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Trying to map moments to a measure that generates them
1 ] {\displaystyle [0,1]} . The moment problem also extends to complex analysis as the trigonometric moment problem in which the Hankel matrices are
Moment_problem
}} , it is referred to as the truncated trigonometric moment problem. The trigonometric moment problem is solvable, that is, { c k } k = 0 n {\displaystyle
Trigonometric_moment_problem
Probability problem
In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m0, m1, m2, ...), does there
Hamburger_moment_problem
Probability problem
In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence (m0, m1,
Hausdorff_moment_problem
Probability of shared birthdays
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday
Birthday_problem
Probability problem
In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (m0, m1, m2
Stieltjes_moment_problem
Mathematical problem involving optimal stopping theory
known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also
Secretary_problem
Probability puzzle
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal
Monty_Hall_problem
Decomposition of periodic functions
of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a
Fourier_series
Problem in statistical estimation
In the statistical theory of estimation, the German tank problem consists of estimating the maximum of a discrete uniform distribution from sampling without
German_tank_problem
Mathematical problem
The Sleeping Beauty problem, also known as the Sleeping Beauty paradox, is a puzzle in decision theory in which an ideally rational epistemic agent is
Sleeping_Beauty_problem
Concept in probability theory and gambling
gambler's ruin problem is a letter from Blaise Pascal to Pierre Fermat in 1656 (two years after the more famous correspondence on the problem of points).
Gambler's_ruin
Mathematical problem
The three prisoners problem appeared in Martin Gardner's "Mathematical Games" column in Scientific American in 1959. It is mathematically equivalent to
Three_prisoners_problem
Problem in probability theory
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory. One of the famous problems that
Problem_of_points
Puzzle in logic and mathematics
The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory and for
Two_envelopes_problem
Problem in probability theory
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following
Coupon_collector's_problem
Question in geometric probability
In probability theory, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: Suppose we have
Buffon's_needle_problem
Paradox in probability theory
theory, which are also known as the two children problem, Mr. Smith's children and the Mrs. Smith problem. The initial formulation of the question dates
Boy_or_girl_paradox
Mental exercise in probability and statistics
In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc
Urn_problem
Mathematical paradox
Monty Hall problem the three prisoners problem the two envelopes problem the Sleeping Beauty problem The Monty Hall and Three Prisoners problems are identical
Bertrand's_box_paradox
Problem asking the probability that the sun will rise tomorrow
present moment can arrest the course of it. E.T. Jaynes noted that Laplace's warning had gone unheeded by workers in the field. A reference class problem arises:
Sunrise_problem
Paradox involving a game with repeated coin flipping
amount of money a casino would need to continue the game indefinitely. The problem was invented by Nicolas Bernoulli, who stated it in a letter to Pierre
St._Petersburg_paradox
Election result probability theorem
In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B receives q votes with
Bertrand's_ballot_theorem
Probability theory paradox
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités
Bertrand paradox (probability)
Bertrand_paradox_(probability)
Variation of Buffon's needle
In geometric probability, the problem of Buffon's noodle is a variation on the well-known problem of Buffon's needle, named after Georges-Louis Leclerc
Buffon's_noodle
Financial phenomenon
identified by economist Jeremy Siegel in 1972. Like the related two envelopes problem, the phenomenon is sometimes labeled a paradox because an agent can seem
Siegel's_paradox
Problem in probability
Banach's match problem is a classic problem in probability attributed to Stefan Banach. Feller says that the problem was inspired by a humorous reference
Banach's_matchbox_problem
Balanced or random resource allocation
balanced allocations) problem is a classic problem in probability theory that has many applications in computer science. The problem involves m balls and
Balls_into_bins_problem
}}(\xi )\,d\xi =\nu (\{0\}).} Lebesgue's decomposition theorem Trigonometric moment problem Furstenberg's Conjecture on 2-3-invariant continuous probability
Wiener's_lemma
In game theory, the Waldegrave problem is a problem first described in the second edition of Pierre Raymond de Montmort`s Essay d'analyse sur les jeux
