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Polynomials in combinatorial mathematics
inversion. The partial or incomplete exponential Bell polynomials are a triangular array of polynomials given by B n , k ( x 1 , x 2 , … , x n − k + 1 )
Bell_polynomials
Polynomial sequence
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets
Hermite_polynomials
Count of the possible partitions of a set
notebook, he investigated both Bell polynomials and Bell numbers. Early references for the Bell triangle, which has the Bell numbers on both of its sides
Bell_number
Relations between power sums and elementary symmetric functions
of symmetric polynomials, namely between power sums and elementary symmetric polynomials. Evaluated at the roots of a monic polynomial P in one variable
Newton's_identities
Sequence of polynomials
Touchard polynomials, studied by Jacques Touchard (1956), also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence
Touchard_polynomials
Scottish-born mathematician and science fiction writer
for convergence. He is the eponym of the Bell polynomials and the Bell numbers of combinatorics. In 1924 Bell was awarded the Bôcher Memorial Prize for
Eric_Temple_Bell
Square matrices satisfy their characteristic equation
the elementary symmetric polynomials of the eigenvalues of A. Using Newton identities, the elementary symmetric polynomials can in turn be expressed in
Cayley–Hamilton_theorem
Topics referred to by the same term
of a jellyfish Bell character, in computing, a device control code Bell number, in mathematics Bell polynomials, in mathematics Bell state, in quantum
Bell_(disambiguation)
Set of quantities in probability theory
moments, given by the polynomials above.[clarification needed][citation needed] For those polynomials, construct a polynomial sequence in the following
Cumulant
Type of polynomial sequence
of the Bell polynomials. Every sequence of binomial type is a Sheffer sequence (but most Sheffer sequences are not of binomial type). Polynomial sequences
Binomial_type
Generalized chain rule in calculus
formula expressed in terms of partial (or incomplete) exponential Bell polynomials B n , k ( x 1 , … , x n − k + 1 ) {\displaystyle B_{n,k}(x_{1},\ldots
Faà_di_Bruno's_formula
For a square matrix, the transpose of the cofactor matrix
represented in terms of traces of powers of A using complete exponential Bell polynomials. The resulting formula is adj ( A ) = ∑ s = 0 n − 1 A s ∑ k 1 , k
Adjugate_matrix
All one polynomials Appell sequence Askey–Wilson polynomials Bell polynomials Bernoulli polynomials Bernstein polynomial Bessel polynomials Binomial
List_of_polynomial_topics
infinite lower triangular matrix whose entries are given by ordinary Bell polynomials evaluated at the coefficients of f {\displaystyle f} . This is why
Jabotinsky_matrix
Square root of the determinant of a skew-symmetric square matrix
s_{l}=-{\tfrac {1}{2}}(l-1)!\,\mathrm {tr} ((AB)^{l})} and Bn(s1,s2,...,sn) are Bell polynomials. For a block-diagonal matrix A 1 ⊕ A 2 = [ A 1 0 0 A 2 ] , {\displaystyle
Pfaffian
Sequence valued in polynomials
All-one polynomials Abel polynomials Bell polynomials Bernoulli polynomials Cyclotomic polynomials Dickson polynomials Fibonacci polynomials Lagrange
Polynomial_sequence
Formula for inverting a Taylor series
then an explicit form of inverse coefficients can be given in term of Bell polynomials: g n = 1 f 1 n ∑ k = 1 n − 1 ( − 1 ) k n k ¯ B n − 1 , k ( f ^ 1 ,
Lagrange_inversion_theorem
Infinite sum approximating a probability distribution in terms of its cumulants
Gram–Charlier A series. Such an expansion can be written compactly in terms of Bell polynomials as exp [ ∑ r = 3 ∞ κ r ( − D ) r r ! ] = ∑ n = 0 ∞ B n ( 0 , 0 ,
Edgeworth_series
consequence of the general relation between Z n {\displaystyle Z_{n}} and Bell polynomials: n ! Z n ( a 1 , … , a n ) = B n ( 0 ! a 1 , 1 ! a 2 , … , ( n − 1
Exponential_formula
Numbers arranged in a triangle
other than numbers; for instance the Bell polynomials form a triangular array in which each array entry is a polynomial. Arrays in which the length of each
Triangular_array
of a partition Solid partition Young tableau Young's lattice Bell number Bell polynomials Dobinski's formula Cumulant Data clustering Equivalence relation
List_of_partition_topics
other special polynomials, are included. Contents: Top 0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Niels Abel: Abel polynomials - Abelian function
List of eponyms of special functions
List_of_eponyms_of_special_functions
Recreational mathematics planar boundary and area problem
}{4}}\right|={\frac {\pi }{4}}} . A solution can also be written using Bell polynomials, which follows from the Lagrange inversion theorem: r = 2 cos ( π
Goat_grazing_problem
Operation on formal power series
generating function is given implicitly through the Bell polynomials by the EGF for these polynomials defined in the previous formula for some sequence
Generating function transformation
Generating_function_transformation
Generalization of the binomial theorem to other polynomials
(2008), "Connection between ordinary multinomials, Fibonacci numbers, Bell polynomials and discrete uniform distribution", Annales Mathematicae et Informaticae
Multinomial_theorem
Mathematical sequences in combinatorics
{1}{j^{k}j!}}} . Bell polynomials Catalan number Cycles and fixed points Pochhammer symbol Polynomial sequence Touchard polynomials Stirling permutation
Stirling_number
Count of permutations by cycles
x^{k}} from the following formal power series (see the non-exponential Bell polynomials and section 3 of ). More generally, sums related to these weighted
Stirling numbers of the first kind
Stirling_numbers_of_the_first_kind
Mathematical approximation of a function
of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function
Taylor_series
Triangular pyramidal number The (incomplete) Bell polynomials from a triangular array of polynomials (see also Polynomial sequence). Heronian triangle Integer
List_of_triangle_topics
Mathematical algorithm
_{k=0}^{n}c_{k}\lambda ^{k}~,} where, evidently, cn = 1 (characteristic polynomials are monic polynomials) and c0 = (−1)n det A. The coefficients cn − i are determined
Faddeev–LeVerrier_algorithm
Numbers parameterizing ways to partition a set
Stirling numbers of the first kind Bell number – the number of partitions of a set with n members Stirling polynomials Twelvefold way Learning materials
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
In mathematics, invariant of square matrices
The formula can be expressed in terms of the complete exponential Bell polynomial of n arguments sl = −(l – 1)! tr(Al) as det ( A ) = ( − 1 ) n n ! B
Determinant
j > n − k + 1 leads to a somewhat simpler formula expressed in terms of Bell polynomials Bn,k(x1,...,xn−k+1): d n d x n f ( g ( x ) ) = ∑ k = 1 n f ( k ) (
Glossary_of_calculus
Polynomial in combinatorial mathematics
_{k=1}^{n}a_{k}^{j_{k}}} that can be also stated in terms of complete Bell polynomials: Z ( S n ) = B n ( 0 ! a 1 , 1 ! a 2 , … , ( n − 1 ) ! a n ) n ! .
Cycle_index
{\displaystyle B_{n}} denotes the n {\displaystyle n} -th Bell polynomial. Each Bell polynomial is a finite sum of monomials of the form ∏ i = 1 n ( g (
Absolutely and completely monotonic functions and sequences
Absolutely_and_completely_monotonic_functions_and_sequences
Extension of the factorial function
function, and B n {\displaystyle B_{n}} is the n {\displaystyle n} th Bell polynomial, we have in particular the Laurent series expansion of the gamma function
Gamma_function
Probability distribution
values of x {\displaystyle x} . The recurrence relation for Hermite polynomials Hen(x) may be used to efficiently construct the Taylor series expansion
Normal_distribution
Boolean polynomials as sums of monomials
they are the polynomial ring over the integers modulo 2. The resulting degeneracies of modular arithmetic result in Zhegalkin polynomials being simpler
Algebraic_normal_form
American mathematician and biomedical engineer
distribution of match counts of pairs of integer multisets in terms of Bell polynomials, a problem directly relevant to physical mapping of DNA. Prior to this
Michael_Christopher_Wendl
Historical term in mathematics
composition of polynomial sequences Calculus of finite differences Pidduck polynomials Symbolic method in invariant theory Narumi polynomials Blissard, John
Umbral_calculus
_{l=1}^{n-1}lk_{l}=n-1} The formula can be rewritten in terms of complete Bell polynomials of arguments t l = − ( l − 1 ) ! tr ( A l ) {\displaystyle t_{l}=-(l-1)
Methods_of_matrix_inversion
In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis
Stirling_polynomials
Automatic mechanical calculator
logarithmic and trigonometric functions, which can be approximated by polynomials, so a difference engine can compute many useful tables. English Wikisource
Difference_engine
Natural number
simple 32-stage cycling shift register; also number of binary irreducible polynomials whose degree divides 32 136,048,896 = 116642 = 1084 136,279,841 = The
100,000,000
went on to give the general solution for this problem in terms of the Bell polynomials, showing the traditional score overpredicts P-values by orders of magnitude
Sulston_score
Method in computational algebra
{\displaystyle f(x)} into powers of irreducible polynomials (recalling that the ring of polynomials over a finite field is a unique factorization domain)
Berlekamp's_algorithm
Audioactive decay Barcode Matrix code QR Code Universal Product Code Bell polynomials Bertrand's ballot theorem Binary matrix Binomial theorem Block design
Index of combinatorics articles
Index_of_combinatorics_articles
Polynomial function of degree 3
one or three real roots (which may not be distinct); all odd-degree polynomials with real coefficients have at least one real root. The graph of a cubic
Cubic_function
Text-string-oriented programming language
to be used by its authors to work with the symbolic manipulation of polynomials. It was written in assembly language for the IBM 7090. It had a simple
SNOBOL
Testable implication of local hidden-variable theories
Clauser–Horne–Shimony–Holt (CHSH) inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum
CHSH_inequality
Indian mathematician (born 1956)
an ISI highly cited researcher. He invented one of the first provably polynomial time algorithms for linear programming, which is generally referred to
Narendra_Karmarkar
Triangle of numbers
In mathematics, the Bell triangle is a triangle of numbers analogous to Pascal's triangle, whose values count partitions of a set in which a given element
Bell_triangle
Natural number
primitive polynomials of degree 27 over GF(2) 4,208,945 = Leyland number 4,210,818 = equal to the sum of the seventh powers of its digits 4,213,597 = Bell number
1,000,000
Mathematical function
Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the
Gaussian_function
Permutation of the elements of a set in which no element appears in its original position
}P_{n_{1}}(x)P_{n_{2}}(x)\cdots P_{n_{r}}(x)\ e^{-x}dx,} for a certain sequence of polynomials Pn, where Pn has degree n. But the above answer for the case r = 2 gives
Derangement
Number divisible only by 1 and itself
quadratic polynomials with integer coefficients in terms of the logarithmic integral and the polynomial coefficients. No quadratic polynomial has been
Prime_number
Formal power series
Appell polynomials Chebyshev polynomials Difference polynomials Generalized Appell polynomials q-difference polynomials Other sequences generated by more
Generating_function
Danish computer scientist, creator of C++ (born 1950)
programming language. He led the Large-scale Programming Research department at Bell Labs, served as a professor of computer science at Texas A&M University,
Bjarne_Stroustrup
Natural number
+ 22 + 33 + 44 + 55 + 66 + 77 + 88 17,820,000 = Number of primitive polynomials of degree 30 over GF(2) 17,850,625 = 42252 = 654 17,896,832 = Number
10,000,000
Number of orderings allowing ties
In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the weak orderings on a set of n {\displaystyle n} elements
Ordered_Bell_number
Cryptography method
feasibly extracted from the ciphertext. Specifically, any probabilistic, polynomial-time algorithm (PPTA) that is given the ciphertext of a certain message
Semantic_security
Natural number
prime numbers having eleven digits 3,697,909,056 : number of primitive polynomials of degree 37 over GF(2) 3,707,398,432 = 825 3,715,891,200 : double factorial
1,000,000,000
1016/S0022-314X(01)92763-5. Berlekamp, E. R. (1967), "Factoring polynomials over finite fields", Bell System Technical Journal, 46 (8): 1853–1859, Bibcode:1967BSTJ
Berlekamp–Zassenhaus algorithm
Berlekamp–Zassenhaus_algorithm
Basic unit of quantum information
two entangled qubits in the | Φ + ⟩ {\displaystyle {|\Phi ^{+}\rangle }} Bell state: 1 2 ( | 00 ⟩ + | 11 ⟩ ) . {\displaystyle {\frac {1}{\sqrt {2}}}({|00\rangle
Qubit
2.71828...; base of natural logarithms
it is transcendental, meaning that it is not a root of any non-zero polynomial with rational coefficients. To 30 decimal places, the value of e is: 2
E_(mathematical_constant)
Computational complexity class of problems
theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability
BQP
Dutch mathematician (born 1956)
Lenstra's most widely cited scientific result is the first polynomial time algorithm to factor polynomials with rational coefficients in the seminal paper that
Arjen_Lenstra
Mathematical description of quantum state
and Laguerre polynomials as well as Chebyshev polynomials, Jacobi polynomials and Hermite polynomials. All of these actually appear in physical problems
Wave_function
Number, approximately 3.14
}e^{-u^{2}}\,du={\sqrt {\pi }},} which says that the area under the basic bell curve in the figure is equal to the square root of π. The central limit theorem
Pi
Topics referred to by the same term
stopping power of hunting cartridges Taylor Series, infinite series of polynomials which asymptotically approaches infinitely differentiable functions Taylor's
Taylor
Function used in signal processing
typical applications, the window functions used are non-negative, smooth, "bell-shaped" curves. Rectangle, triangle, and other functions can also be used
Window_function
German mathematician (1804–1851)
of the first to introduce and study the symmetric polynomials that are now known as Schur polynomials, giving the so-called bialternant formula for these
Carl_Gustav_Jacob_Jacobi
Natural number
= 76 117,800 = harmonic divisor number 120,032 = number of primitive polynomials of degree 22 over GF(2) 120,284 = Keith number 120,960 = highly totient
100,000
Programmable machine that processes data
advanced analog machines that could solve real and complex roots of polynomials, which were published in 1901 by the Paris Academy of Sciences. Charles
Computer
English polymath (1642–1727)
Newton's method, the Newton polygon, and classified cubic plane curves (polynomials of degree three in two variables). Newton is also a founder of the theory
Isaac_Newton
Field of electrical engineering
theory, and transform theory Polynomial signal processing – analysis of systems which relate input and output using polynomials System identification and
Signal_processing
Mathematical concept
the polynomial can be written as k(k−1) + n, using the integers k with −(n−1) < k ≤ 0 produces the same set of numbers as 1 ≤ k < n. These polynomials are
Lucky_numbers_of_Euler
Set of numbers used in the smoothsort algorithm
{5}}\right)/2} are the roots of the quadratic polynomial x 2 − x − 1 = 0 {\displaystyle x^{2}-x-1=0} . The Leonardo polynomials L n ( x ) {\displaystyle L_{n}(x)}
Leonardo_number
American mathematician
regarding Bernoulli numbers Carlitz wrote about Bessel polynomials He introduced Al-Salam–Carlitz polynomials. Carlitz' identity for bicentric quadrilaterals
Leonard_Carlitz
Natural number
number 23976 = pentagonal pyramidal number 24000 = number of primitive polynomials of degree 20 over GF(2) 24211 = Zeisel number 24336 = 1562, palindromic
20,000
Infinite integer series where the next number is the sum of the two preceding it
as Fibonacci polynomials are derived from the Fibonacci numbers, the Lucas polynomials L n ( x ) {\displaystyle L_{n}(x)} are a polynomial sequence derived
Lucas_number
Study of numbers that are not solutions of polynomials with rational coefficients
irrationality 1. Next consider the values of polynomials at a complex number x, when these polynomials have integer coefficients, degree at most n, and
Transcendental_number_theory
Rational number sequence
{B_{k+1+j}}{k+1+j}}={\frac {k!m!}{(k+m+1)!}}.} Bernoulli polynomial Bernoulli polynomials of the second kind Bernoulli umbra Bell number Euler number Genocchi number Kummer's
Bernoulli_number
19th century proposed mechanical computer
trigonometric functions by evaluating finite differences to create approximating polynomials. Construction of this machine was never completed; Babbage had conflicts
Analytical_engine
Figure-eight-shaped curve
of Gerono", An elementary treatise on cubic and quartic curves, Deighton, Bell, pp. 171–172. Chandrasekhar, S (2003), Newton's Principia for the common
Lemniscate
Graphical method of determining the stability of a dynamical system
{\displaystyle {\mathcal {T}}(s)} can be expressed as the ratio of two polynomials: T ( s ) = N ( s ) D ( s ) . {\displaystyle {\mathcal {T}}(s)={\frac
Nyquist_stability_criterion
theorem (polynomials) Polynomial remainder theorem (polynomials) Primitive element theorem (field theory) Rational root theorem (algebra, polynomials) Solutions
List_of_theorems
Theoretical upper limit to non-local correlations in quantum mechanics
correlations between distant events. Given that quantum mechanics violates Bell inequalities (i.e., it cannot be described by a local hidden-variable theory)
Tsirelson's_bound
Complexity class
is the set of problems solvable by an interactive proof system with a polynomial-time verifier and one computationally unbounded prover. Informally, IP
QIP_(complexity)
American computer scientist
terms was no harder than multiplying two N {\displaystyle N} -th degree polynomials. In 1973 Traub invited Henryk Woźniakowski to visit CMU. They pioneered
Joseph_F._Traub
cancer. Tim Barlow, 87, English actor (Derek, Les Misérables, Hot Fuzz). Ted Bell, 76, American novelist, intracerebral hemorrhage. Tom Birmingham, 73, American
Deaths_in_January_2023
Mathematical problem in number theory
problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. Attributed to Archimedes, the problem
Archimedes's_cattle_problem
Description of physical properties at the atomic and subatomic scale
, 2 , … . {\displaystyle n=0,1,2,\ldots .} where Hn are the Hermite polynomials H n ( x ) = ( − 1 ) n e x 2 d n d x n ( e − x 2 ) , {\displaystyle
Quantum_mechanics
French mathematician (1811–1832)
he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem that had been open
Évariste_Galois
Quantum mechanical model
,} where Ln are the Laguerre polynomials. This example illustrates how the Hermite and Laguerre polynomials are linked through the Wigner map. Meanwhile
Quantum_harmonic_oscillator
Product of numbers from 1 to n
to relate certain families of polynomials to each other, for instance in Newton's identities for symmetric polynomials. Their use in counting permutations
Factorial
Computer science
In computational complexity theory, exact quantum polynomial time (EQP or sometimes QP) is the class of decision problems that can be solved by a quantum
Exact_quantum_polynomial_time
Branch of discrete mathematics
and is closely related to q-series, special functions and orthogonal polynomials. Originally a part of number theory and analysis, it is now considered
Combinatorics
American mathematician and educator (1921–2008)
namesake of the Gleason polynomials, a system of polynomials that generate the weight enumerators of linear codes. These polynomials take a particularly simple
Andrew_M._Gleason
Numbers obtained by adding the two previous ones
assigned a variable value x, the result is the sequence of Fibonacci polynomials. Not adding the immediately preceding numbers. The Padovan sequence and
Fibonacci_sequence
BELL POLYNOMIALS
BELL POLYNOMIALS
Surname or Lastname
English and North German
English and North German : metonymic occupational name for a leather belt or strap maker, from Middle English belt(e), Middle Low German balt.German : from a short form of the Germanic personal name Baldher (see Belter).North German : habitational name from a place called Beelte (see Belter 2).
Surname or Lastname
English (chiefly northern)
English (chiefly northern) : topographic name for someone who lived by an area of high ground or by a prominent crag, from northern Middle English fell ‘high ground’, ‘rock’, ