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Srinivasa Ramanujan (1887–1920) was an Indian mathematician.
In biology, binocular vision is a type of vision in which an animal having two eyes is able to perceive a single three-dimensional image of its surroundings. Neurological researcher Manfred Fahle has stated six specific advantages of having two eyes rather than just one:
- It gives a creature a spare eye in case one is damaged.
- It gives a wider field of view. For example, humans have a maximum horizontal field of view of approximately 190 degrees with two eyes, approximately 120 degrees of which makes up the binocular field of view flanked by two uniocular fields of approximately 40 degrees.
- It can give stereopsis in which binocular disparity provided by the two eyes' different positions on the head gives precise depth perception. This also allows a creature to break the camouflage of another creature.
- It allows the angles of the eyes' lines of sight, relative to each other (vergence), and those lines relative to a particular object to be determined from the images in the two eyes. These properties are necessary for the third advantage.
- It allows a creature to see more of, or all of, an object behind an obstacle. This advantage was pointed out by Leonardo da Vinci, who noted that a vertical column closer to the eyes than an object at which a creature is looking might block some of the object from the left eye but that part of the object might be visible to the right eye.
- It gives binocular summation in which the ability to detect faint objects is enhanced.
In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity. As part of mathematics it is a notational subset of Ricci calculus; however, it is often used in applications in physics that do not distinguish between tangent and cotangent spaces. It was introduced to physics by Albert Einstein in 1916.
In numerical analysis, the Kahan summation algorithm significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers, compared to the obvious approach. This is done by keeping a separate running compensation.
Opportunity may refer to:
In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely defined by discrete samples of the original function's Fourier transform. And conversely, the periodic summation of a function's Fourier transform is completely defined by discrete samples of the original function. The Poisson summation formula was discovered by Siméon Denis Poisson and is sometimes called Poisson resummation.
In mathematical analysis, Cesàro summation assigns values to some infinite sums that are not convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series.
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.
Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings.
Ewald summation, named after Paul Peter Ewald, is a method for computing long-range interactions in periodic systems. It was first developed as the method for calculating electrostatic energies of ionic crystals, and is now commonly used for calculating long-range interactions in computational chemistry. Ewald summation is a special case of the Poisson summation formula, replacing the summation of interaction energies in real space with an equivalent summation in Fourier space. In this method, the long-range interaction is divided into two parts: a short-range contribution, and a long-range contribution which does not have a singularity. The short-range contribution is calculated in real space, whereas the long-range contribution is calculated using a Fourier transform. The advantage of this method is the rapid convergence of the energy compared with that of a direct summation. This means that the method has high accuracy and reasonable speed when computing long-range interactions, and it is thus the de facto standard method for calculating long-range interactions in periodic systems. The method requires charge neutrality of the molecular system in order to calculate accurately the total Coulombic interaction. A study of the truncation errors introduced in the energy and force calculations of disordered point-charge systems is provided by Kolafa and Perram.
Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series. Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.
The McClellan oscillator is a market breadth indicator used in technical analysis by financial analysts of the New York Stock Exchange to evaluate the balance between the advancing and declining stocks. The McClellan oscillator is based on the Advance-Decline Data and it could be applied to stock market exchanges, indexes, portfolio of stocks or any basket of stocks.
In ecology, productivity refers to the rate of generation of biomass in an ecosystem. It is usually expressed in units of mass per unit surface per unit time, for instance grams per square metre per day. The mass unit may relate to dry matter or to the mass of carbon generated. Productivity of autotrophs such as plants is called primary productivity, while that of heterotrophs such as animals is called secondary productivity.
In signal processing, any periodic function,
with period P, can be represented by a summation of an infinite number of instances of an aperiodic function,
, that are offset by integer multiples of P. This representation is called periodic summation:
