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Differentiable function whose derivative is not Riemann integrable
In mathematics, Volterra's function, named for Vito Volterra, is a real-valued function V defined on the real line R with the following curious combination
Volterra's_function
Set of real numbers in mathematics
positive area. The Smith–Volterra–Cantor set is used in the construction of Volterra's function (see external link). The Smith–Volterra–Cantor set is an example
Smith–Volterra–Cantor_set
Equations modelling predator–prey cycles
The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear differential equations, frequently
Lotka–Volterra_equations
Italian mathematician and physicist (1860–1940)
dei Lincei. Volterra (crater) Volterra's function Lotka–Volterra equation Smith–Volterra–Cantor set Volterra integral equation Volterra series Product
Vito_Volterra
Model for approximating non-linear effects, similar to a Taylor series
{\displaystyle y} . The function h n ( τ 1 , … , τ n ) {\displaystyle h_{n}(\tau _{1},\dots ,\tau _{n})} is called the n-th-order Volterra kernel. It can be
Volterra_series
Operator equation in the style of Fredholm theory
) {\displaystyle f(t)} is a given function and x ( t ) {\displaystyle x(t)} is to be determined. A linear Volterra equation of the second kind is x (
Volterra_integral_equation
Function that is discontinuous at rationals and continuous at irrationals
Thomae's function is a real-valued function of a real variable that can be defined as: f ( x ) = { 1 q if x = p q ( x is rational), with p ∈ Z and
Thomae's_function
Topics referred to by the same term
predator–prey equations Smith–Volterra–Cantor set, a Cantor set with measure greater than zero Volterra's function, a differentiable function whose derivative is
Volterra_(disambiguation)
Model of multi-species population dynamics
The competitive Lotka–Volterra equations are a simple model of the population dynamics of species competing for some common resource. They can be further
Competitive Lotka–Volterra equations
Competitive_Lotka–Volterra_equations
Method of solution to differential equations
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with
Green's_function
Counterintuitive mathematical object
dense but has positive measure. The Fabius function is everywhere smooth but nowhere analytic. Volterra's function is differentiable with bounded derivative
Pathological_(mathematics)
Indefinite integral
function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function
Antiderivative
Bounded linear operator
the Volterra operator, named after Vito Volterra, is a bounded linear operator on the space L2[0,1] of complex-valued square-integrable functions on the
Volterra_operator
Relationship between derivatives and integrals
differentiating a function (calculating its slopes, or rate of change at every point on its domain) with the concept of integrating a function (calculating
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Real function with finite total variation
In mathematical analysis, a function of bounded variation, also known as BV function, is a real-valued function whose total variation is bounded (finite):
Bounded_variation
model for Langmuir waves in plasmas. The Volterra lattice is the set of ordinary differential equations for functions an: a n ′ = a n ( a n + 1 − a n − 1 )
Volterra_lattice
Integral expressing the amount of overlap of one function as it is shifted over another
mathematician Vito Volterra in 1913. When a function g T {\displaystyle g_{T}} is periodic, with period T {\displaystyle T} , then for functions, f {\displaystyle
Convolution
Relationship of a signal transducer
A linear response function describes the input-output relationship of a signal transducer, such as a radio turning electromagnetic waves into music or
Linear_response_function
Topics referred to by the same term
The Volterra equation may refer to the Volterra integral equation, an integral in the style of Fredholm theory. Product integral, an integral over an
Volterra_equation
System where changes of output are not proportional to changes of input
unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which
Nonlinear_system
Community of living organisms together with the nonliving components of their environment
reorganize, while undergoing change so as to retain essentially the same function, structure, identity, is termed its ecological resilience. Ecosystems can
Ecosystem
Software programming optimization technique
programs. It works by storing the results of expensive calls to pure functions, so that these results can be returned quickly should the same inputs
