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Mathematical functions that quantify complexity
A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of
Height_function
Measure of vertical distance
tree, the height of a vertex is the length of the longest downward path to a leaf from that vertex; In algebraic number theory, a "height function" is a measurement
Height
mathematics, the height zeta function of an algebraic variety or more generally a subset of a variety encodes the distribution of points of given height. If S is
Height_zeta_function
Unsolved problem in number theory
of rational points on an algebraic variety relative to a suitable height function. It was proposed by Yuri I. Manin and his collaborators in 1989 when
Manin_conjecture
Geometric construct
height function associating an integer to the vertices of the grid. For instance, draw a chessboard, fix a node A 0 {\displaystyle A_{0}} with height
Domino_tiling
Canonical height The canonical height on an abelian variety is a height function that is a distinguished quadratic form. See Néron–Tate height. Chabauty's
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Topics referred to by the same term
properties of an element Height (ring theory), a measurement in commutative algebra Height (triangle) or altitude Height function, a function that quantifies the
Height_(disambiguation)
Concept in statistical mechanics
Gaussian random field, a central model of random surfaces (random height functions). The discrete version can be defined on any graph, usually a lattice
Gaussian_free_field
{\displaystyle T_{w}(W_{s}(x_{i}))+T_{w}(W_{u}(x_{j}))=T_{w}(M)} . Any Morse function f on a compact Riemannian manifold M defines a gradient vector field. If
Morse–Smale_system
common, that they have a fluctuating height function or some analogue function, that can be thought of as a function, that models the growth of the model
KPZ_fixed_point
Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the
Function_(mathematics)
Ground device to measure aircraft altitude
[citation needed] Height finding radars of the 1960s and 70s were distinguished by their antenna being tall, but narrow. As beam shape is a function of antenna
Height_finder
The group of K-rational points of an abelian variety is a finitely-generated abelian group
same basic structure. The second half of the proof needs some type of height function, in terms of which to bound the 'size' of points of A(K). Some measure
Mordell–Weil_theorem
Algebraic curve in mathematics
This height function h has the property that h(mP) grows roughly like the square of m. Moreover, only finitely many rational points with height smaller
Elliptic_curve
mathematicians Michael Prähofer and Herbert Spohn. They proved that the height function of a model from the (1+1)-dimensional KPZ universality class - the
Airy_process
Number of independent rational basis points with infinite order
This requires the introduction of a height function on the set of rational elliptic curves. To define such a function, recall that a rational elliptic curve
Rank_of_an_elliptic_curve
candidates of the United States is useful for evaluating what role, if any, height plays in presidential elections in the United States. Some observers have
Heights of presidents and presidential candidates of the United States
Heights_of_presidents_and_presidential_candidates_of_the_United_States
Mathematical function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}
Gaussian_function
on the large sieve method, extends this result, counting points by height function and showing, in a strong sense, that a thin set contains a low proportion
Thin_set_(Serre)
Type of knot in knot theory
2-bridge knot is a knot which can be regular isotoped so that the natural height function given by the z-coordinate has only two maxima and two minima as critical
2-bridge_knot
Mathematics
similar formal properties to the abscissa of convergence of the height zeta function and it is conjectured that they are essentially the same. More precisely
Nevanlinna_invariant
Multivariate derivative (mathematics)
is 40% times the cosine of 60°, or 20%. More generally, if the hill height function H is differentiable, then the gradient of H dotted with a unit vector
Gradient
In number theory, the Néron–Tate height (or canonical height) is a quadratic form on the Mordell–Weil group of rational points of an abelian variety defined
Néron–Tate_height
intended here as enclosed structures with continuously occupiable floors and a height of at least 350 metres (1,148 ft). Such definition excludes non-building
List_of_tallest_buildings
Measure of polynomial height
_{2})\cdots (z-\alpha _{n}).} The Mahler measure can be viewed as a kind of height function. Using Jensen's formula, it can be proved that this measure is also
Mahler_measure
Measurement of the shape of a tooth
specifically for its function and to allow for its self-cleaning ability. The proximal contact areas formed mesially and distally by the height of contour are
Height_of_curvature
Tent function, often used in signal processing
an isosceles triangle of height 1 and base 2 in which case it is referred to as the triangular function. Triangular functions are useful in signal processing
Triangular_function
Vector differential operator
of increase at the point. In particular, if a hill is defined as a height function over a plane h(x,y), the gradient at a given location will be a vector
Del
Line of ultraportable notebook computers by Apple
headphone jack, four-speaker sound system with Spatial Audio, full height function keys, and four finishes (Silver, Space Gray, Starlight, and Midnight)
MacBook_Air
Type of generalization of periodic functions in Euclidean space
operators on G; and to satisfy a "moderate growth" asymptotic condition a height function. It is the first of these that makes F automorphic, that is, satisfy
Automorphic_form
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
Type of energy
However, in this case the barrier height does not depend on We. The barrier height now depends on the work function of the collector, as well as any additional
Work_function
Conjecture on zeros of the zeta function
zeta function. After a suitable rescaling to account for the increasing density of zeros with height, the conjectured pair correlation function agrees
Riemann_hypothesis
Self-balancing binary search tree
the height function of an AVL tree obeys the constraints of a WAVL tree, and we may convert any AVL tree into a WAVL tree by using the height of each
WAVL_tree
Mathematical function with no sudden changes
example, the function H(t) denoting the height of a growing flower at time t would be considered continuous. In contrast, the function M(t) denoting
Continuous_function
Distance over which a quantity decreases by a factor of e
28.964 Da × 1.660×10−27 kg/Da = 4.808×10−26 kg. As a function of temperature, the scale height of Earth's atmosphere is therefore H/T = kB/mg = 1.381×10−23 J⋅K−1
Scale_height
Index of lists with the same name
zeta function of a variety Height zeta function of a variety Hurwitz zeta function, a generalization of the Riemann zeta function Igusa zeta function Ihara
List_of_zeta_functions
Multivalued function in mathematics
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse
Lambert_W_function
Arithmetic operation
exponentiation n − 1 {\displaystyle n-1} times. The number n is called the height of the function, while a is called the base, analogous to exponentiation. It is
Tetration
Mathematical Journal (170(2)): 247–277. Moriwaki, Atsushi (2000). "Arithmetic height functions over finitely generated fields". Inventiones (140(1)): 101–142. Mazur
Bogomolov_conjecture
Type of raster image in computer graphics
displacement or "height" from the "floor" of a surface and sometimes visualized as luma of a grayscale image, with black representing minimum height and white
Heightmap
Integral expressing the amount of overlap of one function as it is shifted over another
mathematical operation on two functions f and g that produces a third function f∗g, as the integral of the product of the two functions after one is reflected
Convolution
Uniform restraint of the change in functions
In mathematics, a real function f {\displaystyle f} of real numbers is said to be uniformly continuous if there is a positive real number δ {\displaystyle
Uniform_continuity
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Variable that represents an argument to a function
variables from a function in C, one may write: int width; int height; f(x, &width, &height); where x is an input parameter and width and height are output parameters;
Parameter (computer programming)
Parameter_(computer_programming)
Derivative of a function with multiple variables
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held
Partial_derivative
S-shaped curve
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac
Logistic_function
On heights of points on algebraic varieties over number fields
absolute value v {\displaystyle v} on F {\displaystyle F} , a local height function λ D , v {\displaystyle \lambda _{D,v}} . Fix a finite set of absolute
Vojta's_conjecture
Proposed lower bound on the Mahler measure for polynomials with integer coefficients
\mathbb {R} } be the canonical height function. The canonical height is the analogue for elliptic curves of the function ( deg P ) − 1 log M ( P (
Lehmer's_conjecture
Mathematical function, denoted exp(x) or e^x
point is equal to its height (its y-coordinate) at that point. There are several equivalent definitions of the exponential function, although of very different
Exponential_function
Method of mathematical integration
of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the x-axis. The
Lebesgue_integral
Operation in calculus
a function f with respect to such a tagged partition is defined as ∑i=1nf(ti)Δi; thus each term of the sum is the area of a rectangle with height equal
