AI & ChatGPT searches , social queries for CLOSED FORM-EXPRESSION
Search references for CLOSED FORM-EXPRESSION. Phrases containing CLOSED FORM-EXPRESSION
See searches and references containing CLOSED FORM-EXPRESSION!
Search references for CLOSED FORM-EXPRESSION. Phrases containing CLOSED FORM-EXPRESSION
See searches and references containing CLOSED FORM-EXPRESSION!CLOSED FORM-EXPRESSION
Mathematical formula involving a given set of operations
In mathematics, a closed form expression or formula is one that is formed with constants, variables, and a set of functions considered as basic and connected
Closed-form_expression
Numbers obtained by adding the two previous ones
recurrence with constant coefficients, the Fibonacci numbers have a closed-form expression. It has become known as Binet's formula, named after French mathematician
Fibonacci_sequence
Czech electrical engineer and Holocaust survivor (1906–1985)
Czech electrical engineer and Holocaust survivor who developed a closed-form expression for the distribution factor of a symmetrical three-phase stator
Vilém_Klíma
Binary sequence from Fibonacci recurrence
trivially, by swapping 0s for 1s and shifting the positions by one. A closed form expression for the so-called rabbit sequence: The nth digit of the word is
Fibonacci_word
Mathematical expression using basic operations
algebraic expression is one that is not rational, such as √x + 4. Algebraic function Analytical expression Closed-form expression Expression (mathematics)
Algebraic_expression
is no closed-form expression for the perimeter of an ellipse. Throughout history, a large number of closed-form approximations and expressions in terms
Perimeter_of_an_ellipse
numerical approximation or a closed-form expression of the roots of a univariate polynomial, i.e., determining approximate or closed form solutions of x {\displaystyle
Polynomial_root-finding
Sequential model-based optimization of expensive black-box functions
derivatives are unavailable or unreliable. The objective need not have a closed-form expression. The method constructs a probabilistic model of the unknown function
Bayesian_optimization
Formula that provides the solutions to a quadratic equation
In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic
Quadratic_formula
Mathematics concept
many cases these sequences have simple, closed form expressions or have a generating function with a simple form. The following rules are notable: The sequence
Elementary_cellular_automaton
Orbit in which natural drifting has been minimized
on the closed form expression for this " J 3 {\displaystyle J_{3}\,} perturbation". With the "modern theory" this explicit closed form expression is not
Frozen_orbit
Topics referred to by the same term
Closed form may refer to: Closed-form expression, a finitary expression Closed differential form, a differential form α {\displaystyle \alpha } whose
Closed_form
Symbolic description of a mathematical object
becoming the standard. Analytic expression Closed-form expression Formal calculation Functional programming Infinite expression Number sentence Rewriting Signature
Expression_(mathematics)
Statistical function that defines the quantiles of a probability distribution
distribution above, which is one of the few distributions where a closed-form expression can be found (others include the uniform, the Weibull, the Tukey
Quantile_function
Mathematical constant described by Marvin Ray Burns
{\displaystyle \sum _{k=1}^{\infty }(-1)^{k}k^{1/k}.} There is no known closed-form expression of the MRB constant, nor is it known whether the MRB constant is
MRB_constant
Type of functional equation (mathematics)
may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated
Differential_equation
Number of partitions of an integer
five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4. No closed-form expression for the partition function is known, but it has both asymptotic
Partition function (number theory)
Partition_function_(number_theory)
Measurement of the harmonic distortion present in a signal
difficult task, and the resulting expressions may be quite laborious to obtain. For example, the closed-form expression for the THDF of the sawtooth wave
Total_harmonic_distortion
Statistical model for a binary dependent variable
estimated by maximum-likelihood estimation (MLE). This does not have a closed-form expression, unlike linear least squares; see § Model fitting. Logistic regression
Logistic_regression
Automated financial tool
{\displaystyle x=1+r} ) is a geometric series, which has a simple closed-form expression obtained from observing that x p N ( x ) − p N ( x ) = x N − 1 {\displaystyle
Mortgage_calculator
Concept in probability theory
