| slovo | definícia |
functions
(mass) | functions
- funkcie |
functions
(encz) | functions,funkce Pavel Machek; Giza |
| | podobné slovo | definícia |
malfunctions
(encz) | malfunctions,poruchy n: pl. Zdeněk Brož |
Calculus of functions
(gcide) | Function \Func"tion\, n. [L. functio, fr. fungi to perform,
execute, akin to Skr. bhuj to enjoy, have the use of: cf. F.
fonction. Cf. Defunct.]
1. The act of executing or performing any duty, office, or
calling; performance. "In the function of his public
calling." --Swift.
[1913 Webster]
2. (Physiol.) 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.
[1913 Webster]
3. The natural or assigned action of any power or faculty, as
of the soul, or of the intellect; the exertion of an
energy of some determinate kind.
[1913 Webster]
As the mind opens, and its functions spread. --Pope.
[1913 Webster]
4. The course of action which peculiarly pertains to any
public officer in church or state; the activity
appropriate to any business or profession.
[1913 Webster]
Tradesmen . . . going about their functions. --Shak.
[1913 Webster]
The malady which made him incapable of performing
his
regal functions. --Macaulay.
[1913 Webster]
5. (Math.) 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 x^2, 3^x, Log. x, and
Sin. x, are all functions of x.
[1913 Webster]
6. (Eccl.) A religious ceremony, esp. one particularly
impressive and elaborate.
Every solemn `function' performed with the
requirements of the liturgy. --Card.
Wiseman.
[Webster 1913 Suppl.]
7. A public or social ceremony or gathering; a festivity or
entertainment, esp. one somewhat formal.
This function, which is our chief social event. --W.
D. Howells.
[Webster 1913 Suppl.]
Algebraic function, a quantity whose connection with the
variable is expressed by an equation that involves only
the algebraic operations of addition, subtraction,
multiplication, division, raising to a given power, and
extracting a given root; -- opposed to transcendental
function.
Arbitrary function. See under Arbitrary.
Calculus of functions. See under Calculus.
Carnot's function (Thermo-dynamics), a relation between the
amount of heat given off by a source of heat, and the work
which can be done by it. It is approximately equal to the
mechanical equivalent of the thermal unit divided by the
number expressing the temperature in degrees of the air
thermometer, reckoned from its zero of expansion.
Circular functions. See Inverse trigonometrical functions
(below). -- Continuous function, a quantity that has no
interruption in the continuity of its real values, as the
variable changes between any specified limits.
Discontinuous function. See under Discontinuous.
Elliptic functions, a large and important class of
functions, so called because one of the forms expresses
the relation of the arc of an ellipse to the straight
lines connected therewith.
Explicit function, a quantity directly expressed in terms
of the independently varying quantity; thus, in the
equations y = 6x^2, y = 10 -x^3, the quantity y is an
explicit function of x.
Implicit function, a quantity whose relation to the
variable is expressed indirectly by an equation; thus, y
in the equation x^2 + y^2 = 100 is an implicit
function of x.
Inverse trigonometrical functions, or Circular functions,
the lengths of arcs relative to the sines, tangents, etc.
Thus, AB is the arc whose sine is BD, and (if the length
of BD is x) is written sin ^-1x, and so of the other
lines. See Trigonometrical function (below). Other
transcendental functions are the exponential functions,
the elliptic functions, the gamma functions, the theta
functions, etc.
One-valued function, a quantity that has one, and only one,
value for each value of the variable. -- {Transcendental
functions}, a quantity whose connection with the variable
cannot be expressed by algebraic operations; thus, y in
the equation y = 10^x is a transcendental function of x.
