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By 1970, a calculator could be made using just a few chips of low power consumption, allowing portable models powered from rechargeable batteries. The first handheld calculator was a 1967 prototype called Cal Tech, whose development was led by Jack Kilby at Texas Instruments in a research project to produce a portable calculator. It could add ...
In mathematics, the Bernoulli numbers B n are a sequence of rational numbers which occur frequently in analysis.The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain ...
= and the power of a diagonal matrix can be calculated by taking the corresponding powers of the diagonal entries, which is much easier than doing the exponentiation for A instead. This can be used to compute the matrix exponential e A , a need frequently arising in solving linear differential equations , matrix logarithms and square roots of ...
This is a list of the most populous municipal corporations of the United States.As defined by the United States Census Bureau, an incorporated place includes cities, towns, villages, boroughs, and municipalities.
The first calendar allegedly dates back to 8th century BC during the Roman Kingdom and included 356 days plus a leap year every other year. [98] In contrast, the lunar calendar of the Republican era contained 355 days, roughly ten-and-one-fourth days shorter than the solar year , a discrepancy that was solved by adding an extra month into the ...
The entropy change of a system excluding its surroundings can be well-defined as a small portion of heat transferred to the system during reversible process divided by the temperature of the system during this heat transfer: = The reversible process is quasistatic (i.e., it occurs without any dissipation, deviating only infinitesimally from the ...
Mathematically, this is the debt divided by the GDP amount. The Congressional Budget Office includes historical budget and debt tables along with its annual "Budget and Economic Outlook". Debt held by the public as a percentage of GDP rose from 34.7% GDP in 2000 to 40.5% in 2008 and 67.7% in 2011. [ 34 ]
Ottoman Empire used colonization as a very effective method to consolidate their position and power in the Balkans. The colonizers that were brought to the Balkans consisted of diverse elements, including groups uneasy for the state, soldiers, nomads, farmers, artisans and merchants, dervishes , preachers and other religious functionaries, and ...