Topic Review
Calendar of 13 Months
Has anyone of us missed an event because he was confused between days and dates? Do we really remember the date of any day if we do not have a calendar? Is the current Gregorian Calendar efficient enough for use, and does it really facilitate our life or make it more complicated?  Have you ever thought about a much simpler way to calculate days and dates in a year? All these questions are answered in this article, in which the author proposes an original calendar that might facilitate our lives if we can apply it.
  • 175.7K
  • 12 Jan 2023
Topic Review
Plus-Minus Sign
The plus-minus sign (±) is a mathematical symbol with multiple meanings. The sign is normally pronounced "plus or minus". In mathematics, it generally indicates a choice of exactly two possible values, one of which is the negation of the other. In experimental sciences, the sign commonly indicates the confidence interval or error in a measurement, often the standard deviation or standard error. The sign may also represent an inclusive range of values that a reading might have. In engineering the sign indicates the tolerance, which is the range of values that are considered to be acceptable, safe, or which comply with some standard, or with a contract. In botany it is used in morphological descriptions to notate "more or less". In chemistry the sign is used to indicate a racemic mixture. In chess, the sign indicates a clear advantage for the white player; the complementary sign ∓ indicates the same advantage for the black player.
  • 50.5K
  • 23 Apr 2023
Topic Review
Planck Length
In physics, the Planck length, denoted ℓP, is a unit of length in the system of Planck units that was originally proposed by physicist Max Planck, equal to 1.616255(18)×10−35 m.[note 1] The Planck length can be defined from three fundamental physical constants: the speed of light, the Planck constant, and the gravitational constant. It is also the reduced Compton wavelength of a particle with Planck mass. Regardless of whether it represents some fundamental limit to the universe, it is a useful unit in theoretical physics.
  • 19.9K
  • 18 Nov 2022
Topic Review
Photo Manipulation
Photo manipulation involves transforming or altering a photograph using various methods and techniques to achieve desired results. Some photo manipulations are considered skillful artwork while others are frowned upon as unethical practices, especially when used to deceive the public. Other examples include being used for political propaganda, or to make a product or person look better, or simply for entertainment purposes or harmless pranks. Depending on the application and intent, some photo manipulations are considered an art form because it involves the creation of unique images and in some instances, signature expressions of art by photographic artists. For example, Ansel Adams employed some of the more common manipulations using darkroom exposure techniques, burning (darkening) and dodging (lightening) a photograph. Other examples of photo manipulation include retouching photographs using ink or paint, airbrushing, double exposure, piecing photos or negatives together in the darkroom, scratching instant films, or through the use of software-based manipulation tools applied to digital images. There are a number of software applications available for digital image manipulation, ranging from professional applications to very basic imaging software for casual users.
  • 17.9K
  • 24 Oct 2022
Topic Review
Vocaloid
Vocaloid is a singing voice synthesizer and the first engine released in the Vocaloid series. It was succeeded by Vocaloid 2. This version was made to be able to sing both English and Japanese.
  • 9.6K
  • 17 Oct 2022
Topic Review
Sigma-Algebra
In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections. The pair (X, Σ) is called a measurable space or Borel space. A σ-algebra is a type of algebra of sets. An algebra of sets needs only to be closed under the union or intersection of finitely many subsets, which is a weaker condition. The main use of σ-algebras is in the definition of measures; specifically, the collection of those subsets for which a given measure is defined is necessarily a σ-algebra. This concept is important in mathematical analysis as the foundation for Lebesgue integration, and in probability theory, where it is interpreted as the collection of events which can be assigned probabilities. Also, in probability, σ-algebras are pivotal in the definition of conditional expectation. In statistics, (sub) σ-algebras are needed for the formal mathematical definition of a sufficient statistic, particularly when the statistic is a function or a random process and the notion of conditional density is not applicable. If X = {a, b, c, d}, one possible σ-algebra on X is Σ = { ∅, {a, b}, {c, d}, {a, b, c, d} }, where ∅ is the empty set. In general, a finite algebra is always a σ-algebra. If {A1, A2, A3, …} is a countable partition of X then the collection of all unions of sets in the partition (including the empty set) is a σ-algebra. A more useful example is the set of subsets of the real line formed by starting with all open intervals and adding in all countable unions, countable intersections, and relative complements and continuing this process (by transfinite iteration through all countable ordinals) until the relevant closure properties are achieved (a construction known as the Borel hierarchy).
  • 9.5K
  • 01 Dec 2022
Topic Review
Snakes and Ladders
Snakes and Ladders, known originally as Moksha Patam, is an ancient Indian board game for two or more players regarded today as a worldwide classic. It is played on a game board with numbered, gridded squares. A number of "ladders" and "snakes" are pictured on the board, each connecting two specific board squares. The object of the game is to navigate one's game piece, according to die rolls, from the start (bottom square) to the finish (top square), helped by climbing ladders but hindered by falling down snakes. The game is a simple race based on sheer luck, and it is popular with young children. The historic version had its roots in morality lessons, on which a player's progression up the board represented a life journey complicated by virtues (ladders) and vices (snakes). The game is also sold under other names such as Chutes and Ladders, Bible Ups and Downs, etc., some with a morality motif; a morality Chutes and Ladders was published by Milton Bradley starting from 1943.
  • 9.1K
  • 09 Oct 2022
Topic Review
Well-Defined
In mathematics, an expression is called well-defined or unambiguous if its definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well-defined, ill-defined or ambiguous. A function is well-defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if f takes real numbers as input, and if f(0.5) does not equal f(1/2) then f is not well-defined (and thus not a function). The term well-defined can also be used to indicate that a logical expression is unambiguous or uncontradictory. A function that is not well-defined is not the same as a function that is undefined. For example, if f(x) = 1/x, then the fact that f(0) is undefined does not mean that the f is not well-defined — but that 0 is simply not in the domain of f.
  • 7.9K
  • 01 Dec 2022
Topic Review
Decimation (Signal Processing)
In digital signal processing, decimation is the process of reducing the sampling rate of a signal.  The term downsampling usually refers to one step of the process, but sometimes the terms are used interchangeably.  Complementary to upsampling, which increases sampling rate, decimation is a specific case of sample rate conversion in a multi-rate digital signal processing system. A system component that performs decimation is called a decimator. When decimation is performed on a sequence of samples of a signal or other continuous function, it produces an approximation of the sequence that would have been obtained by sampling the signal at a lower rate (or density, as in the case of a photograph). The decimation factor is usually an integer or a rational fraction greater than one. This factor multiplies the sampling interval or, equivalently, divides the sampling rate. For example, if compact disc audio at 44,100 samples/second is decimated by a factor of 5/4, the resulting sample rate is 35,280.
  • 7.3K
  • 23 Nov 2022
Topic Review
Partition (Number Theory)
In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.) For example, 4 can be partitioned in five distinct ways: 4 3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1 The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition 2 + 1 + 1. A summand in a partition is also called a part. The number of partitions of n is given by the partition function p(n). So p(4) = 5. The notation λ ⊢ n means that λ is a partition of n. Partitions can be graphically visualized with Young diagrams or Ferrers diagrams. They occur in a number of branches of mathematics and physics, including the study of symmetric polynomials and of the symmetric group and in group representation theory in general.
  • 6.9K
  • 04 Nov 2022
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