See Algebraic function (above). -- {Trigonometrical
function}, a quantity whose relation to the variable is the
same as that of a certain straight line drawn in a circle
whose radius is unity, to the length of a corresponding
are of the circle. Let AB be an arc in a circle, whose
radius OA is unity let AC be a quadrant, and let OC, DB,
and AF be drawnpependicular to OA, and EB and CG parallel
to OA, and let OB be produced to G and F. E Then BD is the
sine of the arc AB; OD or EB is the cosine, AF is the
tangent, CG is the cotangent, OF is the secant OG is the
cosecant, AD is the versed sine, and CE is the coversed
sine of the are AB. If the length of AB be represented by
x (OA being unity) then the lengths of Functions. these
lines (OA being unity) are the trigonometrical functions
of x, and are written sin x, cos x, tan x (or tang x), cot
x, sec x, cosec x, versin x, coversin x. These quantities
are also considered as functions of the angle BOA.
FunctionCalculus \Cal"cu*lus\, n.; pl. Calculi. [L, calculus. See
Calculate, and Calcule.]
1. (Med.) Any solid concretion, formed in any part of the
body, but most frequent in the organs that act as
reservoirs, and in the passages connected with them; as,
biliary calculi; urinary calculi, etc.
[1913 Webster]
2. (Math.) A method of computation; any process of reasoning
by the use of symbols; any branch of mathematics that may
involve calculation.
[1913 Webster]
Barycentric calculus, a method of treating geometry by
defining a point as the center of gravity of certain other
points to which co["e]fficients or weights are ascribed.
Calculus of functions, that branch of mathematics which
treats of the forms of functions that shall satisfy given
conditions.
Calculus of operations, that branch of mathematical logic
that treats of all operations that satisfy given
conditions.
Calculus of probabilities, the science that treats of the
computation of the probabilities of events, or the
application of numbers to chance.
Calculus of variations, a branch of mathematics in which
the laws of dependence which bind the variable quantities
together are themselves subject to change.
Differential calculus, a method of investigating
mathematical questions by using the ratio of certain
indefinitely small quantities called differentials. The
problems are primarily of this form: to find how the
change in some variable quantity alters at each instant
the value of a quantity dependent upon it.
Exponential calculus, that part of algebra which treats of
exponents.
Imaginary calculus, a method of investigating the relations
of real or imaginary quantities by the use of the
imaginary symbols and quantities of algebra.
Integral calculus, a method which in the reverse of the
differential, the primary object of which is to learn from
the known ratio of the indefinitely small changes of two
or more magnitudes, the relation of the magnitudes
themselves, or, in other words, from having the
differential of an algebraic expression to find the
expression itself.
[1913 Webster] |
Circular functions
(gcide) | Function \Func"tion\, n. [L. functio, fr. fungi to perform,
execute, akin to Skr. bhuj to enjoy, have the use of: cf. F.
fonction. Cf. Defunct.]
1. The act of executing or performing any duty, office, or
calling; performance. "In the function of his public
calling." --Swift.
[1913 Webster]
2. (Physiol.) 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.
[1913 Webster]
3. The natural or assigned action of any power or faculty, as
of the soul, or of the intellect; the exertion of an
energy of some determinate kind.
[1913 Webster]
As the mind opens, and its functions spread. --Pope.
[1913 Webster]
4. The course of action which peculiarly pertains to any
public officer in church or state; the activity
appropriate to any business or profession.
[1913 Webster]
Tradesmen . . . going about their functions. --Shak.
[1913 Webster]
The malady which made him incapable of performing
his
regal functions. --Macaulay.
[1913 Webster]
5. (Math.) 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 x^2, 3^x, Log. x, and
Sin. x, are all functions of x.
[1913 Webster]
6. (Eccl.) A religious ceremony, esp. one particularly
impressive and elaborate.
Every solemn `function' performed with the
requirements of the liturgy. --Card.
Wiseman.
[Webster 1913 Suppl.]
7. A public or social ceremony or gathering; a festivity or
entertainment, esp. one somewhat formal.
This function, which is our chief social event. --W.
D. Howells.
[Webster 1913 Suppl.]
Algebraic function, a quantity whose connection with the
variable is expressed by an equation that involves only
the algebraic operations of addition, subtraction,
multiplication, division, raising to a given power, and
extracting a given root; -- opposed to transcendental
function.
Arbitrary function. See under Arbitrary.
Calculus of functions. See under Calculus.