Waldegrave_problem
Determinant of large Toeplitz matrices
_{k=1}^{\infty }k\left|{\widehat {c}}_{k}\right|^{2}\right).} Trigonometric moment problem Verblunsky's theorem Böttcher, Albrecht; Silbermann, Bernd (1990)
Szegő_limit_theorems
Aspect of control theory
In probability theory, the Mabinogion sheep problem or Mabinogian urn is a problem in stochastic control introduced by David Williams (mathematician) in
Mabinogion_sheep_problem
Math puzzle
pill, then it is simply consumed and nothing is returned to the jar. The problem becomes very easy to solve once a binary variable Xk defined as Xk = 1
Pill_puzzle
Problem in geometric probability
In geometric probability, the broken stick problem asks for the probability that one can form a triangle from the three parts of a line segment that has
Broken_stick_problem
Probability problem
The Newton–Pepys problem is a probability problem concerning the probability of throwing sixes from a certain number of dice. In 1693 Samuel Pepys and
Newton–Pepys_problem
are an example of orthogonal polynomials on the unit circle. Trigonometric moment problem Schur class Simon 2005a, p. 43. Simon 2010, p. 44. Simon 2010
Orthogonal polynomials on the unit circle
Orthogonal_polynomials_on_the_unit_circle
mathematical field of combinatorial geometry, the Littlewood–Offord problem is the problem of determining the number of subsums of a set of vectors that fall
Littlewood–Offord_problem
variables Moment problem Hamburger moment problem Carleman's condition Hausdorff moment problem Trigonometric moment problem Stieltjes moment problem Prior
List_of_probability_topics
Problem in geometric probability
Sylvester's four point problem in geometric probability asks for the probability that four randomly chosen points in the Euclidean plane form a convex
Sylvester's four point problem
Sylvester's_four_point_problem
Standard deviation / (1:DCR) Standardized moment / (1:R) Stieltjes moment problem / anl (1:R) Trigonometric moment problem / anl (1:R) Uncorrelated / (2:R) Variance /
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
"Average distance between two points in a box (solution to elementary problem E2629)". American Mathematical Monthly. 85 (4): 277–278. doi:10.2307/2321177
Mean_line_segment_length
Hungarian mathematician
methods of functional analysis. In the early 1920s, he worked on the moment problem, to which he introduced the operator-theoretic approach by proving the
Marcel_Riesz
Class of problems in classical mechanics
the problem can be solved analytically, i.e., in terms of well-studied functions such as trigonometric functions. The solution of this problem is important
Classical central-force problem
Classical_central-force_problem
Method of determining a location
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points.
Triangulation
Mathematical function, inverse of an exponential function
{1}{d}}\log _{10}c}.} Trigonometric calculations were facilitated by tables that contained the common logarithms of trigonometric functions. Another critical
Logarithm
(2)=\sum _{k=1}^{\infty }{\frac {1}{k^{2}}}={\frac {\pi ^{2}}{6}}} (the Basel problem) ζ ( 4 ) = ∑ k = 1 ∞ 1 k 4 = π 4 90 {\displaystyle \zeta (4)=\sum _{k=1}^{\infty
List_of_mathematical_series
Polynomial sequence
the forward and inverse Zernike transform use symmetry properties of trigonometric functions, separability of radial and azimuthal parts of Zernike polynomials
Zernike_polynomials
American theoretical physicist (1918–1988)
saying that his IQ was too low. When Feynman was 15, he taught himself trigonometry, advanced algebra, infinite series, analytic geometry, and both differential
Richard_Feynman
Greek astronomer, geographer and mathematician (c. 190 – c. 120 BCE)
others. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. His other reputed achievements
Hipparchus
polyhedra. Pacific J. Math. 132 (1988), no. 1, 35–62. K. Schmüdgen. "The K-moment problem for compact semi-algebraic sets". Math. Ann. 289 (1991), no. 2, 203–206
Positive_polynomial
2-DoF mechanism with 5 links and 5 joints
be calculated as a function of the x,y coordinates of point D using trigonometric functions. This robotic configuration is a parallel manipulator. It
Five-bar_linkage
Mathematician (1845–1918)
n in the nth derived set Sn of a set S of zeros of a trigonometric series. Given a trigonometric series f(x) with S as its set of zeros, Cantor had discovered
Georg_Cantor
Relation between sides of a right triangle
+r_{2}^{2}-2r_{1}r_{2}\cos \Delta \theta ,\end{aligned}}} using the trigonometric product-to-sum formulas. This formula is the law of cosines, sometimes
Pythagorean_theorem
Swiss mathematician (1707–1783)
applied to the argument x. He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also
Leonhard_Euler
Formulation of classical mechanics
necessary condition describing extremal geometry in generalizations of problems from the calculus of variations. It can be understood as a special case
Hamilton–Jacobi_equation
Method for estimating new data outside known data points
example is truncated power series representations of sin(x) and related trigonometric functions. For instance, taking only data from near the x = 0, we may
Extrapolation
Landmark textbook in classical mechanics by E. T. Whittaker
problem. The last chapter includes discussions of solutions of the problems of previous chapters by integration of series, particularly trigonometric
Analytical Dynamics of Particles and Rigid Bodies
Analytical_Dynamics_of_Particles_and_Rigid_Bodies
Direction that Muslims face while praying salah
allows the exact calculation (hisab) of the qibla using a spherical trigonometric formula that takes the coordinates of a location and of the Kaaba as
Qibla
Analytic function in mathematics
; Titulaer, U. M. (1992). "An accurate two-stream moment method for kinetic boundary layer problems of linear kinetic equations". J. Phys. A: Math. Gen
Riemann_zeta_function
Device used for calculations
markets. For example, there are scientific calculators, which include trigonometric and statistical calculations. Some calculators even have the ability
Calculator
Moment in time used as a reference point in astronomy
In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the
Epoch_(astronomy)
Mathematical treatise by Bhāskara II
childless and unmarried. To avoid this fate, he ascertained an auspicious moment for his daughter's wedding. To alert his daughter at the correct time, he
Līlāvatī
Development of linear transformations forming the Lorentz group
transformations: Minkowski (1907–1908) and Sommerfeld (1909) used imaginary trigonometric functions, Frank (1909) and Varićak (1910) used hyperbolic functions
History of Lorentz transformations
History_of_Lorentz_transformations
Distance from center of Earth to center of Moon
parallax of the Moon as viewed from opposite sides of the Earth, involving trigonometric terms. This is equivalent to a formula for the inverse of the distance
Lunar_distance
Deformation of slabs under load
^{2}w}{\partial x^{2}}}+{\frac {\partial ^{2}w}{\partial y^{2}}}\right)} The twisting moment per unit length is given by M x y = − D ( 1 − ν ) ∂ 2 w ∂ x ∂ y {\displaystyle
Bending_of_plates
Process of steering a ship from a starting point to a destination
triangle by mathematical and trigonometric methods. There are many methods to do this. The manual methods use tables (trigonometric, logarithms, etc.) to facilitate
Marine_navigation
Branch of mathematics
mathematical limit. Calculus is the "mathematical backbone" for solving problems in which variable quantities change with time or another reference value
Calculus
Mathematical conjecture on the Riemann zeta function
ISSN 0065-1036. Kolesnik, G. A. (1973). "On the estimation of some trigonometric sums". Acta Arithmetica (in Russian). 25 (1): 7–30. ISSN 0065-1036.
Lindelöf_hypothesis
Greek mathematician and physicist (c. 287 – 212 BC)
his works. Another story of a problem that Archimedes is credited solving with in service of Hiero II is the "wreath problem." According to Vitruvius, writing
Archimedes
Probability distribution
at t = 1 {\displaystyle t=1} give the expected value of these basic trigonometric and hyperbolic functions over a Gaussian random variable X ∼ N ( μ
Normal_distribution
Study of Earth's spatial information
who found a way for a single man, at a single moment, to measure the earth's circumference, by trigonometric calculations based on angles measured from a
Geography
Number, approximately 3.14
semicircle. The existence of such integrals makes π an algebraic period. The trigonometric functions rely on angles, and mathematicians generally use the radian
Pi
Table of positions of astronomical objects at given times
orbit – Orbital perturbations Ptolemy's table of chords – 2nd century AD trigonometric table Two-line element set – Orbital data format William of Saint-Cloud –
Ephemeris
Dutch computer scientist (1930–2002)
"speak to him for a moment"; when I left his office a number of hours later, I was another person. For after having listened to my problems patiently, he agreed
Edsger_W._Dijkstra
Field of knowledge
served as the basis for initial sunclocks. Nubians also exercised a trigonometric methodology comparable to their Egyptian counterparts. Evidence for
Mathematics
Ancient Egyptian mathematical document
Papyrus". Brooklyn Museum. Retrieved November 1, 2012. Maor, Eli (1998). Trigonometric Delights. Princeton University Press. p. 20. ISBN 0-691-09541-8. Wikimedia
Rhind_Mathematical_Papyrus
Product of a number by itself
same way Lagrange's identity Other Parseval's identity Pythagorean trigonometric identity acceleration, length per square time coupling constant (has
Square_(algebra)
Period of cultural flourishing from 786 to 1258