Memoization
Model in theoretical ecology and statistical mechanics
The random generalized Lotka–Volterra model (rGLV) is an ecological model and random set of coupled ordinary differential equations where the parameters
Random generalized Lotka–Volterra model
Random_generalized_Lotka–Volterra_model
Equations with an unknown function under an integral sign
a linear Volterra integral equation of the second kind for an unknown function y ( t ) {\displaystyle y(t)} and a given continuous function g ( t ) {\displaystyle
Integral_equation
Mathematical function describing predator consumption of prey
predator–prey interaction firstly described by Volterra and Lotka in the Lotka–Volterra equation. A trophic function represents the consumption of prey assuming
Trophic_function
Integral using products instead of sums
mathematician Vito Volterra in 1887 to solve systems of linear differential equations. The classical Riemann integral of a function f : [ a , b ] → R {\displaystyle
Product_integral
In scattering theory, the Jost function is the Wronskian of the regular solution and the (irregular) Jost solution to the differential equation − ψ ″ +
Jost_function
Mutually beneficial interaction between species
example, mutualistic interactions are vital for terrestrial ecosystem function as: about 80% of land plants species rely on mycorrhizal relationships
Mutualism_(biology)
Aspect of ecosystems
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Food_chain
Theory in actuarial science and applied probability
penalty function. Since the function measures the actuarial present value of the penalty that occurs at τ {\displaystyle \tau } , the penalty function is multiplied
Ruin_theory
Virus that infects bacteria
awoken from his coma and become responsive. As his immune system began to function he had to be temporarily removed from the cocktail because his fever was
Bacteriophage
Ecological concept; intake rate of a consumer as a function of food density
A functional response in ecology is the intake rate of a consumer as a function of food density (the amount of food available in a given ecotope). It is
Functional_response
Dynamical system
dynamically on the distribution of population types, making the fitness function an endogenous component of the system. This allows it to model frequency-dependent
Replicator_equation
U.S. information technology company
product offering being built on the platforms of BIG-IP, Shape Security, and Volterra. The primary offering in this suite is the SaaS-based web application and
F5,_Inc.
Differential equation with deviating argument
involve the given function's derivative with delays while neutral differential equations do. Integro-differential equations of Volterra type are functional
Functional differential equation
Functional_differential_equation
Mathematical framework
was an improvement over earlier predator-prey models, notably the Lotka–Volterra equations, by incorporating more realistic biological assumptions and providing
Kolmogorov_population_model
System with self-optimizing transfer function
An adaptive filter is a system with a linear filter that has a transfer function controlled by variable parameters and a means to adjust those parameters
Adaptive_filter
Identification of nonlinear systems
categorized into five basic approaches, each defined by a model class: Volterra series models, Block-structured models, Neural network models, NARMAX models
Nonlinear system identification
Nonlinear_system_identification
Behavior characterized by activity during the night and sleeping during the day
illumination (see metaturnal). Others, such as bushbabies and (some) bats, can function only at night. Many nocturnal creatures including tarsiers and some owls
Nocturnal_animal
Area of mathematics
noun goes back to the calculus of variations, implying a function whose argument is a function. The term was first used in Hadamard's 1910 book on that
Functional_analysis
Beneficial symbiosis between species
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Commensalism
Set of points on a line segment with certain topological properties
be interesting in science." The indicator function of the Cantor set Smith–Volterra–Cantor set Cantor function Cantor cube Antoine's necklace Koch snowflake
Cantor_set
Typically mathematical representation of an ecological system
A spatial model is one that has one or more state variables that are a function of space, or can be related to other spatial variables. After construction
Ecosystem_model
Species introduced by human activity
D. (2020). "Introduced herbivores restore Late Pleistocene ecological functions". Proceedings of the National Academy of Sciences. 117 (14): 7871–7878
Introduced_species
Roman god
closed to mark the arrival of peace. As a god of transitions, he had functions pertaining to birth and to journeys and exchange, and in his association
Janus
Region of Italy
"Federalism" (PDF). idea.int. In rare cases, subnational institutions may function very differently from the national level: in Italy, for example, the national
Tuscany
Equation composed of a function being summed
s,x(s){\bigr )}} where x is the unknown function, s, t are integers, and f, k are known functions. Volterra integral equations on time scales: Basic
Summation_equation
Ecological theory concerning the selection of life history traits
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
R/K_selection_theory
Type of heterotrophic nutrition based on decayed organic matter
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Saprotroph
Basic integral in elementary calculus
Smith–Volterra–Cantor set, and let IC be its indicator function. Because C is not Jordan measurable, IC is not Riemann integrable. Moreover, no function g
Riemann_integral
Numerical integration method
trapezoidal rule works by approximating the region under the graph of the function f ( x ) {\displaystyle f(x)} as a trapezoid and calculating its area. This
Trapezoidal_rule
Ecological communities abruptly losing biodiversity, often irreversibly
characteristics of the previous ecosystem, yet has a greatly altered structure and function. There are exceptions where an ecosystem can be recovered past the point
Ecosystem_collapse
term containing the kernel function (defined below) has constants as integration limits. A closely related form is the Volterra integral equation which has
Fredholm_integral_equation
Predator at the top of a food chain
predators, and may be capable of self-regulation. They are central to the functioning of ecosystems, the regulation of disease, and the maintenance of biodiversity
Apex_predator
Period of Roman history (c. 509 – 27 BC)
Senate... he showed no sign of wanting to replace the Senate in its normal functions". Amid wide-ranging and popular reforms to create grain subsidies, change
Roman_Republic
Biological interaction
Schulze, Ernst-Detlef; Mooney, Harold A. (eds.). Biodiversity and Ecosystem Function. Springer. p. 237. ISBN 978-3-642-58001-7. Botkin, D.; Keller, E. (2003)
Predation
Living creatures that eat organisms from a different population
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Consumer_(food_chain)
Function acting on function spaces
In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly and sometimes
Operator_(mathematics)
Study of distribution of species
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Biogeography
n(t,a)} is a function of age a {\displaystyle a} and time t {\displaystyle t} , and m ( a ) {\displaystyle m(a)} is the death function. When m ( a )
Von_Foerster_equation
Type of environment in which an organism lives
number of deep sea creatures are bioluminescent; this serves a variety of functions including predation, protection and social recognition. In general, the
Habitat
Ecogeographical rule in evolutionary biology
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Foster's_rule
Organism that eats mostly or exclusively plant material
(1 August 2008). "Faunal impact on vegetation structure and ecosystem function in mangrove forests: A review". Aquatic Botany. Mangrove Ecology – Applications
Herbivore
Luxury compact executive car
design alloy wheels, Two-tone Graphite/Black Volterra leather, 3-spoke sports leather/Alcantara multi-function steering wheel with gear knob and hand brake
Audi_A4
Biological process to convert light into chemical energy
quitensis, show a variation of photosynthesis where calcium oxalate crystals function as dynamic carbon pools, supplying carbon dioxide (CO2) to photosynthetic
Photosynthesis
Repetitive variation of some measure about a central value
solution to this differential equation produces a sinusoidal position function: x ( t ) = A cos ( ω t − δ ) {\displaystyle x(t)=A\cos(\omega t-\delta
Oscillation
Rocky pool on a seashore, separated from the sea at low tide, filled with seawater
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Tide_pool
Branch of mathematics
to other fields of mathematics. Unifying the work on function spaces of Georg Cantor, Vito Volterra, Cesare Arzelà, Jacques Hadamard, Giulio Ascoli and
Topology
Legendary Greek king of Ithaca
and the symbol "ΔΗ" (which may indicate "public"), confirms the site's function in formal religious rituals. This indicates that the sanctuary catered
Odysseus
between Green's and Riemann–Volterra methods (in some literature the Riemann function is called the Riemann–Green function ), their application to the
Spacetime triangle diagram technique
Spacetime_triangle_diagram_technique
Mathematical theory on dynamical systems
exists a C 1 {\displaystyle C^{1}} function φ ( x , y ) {\displaystyle \varphi (x,y)} (called the Dulac function) such that the expression ∂ ( φ f )
Bendixson–Dulac_theorem
growth Generalized logistic differential equation for growth modeling Lotka–Volterra equations to describe the dynamics of biological systems in which two species
List of named differential equations
List_of_named_differential_equations
Ecological concept
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Edge_effects
Italian polymath (1452–1519)
skeleton, its parts, and the muscles and sinews. He studied the mechanical functions of the skeleton and the muscular forces that are applied to it in a manner
Leonardo_da_Vinci
Study of organisms and their environment
dimensions are defined as environmental variables and whose size is a function of the number of values that the environmental values may assume for which
Ecology
Organism that eats mostly or exclusively animal tissue
gobiconodontids and Jugulator, with a three-cusp anatomy which nevertheless functioned similarly to carnassials. Mesocarnivore Ullrey, Duane E. "Nutrient". Encyclopedia
Carnivore
Italian mathematician and mathematical physicist
mathematician and mathematical physicist known for her collaboration with Vito Volterra on mathematical analysis and its applications to electromagnetism and biomathematics
Elena_Freda
Type of brain cell
star-shaped glial cells in the brain and spinal cord. They perform many functions, including biochemical control of endothelial cells that form the blood–brain
Astrocyte
Organism using energy from light in metabolic processes
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Phototroph
Animal that can eat and survive on both plants and animals
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Omnivore
Associated populations of species in a given area
Climate change and the introduction of invasive species can affect the functioning of key species and thus have knock-on effects on the community processes
Community_(ecology)
Holy site of Judaism in Jerusalem
of Jerusalem in Jewish sources of the 15th century (e.g., Meshullam of Volterra, Obadiah of Bertinoro, etc.). The name Western Wall, used by Obadiah, refers—as
Western_Wall
Chapel in the Apostolic Palace, Vatican City
centuries ago. While known as the location of papal conclaves, the primary function of the Sistine Chapel is as the chapel of the Papal Chapel (Cappella Pontificia)
Sistine_Chapel
Expansion of the time evolution operator
V(t_{1})U(t_{1},t_{0})},} which is ultimately a type of Volterra integral. An iterative solution of the Volterra equation above leads to the following Neumann series:
Dyson_series
Hypothesis about plant resource use competition in community ecology
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
R*_rule_(ecology)
Non-living factors that affect organisms and ecosystems
physical parts of the environment that affect living organisms and the functioning of ecosystems. Abiotic factors and the phenomena associated with them
Abiotic_component
Urban patriciates of the Papal States' March of Ancona (16th–18th centuries)
concentration of legislative, executive, and first-instance judicial functions. In the sixteenth century these urban elites formally excluded other social
Civic nobility in the Papal States' March of Ancona
Civic_nobility_in_the_Papal_States'_March_of_Ancona
Making predation pressure a function of the ratio of prey to predators contrasts with the prey-dependent Lotka–Volterra equations, where the per capita
Arditi–Ginzburg_equations
Process of progressive accumulation in food chain
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Biomagnification
Integral used in the theory of vibrations
It is the convolution of a linear system's impulse response function with the input function. The response of a linear, viscously-damped, single degree
Duhamel's_integral
Organism type
organisms, called heterotrophs, take in autotrophs as food to carry out functions necessary for their life. Thus, heterotrophs – all animals, almost all
Autotroph
Species that is able to thrive in a wide variety of environmental conditions
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Generalist and specialist species
