Positive feedback is a process that occurs in a feedback loop in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback. Both concepts play an important role in science and engineering, including biology and cybernetics. Mathematically, positive feedback is defined as a positive loop gain around a closed loop of cause and effect; that is, positive feedback is in phase with the input, in the sense that it adds to make the input larger. Positive feedback tends to cause system instability; when the loop gain is positive and above 1, there will be exponential growth, increasing oscillations, chaotic behavior or other divergences from equilibrium. System parameters will accelerate towards extreme values, which may damage or destroy the system, or may end with the system latched into a new stable state.
Positive feedback may be controlled by signals in the system being filtered, damped, or limited, or it can be cancelled or reduced by adding negative feedback. Positive feedback is used in digital electronics to force voltages away from intermediate voltages into'0' and'1' states. On the other hand, thermal runaway is a type of positive feedback that can destroy semiconductor junctions. Positive feedback in chemical reactions can increase the rate of reactions, in some cases can lead to explosions. Positive feedback in mechanical design causes tipping-point, or'over-centre', mechanisms to snap into position, for example in switches and locking pliers. Out of control, it can cause bridges to collapse. Positive feedback in economic systems can cause boom-then-bust cycles. A familiar example of positive feedback is the loud squealing or howling sound produced by audio feedback in public address systems: the microphone picks up sound from its own loudspeakers, amplifies it, sends it through the speakers again.
Positive feedback enhances or amplifies an effect by it having an influence on the process which gave rise to it. For example, when part of an electronic output signal returns to the input, is in phase with it, the system gain is increased; the feedback from the outcome to the originating process can be direct, or it can be via other state variables. Such systems can give rich qualitative behaviors, but whether the feedback is instantaneously positive or negative in sign has an important influence on the results. Positive feedback reinforces and negative feedback moderates the original process. Positive and negative in this sense refer to loop gains greater than or less than zero, do not imply any value judgements as to the desirability of the outcomes or effects. A key feature of positive feedback is thus; when a change occurs in a system, positive feedback causes further change, in the same direction. A simple feedback loop is shown in the diagram. If the loop gain AB is positive a condition of positive or regenerative feedback exists.
If the functions A and B are linear and AB is smaller than unity the overall system gain from the input to output is finite, but can be large as AB approaches unity. In that case, it can be shown that the overall or "closed loop" gain from input to output is: G c = A / When AB > 1, the system is unstable, so does not have a well-defined gain. Thus depending on the feedback, state changes can be divergent; the result of positive feedback is to augment changes, so that small perturbations may result in big changes. A system in equilibrium in which there is positive feedback to any change from its current state may be unstable, in which case the system is said to be in an unstable equilibrium; the magnitude of the forces that act to move such a system away from its equilibrium are an increasing function of the "distance" of the state from the equilibrium. Positive feedback does not imply instability of an equilibrium, for example stable on and off states may exist in positive-feedback architectures.
In the real world, positive feedback loops do not cause ever-increasing growth, but are modified by limiting effects of some sort. According to Donella Meadows: "Positive feedback loops are sources of growth, explosion and collapse in systems. A system with an unchecked positive loop will destroy itself. That's. A negative loop will kick in sooner or later."Hysteresis, in which the starting point affects where the system ends up, can be generated by positive feedback. When the gain of the feedback loop is above 1 the output moves away from the input: if it is above the input it moves towards the nearest positive limit, while if it is below the input it moves towards the nearest negative limit. Once it reaches the limit, it will be stable. However, if the input goes past the limit the feedback will change sign and the output will move in the opposite direction until it hits the opposite limit; the system therefore shows bistable behaviour. The terms positive and negative were first applied to feedback before World War II.