pointer, and equator to accurately show where the stars are at that given moment. Use of the astrolabe is best expressed in Al-Farghani's treatise on the
Islamic_Golden_Age
Fundamental theorem in probability theory and statistics
Theorem 1. Klartag (2007), Theorem 1.1. Zygmund, Antoni (2003) [1959]. Trigonometric Series. Cambridge University Press. vol. II, sect. XVI.5, Theorem 5-5
Central_limit_theorem
Angular distance between the Moon and another celestial body
entire degree. The clearing correction for parallax and refraction is a trigonometric function of the observed lunar distance and the altitudes of the two
Lunar_distance_(navigation)
Russian theoretical physicist
contribution to the three body problem was Brumberg's construction of a series of polynomials converging for any real time moment. Brumberg also worked on the
Victor_Brumberg
Fictional character in The Big Bang Theory and Young Sheldon
forced to break his rule about urinating in a moving vehicle. After this moment Wil Wheaton became number six on Sheldon's mortal enemy list (a list he
Sheldon_Cooper
Description of physical properties at the atomic and subatomic scale
equation relates the collection of probability amplitudes that pertain to one moment of time to the collection of probability amplitudes that pertain to another
Quantum_mechanics
Natural satellite orbiting Earth
shielded from the radio chatter of Earth. The lunar soil, although it poses a problem for any moving parts of telescopes, can be mixed with carbon nanotubes
Moon
Medieval technique of navigational computation
navigational computation that uses compass direction, distance and a simple trigonometric table known as the toleta de marteloio. The rule told mariners how to
Rule_of_marteloio
Integral transform useful in probability theory, physics, and engineering
equation Generating function Hamburger moment problem Hardy–Littlewood Tauberian theorem Laplace–Carson transform Moment-generating function Nonlocal operator
Laplace_transform
First artificial Earth satellite
satellite were initially calculated using arithmometers and six-digit trigonometric tables. More complex calculations were carried out on a newly-installed
Sputnik_1
Mathematical relation defining a sequence
use of complex numbers can be eliminated by rewriting the solution in trigonometric form. In this case we can write the eigenvalues as λ 1 , λ 2 = α ± β
Linear recurrence with constant coefficients
Linear_recurrence_with_constant_coefficients
Aircraft system for aiming bombs
through the sights. The distance between the aircraft and target at that moment is the range, so this angle is often referred to as the range angle, although
Bombsight
Something that has mass and volume
; Quiroga-Nuñez, L. H.; van Langevelde, H. J. (10 November 2019). "Trigonometric Parallaxes of High-mass Star-forming Regions: Our View of the Milky
Matter
Mathematics independent of applications
Nevertheless, almost all mathematical theories remained motivated by problems coming from the real world or from less abstract mathematical theories
Pure_mathematics
Mathematical transform that expresses a function of time as a function of frequency
)\sin(2\pi \lambda t){\bigr )}\,d\lambda .} This is called an expansion as a trigonometric integral, or a Fourier integral expansion. The coefficient functions
Fourier_transform
Geometric representation of the complex numbers
All the familiar properties of the complex exponential function, the trigonometric functions, and the complex logarithm can be deduced directly from the
Complex_plane
Distance measuring technique
position from one point of measurement to another, astronomers can use trigonometry to calculate how far away the star is. The concept hinges on the geometry
Parallax_in_astronomy
1214/aoms/1177728796. Lukacs, Eugene; Szász, Otto (1954). "Nonnegative trigonometric polynomials and certain rational characteristic functions". Journal
Eugene_Lukacs
Mathematical operation on vectors in 3D space
\right\|^{2}\left(1-\cos ^{2}\theta \right).} Invoking the Pythagorean trigonometric identity one obtains: ‖ a × b ‖ = ‖ a ‖ ‖ b ‖ | sin θ | , {\displaystyle
Cross_product
Cohort born from 1946 to 1964
"never before in history had youth been so idealized as they were at this moment." According to her, when Generation X came along, it had much to live up
Baby_boomers
Ethnic group
and Thābit theorem by Thābit ibn Qurra, the discovery of several new trigonometric identities by Ibn Yunus and al-Battani, the mathematical proof for Ceva's
Arabs
British explorer and naval officer (1728–1779)
of the Admiralty and the Royal Society. This acclaim came at a pivotal moment in British overseas exploration, and it led to his commission in 1768 as
James_Cook
Persian polymath and poet (1048–1131)
to derive approximate numerical solutions for cubic equations using trigonometric tables. He also contributed to a deeper understanding of Euclid's parallel
Omar_Khayyam
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