Carnot's function (Thermo-dynamics), a relation between the
amount of heat given off by a source of heat, and the work
which can be done by it. It is approximately equal to the
mechanical equivalent of the thermal unit divided by the
number expressing the temperature in degrees of the air
thermometer, reckoned from its zero of expansion.
Circular functions. See Inverse trigonometrical functions
(below). -- Continuous function, a quantity that has no
interruption in the continuity of its real values, as the
variable changes between any specified limits.
Discontinuous function. See under Discontinuous.
Elliptic functions, a large and important class of
functions, so called because one of the forms expresses
the relation of the arc of an ellipse to the straight
lines connected therewith.
Explicit function, a quantity directly expressed in terms
of the independently varying quantity; thus, in the
equations y = 6x^2, y = 10 -x^3, the quantity y is an
explicit function of x.
Implicit function, a quantity whose relation to the
variable is expressed indirectly by an equation; thus, y
in the equation x^2 + y^2 = 100 is an implicit
function of x.
Inverse trigonometrical functions, or Circular functions,
the lengths of arcs relative to the sines, tangents, etc.
Thus, AB is the arc whose sine is BD, and (if the length
of BD is x) is written sin ^-1x, and so of the other
lines. See Trigonometrical function (below). Other
transcendental functions are the exponential functions,
the elliptic functions, the gamma functions, the theta
functions, etc.
One-valued function, a quantity that has one, and only one,
value for each value of the variable. -- {Transcendental
functions}, a quantity whose connection with the variable
cannot be expressed by algebraic operations; thus, y in
the equation y = 10^x is a transcendental function of x.
See Algebraic function (above). -- {Trigonometrical
function}, a quantity whose relation to the variable is the
same as that of a certain straight line drawn in a circle
whose radius is unity, to the length of a corresponding
are of the circle. Let AB be an arc in a circle, whose
radius OA is unity let AC be a quadrant, and let OC, DB,
and AF be drawnpependicular to OA, and EB and CG parallel
to OA, and let OB be produced to G and F. E Then BD is the
sine of the arc AB; OD or EB is the cosine, AF is the
tangent, CG is the cotangent, OF is the secant OG is the
cosecant, AD is the versed sine, and CE is the coversed
sine of the are AB. If the length of AB be represented by
x (OA being unity) then the lengths of Functions. these
lines (OA being unity) are the trigonometrical functions
of x, and are written sin x, cos x, tan x (or tang x), cot
x, sec x, cosec x, versin x, coversin x. These quantities
are also considered as functions of the angle BOA.
FunctionCircular \Cir"cu*lar\, a. [L. circularis, fr. circulus circle:
cf. F. circulaire. See Circle.]
[1913 Webster]
1. In the form of, or bounded by, a circle; round.
[1913 Webster]
2. repeating itself; ending in itself; reverting to the point
of beginning; hence, illogical; inconclusive; as, circular
reasoning.
[1913 Webster]
3. Adhering to a fixed circle of legends; cyclic; hence,
mean; inferior. See Cyclic poets, under Cyclic.
[1913 Webster]
Had Virgil been a circular poet, and closely adhered
to history, how could the Romans have had Dido?
--Dennis.
[1913 Webster]
4. Addressed to a circle, or to a number of persons having a
common interest; circulated, or intended for circulation;
as, a circular letter.
[1913 Webster]
A proclamation of Henry III., . . . doubtless
circular throughout England. --Hallam.
[1913 Webster]
5. Perfect; complete. [Obs.]
[1913 Webster]
A man so absolute and circular
In all those wished-for rarities that may take
A virgin captive. --Massinger.
[1913 Webster]
Circular are, any portion of the circumference of a circle.
Circular cubics (Math.), curves of the third order which
are imagined to pass through the two circular points at
infinity.
Circular functions. (Math.) See under Function.
Circular instruments, mathematical instruments employed for
measuring angles, in which the graduation extends round
the whole circumference of a circle, or 360[deg].
Circular lines, straight lines pertaining to the circle, as
sines, tangents, secants, etc.
Circular note or Circular letter.
(a) (Com.) See under Credit.
