of 10 minutes each half. While less standardized in sports like , where regulation ends with the final buzzer after four quarters or periods, "full time" occasionally appears in or betting terminology to refer to the end of normal playing time before .

Free throw

A free throw, also known as a foul shot, is an unopposed attempt to score one point by shooting the ball from a designated line on the court, awarded to a player after specific fouls committed by the opposing team. It serves as a penalty mechanism to discourage fouling, providing the fouled team an opportunity to score without defensive interference. The free-throw line is positioned 15 feet (4.57 meters) from the backboard in NBA and NCAA play, and approximately 15.09 feet (4.6 meters) in FIBA-governed international basketball. Free throws are typically awarded for personal fouls, with the number depending on the context and game stage. In the NBA, a player fouled in the act of shooting receives two free throws for a two-point attempt or three for a three-point attempt; non-shooting fouls yield two after the team reaches the bonus (fifth foul in a quarter). Technical fouls grant one or two free throws plus possession, while flagrant fouls can award two or three. FIBA rules align closely but differ in bonus structure: two free throws after five team fouls per period, with one-and-one (one successful throw yields a second) before the seventh foul. Violations during attempts, such as stepping over the line before release or offensive basket interference, nullify the shot and may forfeit subsequent throws. The was not part of James Naismith's original 13 in 1891, where repeated fouling led to disqualification rather than shots. It evolved in the as a compromise: early versions awarded points directly for fouls, but by 1894, rules formalized free throws from 15-20 feet to balance offense and defense. The line's distance was standardized to 15 feet by 1895, reflecting concerns over rough play in the sport's origins. Most players use an overhand set-shot technique, involving a jump stop, elbow alignment, and wrist snap for arc and backspin, which aids entry through the . The underhand "granny" style, popularized by (career 89.9% NBA free-throw ), produces higher success rates due to optimal and reduced variability, as shown in biomechanical analyses where it achieves up to 20-25% better odds for skilled shooters. Despite this, underhand shots remain rare, comprising less than 1% of attempts, attributed to perceived lack of aesthetics and psychological barriers rather than mechanical inferiority. NBA league-average free-throw percentage hovers around 77-78%, stable over decades despite training advances, as pressure and fatigue introduce variability not replicable in practice. Career leaders include at 90.43% (minimum 1,250 attempts) and at 91.0% through 2024. Perfect seasons (100%) are rare, with only players like Micheal Williams (1991-92, 97/97) achieving it under minimum thresholds. Free throws often decide close games, accounting for 20-25% of points in high-stakes NBA contests.

Technology and computing

FaceTime

FaceTime is a proprietary videotelephony service developed by Apple Inc. for use on its iOS, iPadOS, macOS, and visionOS devices, enabling real-time audio and video communication between users over Wi-Fi or cellular networks. Launched alongside the iPhone 4 on June 24, 2010, following its announcement by Steve Jobs at the Worldwide Developers Conference on June 7, 2010, FaceTime initially supported one-to-one video calls using the device's front-facing camera and required Wi-Fi connectivity. Cellular support for video calls was added in 2012 with iOS 6. The service expanded to include audio-only calls (FaceTime Audio) introduced in on September 18, 2013, allowing voice communication without video to conserve bandwidth and battery life. Group , supporting up to 32 participants, debuted in on September 17, 2018, with subsequent updates adding features like screen sharing in (September 24, 2021) and spatial audio for immersive sound positioning. Recent enhancements in (September 18, 2023) introduced reaction effects triggered by hand gestures, such as confetti for thumbs-up or fireworks for raised hands, alongside Live Translation for real-time subtitles in multiple languages during calls. FaceTime employs end-to-end encryption using the (SRTP) to protect call content from interception, with keys negotiated via Apple's push notification service; however, metadata such as call duration and participant identifiers may be accessible to Apple for service operation. Video streams utilize H.264 compression for efficient transmission, while audio employs Adaptive Multi-Rate () or AAC-ELD codecs, resulting in data usage of approximately 120-380 MB per hour for video calls depending on resolution and network conditions. Compatibility requires or later on /, macOS 10.6.6 or later on with a compatible camera and , and an for ; cross-platform web access via browsers was enabled in 2021 for non-Apple users through invite links. Privacy concerns have arisen, notably a in Group discovered on January 19, 2019, by a teenager, which permitted callers to access the recipient's and camera audio before call acceptance, prompting Apple to temporarily disable the group on January 28, 2019, and issue a patch on February 7, 2019. In 18 (September 16, 2024), Apple introduced on-device to detect nudity in video feeds during calls involving minors, automatically blurring content and alerting guardians, a aimed at child safety but criticized for potential overreach in monitoring private communications. These incidents highlight tensions between Apple's emphasis on user —evidenced by default —and the challenges of securing real-time features against exploits, with no verified instances of widespread unauthorized tapping absent device compromise like jailbreaking.

Slang and informal usage

For trade

In online trading communities, particularly those focused on collectibles, items, and marketplaces, the abbreviation "FT" denotes "for trade," signaling that a is offering an item or asset for rather than monetary sale. This usage facilitates bartering arrangements, often paired with complementary abbreviations like "LF" (looking for) to specify desired s. It emerged in digital forums and social platforms where direct sales might violate platform policies or community norms favoring swaps, such as in groups for trading cards, , or . The term is ubiquitous in hobbyist subcultures, including Pokémon card exchanges, , and swaps, where posts might read "Vintage cards FT" to attract potential swappers without implying commercial intent. In these contexts, "FT" helps streamline negotiations by clarifying availability for reciprocal offers, reducing misunderstandings in high-volume listing environments like Reddit's trading subreddits or groups. Unlike formal platforms, this slang promotes community-driven value exchange, though it can overlap with gray-market activities if trades involve undervalued resales. Distinctions from similar abbreviations include "" (for sale) or "WTT" (want to trade), with "FT" emphasizing outbound offers rather than inbound requests or outright s. Its adoption reflects the evolution of vernacular from early systems to modern apps, prioritizing brevity in fast-paced interactions. While not formally standardized, the meaning remains consistent across English-language online spaces as of 2025, with minimal variation in informal dialects.

Featuring

In music credits and titles, "ft." serves as an for "featuring," indicating the participation of a or collaborator on a track, often providing vocals, verses, or contributions. This usage highlights the featured performer's role without implying equal billing to the primary , distinguishing it from co-credits marked by "and" or "&." For instance, a song titled "Track Name ft. Guest Artist" credits the guest with a prominent but secondary appearance, a convention prevalent in genres like , pop, and electronic music since the late . The abbreviation appears informally in digital media, such as streaming platforms, YouTube video titles, and social media posts promoting releases, where space constraints favor brevity over the full "feat." or "featuring." While "feat." remains more formal in official liner notes, "ft." has gained traction in casual online discourse, sometimes extending to non-musical collaborations like podcast episodes or videos denoting guest spots. This informal application underscores its slang-like adaptability, though it originates from standard music industry shorthand rather than vernacular slang.

Other uses

Fort

Ft. is an abbreviation for fort, denoting a fortified military enclosure or structure designed for defense against enemy attack, often incorporating walls, ramparts, moats, or earthworks to protect personnel, supplies, and artillery. This usage appears in geographical nomenclature, particularly in North America, where "Fort" or its abbreviated form prefixes names of settlements originating as trading posts, frontier outposts, or army garrisons during colonial and early American expansion, such as Ft. Wayne, Indiana (established 1794 as a U.S. Army post), and Ft. Smith, Arkansas (founded 1817 for frontier defense). The abbreviation "FT" or "Ft." is standardized in postal and addressing conventions; the United States Postal Service lists "FT" as an approved truncation for "FORT" in street suffixes and place names to ensure efficient mail routing. In military contexts, "Ft." abbreviates "Fort" for U.S. installations, reflecting their historical role as permanent bases evolving from temporary camps built during conflicts like the and . Examples include Ft. Knox, (established 1918, site of the U.S. Bullion Depository since 1936 holding approximately 147.3 million ounces of gold as of 2023), and Ft. Sill, Oklahoma (founded 1869 for Plains Indian campaigns). Official naming conventions now favor the full "Fort" for active bases—over 15 such installations exist, including (formerly Ft. Hood, largest active-duty armored post with 36,000 soldiers as of 2024)—though "Ft." persists in historical records, maps, and informal references. Renamings, such as to in 2023, have shifted some designations away from Confederate-era figures but retain the "Fort" structure for bases emphasizing training and readiness. Dictionaries, including and Collins, explicitly define "ft." as shorthand for "" or "," underscoring its prevalence in English-language abbreviations over alternatives like "F." This contrasts with metric contexts where "ft" denotes "foot," but capitalization and context (e.g., "Ft. Lauderdale") distinguish military-geographical uses. Primary sources like U.S. government postal standards and historical archives provide the most reliable verification, avoiding reliance on secondary interpretations prone to interpretive bias.

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