Integral
Mathematical proof technique using contradiction
explicit the way of quantifying the size of a solution, by means of a height function – a concept that became foundational. To show that A(Q)/2A(Q) is finite
Proof_by_infinite_descent
Polynomial function of degree two
In mathematics, a quadratic function of a single variable is a function of the form f ( x ) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c} with
Quadratic_function
Branch of mathematics
about a manifold is deduced from changes in the rank of the Jacobian of a function. For a list of differential topology topics, see the following reference:
Differential_topology
Analyzes the topology of a manifold by studying differentiable functions on that manifold
studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiable function on a manifold will
Morse_theory
Type of altitude above mean sea level
T} are ambient pressure and temperature, respectively, as functions of geopotential height, and R {\displaystyle R} is the specific gas constant. For
Geopotential_height
Single measure of some attribute of a sample
statistic is used both for the function (e.g., a calculation method of the average) and for the value of the function on a given sample (e.g., the result
Statistic
Self-balancing binary search tree
cases restoring the height for any further ancestor nodes. Join will therefore require at most two rotations. The cost of this function is the difference
AVL_tree
degree to which a tree's stem or bole decreases in diameter as a function of height above ground. Within Forestry and for the purposes of timber production
Tree_taper
Classification of symplectic toric manifolds
\mathbb {CP} ^{1}\cong \mathbb {S} ^{2}} , with moment map given by the height function; its associated Delzant polytope is a segment. The Delzant correspondence
Delzant's_theorem
The study of height and intelligence examines correlations between human height and human intelligence. Some epidemiological research on the subject has
Height_and_intelligence
measurements. Some laser hypsometers have a built in height measurement function. Before using this function the user should read the instructions on how it
Tree_height_measurement
Concept in computer programming
equivalent: MyFunctionCall({ xPosition: 20, yPosition: 50, width: 100, height: 5, drawingNow: true }); MyFunctionCall({ width: 100, height: 5, xPosition:
Named_parameter
Branch of mathematics
distance of 150 miles. Plotting the velocity as a function of time yields a rectangle with a height equal to the velocity and a width equal to the time
Calculus
Mathematical abstraction of level sets
mathematical object reflecting the evolution of the level sets of a real-valued function on a manifold. A similar concept was introduced by G.M. Adelson-Velskii
Reeb_graph
Distance between the base of a tire and the lowest point of the automobile
Ride height or ground clearance is the amount of space between the base of an automobile tire and the lowest point of the automobile, typically the bottom
Ride_height
Enclosed structure
a house or factory. Buildings come in a variety of sizes, shapes, and functions, and have been adapted throughout history in response to numerous factors
Building
On the connectivity of a group of diffeomorphisms of a manifold
the proof is to think of the height function as a 1-parameter family of smooth functions on M by considering the function π [ 0 , 1 ] ∘ f t {\displaystyle
Pseudoisotopy_theorem
Sequence of program instructions invokable by other software
In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-formed
Function (computer programming)
Function_(computer_programming)
French mathematician (1906-1998)
descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which
André_Weil
Shape containing unit line segments in all directions
minimum area for convex sets is achieved by an equilateral triangle of height 1 and area 1/√3, as Gyula Pál showed in 1920. Kakeya seems to have suggested
Kakeya_set
Self-balancing binary search tree data structure
T''[recte T'] */ function joinLeftRB(TL, k, TR): /* symmetric to joinRightRB */ function join(TL, k, TR): if TL.blackHeight>TR.blackHeight: T'=joinRightRB(TL
Red–black_tree
the total floor area, or the total building height in terms of number of floors occupied for the function. However, care should be taken in the case of
History of the world's tallest buildings
History_of_the_world's_tallest_buildings
Shape descriptions in a geometrical/topological sense
Size functions are shape descriptors, in a geometrical/topological sense. They are functions from the half-plane x < y {\displaystyle x<y} to the natural
Size_function
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Small size of an organism, caused by growth deficiency or genetic mutations
humans, it is defined as an adult height of 147 centimetres (4 ft 10 in) or less, regardless of sex; the average adult height among people with dwarfism is
Dwarfism
Italian mathematician (1530–1590)
rational interval in lowest terms; this can be considered an early height function. Isaac Beeckman and Marin Mersenne both adopted this theory in the
Giambattista_Benedetti
Fast-growing function
the similar TREE function Hydra game ^ a Friedman actually writes this as 2[2000], which denotes an exponential stack of 2's of height 2000 using his notation
Friedman's_SSCG_function
Well-quasi-ordering of finite trees
application of the theorem gives the existence of a fast-growing TREE function. TREE(3) is one of the largest simply defined finite numbers, dwarfing
Kruskal's_tree_theorem
Skyscraper in Dubai, United Arab Emirates
world's tallest structure, with a total height of 829.8 m (2,722 ft, or just over half a mile) and a roof height (excluding the antenna, but including a
Burj_Khalifa
Position along a vertical direction above or below a given vertical datum
Drying height Dynamic height Ellipsoidal height Geocentric altitude Geopotential Height above mean sea level Height above average terrain Height above
Vertical_position
Mathematical function
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for
Generalised_logistic_function
Purported type of inferiority complex
significant differences in personality functioning or aspects of daily living were found which could be attributable to height"; these traits included generalizations
Napoleon_complex
Polynomial equation of degree two
called solutions of the equation, and roots or zeros of the quadratic function on its left-hand side. A quadratic equation has at most two solutions.
Quadratic_equation
Key on computer keyboards
overlapping and distinct functions dependent on operating system and application. The return key has its origins in two typewriter functions: carriage return
Enter_and_return_keys
Volume of air in the lungs
relation to height and age ((0.0275* Age [Years]+0.0189*Height [cm]−2.6139) litres for normal-mass individuals and (0.0277*Age [Years]+0.0138*Height [cm]−2
Lung_volumes_and_capacities
Concept in economics and decision theory
such as height, weight, temperature, etc can measure utility. Neoclassical economics has largely retreated from using cardinal utility functions as the
Utility
Change of direction of propagation due to variation of velocity
elastic media (gases, liquids, and solids) in which the wave velocity is a function of spatial coordinates. Bending of acoustic rays in layered inhomogeneous
Refraction_(sound)
Residential skyscraper in the Southbank precinct of Melbourne, Victoria, Australia
building in Australia by roof height, surpassing the Eureka Tower, the second-tallest building in Australia by full height (which includes architectural
Australia_108
Feature observed in spectroscopy
shapes include Lorentzian, Gaussian and Voigt functions, whose parameters are the line position, maximum height and half-width. Actual line shapes are determined
Spectral_line_shape
Concept in geometry
positive root of the cosine function or, equivalently, the half-period of the sine (or cosine) function. The cosine function can be defined either as a
Area_of_a_circle
Probability distribution
real-valued random variable. The general form of its probability density function is f(x)=12πσ2exp(−(x−μ)22σ2). The parameter μ is the mean or expectation
Normal_distribution
Computer modelling of a petroleum reservoir
zones. Using the porosity and permeability models and a saturation height function, initial saturation models are built. If volumetric calculations identify
Reservoir_modeling
Equation to derive time of sunset and sunrise
this gives ψ = 1.75 ′ height in metres {\displaystyle \psi =1.75^{\prime }{\sqrt {\text{height in metres}}}} or ψ = 0.97 ′ height in feet {\displaystyle
Sunrise_equation
Curve along which a 3D surface is at equal elevation
the function has the same particular value. In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above
Contour_line
Variable representing a random phenomenon
may be the person's height. Mathematically, the random variable is interpreted as a function which maps the person to their height. Associated with the
Random_variable
Distance from finger tips to finger tips
parallel to the ground at shoulder height at a 90° angle. The arm span measurement is usually very close to the person's height. Age, sex, and ethnicity have
Arm_span
automatic height controller continuously monitors suspension position and adjusts ride height using electronically controlled actuators. Its main functions include:
Automatic_height_controller
Tool in multivariate statistical analysis
the Matérn covariance, also called the Matérn kernel, is a covariance function used in spatial statistics, geostatistics, machine learning, image analysis
Matérn_covariance_function
travel, tourism, insurance
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travel, tourism, insurance