Generalist_and_specialist_species
Hybrid creature in Ancient Greek folklore
Aristophanes, who used it as one of his favourite insults. The precise function of the Hippalectryon remains a mystery; as an apotropaic and prophylactic
Hippalectryon
Dutch graphic artist (1898–1972)
life, Escher traveled through Italy, visiting Florence, San Gimignano, Volterra, Siena, and Ravello. In the same year, he traveled through Spain, visiting
M._C._Escher
City in New Mexico, United States
neighborhood is located in the foothills of Southeast Albuquerque. The Volterra subdivision lies west of Four Hills. Popular urban neighborhoods that can
Albuquerque,_New_Mexico
Volterra operator, defined as follows: consider the unit square X = [0,1] × [0,1] ⊂ R2, with the Lebesgue measure m. On X, define the kernel function
Nilpotent_operator
Group of separated yet interacting ecological populations
on the Lotka–Volterra equation, which was formulated in the mid-1920s, but no further application had been conducted. The Lotka-Volterra equation suggested
Metapopulation
Ecological competition between different species
have been formalized in a mathematical model called the Competitive Lotka–Volterra equations, which creates a theoretical prediction of interactions. It combines
Interspecific_competition
Scientific discipline
which differs from Lotka-Volterra and SIR models in that it is discrete in time. This model, like that of Lotka-Volterra, tracks both populations explicitly
Theoretical_ecology
Ecological competition between organisms of the same species
Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation Overexploitation
Intraspecific_competition
VOLTERRAS FUNCTION
VOLTERRAS FUNCTION
Biblical
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Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, Functionary of the Interior.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, a great functionary.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a high Egyptian functionary.
Male
Celtic
, great justiciary, or functionary.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
VOLTERRAS FUNCTION
VOLTERRAS FUNCTION
Boy/Male
American, Australian, Portuguese, Spanish
Liberator
Boy/Male
American, Chinese, Danish, Dutch, French, German, Latin, Teutonic
Eager to Please; Industrious
Boy/Male
Latin English French
Enduring.
Boy/Male
Hebrew
Cherished. Famous bearers: British pop star David Bowie, American talk-show host David Letterman.
Boy/Male
Shakespearean
The Tragedy of Othello' A Cypriot official.
Boy/Male
Arabic, Hindu, Indian, Marathi, Muslim, Tamil
Compromise; One who Shines
Biblical
same as Nephishesim
Boy/Male
American, British, English
Lives at the Castle Ford
Boy/Male
English American
From the valley.
Boy/Male
British, English
Prayer
VOLTERRAS FUNCTION
VOLTERRAS FUNCTION
VOLTERRAS FUNCTION
VOLTERRAS FUNCTION
VOLTERRAS FUNCTION
prep.
Acting as a substitute; -- said of abnormal action which replaces a suppressed normal function; as, vicarious hemorrhage replacing menstruation.
v. i.
Alt. of Functionate
a.
Destitute of function, or of an appropriate organ. Darwin.
a.
Of, pertaining to, or designating, certain secret tribunals which flourished in Germany from the end of the 12th century to the middle of the 16th, usurping many of the functions of the government which were too weak to maintain law and order, and inspiring dread in all who came within their jurisdiction.
a.
Having relation to growth or nutrition; partaking of simple growth and enlargement of the systems of nutrition, apart from the sensorial or distinctively animal functions; vegetal.
n.
Fig.: Any cavity, or hollow place, in which any function may be conceived of as operating.
a.
Of or pertaining to the vessels of animal and vegetable bodies; as, the vascular functions.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.
adv.
In a functional manner; as regards normal or appropriate activity.
a.
Belonging or relating to life, either animal or vegetable; as, vital energies; vital functions; vital actions.
n.
The doctrine that all the functions of a living organism are due to an unknown vital principle distinct from all chemical and physical forces.
n.
One deputed or authorized to perform the functions of another; a substitute in office; a deputy.
v. i.
To execute or perform a function; to transact one's regular or appointed business.
v. t.
To assign to some function or office.
pl.
of Functionary
a.
Pertaining to the function of an organ or part, or to the functions in general.
a.
Pertaining to, or connected with, a function or duty; official.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.