\theta )} . A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary
Conjugate_prior
Addition of several numbers or other values
(defined with ellipses or Σ notation), it is a common problem to find closed-form expressions for the result. For example, ∑ i = 1 n i = n ( n + 1 ) 2 . {\displaystyle
Summation
Mathematical equation related to human death rate
defined as the inverse of the cumulative distribution function. A closed-form expression for Q ( u ) {\displaystyle Q(u)} can be written using the principal
Gompertz–Makeham law of mortality
Gompertz–Makeham_law_of_mortality
Radiometric dating method
2^{t/245000-t/75000}} Unfortunately there is no closed-form expression for the age, t, but it is easily found using equation solving algorithms
Uranium–thorium_dating
Pattern defining an infinite sequence of numbers
recurrences, one can express the general term of the sequence as a closed-form expression of n {\displaystyle n} . As well, linear recurrences with polynomial
Recurrence_relation
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
analytic function. For example, in principle the Jordan form could give a closed-form expression for the exponential exp(A). The number of Jordan blocks
Jordan_normal_form
Probabilistic classification algorithm
problem. Maximum-likelihood training can be done by evaluating a closed-form expression (simply by counting observations in each group), rather than the
Naive_Bayes_classifier
Moment of inertia of diff geometric shapes
symmetry, one can often determine the moment of inertia in an exact closed-form expression. Typically this occurs when the mass density is constant, but in
List_of_moments_of_inertia
Family of functions in mathematics
kernel F n ( x ) {\displaystyle F_{n}(x)} may also be written in a closed form expression as follows F n ( x ) = 1 n ( sin ( n x 2 ) sin ( x 2 ) ) 2 =
Fejér_kernel
Mathematical constant
role both in mathematics and in physics. It appears when giving a closed form expression for Porter's constant, when estimating the efficiency of the Euclidean
Glaisher–Kinkelin_constant
Kind of probability distribution
the second expression (quadratic form of a normal vector). The parameters of the second expression (quadratic form of a normal vector) can also be calculated
Generalized chi-squared distribution
Generalized_chi-squared_distribution
Distribution of variables which satisfies a stability property under linear combinations
the closed form expression is often in terms of less complicated special functions. Several closed form expressions having rather simple expressions in
Stable_distribution
Number constructible via compass and straightedge
r {\displaystyle r} is constructible if and only if there is a closed-form expression for r {\displaystyle r} using only integers and the operations for
Constructible_number
Probability distribution
closed-form expression for the estimates is available unless α = 0 {\displaystyle \alpha =0} . In contrast, the method of moments has a closed-form expression
Skew_normal_distribution
French mathematician (1667–1754)
prized by gamblers. De Moivre first discovered Binet's formula, the closed-form expression for Fibonacci numbers linking the nth power of the golden ratio
Abraham_de_Moivre
Process of repeating items in a self-similar way
relation can be "solved" to obtain a non-recursive definition (e.g., a closed-form expression). Use of recursion in an algorithm has both advantages and disadvantages
Recursion
Branch of mathematics
nonzero if the scalars belong to a field). Cramer's rule is a closed-form expression, in terms of determinants, of the solution of a system of n linear
Linear_algebra
Stochastic transitivity mathematical model
applicability scoring. In Chapter 7 of this book[citation needed], a closed form expression, derived in 1988, is given for a Euclidean-Gaussian similarity model
Thurstonian_model
Topics referred to by the same term
Tractable, ease of obtaining a mathematical solution such as a closed-form expression Tractable (company), an artificial intelligence company from the
Tractable
Computing joint values of a kinematic chain from a known end position
needed] An analytic solution to an inverse kinematics problem is a closed-form expression that takes the end-effector pose as input and gives joint positions
Inverse_kinematics
Size of a mathematical ball
V_{n}} can be expressed via a two-dimension recurrence relation. Closed-form expressions involve the gamma, factorial, or double factorial function. The
Volume_of_an_n-ball
Combinatorial sequence of numbers
expression as a summation are known. However Dedekind's problem of computing the values of M ( n ) {\displaystyle M(n)} remains difficult: no closed-form
Dedekind_number
Concept in information theory
2159046. S2CID 14238708. Nielsen, Frank; Nock, Richard (2012). "A closed-form expression for the Sharma–Mittal entropy of exponential families". Journal
Rényi_entropy
Sphere tangent to every edge of a polyhedron
cannot be represented exactly as a closed-form expression. Any canonical polyhedron and its polar dual can be used to form two opposite faces of a four-dimensional
Midsphere
Type of regression analysis
provided as a starting point for symbolic regression. Instead, initial expressions are formed by randomly combining mathematical building blocks such as mathematical
Symbolic_regression
Probability distribution
is no general closed-form expression for the median of the beta distribution for arbitrary values of α and β. Closed-form expressions for particular
Beta_distribution
Generalization of the standard Boltzmann–Gibbs entropy
(PDF). Kybernetika. 3 (1): 30–35. Nielsen, F.; Nock, R. (2012). "A closed-form expression for the Sharma–Mittal entropy of exponential families". Journal
Tsallis_entropy
Natural number
Integer Sequences. OEIS Foundation. Messer, Peter W. (2002). "Closed-Form Expressions for Uniform Polyhedra and Their Duals". Discrete & Computational
44_(number)
Integrals not expressible in closed-form from elementary functions
Liouvillian functions. Algebraic function – Mathematical function Closed-form expression – Mathematical formula involving a given set of operations Derivative –
Nonelementary_integral
Type of mathematical function
elementary for applying Liouville's theorem. Algebraic function Closed-form expression – Mathematical formula involving a given set of operations Differential
Elementary_function
Class of statistical models
linear model has a closed form expression for the maximum-likelihood estimates, which is convenient. Most other GLMs lack closed form estimates. When the
Generalized_linear_model
Decomposition of an integer as a sum of positive integers
_{i=0}^{\infty }q^{ji}=\prod _{j=1}^{\infty }(1-q^{j})^{-1}.} No closed-form expression for the partition function is known, but it has both asymptotic
Integer_partition
Family of geometric shapes
is its conciseness and expressiveness in shape. Furthermore, a closed-form expression of the Minkowski sum between two superellipsoids is available. This
Superellipsoid
Numerical simulations of physical problems via computers
This can occur, for instance, when the solution does not have a closed-form expression, or is too complicated. In such cases, numerical approximations
Computational_physics
Probability distribution of energy states of a system
not follow Maxwell–Boltzmann statistics, and there is no simple closed form expression for quantum gases in the canonical ensemble. In the grand canonical
Boltzmann_distribution
Distance along a curve
speed. This defining integral of arc length does not always have a closed-form expression, and numerical integration may be used instead to obtain numerical
Arc_length
Measure of how much of an antenna's signal is transmitted in one direction
The actual result is in fact, 33.1 dBi. For antenna arrays, the closed form expression for Directivity for progressively phased array of isotropic sources
Directivity
Criterion for integration in terms of elementary functions
Liouville's theorem. Algebraic function – Mathematical function Closed-form expression – Mathematical formula involving a given set of operations Differential
Liouville's theorem (differential algebra)
Liouville's_theorem_(differential_algebra)
Maximum eccentricity for which a power series for Kepler's equation converges
{\displaystyle {\frac {x\exp({\sqrt {1+x^{2}}})}{1+{\sqrt {1+x^{2}}}}}=1} A closed-form expression in terms of r-Lambert special function and an infinite series representation
Laplace_limit
Australian synthpop band
The Expression were an Australian synthpop band formed in Sydney in 1981 and disbanded in 1985. Their best known single, "With Closed Eyes", was released
The_Expression
Technique used to determine mass of hadrons
theory. This procedure makes it possible to find analytic solutions (closed-form expression) in situations where strong coupling occurs (the "strongly coupled
Light_front_holography
Property of a model
is taken over the possible labeling of a fixed training set, a closed-form expression exists that relates the bias–variance decomposition to the parameter
Bias–variance_tradeoff
Lower bound on the log-likelihood of some observed data
since then the KL term (though it is itself an expectation) has a closed-form expression, so only the first expectation term needs to be estimated by sampling
Evidence_lower_bound
Association of one output to each input
Homomorphism Morphism Microfunction Distribution Functor Associative array Closed-form expression Elementary function Functional Functional decomposition Functional
Function_(mathematics)
Probability distribution
and can be expressed as a function of the chi-squared divergence. Closed-form expression for the total variation, Jensen–Shannon divergence, Hellinger distance
Cauchy_distribution
Type of queue model in queueing theory
elementary of queueing models and an attractive object of study as closed-form expressions can be obtained for many metrics of interest in this model. An
M/M/1_queue
Mathematical constant related to the cosine function
and Bertrand's circle problems. The Dottie number appears in the closed form expression of some integrals: ∫ 0 ∞ ln ( 4 ( x + sinh x ) 2 + π 2 4 ( x
Dottie_number
Wavelet constructed using a spline function
− 1 ) {\displaystyle \psi _{C,1}(x)=N_{1}(2x)-N_{1}(2x-1)} The closed form expression for compactly supported B-spline wavelet of order 1 is ψ C , 1 (
Spline_wavelet
Technique in numerical linear algebra
image form. Minimization with respect to the L {\displaystyle L} variable (a linear least squares problem) leads to the closed form expression of the
Low-rank_approximation
Rational number sequence
{B_{k}^{+}}{kz^{k}}}} Bernoulli numbers feature prominently in the closed form expression of the sum of the mth powers of the first n positive integers. For
Bernoulli_number
Probability distribution in physics
is one of the few examples of a stable distribution for which a closed form expression of the probability density function is known. However, its probability
Holtsmark_distribution
Positive real number which when multiplied by itself gives 5
\end{aligned}}} 5 {\displaystyle {\sqrt {5}}} then figures in the closed form expression for the Fibonacci numbers: F ( n ) = φ n − φ ¯ n 5 . {\displaystyle
Square_root_of_5
Iterative method for finding maximum likelihood estimates in statistical models
linear function. In such a case, it is usually possible to derive closed-form expression updates for each step, using the Sundberg formula (proved and published
Expectation–maximization algorithm
Expectation–maximization_algorithm
Numerical approximation algorithm
especially the elliptic type.[citation needed] Mathematics portal Closed-form expression Iterative refinement Kaczmarz method Non-linear least squares Numerical
Iterative_method
Probability distribution
1 8 . {\displaystyle \operatorname {var} (X)={\frac {1}{8}}.} A closed-form expression for any even central moment can be found by first obtaining the
Cantor_distribution
Mathematical series
propagation graphs which takes advantage of Neumann series to derive closed form expressions for transfer functions. Wu, M.; Yin, B.; Vosoughi, A.; Studer,
Neumann_series
Geographical point
of minimum aggregate travel. Unfortunately, there is no direct closed-form expression for the geometric median; it is typically computed using iterative
Center_of_population
Stochastic model for the evolution of financial interest rates
special case of a basic affine jump diffusion, which still permits a closed-form expression for bond prices. Time varying functions replacing coefficients can
Cox–Ingersoll–Ross_model
Least squares approximation of linear functions to data
OLS method minimizes the sum of squared residuals, and leads to a closed-form expression for the estimated value of the unknown parameter vector β: β ^ =
Linear_least_squares
Mathematical concept
portion. There is no known closed-form expression that diagonalizes this operator; that is, there are no closed-form expressions known for the eigenvectors
Gauss–Kuzmin–Wirsing_operator
Probability distribution
_{j=1}^{n}X_{j}} . The distribution of Y {\displaystyle Y} has no closed-form expression, but can be reasonably approximated by another log-normal distribution
Log-normal_distribution
Distance between the nearest and the furthest objects that are in focus in an image
Field in Depth. Peterson does not give a closed-form expression for the minimum f-number, though such an expression obtains from simple algebraic manipulation
Depth_of_field
Number of paths between grid corners, allowing diagonal steps
n-k}}={\binom {m+n-k}{m}}{\binom {m}{k}}} . Hence, one gets the closed-form expression D ( m , n ) = ∑ k = 0 min ( m , n ) ( m + n − k m ) ( m k ) . {\displaystyle
Delannoy_number
Integrated circuit reliability metric
function g ( v ) {\displaystyle g(\mathbf {v} )} does not have a closed-form expression and must be estimated using numerical methods. Currently, the industrial
Yield_(metric)
Spiral
general, the arc length of the lituus spiral cannot be expressed as a closed-form expression, but the arc length of the lituus spiral can be represented as a
Lituus_(mathematics)
Mathematical procedure
constants. If an integer relation is found, this suggests a possible closed-form expression for the original series, product or integral. This conjecture can
Integer_relation_algorithm
Elementary functions and their finitely iterated integrals
transcendental functions, such as: the gamma function; the zeta function. Closed-form expression – Mathematical formula involving a given set of operations Differential
Liouvillian_function
Probability distribution
bounds that are not closed-form expressions, including this one involving the gamma function, based on solving the integral expression substituting 1 for
Gamma_distribution
Function in statistics
half-integer values ν = n + 1 / 2 {\displaystyle \nu =n+1/2} , we have a closed form expression for the generalized Marcum Q-function as Q n + 1 / 2 ( a , b ) =
Marcum_Q-function
Boolean polynomials as sums of monomials
normal form (a fully expanded disjunctive normal form) is computed first. Then the negations in this expression are replaced by an equivalent expression using
Algebraic_normal_form
Generalized sphere of dimension n (mathematics)
s_{n-2})|J_{n-1}|.\end{aligned}}} Induction then gives a closed-form expression for the volume element in spherical coordinates d n V = | det ∂
N-sphere
Function in discrete mathematics
}\exp \left(-{\frac {\pi \cdot (m+N\cdot k)^{2}}{N}}\right).} The closed form expression for the series can be expressed by Jacobi theta functions as F (
Discrete_Fourier_transform
Decomposition of periodic functions
nontrivial. The function T {\displaystyle T} cannot be written as a closed-form expression. This method of solving the heat problem was made possible by Fourier's
Fourier_series
Measure for evaluating probabilistic forecasts
_{i})(q_{i}-y)_{+}} For many popular families of distributions, closed-form expressions for the continuous ranked probability score have been derived.
Scoring_rule
Generalization of the one-dimensional normal distribution to higher dimensions
estimating the parameters of a multivariate normal distribution has a closed form expression. This can be used, for example, to compute the Cramér–Rao bound
Multivariate normal distribution
Multivariate_normal_distribution
French mathematician, physicist and astronomer (1786-1856)
u_{n}=u_{n-1}+u_{n-2},{\text{ for }}n>1} Binet's formula provides a closed-form expression for the n th {\displaystyle n^{\text{th}}} term in this sequence:
Jacques_Philippe_Marie_Binet
Multivalued function in mathematics
62, IV: 607–616. Nielsen, F. (July 2013). "Jeffreys centroids: A closed-form expression for positive histograms and a guaranteed tight approximation for
Lambert_W_function
stochastic geometry can then allow for the derivation of closed-form or semi-closed-form expressions for these quantities without resorting to simulation
Stochastic geometry models of wireless networks
Stochastic_geometry_models_of_wireless_networks
Statistical transformation
although they greatly complicate the computation of the inverse – a closed-form expression is not available. The near-constant variance of the transformation
Fisher_transformation
German polymath and scholar (1777–1855)
theory, the "Theoria attractionis..." (1813), Gauss provided a closed-form expression to the gravitational attraction of a homogeneous triaxial ellipsoid
Carl_Friedrich_Gauss
CLOSED FORM-EXPRESSION
CLOSED FORM-EXPRESSION
Female
English
Old English flower name, CLOVER means simply "clover."
Surname or Lastname
English
English : topographic name for someone who lived by an enclosure of some sort, such as a courtyard set back from the main street or a farmyard, from Middle English clos(e) (Old French clos, from Late Latin clausum, past participle of claudere ‘to close’).English : from Middle English clos(e) ‘secret’, applied as a nickname for a reserved or secretive person.Dutch : variant of Claeys.Altered spelling of German Klose.
Male
English
English surname transferred to forename use, from the Old English word ford, FORD means "ford, river crossing."
Surname or Lastname
English, French, and Catalan
English, French, and Catalan : nickname from Old French, Middle English, Catalan fort, ‘strong’, ‘brave’ (Latin fortis). In some cases it may be from the Latin personal name derived from this word; this was borne by an obscure saint whose cult was popular during the Middle Ages in southern and southwestern France.English and French : topographic name for someone who lived near a fortress or stronghold, or an occupational name for someone employed in one. Compare Fortier 1.Czech (Fořt) : variant of Forst.
Boy/Male
Australian, British, Christian, English, French
Man of the North; From the North
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
Close; Clove
Girl/Female
Indian
Fragrance
Boy/Male
English American Shakespearean
River crossing.
Surname or Lastname
English
English : topographic name for someone who lived near a ford, Middle English, Old English ford, or a habitational name from one of the many places named with this word, such as Ford in Northumberland, Shropshire, and West Sussex, or Forde in Dorset.Irish : Anglicized form (quasi-translation) of various Gaelic names, for example Mac Giolla na Naomh ‘son of Gilla na Naomh’ (a personal name meaning ‘servant of the saints’), Mac Conshámha ‘son of Conshnámha’ (a personal name composed of the elements con ‘dog’ + snámh ‘to swim’), in all of which the final syllable was wrongly thought to be áth ‘ford’, and Ó Fuar(th)áin (see Foran).Jewish : Americanized form of one or more like-sounding Jewish surnames.Translation of German Fürth (see Furth).
Surname or Lastname
English
English : occupational name for a nailer, from an agent derivative of Old French clou ‘nail’. Compare Cloutier.Americanized spelling of German Klauer (or the variant Clauer) or of Glauer, a nickname from Middle High German glau, glou ‘intelligent’, ‘circumspect’.
Girl/Female
American, Anglo, Australian, British, Christian, English, Jamaican, Portuguese
Clover; Flower Name; Fortunate; Mind; Heart; Spirit
Boy/Male
Hindu, Indian
Fragrance
Male
English
Anglicized form of Hebrew Kesed, CHESED means "increase." In the bible, this is the name of the 4th son of Nahor.
Girl/Female
Anglo Saxon English
Clover.
Boy/Male
French
From the north.
Surname or Lastname
English
English : variant of Close 1.German : variant of Kloss.
Boy/Male
American, Australian, British, Christian, English, Jamaican, Shakespearean
From the River Crossing
Girl/Female
Shakespearean
The Merry Wives of Windsor' Mistress Ford.
Male
English
Short form of English Norman, NORM means "northman."
Surname or Lastname
German and Danish
German and Danish : variant of Wurm.English : nickname from Middle English wurm ‘serpent’, ‘dragon’ (Old English wyrm).
CLOSED FORM-EXPRESSION
CLOSED FORM-EXPRESSION
Female
English
English variant spelling of Arabic Aisha, AYEESHA means "alive."Â
Girl/Female
Australian, Hindu, Indian, Marathi
Happiness
Girl/Female
Bengali, Indian, Tamil, Telugu
Favour
Boy/Male
Tamil
Ascetic
Boy/Male
Arabic, Muslim
Slave of the Originator
Girl/Female
Irish
Ancient Irish name from the noun aine that means “splendor, radiance, brilliance.†Aine is connected with fruitfulness and prosperity. The queen of the Munster fairies was called Aine as was one of the wives of Fionn Mac Cool (read the legend). Aine appears in folktales as “the best-hearted woman who ever lived – lucky in love and in money.â€
Boy/Male
Muslim
Commodities
Female
English
Variant spelling of English Alice, ALYSE means "noble sort."
Male
English
Anglicized form of Hebrew Chanowk, HANOCH means "dedicated" or "initiated." In the bible, this is the name of the eldest son of Cain, and a son of Jared the father of Methuselah.
Boy/Male
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Tamil, Telugu
Ocean; Lord Vishnu; White
CLOSED FORM-EXPRESSION
CLOSED FORM-EXPRESSION
CLOSED FORM-EXPRESSION
CLOSED FORM-EXPRESSION
CLOSED FORM-EXPRESSION
v. i.
To run to a form, as a hare.
n.
The combination of planes included under a general crystallographic symbol. It is not necessarily a closed solid.
v. t.
To make into a closet for a secret interview.
n.
To stop, or fill up, as an opening; to shut; as, to close the eyes; to close a door.
v. t.
Shut fast; closed; tight; as, a close box.
imp. & p. p.
of Close
adv.
In a close manner.
adv.
Close; closely.
a.
Firmly barred or closed.
n.
One who, or that which, closes; specifically, a boot closer. See under Boot.
v. t.
Short; as, to cut grass or hair close.
v. t.
Strictly confined; carefully quarded; as, a close prisoner.
adv.
In a close manner.
n.
To provide with a form, as a hare. See Form, n., 9.
v. t.
Concise; to the point; as, close reasoning.
v. t.
To make close.
v. t.
Narrow; confined; as, a close alley; close quarters.
v. t.
Difficult to obtain; as, money is close.
superl.
Fixed; hence, closely compressed; compact; substantial; hard; solid; -- applied to the matter of bodies; as, firm flesh; firm muscles, firm wood.
v. i.
To take a form, definite shape, or arrangement; as, the infantry should form in column.