(b) (Diplomacy) A letter addressed in identical terms to a
number of persons.
Circular numbers (Arith.), those whose powers terminate in
the same digits as the roots themselves; as 5 and 6, whose
squares are 25 and 36. --Bailey. --Barlow.
Circular points at infinity (Geom.), two imaginary points
at infinite distance through which every circle in the
plane is, in the theory of curves, imagined to pass.
Circular polarization. (Min.) See under Polarization.
Circular sailing or Globular sailing (Naut.), the method
of sailing by the arc of a great circle.
Circular saw. See under Saw.
[1913 Webster] |
Elliptic functions
(gcide) | Function \Func"tion\, n. [L. functio, fr. fungi to perform,
execute, akin to Skr. bhuj to enjoy, have the use of: cf. F.
fonction. Cf. Defunct.]
1. The act of executing or performing any duty, office, or
calling; performance. "In the function of his public
calling." --Swift.
[1913 Webster]
2. (Physiol.) 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.
[1913 Webster]
3. The natural or assigned action of any power or faculty, as
of the soul, or of the intellect; the exertion of an
energy of some determinate kind.
[1913 Webster]
As the mind opens, and its functions spread. --Pope.
[1913 Webster]
4. The course of action which peculiarly pertains to any
public officer in church or state; the activity
appropriate to any business or profession.
[1913 Webster]
Tradesmen . . . going about their functions. --Shak.
[1913 Webster]
The malady which made him incapable of performing
his
regal functions. --Macaulay.
[1913 Webster]
5. (Math.) 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 x^2, 3^x, Log. x, and
Sin. x, are all functions of x.
[1913 Webster]
6. (Eccl.) A religious ceremony, esp. one particularly
impressive and elaborate.
Every solemn `function' performed with the
requirements of the liturgy. --Card.
Wiseman.
[Webster 1913 Suppl.]
7. A public or social ceremony or gathering; a festivity or
entertainment, esp. one somewhat formal.
This function, which is our chief social event. --W.
D. Howells.
[Webster 1913 Suppl.]
Algebraic function, a quantity whose connection with the
variable is expressed by an equation that involves only
the algebraic operations of addition, subtraction,
multiplication, division, raising to a given power, and
extracting a given root; -- opposed to transcendental
function.
Arbitrary function. See under Arbitrary.
Calculus of functions. See under Calculus.
Carnot's function (Thermo-dynamics), a relation between the
amount of heat given off by a source of heat, and the work
which can be done by it. It is approximately equal to the
mechanical equivalent of the thermal unit divided by the
number expressing the temperature in degrees of the air
thermometer, reckoned from its zero of expansion.
Circular functions. See Inverse trigonometrical functions
(below). -- Continuous function, a quantity that has no
interruption in the continuity of its real values, as the
variable changes between any specified limits.
Discontinuous function. See under Discontinuous.
Elliptic functions, a large and important class of
functions, so called because one of the forms expresses
the relation of the arc of an ellipse to the straight
lines connected therewith.
Explicit function, a quantity directly expressed in terms
of the independently varying quantity; thus, in the
equations y = 6x^2, y = 10 -x^3, the quantity y is an
explicit function of x.
Implicit function, a quantity whose relation to the
variable is expressed indirectly by an equation; thus, y
in the equation x^2 + y^2 = 100 is an implicit
function of x.
Inverse trigonometrical functions, or Circular functions,
the lengths of arcs relative to the sines, tangents, etc.
Thus, AB is the arc whose sine is BD, and (if the length
of BD is x) is written sin ^-1x, and so of the other
lines. See Trigonometrical function (below). Other
transcendental functions are the exponential functions,
the elliptic functions, the gamma functions, the theta
functions, etc.
One-valued function, a quantity that has one, and only one,
value for each value of the variable. -- {Transcendental
functions}, a quantity whose connection with the variable
cannot be expressed by algebraic operations; thus, y in
the equation y = 10^x is a transcendental function of x.
See Algebraic function (above). -- {Trigonometrical
function}, a quantity whose relation to the variable is the
same as that of a certain straight line drawn in a circle
whose radius is unity, to the length of a corresponding
are of the circle. Let AB be an arc in a circle, whose
radius OA is unity let AC be a quadrant, and let OC, DB,
and AF be drawnpependicular to OA, and EB and CG parallel
to OA, and let OB be produced to G and F. E Then BD is the
sine of the arc AB; OD or EB is the cosine, AF is the
tangent, CG is the cotangent, OF is the secant OG is the
cosecant, AD is the versed sine, and CE is the coversed
sine of the are AB. If the length of AB be represented by
x (OA being unity) then the lengths of Functions. these
lines (OA being unity) are the trigonometrical functions
of x, and are written sin x, cos x, tan x (or tang x), cot
x, sec x, cosec x, versin x, coversin x. These quantities
are also considered as functions of the angle BOA.
Function |
Hyperbolic functions
(gcide) | Hyperbolic \Hy`per*bol"ic\, Hyperbolical \Hy`per*bol"ic*al\, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
[1913 Webster]
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression. "This
hyperbolical epitaph." --Fuller.
[1913 Webster]
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector.
[1913 Webster] |
Inverse trigonometrical functions
(gcide) | Function \Func"tion\, n. [L. functio, fr. fungi to perform,
execute, akin to Skr. bhuj to enjoy, have the use of: cf. F.
fonction. Cf. Defunct.]
1. The act of executing or performing any duty, office, or
calling; performance. "In the function of his public
calling." --Swift.
[1913 Webster]
2. (Physiol.) 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.
[1913 Webster]
3. The natural or assigned action of any power or faculty, as
of the soul, or of the intellect; the exertion of an
energy of some determinate kind.
[1913 Webster]
As the mind opens, and its functions spread. --Pope.
[1913 Webster]
4. The course of action which peculiarly pertains to any
public officer in church or state; the activity
appropriate to any business or profession.
[1913 Webster]
Tradesmen . . . going about their functions. --Shak.
[1913 Webster]
The malady which made him incapable of performing
his
regal functions. --Macaulay.
[1913 Webster]
5. (Math.) 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 x^2, 3^x, Log. x, and
Sin. x, are all functions of x.
[1913 Webster]
6. (Eccl.) A religious ceremony, esp. one particularly
impressive and elaborate.
Every solemn `function' performed with the
requirements of the liturgy. --Card.
Wiseman.
[Webster 1913 Suppl.]
7. A public or social ceremony or gathering; a festivity or
entertainment, esp. one somewhat formal.
This function, which is our chief social event. --W.
D. Howells.
[Webster 1913 Suppl.]
Algebraic function, a quantity whose connection with the
variable is expressed by an equation that involves only
the algebraic operations of addition, subtraction,
multiplication, division, raising to a given power, and
extracting a given root; -- opposed to transcendental
function.
Arbitrary function. See under Arbitrary.
Calculus of functions. See under Calculus.
Carnot's function (Thermo-dynamics), a relation between the
amount of heat given off by a source of heat, and the work
which can be done by it. It is approximately equal to the
mechanical equivalent of the thermal unit divided by the
number expressing the temperature in degrees of the air
thermometer, reckoned from its zero of expansion.
Circular functions. See Inverse trigonometrical functions
(below). -- Continuous function, a quantity that has no
interruption in the continuity of its real values, as the
variable changes between any specified limits.
Discontinuous function. See under Discontinuous.
Elliptic functions, a large and important class of
functions, so called because one of the forms expresses
the relation of the arc of an ellipse to the straight
lines connected therewith.
Explicit function, a quantity directly expressed in terms
of the independently varying quantity; thus, in the
equations y = 6x^2, y = 10 -x^3, the quantity y is an
explicit function of x.
Implicit function, a quantity whose relation to the
variable is expressed indirectly by an equation; thus, y
in the equation x^2 + y^2 = 100 is an implicit
function of x.
Inverse trigonometrical functions, or Circular functions,
the lengths of arcs relative to the sines, tangents, etc.
Thus, AB is the arc whose sine is BD, and (if the length
of BD is x) is written sin ^-1x, and so of the other
lines. See Trigonometrical function (below). Other
transcendental functions are the exponential functions,
the elliptic functions, the gamma functions, the theta
functions, etc.
One-valued function, a quantity that has one, and only one,
value for each value of the variable. -- {Transcendental
functions}, a quantity whose connection with the variable
cannot be expressed by algebraic operations; thus, y in
the equation y = 10^x is a transcendental function of x.
See Algebraic function (above). -- {Trigonometrical
function}, a quantity whose relation to the variable is the
same as that of a certain straight line drawn in a circle
whose radius is unity, to the length of a corresponding
are of the circle. Let AB be an arc in a circle, whose
radius OA is unity let AC be a quadrant, and let OC, DB,
and AF be drawnpependicular to OA, and EB and CG parallel
to OA, and let OB be produced to G and F. E Then BD is the
sine of the arc AB; OD or EB is the cosine, AF is the
tangent, CG is the cotangent, OF is the secant OG is the
cosecant, AD is the versed sine, and CE is the coversed
sine of the are AB. If the length of AB be represented by
x (OA being unity) then the lengths of Functions. these
lines (OA being unity) are the trigonometrical functions
of x, and are written sin x, cos x, tan x (or tang x), cot
x, sec x, cosec x, versin x, coversin x. These quantities
are also considered as functions of the angle BOA.
Function |
Sustentative functions
(gcide) | Sustentative \Sus"ten*ta*tive\, a.
Adapted to sustain, strengthen, or corroborate; as,
sustentative citations or quotations.
[1913 Webster]
Sustentative functions (Physiol.), those functions of the
body which affect its material composition and thus
determine its mass.
[1913 Webster] |
Transcendental functions
(gcide) | Function \Func"tion\, n. [L. functio, fr. fungi to perform,
execute, akin to Skr. bhuj to enjoy, have the use of: cf. F.
fonction. Cf. Defunct.]
1. The act of executing or performing any duty, office, or
calling; performance. "In the function of his public
calling." --Swift.
[1913 Webster]
2. (Physiol.) 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.
[1913 Webster]
3. The natural or assigned action of any power or faculty, as
of the soul, or of the intellect; the exertion of an
energy of some determinate kind.
[1913 Webster]
As the mind opens, and its functions spread. --Pope.
[1913 Webster]
4. The course of action which peculiarly pertains to any
public officer in church or state; the activity
appropriate to any business or profession.
[1913 Webster]
Tradesmen . . . going about their functions. --Shak.
[1913 Webster]
The malady which made him incapable of performing
his
regal functions. --Macaulay.
[1913 Webster]
5. (Math.) 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 x^2, 3^x, Log. x, and
Sin. x, are all functions of x.
[1913 Webster]
6. (Eccl.) A religious ceremony, esp. one particularly
impressive and elaborate.
Every solemn `function' performed with the
requirements of the liturgy. --Card.
Wiseman.
[Webster 1913 Suppl.]
7. A public or social ceremony or gathering; a festivity or
entertainment, esp. one somewhat formal.
This function, which is our chief social event. --W.
D. Howells.
[Webster 1913 Suppl.]
Algebraic function, a quantity whose connection with the
variable is expressed by an equation that involves only
the algebraic operations of addition, subtraction,
multiplication, division, raising to a given power, and
extracting a given root; -- opposed to transcendental
function.
Arbitrary function. See under Arbitrary.
Calculus of functions. See under Calculus.
Carnot's function (Thermo-dynamics), a relation between the
amount of heat given off by a source of heat, and the work
which can be done by it. It is approximately equal to the
mechanical equivalent of the thermal unit divided by the
number expressing the temperature in degrees of the air
thermometer, reckoned from its zero of expansion.
Circular functions. See Inverse trigonometrical functions
(below). -- Continuous function, a quantity that has no
interruption in the continuity of its real values, as the
variable changes between any specified limits.
Discontinuous function. See under Discontinuous.
Elliptic functions, a large and important class of
functions, so called because one of the forms expresses
the relation of the arc of an ellipse to the straight
lines connected therewith.
Explicit function, a quantity directly expressed in terms
of the independently varying quantity; thus, in the
equations y = 6x^2, y = 10 -x^3, the quantity y is an
explicit function of x.
Implicit function, a quantity whose relation to the
variable is expressed indirectly by an equation; thus, y
in the equation x^2 + y^2 = 100 is an implicit
function of x.
Inverse trigonometrical functions, or Circular functions,
the lengths of arcs relative to the sines, tangents, etc.
Thus, AB is the arc whose sine is BD, and (if the length
of BD is x) is written sin ^-1x, and so of the other
lines. See Trigonometrical function (below). Other
transcendental functions are the exponential functions,
the elliptic functions, the gamma functions, the theta
functions, etc.
One-valued function, a quantity that has one, and only one,
value for each value of the variable. -- {Transcendental
functions}, a quantity whose connection with the variable
cannot be expressed by algebraic operations; thus, y in
the equation y = 10^x is a transcendental function of x.
See Algebraic function (above). -- {Trigonometrical
function}, a quantity whose relation to the variable is the
same as that of a certain straight line drawn in a circle
whose radius is unity, to the length of a corresponding
are of the circle. Let AB be an arc in a circle, whose
radius OA is unity let AC be a quadrant, and let OC, DB,
and AF be drawnpependicular to OA, and EB and CG parallel
to OA, and let OB be produced to G and F. E Then BD is the
sine of the arc AB; OD or EB is the cosine, AF is the
tangent, CG is the cotangent, OF is the secant OG is the
cosecant, AD is the versed sine, and CE is the coversed
sine of the are AB. If the length of AB be represented by
x (OA being unity) then the lengths of Functions. these
lines (OA being unity) are the trigonometrical functions
of x, and are written sin x, cos x, tan x (or tang x), cot
x, sec x, cosec x, versin x, coversin x. These quantities
are also considered as functions of the angle BOA.
Function |
Vital functions
(gcide) | Vital \Vi"tal\, a. [F., fr. L. vitalis, fr. vita life; akin to
vivere to live. See Vivid.]
1. Belonging or relating to life, either animal or vegetable;
as, vital energies; vital functions; vital actions.
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2. Contributing to life; necessary to, or supporting, life;
as, vital blood.
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Do the heavens afford him vital food? --Spenser.
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And vital virtue infused, and vital warmth.
--Milton.
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3. Containing life; living. "Spirits that live throughout,
vital in every part." --Milton.
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4. Being the seat of life; being that on which life depends;
mortal.
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The dart flew on, and pierced a vital part. --Pope.
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5. Very necessary; highly important; essential.
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A competence is vital to content. --Young.
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6. Capable of living; in a state to live; viable. [R.]
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Pythagoras and Hippocrates . . . affirm the birth of
the seventh month to be vital. --Sir T.
Browne.
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Vital air, oxygen gas; -- so called because essential to
animal life. [Obs.]
Vital capacity (Physiol.), the breathing capacity of the
lungs; -- expressed by the number of cubic inches of air
which can be forcibly exhaled after a full inspiration.
Vital force. (Biol.) See under Force. The vital forces,
according to Cope, are nerve force (neurism), growth force
(bathmism), and thought force (phrenism), all under the
direction and control of the vital principle. Apart from
the phenomena of consciousness, vital actions no longer
need to be considered as of a mysterious and unfathomable
character, nor vital force as anything other than a form
of physical energy derived from, and convertible into,
other well-known forces of nature.
Vital functions (Physiol.), those functions or actions of
the body on which life is directly dependent, as the
circulation of the blood, digestion, etc.
Vital principle, an immaterial force, to which the
functions peculiar to living beings are ascribed.
Vital statistics, statistics respecting the duration of
life, and the circumstances affecting its duration.
Vital tripod. (Physiol.) See under Tripod.
Vital vessels (Bot.), a name for latex tubes, now disused.
See Latex.
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logic for computable functions
(foldoc) | Logic for Computable Functions
LCF
(LCF) Part of the Edinburgh proof assistant.
[What is it? Address?]
(1995-01-06)
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