Explore topic-wise fullforms in Maths

INFO: Full form for HVDM is Heterogeneous Value Difference Metric in Maths category
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INFO: Full form for STLC is Simply-typed Lambda-calculus in Maths category
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INFO: Full form for SELA is Stochastic Estimator Learning Algorithm in Maths category
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INFO: Full form for UGIT is Universal Graph Isomorphism Tuple in Maths category
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INFO: Full form for XNR is X Converted To A Number in Maths category
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INFO: Full form for RTPG is Relaxed Temporal Planning Graph in Maths category
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INFO: Full form for RGML is Rdf Graph Modeling Language in Maths category
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INFO: Full form for QVR is Quantity Variances Function in Maths category
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INFO: Full form for XGMML is Extensible Graph Markup and Modeling Language in Maths category
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INFO: Full form for RTPG is Refined Type Pose Geometry in Maths category
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INFO: Full form for FESE is First Even Second Even in Maths category
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INFO: Full form for ATFT is Adaptive Time Frequency Transform in Maths category
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INFO: Full form for AAGR is As A General Rule in Maths category
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INFO: Full form for QFD is Quadratic Finite Difference in Maths category
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INFO: Full form for VBEG is Vectoralized Blume Emery Griffiths in Maths category
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INFO: Full form for SPDE is Sampling Point Data Entry in Maths category
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INFO: Full form for UUB is Uehling- Uhlenbeck- Boltzmann Equation in Maths category
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INFO: Full form for WBFT is Wavelet-based Fourier Transform in Maths category
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INFO: Full form for TMAX is Total Maximum in Maths category
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INFO: Full form for DERD is Delta Encoding Via Resemblance Detection in Maths category
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INFO: Full form for HBOA is Hierarchical Bayesian Optimization Algorithm in Maths category
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INFO: Full form for P(E) is The Perimeter of E in Maths category

INFO: Full form for FUF is Functional Unification Formalism in Maths category
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INFO: Full form for QPCA is Quadtree Principal Components Analysis in Maths category
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INFO: Full form for LPDE is Linear Partial Differential Equation in Maths category
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INFO: Full form for QPCA is Quadratic Principal Component Analysis in Maths category
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INFO: Full form for SPDE is Stochastic Partial Differential Equation in Maths category
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INFO: Full form for PILP is Parametric Integer Linear Program in Maths category
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INFO: Full form for HTMC is High-throughput Monte-carlo in Maths category
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INFO: Full form for FLASH is Factual Lines About Submarine Hazards in Maths category
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INFO: Full form for TXZ is Tensor X-z Plane in Maths category
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INFO: Full form for TXZ is Transfer, From X To Z in Maths category
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INFO: Full form for XY is Horizontal Vertical in Maths category
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INFO: Full form for WXT is Windowed Xray Transform in Maths category
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INFO: Full form for XLV is Roman Numeral 45 in Maths category
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INFO: Full form for XM is X Midpoint in Maths category
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INFO: Full form for XV is Roman Numeral 15 in Maths category
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INFO: Full form for XX is Roman Numeral 20 in Maths category
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INFO: Full form for QOV is Quasi-option Value in Maths category
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INFO: Full form for QOV is Quasi Optimal Value in Maths category
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INFO: Full form for WBTS is Water Balance Time Series in Maths category
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The Planck constant, or Planck's constant, is a fundamental physical constant denoted h {\displaystyle h} , and is of fundamental importance in quantum mechanics. A photon's energy is equal to its frequency multiplied by the Planck constant. Due to mass–energy equivalence, the Planck constant also relates mass to frequency.

In metrology it is used, together with other constants, to define the kilogram, an SI unit. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value h {\displaystyle h} = 6.62607015×10−34 J⋅Hz−1.

At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but predictions of the frequency distribution of the radiation by then-existing theories diverged significantly at higher frequencies. In 1900, Max Planck empirically derived a formula for the observed spectrum. He assumed a hypothetical electrically charged oscillator in a cavity that contained black-body radiation could only change its energy in a minimal increment, E , {\displaystyle E,} that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant from the experimental measurements, and that constant is named in his honor. In 1905, Albert Einstein determined a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, and was eventually called a photon. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".

Confusion can arise when dealing with frequency or the Planck constant because the units of angular measure (cycle or radian) are omitted in SI. In the language of quantity calculus, the expression for the value of the Planck constant, or a frequency, is the product of a numerical value and a unit of measurement. The symbol f (or ν), when used for the value of a frequency, implies cycles per second or hertz as the unit. When the symbol ω is used for the frequency's value it implies radians per second as the unit. The numerical values of these two ways of expressing the frequency have a ratio of 2π. Omitting the units of angular measure "cycle" and "radian" can lead to an error of 2π. A similar state of affairs occurs for the Planck constant. The symbol h is used to express the value of the Planck constant in J⋅s/cycle, and the symbol ħ ("h-bar") is used to express its value in J⋅s/rad. Both represent the value of the Planck constant, but, as discussed above, their numerical values have a ratio of 2π. In this article the word "value" as used in the tables means "numerical value", and the equations involving the Planck constant and/or frequency actually involve their numerical values using the appropriate implied units.

50 (fifty) is the natural number following 49 and preceding 51.

Infinity is that which is boundless or endless, or something that is larger than any real or natural number. It is often denoted by the infinity symbol.

Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all of its points, their infinite number (i.e., the cardinality of the line) is larger than the number of integers. In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object.

The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets. Among the axioms of Zermelo–Fraenkel set theory, on which most of modern mathematics can be developed, is the axiom of infinity, which guarantees the existence of infinite sets. The mathematical concept of infinity and the manipulation of infinite sets are used everywhere in mathematics, even in areas such as combinatorics that may seem to have nothing to do with them. For example, Wiles's proof of Fermat's Last Theorem implicitly relies on the existence of very large infinite sets for solving a long-standing problem that is stated in terms of elementary arithmetic.

In physics and cosmology, whether the Universe is infinite is an open question.

INFO: Full form for SIM is Simple Integration Method in Maths category
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INFO: Full form for ERP is Error Reduction Parameter in Maths category
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INFO: Full form for GSM is Generalized Second Moment in Maths category
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INFO: Full form for NCR is The Number of Combinations of R in Maths category
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INFO: Full form for MIS is Mathematics In The Sciences in Maths category
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In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be close to that sample. In other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample.

In a more precise sense, the PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and its integral over the entire space is equal to 1.

The terms "probability distribution function" and "probability function" have also sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. In other sources, "probability distribution function" may be used when the probability distribution is defined as a function over general sets of values or it may refer to the cumulative distribution function, or it may be a probability mass function (PMF) rather than the density. "Density function" itself is also used for the probability mass function, leading to further confusion. In general though, the PMF is used in the context of discrete random variables (random variables that take values on a countable set), while the PDF is used in the context of continuous random variables.