The idea of positive feedback was current in the 1920s with the introduction of the regenerative circuit. Friis & Jensen described regeneration in a set of electronic amplifiers as a case where the "feed-back" action is positive in contrast to negative feed-back action, which they mention only in passing. Harold Stephen Black's classic 1934 paper first details the use of negative feedback in electronic amp
A weighing scale is a device to measure weight or mass. These are known as mass scales, weight scales, mass balance, weight balance, or scale, balance, or balance scale; the traditional scale bowls suspended at equal distances from a fulcrum. One plate holds an object of unknown mass, while known masses are added to the other plate until static equilibrium is achieved and the plates level off, which happens when the masses on the two plates are equal. A spring scale will make use of a spring of known stiffness to determine mass. Suspending a certain mass will extend the spring by a certain amount depending on the spring's stiffness; the heavier the object, the more the spring stretches, as described in Hooke's law. Other types of scale making use of different physical principles exist; some scales can be calibrated to read in units of force such as newtons instead of units of mass such as kilograms. Scales and balances are used in commerce, as many products are sold and packaged by mass; the balance scale is such a simple device that its usage far predates the evidence.
What has allowed archaeologists to link artifacts to weighing scales are the stones for determining absolute mass. The balance scale itself was used to determine relative mass long before absolute mass; the oldest evidence for the existence of weighing scales dates to c. 2400–1800 B. C. in the Indus River valley. Prior to that, no banking was performed due to lack of scales. Uniform, polished stone cubes discovered in early settlements were used as mass-setting stones in balance scales. Although the cubes bear no markings, their masses are multiples of a common denominator; the cubes are made of many different kinds of stones with varying densities. Their mass, not their size or other characteristics, was a factor in sculpting these cubes. In Egypt, scales can be traced to around 1878 B. C. but their usage extends much earlier. Carved stones bearing marks denoting mass and the Egyptian hieroglyphic symbol for gold have been discovered, which suggests that Egyptian merchants had been using an established system of mass measurement to catalog gold shipments or gold mine yields.
Although no actual scales from this era have survived, many sets of weighing stones as well as murals depicting the use of balance scales suggest widespread usage. In China, the earliest weighing balance excavated was from a tomb of the State of Chu of the Chinese Warring States Period dating back to the 3rd to 4th century BC in Mount Zuojiagong near Changsha, Hunan; the balance was made of wood and used bronze masses. Variations on the balance scale, including devices like the cheap and inaccurate bismar, began to see common usage by c. 400 B. C. by many small merchants and their customers. A plethora of scale varieties each boasting advantages and improvements over one another appear throughout recorded history, with such great inventors as Leonardo da Vinci lending a personal hand in their development. With all the advances in weighing scale design and development, all scales until the seventeenth century AD were variations on the balance scale; the standardization of the weights used – and ensuring traders used the correct weights – was a considerable preoccupation of governments throughout this time.
The original form of a balance consisted of a beam with a fulcrum at its center. For highest accuracy, the fulcrum would consist of a sharp V-shaped pivot seated in a shallower V-shaped bearing. To determine the mass of the object, a combination of reference masses was hung on one end of the beam while the object of unknown mass was hung on the other end. For high precision work, such as empirical chemistry, the center beam balance is still one of the most accurate technologies available, is used for calibrating test masses; the balance was the first mass measuring instrument invented. In its traditional form, it consists of a pivoted horizontal lever with arms of equal length – the beam – and a weighing pan suspended from each arm; the unknown mass is placed in one pan and standard masses are added to the other pan until the beam is as close to equilibrium as possible. In precision balances, a more accurate determination of the mass is given by the position of a sliding mass moved along a graduated scale.
Technically, a balance compares weight rather than mass, but, in a given gravitational field, the weight of an object is proportional to its mass, so the standard masses used with balances are labeled in units of mass. Unlike spring-based scales, balances are used for the precision measurement of mass as their accuracy is not affected by variations in the local gravitational field. A change in the strength of the gravitational field caused by moving the balance does not change the measured mass, because the moments of force on either side of the beam are affected equally. A balance will render an accurate measurement of mass at any location experiencing a constant gravity or acceleration. Precise measurements are achieved by ensuring that the balance's fulcrum is friction-free, by attaching a pointer to the beam which amplifies any deviation from a balance position. For greatest accuracy, there needs to be an allowance for the bu
United States Department of the Treasury
The Department of the Treasury is an executive department and the treasury of the United States federal government. Established by an Act of Congress in 1789 to manage government revenue, the Treasury prints all paper currency and mints all coins in circulation through the Bureau of Engraving and Printing and the United States Mint, respectively. S. government debt instruments. The Department is administered by the Secretary of the Treasury, a member of the Cabinet. Senior advisor to the Secretary is the Treasurer of the United States. Signatures of both officials appear on all Federal Reserve notes; the first Secretary of the Treasury was Alexander Hamilton, sworn into office on September 11, 1789. Hamilton was appointed by President George Washington on the recommendation of Robert Morris, Washington's first choice for the position, who had declined the appointment. Hamilton established—almost singlehandedly—the nation's early financial system and for several years was a major presence in Washington's administration.
His portrait appears on the obverse of the ten-dollar bill, while the Treasury Department building is depicted on the reverse. The current Secretary of the Treasury is Steven Mnuchin, confirmed by the United States Senate on February 13, 2017. Jovita Carranza, appointed on April 28, 2017, is the incumbent treasurer; the history of the Department of the Treasury began in the turmoil of the American Revolution, when the Continental Congress at Philadelphia deliberated the crucial issue of financing a war of independence against Great Britain. The Congress had no power to levy and collect taxes, nor was there a tangible basis for securing funds from foreign investors or governments; the delegates resolved to issue paper money in the form of bills of credit, promising redemption in coin on faith in the revolutionary cause. On June 22, 1775—only a few days after the Battle of Bunker Hill—Congress issued $2 million in bills. On July 29, 1775, the Second Continental Congress assigned the responsibility for the administration of the revolutionary government's finances to joint Continental treasurers George Clymer and Michael Hillegas.
The Congress stipulated. To ensure proper and efficient handling of the growing national debt in the face of weak economic and political ties between the colonies, the Congress, on February 17, 1776, designated a committee of five to superintend the Treasury, settle accounts, report periodically to the Congress. On April 1, a Treasury Office of Accounts, consisting of an Auditor General and clerks, was established to facilitate the settlement of claims and to keep the public accounts for the government of the United Colonies. With the signing of the Declaration of Independence on July 4, 1776, the newborn republic as a sovereign nation was able to secure loans from abroad. Despite the infusion of foreign and domestic loans, the united colonies were unable to establish a well-organized agency for financial administration. Michael Hillegas was first called Treasurer of the United States on May 14, 1777; the Treasury Office was reorganized three times between 1778 and 1781. The $241.5 million in paper Continental bills devalued rapidly.
By May 1781, the dollar collapsed at a rate of from 500 to 1000 to 1 against hard currency. Protests against the worthless money swept the colonies, giving rise to the expression "not worth a Continental". Robert Morris was designated Superintendent of Finance in 1781 and restored stability to the nation's finances. Morris, a wealthy colonial merchant, was nicknamed "the Financier" because of his reputation for procuring funds or goods on a moment's notice, his staff included a comptroller, a treasurer, a register, auditors, who managed the country's finances through 1784, when Morris resigned because of ill health. The treasury board, consisting of three commissioners, continued to oversee the finances of the confederation of former colonies until September 1789; the First Congress of the United States was called to convene in New York on March 4, 1789, marking the beginning of government under the Constitution. On September 2, 1789, Congress created a permanent institution for the management of government finances:Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled, That there shall be a Department of Treasury, in which shall be the following officers, namely: a Secretary of the Treasury, to be deemed head of the department.
Alexander Hamilton took the oath of office as the first Secretary of the Treasury on September 11, 1789. Hamilton had served as George Washington's aide-de-camp during the Revolution and was of great importance in the ratification of the Constitution; because of his financial and managerial acumen, Hamilton was a logical choice for solving the problem of the new nation's heavy war debt. Hamilton's first official act was to submit a report to Congress in which he laid the foundation for the nation's financial health. To the surprise of many legislators, he insisted upon federal assumption and dollar-for-dollar repayment of the country's $75 million debt in order to revitalize the public credit: "he debt of the United States was the price of liberty; the faith of America has been pledged for it, with solemnities that give peculiar force to the obligation." Hami
W & T Avery
W & T Avery Ltd. is a British manufacturer of weighing machines. The company was founded in the early 18th century and took the name W & T Avery in 1818. Having been taken over by GEC in 1979 the company was renamed into GEC-Avery; the company became Avery Berkel in 1993. After the take over by Weigh-Tronix in 2000 the company was again renamed to be called Avery Weigh-Tronix; the company is based in United Kingdom. The undocumented origin of the company goes back to 1730 when James Ford established the business in Digbeth. On Joseph Balden the owner's death in 1813 William and Thomas Avery took over his scalemaking business and in 1818 renamed it W & T Avery; the business expanded and in 1885 they owned three factories: the Atlas Works in West Bromwich, the Mill Lane Works in Birmingham and the Moat Lane Works in Digbeth. In 1891 the business became a limited company with a board of directors and in 1894 the shares were quoted on the London Stock Exchange. In 1895 the company bought the legendary Soho Foundry in Smethwick, a former steam engine factory owned by James Watt & Co.
In 1897 the move was complete and the steam engine business was converted to pure manufacture of weighing machines. The turn of the century was marked by managing director William Hipkins' determined efforts in broadening the renown of the Avery brand and transforming the business into a specialist manufacturer of weighing machines. By 1914 the company had some 3000 employees. In the inter-war period the growth continued with the addition of specialised shops for cast parts, enamel paints and weighbridge assembly and the product range diversified into counting machines, testing machines, automatic packing machines and petrol pumps. During the second world war the company produced various types of heavy guns. At that time the site underwent severe damage from incendiary bombs. From 1931 to 1973 the company occupied the 18th-century Middlesex Sessions House in Clerkenwell as its headquarters. Changes in weighing machine technology after World War II led to the closure of the foundry, the introduction of load cells and electronic weighing with the simultaneous gradual disappearance of purely mechanical devices.
The continued expansion was achieved through a series of acquisitions of other companies. The most important are: Co 1899 Parnall & Sons Ltd.. 1920/1928 Southall and Smith Ltd. 1920 Saml. Denison & Son Ltd. 1925 Oertling Ltd. 1931 The Tan Sad Chair Co. Ltd. 1932 Avery-Hardoll Ltd. 1953/1976 Pump Maintenance Ltd. 1959 Geo Driver & Son Ltd.. After a century of national and international expansion the company was taken over by GEC in 1979. Keith Hodgkinson, managing director at the time, completed the turn-around from mechanical to electronic weighing with a complete overhaul of the product range of retail scales and industrial platform scales. In 1993 GEC took over the Dutch-based company Berkel and the Avery-Berkel name was introduced. In 2000 the business was in turn acquired by the US-American company Weigh-Tronix, who owned Salter, is today operating as Avery Weigh-Tronix. In 2008 Illinois Tool Works Inc. purchased Avery Weigh-Tronix from its owners, European Capital. Roberval Balance Weighbridge Ernest Pendarves Leigh-Bennett, Weighing the World: an impression after two hundred years of the past history of an English house of business, of its present activities and influence throughout the world of weighing, 1730-1930, Birmingham, 1930 Walter Keith Vernon Gale, Soho Foundry, Birmingham, 1948 Monopolies and Mergers Commission, The General Electric Company Limited and Averys Limited: a report on the proposed merger, London, 1979, ISBN 0-10-176530-4 L H Broadbent, "The Avery Business", W & T Avery, Birmingham, 1949 www.averyweigh-tronix.com Corporate website Avery Chronology of the Avery company The Soho Foundry History of the company's main site The General Electric Company Limited and Averys Limited Chapter One of The General Electric Company Limited and Averys Limited: A Report on the Proposed Merger Averys Limited Chapter Four of The General Electric Company Limited and Averys Limited: A Report on the Proposed Merger Names on Weights A list of manufacturers whose names appears on British weights Sir William Beilby Avery
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number", it was the Pythagoreans who coined the term "mathematics", with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria, she succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; as these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, proceed to specialize in topics of their own choice at the graduate level.
In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns