title: Music sequencer

text: The advent of Musical Instrument Digital Interface (MIDI) and the Atari ST home computer in the 1980s gave programmers the opportunity to design software that could more easily record and play back sequences of notes played or programmed by a musician. This software also improved on the quality of the earlier sequencers which tended to be mechanical sounding and were only able to play back notes of exactly equal duration. Software-based sequencers allowed musicians to program performances that were more expressive and more human. These new sequencers could also be used to control external synthesizers, especially rackmounted sound modules, and it was no longer necessary for each synthesizer to have its own devoted keyboard.


title: Music sequencer

text: As the technology matured, sequencers gained more features, such as the ability to record multitrack audio. Sequencers used for audio recording are called digital audio workstations (or DAWs).


title: Music sequencer

text: Many modern sequencers can be used to control virtual instruments implemented as software plug-ins. This allows musicians to replace expensive and cumbersome standalone synthesizers with their software equivalents.


title: Music sequencer

text: Today the term "sequencer" is often used to describe software. However, hardware sequencers still exist. Workstation keyboards have their own proprietary built-in MIDI sequencers. Drum machines and some older synthesizers have their own step sequencer built in. There are still also standalone hardware MIDI sequencers, although the market demand for those has diminished greatly due to the greater feature set of their software counterparts.


title: Music sequencer

text: Realtime sequencers record the musical notes in real-time as on audio recorders, and play back musical notes with designated tempo, quantizations, and pitch. For editing, usually "punch in/punch out" features originated in the tape recording are provided, although it requires sufficient skills to obtain the desired result. For detailed editing, possibly another visual editing mode under graphical user interface may be more suitable. Anyway, this mode provides usability similar to audio recorders already familiar to musicians, and it is widely supported on software sequencers, DAWs, and built-in hardware sequencers.


title: Music sequencer

text: Analog sequencers are typically implemented with analog electronics, and play the musical notes designated by a series of knobs or sliders corresponding to each musical note (step). It is designed for both composition and live performance; users can change the musical notes at any time without regarding recording mode. And also possibly, the time-interval between each musical note (length of each step) can be independently adjustable. Typically, analog sequencers are used to generate the repeated minimalistic phrases which may be reminiscent of Tangerine Dream, Giorgio Moroder or trance music.


title: Music sequencer

text: On step sequencers, musical notes are rounded into steps of equal time-intervals, and users can enter each musical note without exact timing; instead, the timing and duration of each step can be designated in several different ways:


title: Music sequencer

text: In general, step mode, along with roughly quantized semi-realtime mode, is often supported on the drum machines, bass machines and several groove machines.


title: Music sequencer

text: Software sequencer is a class of application software providing a functionality of music sequencer, and often provided as one feature of the DAW or the integrated music authoring environments. The features provided as sequencers vary widely depending on the software; even an analog sequencer can be simulated. The user may control the software sequencer either by using the graphical user interfaces or a specialized input devices, such as a MIDI controller.


title: Music sequencer

text: The early music sequencers were sound producing devices such as , music boxes, mechanical organs, player pianos, and Orchestrions. Player pianos, for example, had much in common with contemporary sequencers. Composers or arrangers transmitted music to piano rolls which were subsequently edited by technicians who prepared the rolls for mass duplication. Eventually consumers were able to purchase these rolls and play them back on their own player pianos.


title: Music sequencer

text: The origin of automatic musical instruments seems remarkably old. As early as the 9th century, the Persian (Iranian) Banū Mūsā brothers invented a hydropowered organ using exchangeable cylinders with pins, and also an automatic flute playing machine using steam power, as described in their "Book of Ingenious Devices". The Banu Musa brothers' automatic flute player was the first programmable music sequencer device, and the first example of repetitive music technology, powered by hydraulics.


title: Music sequencer

text: In 1206, Al-Jazari, an Arab engineer, invented programmable musical automata, a "robot band" which performed "more than fifty facial and body actions during each musical selection." It was notably the first programmable drum machine. Among the four automaton musicians were two drummers. It was a drum machine where (cams) bump into little levers that operated the percussion. The drummers could be made to play different rhythms and different drum patterns if the pegs were moved around.


title: Music sequencer

text: In the 14th century, rotating cylinders with pins were used to play a carillon (steam organ) in Flanders, and at least in the 15th century, barrel organs were seen in the Netherlands.


title: Music sequencer

text: In the late-18th or early-19th century, with technological advances of the Industrial Revolution various automatic musical instruments were invented. Some examples: music boxes, barrel organs and barrel pianos consisting of a barrel or cylinder with pins or a flat metal disc with punched holes; or mechanical organs, player pianos and orchestrions using book music / music rolls (piano rolls) with punched holes, etc. These instruments were disseminated widely as popular entertainment devices prior to the inventions of phonographs, radios, and sound films which eventually eclipsed all such home music production devices.


title: Music sequencer

text: Of them all, punched-paper-tape media had been used until the mid-20th century. The earliest programmable music synthesizers including the RCA Mark II Sound Synthesizer in 1957, and the Siemens Synthesizer in 1959, were also controlled via punch tapes similar to piano rolls.


title: Music sequencer

text: Additional inventions grew out of sound film audio technology. The drawn sound technique which appeared in the late 1920s, is notable as a precursor of today's intuitive graphical user interfaces. In this technique, notes and various sound parameters are triggered by hand-drawn black ink waveforms directly upon the film substrate, hence they resemble piano rolls (or the 'strip charts' of the modern sequencers/DAWs). Drawn soundtrack was often used in early experimental electronic music, including the Variophone developed by Yevgeny Sholpo in 1930, and the Oramics designed by Daphne Oram in 1957, and so forth.


title: Music sequencer

text: During the 1940s–1960s, Raymond Scott, an American composer of electronic music, invented various kind of music sequencers for his electric compositions. The "Wall of Sound", once covered on the wall of his studio in New York during the 1940s–1950s, was an electro-mechanical sequencer to produce rhythmic patterns, consisting of stepping relays (used on dial pulse telephone exchange), solenoids, control switches, and tone circuits with 16 individual oscillators. Later, Robert Moog would explain it in such terms as "the whole room would go 'clack - clack - clack', and the sounds would come out all over the place".


title: Music sequencer

text: The Circle Machine, developed in 1959, had incandescent bulbs each with its own rheostat, arranged in a ring, and a rotating arm with photocell scanning over the ring, to generate an arbitrary waveform. Also, the rotating speed of the arm was controlled via the brightness of lights, and as a result, arbitrary rhythms were generated.


title: Music sequencer

text: Clavivox, developed since 1952, was a kind of keyboard synthesizer with sequencer. On its prototype, a theremin manufactured by young Robert Moog was utilized to enable portamento over 3-octave range, and on later version, it was replaced by a pair of photographic film and photocell for controlling the pitch by voltage.


title: Music sequencer

text: In 1968 Ralph Lundsten and Leo Nilsson had a polyphonic synthesizer with sequencer called Andromatic built for them by Erkki Kurenniemi.


title: Music sequencer

text: The step sequencers played rigid patterns of notes using a grid of (usually) 16 buttons, or steps, each step being 1/16 of a measure. These patterns of notes were then chained together to form longer compositions. Sequencers of this kind are still in use, mostly built into drum machines and grooveboxes. They are monophonic by nature, although some are multi-timbral, meaning that they can control several different sounds but only play one note on each of those sounds.


title: Music sequencer

text: On the other hand, software sequencers were continuously utilized since the 1950s in the context of computer music, including computer-"played" music (software sequencer), computer-"composed" music (music synthesis), and computer "sound generation" (sound synthesis). In June 1951, the first computer music "Colonel Bogey" was played on CSIRAC, Australia's first digital computer. In 1956, Lejaren Hiller at the University of Illinois at Urbana–Champaign wrote one of the earliest programs for computer music composition on ILLIAC, and collaborated on the first piece, "Illiac Suite for String Quartet", with Leonard Issaction. In 1957 Max Mathews at Bell Labs wrote MUSIC, the first widely used program for sound generation, and a 17-second composition was performed by the IBM 704 computer. Subsequently, computer music was mainly researched on the expensive mainframe computers in computer centers, until the 1970s when minicomputers and then microcomputers became available in this field.


title: Music sequencer

text: In Japan, experiments in computer music date back to 1962, when Keio University professor Sekine and Toshiba engineer Hayashi experimented with the computer. This resulted in a piece entitled "TOSBAC Suite".


title: Music sequencer

text: In 1971, Electronic Music Studios (EMS) released one of the first digital sequencer products as a module of Synthi 100, and its derivation, Synthi Sequencer series.


title: Music sequencer

text: After then, Oberheim released the DS-2 Digital Sequencer in 1974, and Sequential Circuits released Model 800 in 1977


title: Music sequencer

text: In 1975, New England Digital (NED) released ABLE computer (microcomputer) as a dedicated data processing unit for Dartmouth Digital Synthesizer (1973), and based on it, later Synclavier series were developed.


title: Music sequencer

text: The Synclavier I, released in September 1977, was one of the earliest digital music workstation product with multitrack sequencer. Synclavier series evolved throughout the late-1970s to the mid-1980s, and they also established integration of digital-audio and music-sequencer, on their Direct-to-Disk option in 1984, and later Tapeless Studio system.


title: Music sequencer

text: In 1982, renewed the Fairlight CMI Series II and added new sequencer software "Page R", which combined step sequencing with sample playback.


title: Music sequencer

text: Yamaha's GS-1, their first FM digital synthesizer, was released in 1980. To program the synthesizer, Yamaha built a custom computer workstation . It was only available at Yamaha's headquarters in Japan (Hamamatsu) and the United States (Buena Park).


title: Music sequencer

text: While there were earlier microprocessor-based sequencers for digital polyphonic synthesizers, their early products tended to prefer the newer internal digital buses than the old-style analogue CV/Gate interface once used on their prototype system. Then in the early-1980s, they also re-recognized the needs of CV/Gate interface, and supported it along with MIDI as options.


title: Music sequencer

text: In 1977, Roland Corporation released the MC-8 Microcomposer, also called "computer music composer" by Roland. It was an early stand-alone, microprocessor-based, digital CV/Gate sequencer, and an early polyphonic sequencer. It equipped a keypad to enter notes as numeric codes, 16 KB of RAM for a maximum of 5200 notes (large for the time), and a polyphony function which allocated multiple pitch CVs to a single Gate. It was capable of eight-channel polyphony, allowing the creation of polyrhythmic sequences. The MC-8 had a significant impact on popular electronic music, with the MC-8 and its descendants (such as the Roland MC-4 Microcomposer) impacting popular electronic music production in the 1970s and 1980s more than any other family of sequencers. The MC-8's earliest known users were Yellow Magic Orchestra in 1978.


title: Music sequencer

text: In June 1981, Roland Corporation founder Ikutaro Kakehashi proposed the concept of standardization between different manufacturers' instruments as well as computers, to Oberheim Electronics founder Tom Oberheim and Sequential Circuits president Dave Smith. In October 1981, Kakehashi, Oberheim and Smith discussed the concept with representatives from Yamaha, Korg and Kawai. In 1983, the MIDI standard was unveiled by Kakehashi and Smith. The first MIDI sequencer was the Roland MSQ-700, released in 1983.


title: Music sequencer

text: It was not until the advent of MIDI that general-purpose computers started to play a role as sequencers. Following the widespread adoption of MIDI, computer-based MIDI sequencers were developed. MIDI-to-CV/Gate converters were then used to enable analogue synthesizers to be controlled by a MIDI sequencer. Since its introduction, MIDI has remained the musical instrument industry standard interface through to the present day.


title: Music sequencer

text: In 1978, Japanese personal computers such as the Hitachi equipped the low-bit D/A converter to generate sound which can be sequenced using Music Macro Language (MML). This was used to produce chiptune video game music.


title: Music sequencer

text: It was not until the advent of MIDI, introduced to the public in 1983, that general-purpose computers really started to play a role as software sequencers. NEC's personal computers, the PC-88 and PC-98, added support for MIDI sequencing with MML programming in 1982. In 1983, Yamaha modules for the MSX featured music production capabilities, real-time FM synthesis with sequencing, MIDI sequencing, and a graphical user interface for the software sequencer. Also in 1983, Roland Corporation's CMU-800 sound module introduced music synthesis and sequencing to the PC, Apple II, and Commodore 64.


title: Music sequencer

text: The spread of MIDI on personal computers was facilitated by Roland's MPU-401, released in 1984. It was the first MIDI-equipped PC sound card, capable of MIDI sound processing and sequencing. After Roland sold MPU sound chips to other sound card manufacturers, it established a universal standard MIDI-to-PC interface. Following the widespread adoption of MIDI, computer-based MIDI software sequencers were developed.


title: Music sequencer

text: In 1987, software sequencers called trackers were developed to realize the low-cost integration of sampling sound and interactive digital sequencer as seen on Fairlight CMI II "Page R". They became popular in the 1980s and 1990s as simple sequencers for creating computer game music, and remain popular in the demoscene and chiptune music.


title: Health economics

text: Health economics is a branch of economics concerned with issues related to efficiency, effectiveness, value and behavior in the production and consumption of health and healthcare. Health economics is important in determining how to improve health outcomes and lifestyle patterns through interactions between individuals, healthcare providers and clinical settings. In broad terms, health economists study the functioning of healthcare systems and health-affecting behaviors such as smoking, diabetes, and obesity.


title: Health economics

text: One of the biggest difficulties regarding healthcare economics is that it does not follow normal rules for economics. Price and Quality are often hidden by the third-party payer system of insurance companies and employers. Additionally, QALY (Quality Adjusted Life Years), one of the most commonly used measurements for treatments, is very difficult to measure and relies upon assumptions that are often unreasonable.


title: Health economics

text: A seminal 1963 article by Kenneth Arrow is often credited with giving rise to health economics as a discipline. His theory drew conceptual distinctions between health and other goods. Factors that distinguish health economics from other areas include extensive government intervention, intractable uncertainty in several dimensions, asymmetric information, barriers to entry, externality and the presence of a third-party agent. In healthcare, the third-party agent is the patient's health insurer, who is financially responsible for the healthcare goods and services consumed by the insured patient.


title: Health economics

text: Uncertainty is intrinsic to health, both in patient outcomes and financial concerns. The knowledge gap that exists between a physician and a patient creates a situation of distinct advantage for the physician, which is called "asymmetric information".


title: Health economics

text: Externalities arise frequently when considering health and health care, notably in the context of the health impacts as with infectious disease or opioid abuse . For example, making an effort to avoid catching the common cold affects people other than the decision maker or finding sustainable, humane and effective solutions to the opioid epidemic.


title: Health economics

text: The scope of health economics is neatly encapsulated by Alan Williams' "plumbing diagram" dividing the discipline into eight distinct topics:


title: Health economics

text: In the third century BC, Aristotle, an ancient Greek thinker, once talked about the relationship between farmers and doctors in production and exchange. In the 17th century, William Petty, a British classical economist, pointed out that the medical and health expenses spent on workers would bring economic benefits.


title: Health economics

text: Nowadays, modern health economics has developed into a leading interdisciplinary science, which bridges the gap between economic theory and health care practice, and the wide diversification in various sub-disciplines and research fields has been clearly visible. Few would argue that the actual cradle of this knowledge was the academic tradition of the U.S.


title: Health economics

text: The American Medical Association (AMA) was created in 1848, having as main goals scientific advancement, creation of standards for medical education, launching a program of medical ethics, and obtaining improved public health. Yet, it was only in 1931 that economic concerns came to the agenda, with the creation of the AMA Bureau of Medical Economics, established to study all economic matters affecting the medical profession.


title: Health economics

text: After the Second World War, amid the rapid improvement of the level of medical research technology, the modernization of diagnosis and treatment means and health facilities and equipment, the aging of the population, the sharp increase of chronic diseases, and the improvement of people's demand for health care and other reasons, medical and health expenses increased significantly. For example, total U.S. health expenditures steadily increased as a share of gross domestic product (GDP), demonstrating the increased importance that society placed on health care relative to other non-health goods and services. Between 1960 and 2013, health spending as a share of GDP increased from 5.0 to 17.4 percent. Over the same period, the average annual growth in nominal national health expenditures was 9.2 percent compared to nominal GDP


title: Health economics

text: At the same time, the expenditure on health care in many European countries also increased, accounting for about 4% of GDP in the 1950s and 8% by the end of the 1970s. In terms of growth rate, the proportion of health care expenditure in GNP (gross national product) in many countries increased by 1% in the 1950s, 1.5% in the 1960s, and 2% in the 1970s. This high medical and health expenditure was a heavy economic burden on government, business owners, workers, and families, which required a way to restrain its growth.


title: Health economics

text: In addition, the scale of health service increased, technical equipment became more advanced, and division of labor and specialization saw increases, too. The medical and health service developed into a "healthcare industry" which occupies a considerable amount of capital and labor and occupies an important position in social and economic life. The research on economic problems of the health sector became an important topic of economic research.


title: Health economics

text: Selma Muskin published "Towards the definition of health economics" in 1958 and, four years the, "Health as an Investment." At that time, health was broadly regarded as rather a consumptive branch of the economy. Muhkin's analysis was the first understanding that health investment had long-term beneficial consequences for the community. Probably, the single most famous and cited contribution to the discipline was Kenneth Arrow's "Uncertainty and the welfare economics of medical care," published in 1963.


title: Health economics

text: After the 1960s, research in health economics developed further, and a second academic seminar on health economics was held in the United States in 1962 followed by a third in 1968. In 1968, the World Health Organization held its first international health economics seminar in Moscow. The convening of the three meetings showed that health economics had boarded an academic forum as an independent discipline, which also marked the official formation of health economics.


title: Health economics

text: After the 1970s, the health economy entered a period of rapid development and nursing economics gradually emerged. In 1979, Paul Feldstein, a famous American health economist, first used the principles of economics to discuss the long-term care market, registered market, and other nursing economy issues, laying the foundation for the emergence of nursing economics.


title: Health economics

text: In 1983, Nursing Economic Magazine was founded in the United States, and its main research content included nursing market development, nursing cost accounting, policies related to nursing services, nursing economic management, etc. The magazine's publication was a mark of the formal formation of nursing economics. In 1993, The University of Iowa Cost Research Center conducted a systematic nursing cost study, simply the NIC System. The specific practice consisted of establishing a special research institution equipped with full-time researchers, sorting out the nursing cost accounting content, and, finally, identifying 433 items in 6 categories. At the same time, the Center adopted computer technology to carry out nursing cost management, including cost assessment, reasonable budget, decision making, etc., which played a crucial role in improving the efficiency of nursing management and alleviating the nursing management crisis.


title: Health economics

text: The demand for healthcare is a derived demand from the demand for health. Healthcare is demanded as a means for consumers to achieve a larger stock of "health capital." The demand for health is unlike most other goods because individuals allocate resources in order to both consume and produce health.


title: Health economics

text: The above description gives three roles of persons in health economics. The World Health Report (p. 52) states that people take four roles in the healthcare:


title: Health economics

text: Michael Grossman's 1972 model of health production has been extremely influential in this field of study and has several unique elements that make it notable. Grossman's model views each individual as both a producer and a consumer of health. Health is treated as a stock which degrades over time in the absence of "investments" in health, so that health is viewed as a sort of capital. The model acknowledges that health is both a consumption good that yields direct satisfaction and utility, and an investment good, which yields satisfaction to consumers indirectly through fewer sick days. Investment in health is costly as consumers must trade off time and resources devoted to health, such as exercising at a local gym, against other goals. These factors are used to determine the optimal level of health that an individual will demand. The model makes predictions over the effects of changes in prices of healthcare and other goods, labour market outcomes such as employment and wages, and technological changes. These predictions and other predictions from models extending Grossman's 1972 paper form the basis of much of the econometric research conducted by health economists.


title: Health economics

text: In Grossman's model, the optimal level of investment in health occurs where the marginal cost of health capital is equal to the marginal benefit. With the passing of time, health depreciates at some rate formula_1. The interest rate faced by the consumer is denoted by formula_2. The marginal cost of health capital can be found by adding these variables: formula_3. The marginal benefit of health capital is the rate of return from this capital in both market and non-market sectors. In this model, the optimal health stock can be impacted by factors like age, wages and education. As an example, formula_4 increases with age, so it becomes more and more costly to attain the same level of health capital or health stock as one ages. Age also decreases the marginal benefit of health stock. The optimal health stock will therefore decrease as one ages.


title: Health economics

text: Beyond issues of the fundamental, "real" demand for medical care derived from the desire to have good health (and thus influenced by the production function for health) is the important distinction between the "marginal benefit" of medical care (which is always associated with this "real demand" curve based on derived demand), and a separate "effective demand" curve, which summarizes the amount of medical care demanded at particular market prices. Because most medical care is not purchased from providers directly, but is rather obtained at subsidized prices due to insurance, the out-of-pocket prices faced by consumers are typically much lower than the market price. The consumer sets formula_5 out of pocket, and so the "effective demand" will have a separate relationship between price and quantity than will the "marginal benefit curve" or real demand relationship. This distinction is often described under the rubric of "ex-post moral hazard" (which is again distinct from ex-ante moral hazard, which is found in any type of market with insurance).


title: Health economics

text: Economic evaluation, and in particular cost-effectiveness analysis, has become a fundamental part of technology appraisal processes for agencies in a number of countries. The Institute for Quality and Economy in Health Services (Institut für Qualität und Wirtschaftlichkeit im Gesundheitswesen – IQWiG) in Germany and the National Institute for Health and Care Excellence (NICE) in the United Kingdom, for example, both consider the cost-effectiveness of new pharmaceuticals entering the market.


title: Health economics

text: Some agencies, including NICE, recommend the use of cost–utility analysis (CUA). This approach measures outcomes in a composite metric of both length and quality of life, the Quality-adjusted life year (QALY).


title: Health economics

text: Although assumptions of textbook models of economic markets apply reasonably well to healthcare markets, there are important deviations. Many states have created risk pools in which relatively healthy enrollees subsidise the care of the rest. Insurers must cope with adverse selection which occurs when they are unable to fully predict the medical expenses of enrollees; adverse selection can destroy the risk pool. Features of insurance market risk pools, such as group purchases, preferential selection ("cherry-picking"), and preexisting condition exclusions are meant to cope with adverse selection.


title: Health economics

text: Insured patients are naturally less concerned about healthcare costs than they would if they paid the full price of care. The resulting moral hazard drives up costs, as shown by the famous RAND Health Insurance Experiment. Insurers use several techniques to limit the costs of moral hazard, including imposing copayments on patients and limiting physician incentives to provide costly care. Insurers often compete by their choice of service offerings, cost-sharing requirements, and limitations on physicians.


title: Health economics

text: Consumers in healthcare markets often lack adequate information about what services they need to buy and which providers offer the best value proposition. Health economists have documented a problem with supplier induced demand, whereby providers base treatment recommendations on economic, rather than medical criteria. Researchers have also documented substantial "practice variations", whereby the treatment also on service availability to rein in inducement and practice variations.


title: Health economics

text: Some economists argue that requiring doctors to have a medical license constrains inputs, inhibits innovation, and increases cost to consumers while largely only benefiting the doctors themselves.


title: Health economics

text: Folland, Godman, and Stino the authors of the book, The Economics of Health and Health Care lists several separate and independent reasons for governments intervening in health-care systems rather than leaving it to the private market forces.


title: Health economics

text: 1. The first is to ensure that the optimum level of production and consumption of public goods (hospitals, vaccines) and goods with a partially public character are available.


title: Health economics

text: 2. Secondly, the rationale is to increase the quality and equity of insurance for those services that can be produced in the private sector but require risk-sharing due to the expense and uncertainties about needs. For example; investing in research and development for new cures and health care equipment. Governments usually subsidize for those who cannot afford insurance or, in certain situations, those low-cost activities and facilities that non-poor citizens can afford on their own. For example; the largest health insurance scheme in the world was launched in India by the name Ayushman Bharat in 2018.


title: Health economics

text: 3. The third reason for which the government might want to intervene is to prevent market failure. A classic example of market failure is Monopoly Power. Several health-care markets tend to have the potential for monopoly control to be exercised. Medical care in markets with few hospitals, patent-protected prescription products, and some health insurance markets is the major reason for higher costs and especially in cases where the providers are private companies.


title: Health economics

text: 4. Knowledge can be perceived as a public good with a strong economic value. The information provided by one user does not restrict the information available to another. While those who do not pay are often denied access to information and the marginal cost of providing information to another person is frequently low. As a result, one might argue that private markets would under-produce knowledge, necessitating government intervention to increase its availability. Government intervention, in this case, can be seen as assisting in the public distribution of established information, either directly or by subsidizing private sector operations.


title: Health economics

text: 5. The last point in this section is related to incomplete markets. Incomplete markets may arise when private markets struggle to satisfy existing demand. This situation can arise when the cure of disease is very expensive, such as cancer or a wide spread of new diseases such as HIV/AIDS or Covid-19. In such cases either private insurers require a high premium as the risk factor and costs are high or they may not insure the people for a particular case. This leads to a void in the market where a certain section of the population will not be able to afford healthcare. Certain insurance markets, such as those for patients with HIV/AIDS, cancer, or other pre-existing conditions who are searching for new coverage, may be incomplete in the sense that those patients may be unable to afford coverage at any price. In such cases, the government usually intervenes and provides health care for such cases. For example, during the Covid-19 pandemic, no private insurance company predicted (or could have predicted) that such an outbreak would occur; as a result, state intervention became necessary to treat people.


title: Health economics

text: Often used synonymously with health economics, "medical economics", according to Culyer, is the branch of economics concerned with the application of economic theory to phenomena and problems associated typically with the second and third health market outlined above: physician and institutional service providers. Typically, however, it pertains to cost–benefit analysis of pharmaceutical products and cost-effectiveness of various medical treatments. Medical economics often uses mathematical models to synthesise data from biostatistics and epidemiology for support of medical decision-making, both for individuals and for wider health policy.


title: Health economics

text: Mental health economics incorporates a vast array of subject matters, ranging from pharmacoeconomics to labor economics and welfare economics. Mental health can be directly related to economics by the potential of affected individuals to contribute as human capital. In 2009 Currie and Stabile published "Mental Health in Childhood and Human Capital" in which they assessed how common childhood mental health problems may alter the human capital accumulation of affected children. Externalities may include the influence that affected individuals have on surrounding human capital, such as at the workplace or in the home. In turn, the economy also affects the individual, particularly in light of globalization. For example, studies in India, where there is an increasingly high occurrence of western outsourcing, have demonstrated a growing hybrid identity in young professionals who face very different sociocultural expectations at the workplace and in at home.


title: Health economics

text: Mental health economics presents a unique set of challenges to researchers. Individuals with cognitive disabilities may not be able to communicate preferences. These factors represent challenges in terms of placing value on the mental health status of an individual, especially in relation to the individual's potential as human capital. Further, employment statistics are often used in mental health economic studies as a means of evaluating individual productivity; however, these statistics do not capture "presenteeism", when an individual is at work with a lowered productivity level, quantify the loss of non-paid working time, or capture externalities such as having an affected family member. Also, considering the variation in global wage rates or in societal values, statistics used may be contextually, geographically confined, and study results may not be internationally applicable.


title: Health economics

text: Though studies have demonstrated mental healthcare to reduce overall healthcare costs, demonstrate efficacy, and reduce employee absenteeism while improving employee functioning, the availability of comprehensive mental health services is in decline. Petrasek and Rapin (2002) cite the three main reasons for this decline as (1) stigma and privacy concerns, (2) the difficulty of quantifying medical savings and (3) physician incentive to medicate without specialist referral. Evers et al. (2009) have suggested that improvements could be made by promoting more active dissemination of mental health economic analysis, building partnerships through policy-makers and researchers, and employing greater use of knowledge brokers.


title: Health economics

text: Generally, economists assume that individuals act rationally with the aim of maximizing their lifetime utility, while all are subject to the fact that they cannot buy more than their resources allow. However, this model gets complex as there exists the uncertainty over individuals' lifetime. As such, we should split the issue into two parts: 1. How does health produce utility and 2. What affects health (e.g., medical care and life-style choices).


title: Health economics

text: Probably the most fundamental thing in consumer demand theory is that the good increases an individual's utility. Health is not really a good in the traditional sense, but health in itself produces happiness. We can think of health as a durable good, much like for instance a car, a house or an education. We all come into the world with some inherent "stock" of health, and a healthy baby has a fairly high stock of health. Basically, every decision we take during our lifetime will affect our stock of health.


title: Health economics

text: Consider X as a bundle of other goods, and H as a stock of health. With this in mind we can get the formula for an individual's utility as: "Utility = U(X, H)." For simplicity, continue to think the stock of health produces utility, but technically, it is the flow of services created by the stock of health that produces utility. As the traditional fashion for goods, "more is better", in other words an increase in health leads to an increase in utility. With this in mind it seems logical that X grows with health, for instance it is more enjoyable to visit the zoo when not experiencing a headache.


title: Health economics

text: Like other durable goods, the stock of health wears out over time, much like other durable goods. This process can be called aging. When our stock of health has dropped low enough, we will lose our ability to function. We can say, in economic terminology that the stock of health depreciates. Since life expectancy has risen a lot during this century, it implies that e.g., the depreciation rate has decreased during this time. Public-health care efforts and individual medical care are in place to restore the stock of health or to decrease the depreciation rate on the stock of health. If we were to plot an individual's stock of health throughout its lifetime in a graph, it would steadily increase in the beginning during its childhood, and after that gradually decline because of aging, meanwhile sudden drops created by random events, such as injury or illness.


title: Health economics

text: There are many other things than "random" health care events, which individuals consume or do during their lives that affect the speed of aging and the severity and frequency of the drops. Lifestyle choices can deeply better or worse our health. If we go back to X, the bundle of goods and services, can undertake numerous characteristics, some add value while others noticeably decrease our stock of health. Outstanding among such lifestyle choices are the decision to consume alcohol, smoke tobacco, use drugs, composition of diet, amount of exercise and so on. Not only can X and H work as substitutes for one another in producing utility, but X can also affect H in a production sense as well. X can then be split into different categories depending on which effect it has on H, for instance "good" types (e.g., moderate exercise), "bad" types (e.g., food with high cholesterol) and "neutral" types (e.g., concerts and books). Neutral goods do not have an apparent effect on individuals' health.


title: Iruttu Araiyil Murattu Kuththu

text: Iruttu Araiyil Murattu Kuthu () is a 2018 Indian Tamil-language adult horror comedy film written and directed by Santhosh P. Jayakumar and produced by K. E. Gnanavel Raja. The film stars Gautham Karthik and VJ Sha Ra, with Yashika Anand, Chandrika Ravi, and Vaibhavi Shandilya are in the female leads. The music was composed by Balamurali Balu with cinematography by Ballu and editing by Prasanna GK. The film was released on 4 May 2018.


title: Iruttu Araiyil Murattu Kuththu

text: The film was later remade in Telugu as "Chikati Gadilo Chithakotudu" by Jayakumar himself, while a spiritual sequel "Irandam Kuththu" was released in November 2020.


title: Iruttu Araiyil Murattu Kuththu

text: Veera is a playboy who is rejected by every potential bride because of that reason. Thendral accepts his marriage proposal with one condition. She demands that he impress her and asks him to take her on a trip in order to know each other better. She also suggests him to bring along another couple. Veera informs his friend Vasu, who tells him that he has a girlfriend named Kavya, who is Veera's ex-girlfriend. When Kavya learns about Vasu's friendship with Veera, she vows to get her hands on him during the trip. The couple then travels to Thailand and rents a bungalow. Their host asks them not to go into a particular room in that bungalow.


title: Iruttu Araiyil Murattu Kuththu

text: One day, Veera and Vasu consume Viagra by accident, and when their girlfriends arrive earlier than expected, they run into the closed room to hide their arousal. There, they find a portrait of an under-dressed woman and masturbate, thereby arousing a ghost. The ghost begins to haunt them. She reveals that she died in an accident as a virgin and will have sex with a virgin to rest her soul. Since both of them are virgins, they are unable to leave the house. The ghost tries several attempts to have sex with Vasu and Veera but fails. They make fun of the ghost, but all their plans go in vain as she takes the form of a beautiful woman.


title: Iruttu Araiyil Murattu Kuththu

text: Since Veera and Vasu's wives know that the ghost is present, they call Jack and Rose, two conmen disguised as Father and nun, respectively. When Jack and Rose encounter the ghost, they too are trapped because they are virgins. For pacifying the ghost, they hire a cook named Babyshri. There, Babyshri falls in love with Jack. From somewhere, another virgin man named Girish Kalyan comes and gets trapped in the house. To execute the plan, they come up with a plan to have a party in which they invite boys and girls, hoping that one of them should be a virgin, but no one is. Veera thinks that his playboy nature is responsible for all this fiasco and decides to have sex with the ghost. Veera almost seduces the ghost, but in the process puts a fire boundary around the ghost on the advice of a Buddhist priest named Swamy. While Swamy controls the ghost, all the others (Veera-Thendral, Vasu-Kavya, Jack-Babyshri & Rose-Swamy's assistant) have sex and lose their virginities, which, in turn, results in the ghost getting killed. While taming the ghost, it is revealed that Swamy and Girish are homosexual men.


title: Iruttu Araiyil Murattu Kuththu

text: Following the success of the adult comedy "Hara Hara Mahadevaki" (2017), K. E. Gnanavel Raja chose to associate with director Santhosh P. Jayakumar and actor Gautham Karthik for another film in the same genre. Titled "Iruttu Araiyil Murattu Kuththu", Santhosh stated it would be one of the first "adult horror comedy" films shot in the Tamil film industry. Production was briefly delayed due to the FEFSI strike in September 2017, but it duly began later that month. The makers initially attempted to cast Oviya in a lead role, following her rise to fame through the reality show "Bigg Boss" (2017), but she turned down the offer. Vaibhavi Shandilya was subsequently cast as the lead actress and began shooting for the film in Chennai for a five-day schedule. The team later moved to Thailand to shoot the rest of the film. Actresses Rashmi Gautham and Chandrika Ravi joined the team during the Thailand schedule, with Rashmi later replaced by Yaashika Aanand.


title: Iruttu Araiyil Murattu Kuththu

text: The soundtrack was composed by Balamurali Balu in his second collaboration with actor Gautham Karthik and director Santhosh P. Jayakumar.


title: Iruttu Araiyil Murattu Kuththu

text: Iruttu Araiyil Murattu Kuththu received mixed reviews and become commercial successful venture. Tamil Nadu theatrical rights of the film were sold for 5.25 crore.


title: Dance of the Seven Veils

text: The Dance of the Seven Veils is Salome's dance performed before King Herod Antipas, in modern stage, literature and visual arts. It is an elaboration on the New Testament story of the Feast of Herod and the execution of John the Baptist, which refers to Salome dancing before the king, but does not give the dance a name.


title: Dance of the Seven Veils

text: The name "Dance of the Seven Veils" originates with the 1893 English translation of Oscar Wilde's 1891 French play "Salome" in the stage direction "Salome dances the dance of the seven veils". The dance was also incorporated into Richard Strauss's 1905 opera "Salome".


title: Dance of the Seven Veils

text: According to ten verses of Matthew 14, John was imprisoned for criticizing King Herod Antipas's marriage to Herodias, the former wife of Antipas's half-brother Herod II. Herod offered his niece a reward of her choice for performing a dance for his guests on his birthday. Herodias persuaded her daughter to ask for John the Baptist's head on a platter. Against his better judgment, Herod reluctantly acceded to her request.


title: Dance of the Seven Veils

text: The Romano-Jewish historian Josephus lists Antipas's stepdaughter's name as Salome, but makes no mention of a dance nor makes any connection between Salome and John the Baptist.


title: Dance of the Seven Veils

text: The idea that Salome's dance involves "seven veils" originates with Wilde's 1891 play "Salomé". Wilde was influenced by earlier French writers who had transformed the image of Salome into an incarnation of female lust. Rachel Shteir writes that,


title: Dance of the Seven Veils

text: Wilde was especially influenced by Gustave Flaubert's story "Herodias" in which Salome dances on her hands to please Antipas. The type of dance was common among "gypsy" acrobats in the 19th century. Wilde at first intended to follow Flaubert's version, but changed his mind. Shireen Malik says he may have been influenced by the 1870 poem "The Daughter of Herodias" by Arthur O'Shaughnessy which describes Salome dancing:


title: Dance of the Seven Veils

text: Wilde transforms the dance from a public performance for his guests, as in the Bible, to a personal dance for the king himself. He gives no description of the dance beyond the name, but the idea of a series of veils has been connected to a process of unveiling. As Malik says, "although Wilde does not describe Salome's dance or suggest that she remove any veils, her dance is invariably assumed to be one of unveiling, thus revealing herself." Wilde's play has even been proposed as the origin of striptease. Toni Bentley writes "Wilde's bracketed brevity allowed for a world of interpretation. Can the invention of striptease be traced to a single innocuous stage direction in a censored play that could barely find a theater or audience? Can Oscar Wilde be considered the unlikely father of modern striptease?"


title: Dance of the Seven Veils

text: In one of Aubrey Beardsley's illustrations to the play, he depicts what he calls a "stomach dance" (i.e., a belly dance), in which Salome is depicted with exposed breasts and undulating belly, wearing transparent pantaloons. Wilde wrote a note in appreciation of Beardsley's design, saying: "For Aubrey: for the only artist who, besides myself, knows what the dance of the seven veils is, and can see that invisible dance." The concept of "belly dancing" had become widely known in 1893, the year before Beardsley created his designs, when it was featured at the World's Fair in Chicago that year.


title: Dance of the Seven Veils

text: Bentley notes that the Mesopotamian goddess Inanna "performed the first documented striptease" when she descended into the "Kur" (underworld), ruled by her sister Ereshkigal, in search of her faithless lover Dumuzid. Inanna had to divest herself of the mysterious "seven "mé" " (conjecturally, her various jewels and robes) in her descent through seven successive gates leading ever deeper into the underworld until at last she stood naked in the 'land of no return.' Oscar Wilde assigned this symbolic descent to the underworld of the unconscious, a ceremony that equates stripping naked to being in a state of truth, the ultimate unveiling, to Salome." Writing from a Jungian perspective, Perera has demonstrated the same for the far older Sumerian myth of the descent of Inanna.


title: Dance of the Seven Veils

text: Wilde's concept of "seven veils" is believed to be derived from the popularity of what were known as "veil dances" at the time. These were westernised versions of imagined Middle Eastern styles of dance. The dancer Loïe Fuller was especially associated with such dances. In 1886, Fuller appeared at New York's Standard Theater in a show called "The Arabian Nights". According to Rhonda Garelick, this "featured fourteen different Oriental dance numbers, including the 'Veil of Vapor' dance, done with clouds of steam instead of fabric veils."


title: Dance of the Seven Veils

text: The Hebrew word chuwl, meaning to twist or whirl (in a circular or spiral manner), is used in Judges 21:21-23, Judges 11.34, and I Samuel 18.6-7. In these instances it refers to a type of erotic dance done during biblical ceremonies, and performed by women. Most notably, in Canaan before 900 BC, a small piece of cloth worn around the hips (ḥagor), would have been all that was worn.


title: Dance of the Seven Veils

text: Strauss's operatic adaptation of the play also features the Dance of the Seven Veils. The dance remains unnamed except in the acting notes, but Salome's sexual fascination with John seems to motivate the request—though Herod is portrayed as pleased. The music for the dance comes from near the climax of the opera. The visual content of that scene (about seven minutes long with standard tempi) has varied greatly depending on the aesthetic notions of the stage director, choreographer, and soprano, and on the choreographic skills and body shape of that singer. Strauss himself stipulated that the dance should be "thoroughly decent, as if it were being done on a prayer mat." Nevertheless, many productions made the dance explicitly erotic. In a 1907 production in New York the dancer "spared the audience nothing in active and suggestive detail", to such an extent that some ladies in the audience "covered their eyes with their programs."


title: Dance of the Seven Veils

text: Ernst Krause argues that Strauss's version of the dance "established the modern musical formula for the portrayal of ecstatic sensual desire and brought it to perfection." In Derek B Scott's view, "The eroticism of the 'Dance of the Seven Veils' is encoded in the sensual richness (timbral and textual) of a huge orchestra, the quasi-Oriental embellishment of melody (intimations of 'exotic' sensuality), and the devices of crescendo and quickening pace (suggestive of growing excitement)."


title: Dance of the Seven Veils

text: The Wilde play and the Strauss opera led to the phenomenon of "Salomania", in which various performers put on acts inspired by Salome's erotic dance. Several of these were criticised for being salacious and close to stripping, leading to "insistent vogue for women doing glamorous and exotic 'oriental' dances in striptease". In 1906 Maude Allan's production "Vision of Salomé" opened in Vienna. Based loosely on Wilde's play, her version of the Dance of the Seven Veils became famous (and to some notorious) and she was billed as "The Salomé Dancer". Her version was praised for the "eastern spirit" of her dancing without the "vulgarities familiar to the tourists in Cairo or Tangier". The dance first appeared in film in 1908 in a Vitagraph production entitled "Salome, or the Dance of the Seven Veils".


title: Dance of the Seven Veils

text: In the 1953 film "Salome", Rita Hayworth performs the dance as a strip dance. She stops the dance before removing her last veil when she sees John's head being delivered on a platter, as she did not want him to be killed in this version of the story.


title: Dance of the Seven Veils

text: In the 1961 film "King of Kings", Salomé, portrayed by Brigid Bazlen, performs a similar dance; her voluptuous seduction of a drunken lascivious Herod Antipas remains highly praised and is now widely regarded as Bazlen's best performance.


title: Dance of the Seven Veils

text: Salome and the dance are recurring thematic and plot elements in Tom Robbins's 1990 novel "Skinny Legs and All".


title: Coleman Hughes

text: Coleman Cruz Hughes (born February 25, 1996) is an American writer and podcast host. He was a fellow at the Manhattan Institute for Policy Research and a fellow and contributing editor at their "City Journal", and is the host of the podcast "Conversations with Coleman".


title: Coleman Hughes

text: Hughes is of African American and Puerto Rican descent, and grew up in Montclair, New Jersey. He is a graduate of Newark Academy and was selected as a United States Presidential Scholar in 2014. He graduated from Columbia University in 2020 with a B.A. in philosophy.


title: Coleman Hughes

text: On June 19, 2019, Hughes testified before a U.S. House Judiciary subcommittee at a hearing on reparations for slavery, arguing against the campaign. He argued that "[i]f we were to pay reparations today, we would only divide the country further, making it harder to build the political coalitions required to solve the problems facing black people today." In this vein, he highlighted mass incarceration and high homicide victimization rates as problems affecting black Americans today. He suggested an alternate proposal of paying reparations to black Americans who personally grew up under Jim Crow. Hughes went on to say that reparations to the descendants of slaves would insult many black Americans and claimed they would make him and the "one-third of black Americans who poll against reparations into victims without their consent."


title: Coleman Hughes

text: In addition to writing for "Quillette", Hughes has contributed to publications including "The Spectator", "The New York Times", "The Wall Street Journal", "National Review", the "Washington Examiner", and the Heterodox Academy blog. In May 2020, he became a fellow of the Manhattan Institute for Policy Research and contributing editor of their "City Journal". Hughes is listed as a scholar for the 1776 Unites project. In February 2020, Hughes debated Julianne Malveaux on iHeartRadio's Munk Debates regarding the topic of slavery reparations.


title: Coleman Hughes

text: Hughes says he formerly accepted the premise of Black Lives Matter—that, in his words, "racist cops are killing unarmed black people"—but now believes that the existence of racial bias in deadly shootings does not survive scrutiny once factors other than race are taken into account. He has cited research from Roland G. Fryer Jr. and Sendhil Mullainathan, among others, in support of his stance.


title: Coleman Hughes

text: Writing in "The Washington Post" in 2018, Megan McArdle called Hughes "an undergraduate at Columbia University but already a thinker to be reckoned with." Nick Gillespie wrote in "Reason" in 2019 that Hughes had "emerged over the past year as one of the most prolific and insightful commentators on race and class in the United States." In 2020, Christopher Bollen wrote in "Interview" that Hughes "has become one of the most compelling and promising voices on the political landscape." In September 2020, Stéphanie Chayet, writing in the French newspaper "Le Monde", identified Hughes as one of four "anti-conformists of anti-racism" along with Glenn Loury, Thomas Chatterton Williams and John McWhorter. In December 2020, Hughes was listed on the "Forbes" 30-under-30 list for 2021 in the Media category.


title: Coleman Hughes

text: Hughes began studying violin at age three. He is a hobbyist rapper—in 2021 and 2022, he released several rap singles on YouTube and Spotify, using the moniker COLDXMAN, including a music video for a track titled "Blasphemy", which appeared in January 2022. Hughes also plays jazz trombone with a Charles Mingus tribute band that plays regularly at the Jazz Standard in New York City.


title: Camp Half-Blood Chronicles

text: Camp Half-Blood Chronicles is a media franchise created by author Rick Riordan, encompassing three five-part novel series, two short-story collections, two myth anthology books, a stand-alone short story, three crossover short stories, an essay collection, multiple guides, seven graphic novels, two films, a video game, a musical, and other media. Set in the modern world, it focuses on groups of demigod teenagers, and features many characters from Greek and Roman mythology. The first series, "Percy Jackson & the Olympians", follows the adventures of a teen named Percy Jackson at a summer camp for Greek demigods. The second series, "The Heroes of Olympus", introduces several more lead characters and a second camp for Roman demigods named Camp Jupiter. The third series, "The Trials of Apollo", follows the now-mortal god Apollo, with appearances by many characters from the first and second series.


title: Camp Half-Blood Chronicles

text: The franchise takes place in the same fictional universe as two of Riordan's other series, "The Kane Chronicles" (which centers on Egyptian mythology) and "Magnus Chase and the Gods of Asgard" (set in the world of Norse mythology). Three short stories have been published which join "The Kane Chronicles" and the "Camp Half-Blood Chronicles"; "Camp Half-Blood" characters have also appeared in both the "Magnus" and "Kane" books.


title: Camp Half-Blood Chronicles

text: "Percy Jackson & the Olympians" is a pentalogy of adventure and fiction books written by Rick Riordan. Set in the United States, the books are predominantly based on Greek mythology and deal with a demigod, Percy Jackson, and his quest to stop the rise of the Titan lord Kronos from rising from Tartarus. All five books are seen from Percy's witty and sardonic point of view. The series tackles themes like coming of age, love and teenage angst. More than 69 million copies of the books have been sold in more than 35 countries.


title: Camp Half-Blood Chronicles

text: As of July 19, 2020, the series has been on "the New York Times" best seller list for children's book series for 538 weeks.


title: Camp Half-Blood Chronicles

text: "The Lightning Thief" is the first book in the "Percy Jackson and the Olympians" series. It introduces Percy Jackson, Annabeth Chase, and Grover Underwood, and follows their quest to recover Zeus' stolen master bolt, which was thought to be stolen by Hades. It was released on July 1, 2005.


title: Camp Half-Blood Chronicles

text: "The Sea of Monsters" is the second book in the "Percy Jackson and the Olympians" series. In this book, Percy, Annabeth, and Tyson, Percy's cyclops brother, need to go to the Bermuda Triangle, also known as the Sea of Monsters, in order to find the Golden Fleece to save their camp and to rescue their satyr friend Grover from the cyclops Polyphemus. It was released April 1, 2006.


title: Camp Half-Blood Chronicles

text: "The Titan's Curse" is the third book in the "Percy Jackson and the Olympians" series. The book features Percy, Grover, Thalia Grace, Zoë Nightshade, and Bianca di Angelo traveling to San Francisco in order to rescue the goddess Artemis and Annabeth. It was released on May 11, 2007.


title: Camp Half-Blood Chronicles

text: "The Battle of the Labyrinth" is the fourth book in the "Percy Jackson and the Olympians" series. In the book, Percy, Annabeth, Grover, Tyson, Nico di Angelo, and Rachel Elizabeth Dare are tasked with finding Daedalus in the Labyrinth so he can help them keep their camp safe against the Titan army. In this book, Percy also meets Calypso. The book was released on May 6, 2008.


title: Camp Half-Blood Chronicles

text: "The Last Olympian" is the fifth and final book in the "Percy Jackson and the Olympians" series. In the book, all the demigods from Camp Half-Blood help defend Manhattan, in particular the Empire State Building a.k.a. Mount Olympus against Kronos and his army while the gods fight Typhon. The book was released on May 5, 2009.


title: Camp Half-Blood Chronicles

text: "The Heroes of Olympus" is a pentalogy of books written by Riordan. It chronicles the events of seven demigods and their obstacles involving the waking of the earth goddess, Gaea, and their efforts to stop her. It picks up a year after the end of the "Percy Jackson & the Olympians" series. Themes include love and teenage angst, as well as dealing with homosexuality.


title: Camp Half-Blood Chronicles

text: Riordan based some of his series on "The Golden Fleece and the Heroes Who Lived Before Achilles" by Padraic Colum.


title: Camp Half-Blood Chronicles

text: "The Lost Hero" is the first book in "The Heroes of Olympus" series. It features three new heroes, Roman demigod Jason Grace, as well as Greek demigods Piper McLean and Leo Valdez travelling to California in order to rescue Hera from being consumed by the giants and to defeat the king of giants, Porphyrion. It was released on October 12, 2010.


title: Camp Half-Blood Chronicles

text: "The Son of Neptune" is the second book in "The Heroes of Olympus" series. The book features Percy Jackson and two new heroes, Roman demigods Hazel Levesque and Frank Zhang traveling to Alaska to free Thanatos, the God of Death, from the giant Alcyoneus. It was released on October 4, 2011.


title: Camp Half-Blood Chronicles

text: "The Mark of Athena" is the third book in "The Heroes of Olympus" series. The book features Percy Jackson, Annabeth Chase, Jason Grace, Piper McLean, Leo Valdez, Hazel Levesque, and Frank Zhang traveling to Greece to prevent Gaea's awakening while simultaneously also trying to uncover the gigantic long-lost statue of Athena, the Athena Parthenos, in Rome. It was released on October 2, 2012.


title: Camp Half-Blood Chronicles

text: "The House of Hades" is the fourth book in "The Heroes of Olympus" series. It features Jason Grace, Piper McLean, Leo Valdez, Hazel Levesque, Frank Zhang, and Nico di Angelo as they continue to set sail towards Greece with the rescue of Percy Jackson and Annabeth Chase, both of whom have fallen to Tartarus in the previous book's epilogue, in mind; the latter couple in turn also try to find their own way out of the hellish realm. The book also reintroduces Calypso. The book was released on October 8, 2013.


title: Camp Half-Blood Chronicles

text: "The Blood of Olympus" is the fifth and final book in "The Heroes of Olympus" series. It features two parallel stories: the first has the seven demigods finally reaching Greece and working to defeat the giants at the Acropolis of Athens, while the second has Reyna Ramírez-Arellano, Nico di Angelo, and Coach Gleeson Hedge delivering the Athena Parthenos back to Camp Half-Blood with the clash of the Greek and Roman camps in the horizon. The book was released on October 7, 2014.


title: Camp Half-Blood Chronicles

text: "The Trials of Apollo" is a pentalogy of books written by Riordan. It chronicles the life of Apollo after his being made mortal by Zeus as a punishment for his actions during "The Heroes of Olympus" series. The first book, "The Hidden Oracle," was featured on May 5, 2016. It also features most of the characters from "The Heroes of Olympus" and "Percy Jackson and the Olympians" series.


title: Camp Half-Blood Chronicles

text: "The Hidden Oracle" is the first book in "The Trials of Apollo" series. It was released on May 3, 2016. It features Apollo as a 16 year old mortal named Lester Papadopoulos and introduces a new demigod Meg McCaffrey as they travel to Camp Half-Blood and fight monsters sent by Emperor Nero in order to save the Oracle of Dodona. It also sees the return of Leo Valdez who was presumed to be dead and was resurrected in the last book of Heroes of Olympus, Blood of Olympus.


title: Camp Half-Blood Chronicles

text: "The Dark Prophecy" is the second book in "The Trials of Apollo" series. It was released on May 2, 2017. It features Apollo going on a journey with Leo Valdez and Calypso to find Oracle of Trophonius and preventing it from falling to the hand of Emperor Commodus.


title: Camp Half-Blood Chronicles

text: "The Burning Maze" is the third book in "The Trials of Apollo" series. It was released on May 1, 2018. It features Apollo, Meg, Grover, Piper McLean, and Jason Grace as they go to free the Oracle of Erythraea who has been imprisoned by Emperor Caligula. They also stop Caligula’s plan to make himself the sun god with Apollo’s and Helios’s essence.


title: Camp Half-Blood Chronicles

text: "The Tyrant's Tomb" is the fourth book in "The Trials of Apollo" series. It was released on September 24, 2019. It features Apollo, Meg, Hazel Levesque, Reyna Ramirez-Arellano, and new hero Lavinia Asimov as they race to free the god Harpocrates and save Camp Jupiter from King Tarquin, Emperors Commodus and Caligula, and their respective armies. The goddess Diana, the Roman form of Apollo's twin sister, also made an appearance.


title: Camp Half-Blood Chronicles

text: "The Tower of Nero" is the fifth and final book in "The Trials of Apollo" series. It was released on October 6, 2020. It features Apollo, Meg, Rachel Elizabeth Dare, Nico di Angelo, and his boyfriend and Apollo's son Will Solace as they fight to prevent Emperor Nero from burning New York City. Apollo must also defeat his nemesis Python, who has been controlling Apollo's source of prophetic prowess in the caves of Delphi, and regain his immortality.


title: Camp Half-Blood Chronicles

text: On October 6, 2021, it was announced that Riordan would write a new book centered on Nico di Angelo and Will Solace, continuing story threads hinted in "The Tower of Nero". He will collaborate with writer Mark Oshiro. The book was announced to bear the title "The Sun and the Star" on September 23, 2022, with its release set for May 2, 2023.


title: Camp Half-Blood Chronicles

text: A standalone novel, "Percy Jackson and the Chalice of the Gods", was announced in October 2022, with a release date of September 26, 2023. The book covers events that take place between "The Heroes of Olympus" and "The Trials of Apollo". The novel will be written from Percy's point of view, much like in the "Percy Jackson & the Olympians" series.


title: Camp Half-Blood Chronicles

text: "The Demigod Files" is a collection published by Hyperion on February 10, 2009, written entirely by Riordan. It is a companion book to the first series, "Percy Jackson & the Olympians", and its main contents are four short stories: "Percy Jackson and the Stolen Chariot", "Percy Jackson and the Bronze Dragon", and "Percy Jackson and the Sword of Hades", and the first chapter of "The Last Olympian" (the fifth novel, published a few months later). Additional contents include interviews with some of the campers, a drawing of Annabeth's open camp trunk and a "Map of Camp Half-Blood" by Steve James, glossy color illustrations of eight characters by Antonio Caparo, and various crossword puzzles and other activities. The narrative setting is between the fourth and fifth novels.


title: Camp Half-Blood Chronicles

text: "The Demigod Diaries" is a collection published by Hyperion on August 14, 2012, written by Rick and his son Haley Riordan. It is a companion to the second series, "The Heroes of Olympus", nearly identical in structure to "The Demigod Files". The main contents are four stories: "The Diary of Luke Castellan", "Percy Jackson and the Staff of Hermes", "Leo Valdez and the Quest for Buford" and, by Haley Riordan, "Son of Magic". It contains puzzles, games, black-and-white drawings by Steve James, and glossy color illustrations of characters by Antonio Caparo.


title: Camp Half-Blood Chronicles

text: "Percy Jackson and the Singer of Apollo" is a short story appearing in the Guys Read anthology "Other Worlds". It features Percy Jackson and Grover Underwood in New York City trying to recover the gold Singer of Apollo.


title: Camp Half-Blood Chronicles

text: The "Camp Half-Blood/Kane Chronicles" crossovers are a series of short stories that feature two characters each, one from "Percy Jackson & the Olympians" and one from "The Kane Chronicles". They were published in a collection titled "Demigods and Magicians" on April 5, 2016.


title: Camp Half-Blood Chronicles

text: "The Son of Sobek" is a 2013 crossover novel between the "Percy Jackson" and the "Kane Chronicles" series. It features Percy Jackson and Carter Kane fighting a giant crocodile in Long Island. It was originally published in the paperback edition of "The Serpent's Shadow" and was later published as an e-short.


title: Camp Half-Blood Chronicles

text: "The Staff of Serapis" is a continuation of "The Son of Sobek", published in 2014. It features Annabeth Chase and Sadie Kane battling the god Serapis in Rockaway Beach in Queens. It was originally published in the paperback edition of "The Mark of Athena" and was later published as an e-short.


title: Camp Half-Blood Chronicles

text: "The Crown of Ptolemy", published in 2015, features all four characters that were in the first two stories. They need to stop the evil magician Setne from collecting the Upper and Lower Crowns of Egypt and becoming a god. The short was originally published in the paperback edition of "The House of Hades" along with the short story "Percy Jackson and the Sword of Hades". It was later published as an e-short.


title: Camp Half-Blood Chronicles

text: "Demigods of Olympus" is an interactive e-series in which the reader is the main character. The first three stories were published in Rick Riordan's application, "Demigods of Olympus" and the fourth was original to a collection of all four on July 14, 2015.


title: Camp Half-Blood Chronicles

text: This book is a retelling of several mythological stories about the Greek Gods as narrated by Percy Jackson. It was released on August 19, 2014.


title: Camp Half-Blood Chronicles

text: This book is a retelling of several mythological stories about various Greek heroes as narrated by Percy Jackson. It is the sequel to "Percy Jackson’s Greek Gods". It was released on August 18, 2015.


title: Camp Half-Blood Chronicles

text: "Demigods and Monsters: Your Favorite Authors on Rick Riordan's Percy Jackson and the Olympians Series" is a collection of essays "edited by Rick Riordan with Leah Wilson" and published by Borders Group in 2008; an expanded edition was published by BenBella Books in 2013. The second edition front cover promotes both an "original introduction by Rick Riordan" and "New Essays: Updated through "The Last Olympian"". Leah Wilson is editor-in-chief of the Smart Pop series in which both the paperback first edition (2009) and the second edition were issued by BenBella.


title: Camp Half-Blood Chronicles

text: "Percy Jackson and the Olympians: The Ultimate Guide" is a guide to the world of Percy Jackson written by Mary-Jane Knight, who is not credited on the front cover. It features illustrations of characters in the series by Antonio Caparo (as trading cards in pockets) and chapters about Percy Jackson, Camp Half-Blood, and places, gods, monsters, and items from mythology. It was released by Hyperion on January 18, 2010 (156 pp; 1-4231-2171-6) and termed Book 8 in the Percy Jackson series by Amazon or the publisher. The British edition was published by Puffin Books in March as "Percy Jackson: The Ultimate Guide".


title: Camp Half-Blood Chronicles

text: "Camp Half-Blood Confidential" is a companion guide to the "Trials of Apollo" book series. Released on August 15, 2017, the guide follows the campers of Camp Half-Blood as they rediscover the lost Camp Half-Blood orientation video, directed and produced by the god Apollo. The book features transcripts, interviews, and a short story about the video and the campers who are watching it.


title: Camp Half-Blood Chronicles

text: "Camp Jupiter Classified: A Probatio's Journal" is a companion book to the "Trials of Apollo" series. Released on May 5, 2020, the short story follows a "Probatio" at Camp Jupiter named Claudia as she deals with the daily duties of being a member of the Twelfth Legion of Rome. The book offers an insight at the lives of campers at Camp Jupiter and the havoc that the battle with Gaea left on the camp.


title: Camp Half-Blood Chronicles

text: "The Lightning Thief Graphic Novel" is an adaptation of "The Lightning Thief" into a graphic novel. It was adapted by Robert Venditti, illustrated by Attila Futaki, and colored by José Villarrubia, and was published on October 12, 2010.


title: Camp Half-Blood Chronicles

text: "The Sea of Monsters Graphic Novel" is the graphic novel version of "The Sea of Monsters." It was adapted by Robert Venditti, illustrated by Attila Futaki, and colored by Tamás Gáspár, and was published on July 2, 2013.


title: Camp Half-Blood Chronicles

text: "The Titan's Curse Graphic Novel" is the graphic novel of "The Titan's Curse". It was adapted by Robert Venditti, illustrated by Attila Futaki, and colored by Greg Guilhaumond, and was published on October 8, 2013.


title: Camp Half-Blood Chronicles

text: "The Lost Hero Graphic Novel" is the adaptation of "The Lost Hero" into a graphic novel. It was adapted by Robert Venditti, illustrated by Nate Powell, and colored by Orpheus Collar, and was published on October 7, 2014.


title: Camp Half-Blood Chronicles

text: "The Son of Neptune Graphic Novel" is the adaptation of "The Son of Neptune" into a graphic novel. It was adapted by Robert Venditti, illustrated by Antoine Dod, and colored by Orpheus Collar, and was published on February 21, 2017.


title: Camp Half-Blood Chronicles

text: "Percy Jackson & the Olympians: The Lightning Thief" (also known as "Percy Jackson & The Lightning Thief") is a 2010 fantasy film directed by Chris Columbus. The film is loosely based on "The Lightning Thief", the first novel in the "Percy Jackson & the Olympians" series by Rick Riordan. It stars Logan Lerman as Percy Jackson alongside an ensemble cast that includes Brandon T. Jackson, Alexandra Daddario, Jake Abel, Rosario Dawson, Steve Coogan, Uma Thurman, Catherine Keener, Kevin McKidd, Sean Bean and Pierce Brosnan. It was released to theaters on February 12, 2010. The film grossed $226,497,209 worldwide against a production budget of $95 million.


title: Camp Half-Blood Chronicles

text: "Percy Jackson: Sea of Monsters" (also known as "Percy Jackson & The Sea of Monsters") is a 2013 fantasy film and the sequel to the 2010 film "". It continues the adventures of Percy Jackson (Logan Lerman) and his friends, as they look for the golden fleece, in order to save Camp Half-Blood's magical borders from monsters. The film is based on the book "The Sea of Monsters", and was released on August 7, 2013.


title: Camp Half-Blood Chronicles

text: "The Lightning Thief" is a two-hour-long 2017 Off-Broadway musical adaptation of the first Percy Jackson novel by Theatreworks USA. The stage play was written by Joe Tracz, with lyrics and music by Rob Rokicki, and the performance was directed by Stephen Brackett. The production had a 2019 US tour, touring 31 US cities. Following the tour, "the Lighting Thief" had a limited 16-week Broadway run at the Longacre Theatre and closed on January 5th, 2020.


title: Camp Half-Blood Chronicles

text: 2018 Interactive theatre performance touring UK Theatres, Schools, and literacy festivals. Following permission from Rick Riordan and Puffin books, the show was designed by Pushforward to encourage a love of reading and English literature. The show features stars such as UK actor Paul Andrew Goldsmith as Hermes.


title: Camp Half-Blood Chronicles

text: The Percy Jackson video game was created by Activision for the Nintendo DS and was released on February 9, 2010. The game was based mostly on the and featured players that were neither in the book nor the movie.


title: Camp Half-Blood Chronicles

text: A streaming television adaptation is currently in production and is scheduled to be released on Disney+ in early 2024.


title: Adamstown, Pitcairn Islands

text: Adamstown is the capital of, and the only settlement on, the Pitcairn Islands, the only British Overseas Territory that is located in the Pacific Ocean.


title: Adamstown, Pitcairn Islands

text: Adamstown has a population of 40, which is the entire population of the Pitcairn Islands. All the other islands in the group are uninhabited. Adamstown is where most residents live, while they grow food in other areas of the island.


title: Adamstown, Pitcairn Islands

text: Adamstown is the second smallest capital in the world by population. It has access to television, satellite Internet, and a telephone; however, the main means of communication remains ham radio. The "Hill of Difficulty" connects the island's jetty to the town.


title: Adamstown, Pitcairn Islands

text: The history of the Pitcairn Islands begins with the settlement of the islands by Polynesians in the 11th century. The Polynesians established a culture that flourished for four centuries and then vanished. Pitcairn was settled again in 1790 by a group of British mutineers on HMS "Bounty" and Tahitians. Adamstown is named for the last surviving mutineer, John Adams.


title: Adamstown, Pitcairn Islands

text: The settlement is located on the central-north side of the island of Pitcairn, facing the Pacific Ocean and close to the Bounty Bay, the only seaport of the island.


title: Adamstown, Pitcairn Islands

text: Adamstown has a tropical rainforest climate ("Af") under the Köppen climate classification system. The hamlet features a wet, very warm climate averaging of rain a year. The wettest month is December and temperatures do not vary significantly throughout the year.


title: Glaceau Smartwater

text: Glaceau Smartwater (stylized as smartwater) is a brand of bottled water owned by Energy Brands, a subsidiary of The Coca-Cola Company. Introduced in 1996 in the United States, by 2016 it was one of the top five brands of bottled water in that country with sales worth nearly $830 million in 2017.


title: Glaceau Smartwater

text: The brand is also available in other countries including the United Kingdom, France, India, Australia, Argentina, Brazil, Chile, The United Arab Emirates, Croatia, Singapore, Serbia, Romania, Malaysia and Canada.


title: Glaceau Smartwater

text: Smartwater is manufactured by distillation. This process removes most inorganic impurities, such as naturally dissolved minerals, but may let low boiling-point organic matter through. Afterwards, certain mineral electrolytes such as potassium, calcium and magnesium are added back. There are no known benefits of distilling potable water combined with the readdition of ingredients lost in this process.


title: Glaceau Smartwater

text: Globally, the brand has several variants introduced in 2017, such as Glaceau Smartwater Sparkling Green Apple, Lemon, and Berry & Kiwi. In 2020, four new combination flavors were introduced: Cucumber Lime, Strawberry Blackberry, Pineapple Kiwi, and Watermelon Mint.


title: Glaceau Smartwater

text: Starting in 2008, American actress Jennifer Aniston was the ambassador for the brand globally and was involved in a number of campaigns as the face of the product. She was succeeded in 2020 by Israeli actress Gal Gadot.


title: Glaceau Smartwater

text: In June 2022, Zendaya was announced as the global brand ambassador of Glaceau SmartWater and the face of its new campaign "Smart Solutions: Global Water Challenge (GWC)".


title: Glaceau Smartwater

text: Smartwater was launched in India through its association with TED Talks India Nayi Soch as the official sponsor for property.


title: Glaceau Smartwater

text: In 2018, Smartwater was awarded the German "Goldener Windbeutel" ("Golden Windbag") anti-award by the consumer rights advocacy group Foodwatch Germany for "the most brazen lie in food advertising" that year. The group said that Smartwater is "nothing but ordinary water" sold by advertising a "scientifically-sounding but completely unnecessary production process" which yields no proven nutritional benefits, for as much as seven times the price of regular water. The product also won the Dutch "Gouden Windei" ("Golden Windbag") prize that year.


title: Glaceau Smartwater

text: The Coca-Cola Company repudiated the criticism and said that it followed all applicable food labeling regulations in a transparent manner, that Foodwatch had nominated Coca-Cola in order to attract attention to itself, and that "the success of the water with consumers proved that they liked the product for the taste."


title: Münster rebellion

text: The Münster rebellion (, "Anabaptist dominion of Münster") was an attempt by radical Anabaptists to establish a communal sectarian government in the German city of Münster then under the large Prince-Bishopric of Münster in the Holy Roman Empire.


title: Münster rebellion

text: The city was under Anabaptist rule from February 1534, when the city hall was seized and Bernhard Knipperdolling installed as mayor, until its fall in June 1535. It was Melchior Hoffman, who initiated adult baptism in Strasbourg in 1530, and his line of eschatological Anabaptism, that helped lay the foundations for the events of 1534–35 in Münster.


title: Münster rebellion

text: After the German Peasants' War (1524–1525), a forceful attempt to establish theocracy was made at Münster, in Westphalia (1532–1535). Here the Anabaptists had gained considerable influence, through the adhesion of Bernhard Rothmann, the Lutheran pastor, and several prominent citizens and leaders, including Jan Matthys (also spelled Matthijs, Mathijsz, Matthyssen, Mathyszoon), a baker from Haarlem, and Jan Bockelson (or Beukelszoon), a tailor from Leiden. Bernhard Rothmann was a tireless and vitriolic opponent of Catholicism and a writer of pamphlets that were published by his ally, the wealthy wool merchant Bernhard Knipperdolling. The pamphlets at first denounced Catholicism from a radical Lutheran perspective, but soon started to proclaim that the Bible called for the absolute equality of man in all matters, including the distribution of wealth. The pamphlets, which were distributed throughout northern Germany, called upon the poor of the region to join the citizens of Münster to share the wealth of the town and benefit spiritually from being the elect of Heaven.


title: Münster rebellion

text: With so many Anabaptist adherents in the town, Rothmann and his allies had little difficulty obtaining possession of it at the elections for the magistracy and placing Bernhard Knipperdolling as the mayor, after deposing the mainly Lutheran magistrates, who, until then, had seen him as an ally in their own distrust of, and dislike for, Catholics. Matthys was a follower of Melchior Hoffman, and after Hoffman's imprisonment at Strasbourg Matthys obtained a considerable following in the Low Countries, including Bockelson, who became known as John of Leiden. John of Leiden and Gerrit Boekbinder had visited Münster, and returned with a report that Bernhard Rothmann was in Münster teaching doctrines similar to their own. Matthys identified Münster as the "New Jerusalem", and on January 5, 1534, a number of his disciples entered the city and introduced adult baptism. Rothmann apparently accepted "baptism" that day, and well over 1000 adults were soon baptised. Vigorous preparations were made not only to hold what had been gained but to spread their beliefs to other areas. The many Lutherans who left were outnumbered by the arriving Anabaptists. There was an orgy of iconoclasm in cathedrals and monasteries, and rebaptism became compulsory. The property of emigrants was shared out with the poor, and soon a proclamation was issued that all property was to be held in common.


title: Münster rebellion

text: The city was besieged by Franz von Waldeck, its expelled bishop. In April 1534, on Easter Sunday, Matthys, who had prophesied God's judgment to come on the wicked on that day, led a procession from the city with twelve followers, as he believed himself the second Gideon. He and his followers were cut off and taken. Matthys was killed, his head placed on a pole for all in the city to see, and his genitals nailed to the city gate.


title: Münster rebellion

text: The 25-year-old John of Leiden was subsequently recognized as Matthys' religious and political successor, justifying his authority and actions by claiming visions from heaven. His authority grew until eventually he proclaimed himself the successor of David and adopted royal regalia, honors, and absolute power in the new "Zion". There were now in the town at least three times as many women of marriageable age as men, so he made polygamy compulsory, and he himself took sixteen wives. (John is said to have beheaded Elisabeth Wandscherer in the marketplace for refusing to marry him, though this act might have been falsely attributed to him after his death.) Meanwhile, most of the residents of Münster were starving as a result of the year-long siege.


title: Münster rebellion

text: After lengthy resistance, the city was taken by the besiegers on June 24, 1535, and John of Leiden and several other prominent Anabaptist leaders were captured and imprisoned. In January 1536 John of Leiden, Bernhard Knipperdolling and one more prominent follower, Bernhard Krechting, were tortured and executed in the marketplace of Münster. Their bodies were exhibited in cages which hung from the steeple of St. Lambert's Church. The bones were removed later, but the cages hang there still.


title: Münster rebellion

text: The Münster Rebellion was a turning point for the Anabaptist movement. It never again had the opportunity of assuming political importance, as both Catholic and Lutheran civil powers adopted stringent measures to counter this. It is difficult to trace the subsequent history of the group as a religious body, through changes in the names used and beliefs held.


title: Münster rebellion

text: The Batenburgers under Jan van Batenburg preserved the violent millennialist stream of Anabaptism seen at Münster. They were polygamous and believed force was justified against anyone not in their sect. Their movement went underground after the suppression of the Münster Rebellion, with members posing as Catholics or Lutherans as necessary. Some nonresistant Anabaptists found leaders in Menno Simons and the brothers Obbe and Dirk Philips, Dutch Anabaptist leaders who repudiated the distinctive doctrines of the Münster Anabaptists. This group eventually became known as the Mennonites after Simons. They rejected any use of violence and preached a faith based on compassion and love of enemy.


title: Münster rebellion

text: In August 1536 the leaders of Anabaptist groups influenced by Melchior Hoffman met in Bocholt in an attempt to maintain unity. The meeting included followers of Batenburg, survivors of Münster, David Joris and his sympathisers, and the nonresistant Anabaptists. At this meeting the major areas of dispute between the sects were polygamous marriage and the use of force against non-believers. Joris proposed compromise by declaring the time had not yet come to fight against the authorities, and that it would be unwise to kill any non-Anabaptists. The gathered Anabaptists agreed to the compromise of no more force, but the meeting did not prevent the fragmentation of Anabaptism.


title: Absolute continuity

text: In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity. The notion of absolute continuity allows one to obtain generalizations of the relationship between the two central operations of calculus—differentiation and integration. This relationship is commonly characterized (by the fundamental theorem of calculus) in the framework of Riemann integration, but with absolute continuity it may be formulated in terms of Lebesgue integration. For real-valued functions on the real line, two interrelated notions appear: absolute continuity of functions and absolute continuity of measures. These two notions are generalized in different directions. The usual derivative of a function is related to the "Radon–Nikodym derivative", or "density", of a measure.


title: Absolute continuity

text: A continuous function fails to be absolutely continuous if it fails to be uniformly continuous, which can happen if the domain of the function is not compact – examples are tan("x") over , "x" over the entire real line, and sin(1/"x") over (0, 1]. But a continuous function "f" can fail to be absolutely continuous even on a compact interval. It may not be "differentiable almost everywhere" (like the Weierstrass function, which is not differentiable anywhere). Or it may be differentiable almost everywhere and its derivative "f" ′ may be Lebesgue integrable, but the integral of "f" ′ differs from the increment of "f" (how much "f" changes over an interval). This happens for example with the Cantor function.


title: Absolute continuity

text: Let formula_2 be an interval in the real line formula_3. A function formula_4 is absolutely continuous on formula_2 if for every positive number formula_6, there is a positive number formula_7 such that whenever a finite sequence of pairwise disjoint sub-intervals formula_8 of formula_2 with formula_10 satisfies


title: Absolute continuity

text: The following conditions on a real-valued function "f" on a compact interval ["a","b"] are equivalent:


title: Absolute continuity

text: Equivalence between (1) and (3) is known as the fundamental theorem of Lebesgue integral calculus, due to Lebesgue.


title: Absolute continuity

text: For an equivalent definition in terms of measures see the section Relation between the two notions of absolute continuity.


title: Absolute continuity

text: The following functions are absolutely continuous and α-Hölder continuous but not Lipschitz continuous:


title: Absolute continuity

text: Let ("X", "d") be a metric space and let "I" be an interval in the real line R. A function "f": "I" → "X" is absolutely continuous on "I" if for every positive number formula_22, there is a positive number formula_7 such that whenever a finite sequence of pairwise disjoint sub-intervals ["x", "y"] of "I" satisfies


title: Absolute continuity

text: A measure formula_28 on Borel subsets of the real line is absolutely continuous with respect to the Lebesgue measure formula_20 if for every formula_20-measurable set formula_31 formula_32 implies formula_33 This is written as formula_34 We say formula_28 is "dominated" by formula_36


title: Absolute continuity

text: In most applications, if a measure on the real line is simply said to be absolutely continuous — without specifying with respect to which other measure it is absolutely continuous — then absolute continuity with respect to the Lebesgue measure is meant.


title: Absolute continuity

text: The following conditions on a finite measure formula_28 on Borel subsets of the real line are equivalent:


title: Absolute continuity

text: For an equivalent definition in terms of functions see the section Relation between the two notions of absolute continuity.


title: Absolute continuity

text: Any other function satisfying (3) is equal to formula_45 almost everywhere. Such a function is called Radon–Nikodym derivative, or density, of the absolutely continuous measure formula_49


title: Absolute continuity

text: Thus, the absolutely continuous measures on formula_50 are precisely those that have densities; as a special case, the absolutely continuous probability measures are precisely the ones that have probability density functions.


title: Absolute continuity

text: If formula_28 and formula_54 are two measures on the same measurable space formula_55 formula_28 is said to be with respect to formula_54 if formula_58 for every set formula_43 for which formula_60 This is written as "formula_61". That is:


title: Absolute continuity

text: Absolute continuity of measures is reflexive and transitive, but is not antisymmetric, so it is a preorder rather than a partial order. Instead, if formula_66 and formula_67 the measures formula_28 and formula_54 are said to be equivalent. Thus absolute continuity induces a partial ordering of such equivalence classes.


title: Absolute continuity

text: If formula_28 is a signed or complex measure, it is said that formula_28 is absolutely continuous with respect to formula_54 if its variation formula_73 satisfies formula_74 equivalently, if every set formula_43 for which formula_76 is formula_28-null.


title: Absolute continuity

text: The Radon–Nikodym theorem states that if formula_28 is absolutely continuous with respect to formula_79 and both measures are σ-finite, then formula_28 has a density, or "Radon-Nikodym derivative", with respect to formula_79 which means that there exists a formula_54-measurable function formula_83 taking values in formula_84 denoted by formula_85 such that for any formula_54-measurable set formula_43 we have


title: Absolute continuity

text: Via Lebesgue's decomposition theorem, every σ-finite measure can be decomposed into the sum of an absolutely continuous measure and a singular measure with respect to another σ-finite measure. See singular measure for examples of measures that are not absolutely continuous.


title: Absolute continuity

text: A finite measure "μ" on Borel subsets of the real line is absolutely continuous with respect to Lebesgue measure if and only if the point function


title: Absolute continuity

text: More generally, a function is locally (meaning on every bounded interval) absolutely continuous if and only if its distributional derivative is a measure that is absolutely continuous with respect to the Lebesgue measure.


title: Absolute continuity

text: If absolute continuity holds then the Radon–Nikodym derivative of "μ" is equal almost everywhere to the derivative of "F".


title: Absolute continuity

text: More generally, the measure "μ" is assumed to be locally finite (rather than finite) and "F"("x") is defined as "μ"((0,"x"]) for , 0 for , and −"μ"(("x",0]) for . In this case "μ" is the Lebesgue–Stieltjes measure generated by "F".


title: Strive Masiyiwa

text: Strive Masiyiwa (born 29 January 1961) is a London-based Zimbabwean billionaire businessman and philanthropist. He is the founder and executive chairman of international technology groups Econet Global and Cassava Technologies.


title: Strive Masiyiwa

text: Masiyiwa has provided scholarships to more than 250,000 young Africans over the past 20 years through his family foundation. He has supported more than 40,000 orphans with educational initiatives and sponsored students at universities in America, the United Kingdom, and China.


title: Strive Masiyiwa

text: Strive Masiyiwa was born in Zimbabwe, on 29 January 1961. When he was seven, his family left the country after Prime Minister Ian Smith's government declared a Unilateral Declaration of Independence from the United Kingdom. The family settled in Kitwe, a city in north central Zambia known for its copper mines. It was here that he attended primary school, before completing his secondary education in Scotland. Masiyiwa's mother was an entrepreneur. By the time Masiyiwa was 12 years old, his parents could afford to provide him with a European education.


title: Strive Masiyiwa

text: They sent him to private school in Edinburgh, Scotland. When he graduated in 1978, he travelled back to Rhodesia, intending to join Robert Mugabe and Joshua Nkomo's anti-government guerrilla forces. However, he returned to school in Britain, and earned a degree in electrical engineering from the University of Wales in 1983. He worked briefly in the computer industry in Cambridge, England, but returned to Zimbabwe in 1984, hoping to aid the country's recovery following the end of the Rhodesian Bush War and universal franchise elections in 1980.


title: Strive Masiyiwa

text: Masiyiwa's international appointments and board memberships over the years include: Unilever (board member), Netflix (board member), Bill & Melinda Gates Foundation (trustee), the National Geographic Society (trustee), Bank of America (Global Advisory Council), UN Commission on Adaptation (former Commissioner), Generation Africa (co-founder), Pathways for Prosperity Commission on Technology and Inclusive Development (co-chair), The Rockefeller Foundation (former board member), US Council on Foreign Relations (Global Advisory Board), the Asia Society (former board member), Stanford University (Global Advisory Board), the Africa Progress Panel, Alliance for a Green Revolution in Africa (chair, now Chair Emeritus), The Micronutrient Initiative of Canada (former board member), Grow Africa, the African Union's Ebola Fund (co-founder), Morehouse College(former Trustee), the African Academy of Sciences (Honorary Fellow) and the Pan African Strategic Institute. He was recently involved in helping to organize the Global Africa Business Initaitive launched in New York in 2022.


title: Strive Masiyiwa

text: Masiyiwa is the only African member of the United States Holocaust Memorial Museum's Committee on Conscience. Masiyiwa also served on two UN Advisory Panels.


title: Strive Masiyiwa

text: In 2014, "Fortune Magazine" named Masiyiwa one of the 50 most influential business leaders in the world, and he was cited as one of the Top 100 most influential Africans by New African magazine.


title: Strive Masiyiwa

text: In September 2014, the Chair of the African Union (AU), Nkosazana Dlamini-Zuma, asked Masiyiwa to help mobilise resources for Africa's response to the Ebola outbreak. This was the first time The AU had asked a business leader to undertake such a role. Masiyiwa, with the help of other leaders, set up the first ever Pan-African fund-raising campaign known as #AfricaAgainstEbola Solidarity Fund.