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Paramecium ( / ˌpærəˈmiːs ( i) əm / PARR-ə-MEE-s (ee-)əm, /- siəm / -see-əm, plural "paramecia" only when used as a vernacular name) [2] is a genus of eukaryotic, unicellular ciliates, commonly studied as a model organism of the ciliate group. Paramecium are widespread in freshwater, brackish, and marine environments and are often ...
Exponential decay. A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant ( λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has. where e is the base of the natural logarithm, i is the imaginary unit, and ...
The form is similar to the Lotka–Volterra equations for predation in that the equation for each species has one term for self-interaction and one term for the interaction with other species. In the equations for predation, the base population model is exponential. For the competition equations, the logistic equation is the basis.
The Baker–Campbell–Hausdorff formula can be used to give comparatively simple proofs of deep results in the Lie group–Lie algebra correspondence . If and are sufficiently small matrices, then can be computed as the logarithm of , where the exponentials and the logarithm can be computed as power series. The point of the Baker–Campbell ...
n {\displaystyle n} is the ideality factor, also known as the quality factor or emission coefficient. The equation is called the Shockley ideal diode equation when the ideality factor equals 1, thus is sometimes omitted. The ideality factor typically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process ...
A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity can thereby move due to the ...
Exponential growth. Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential ...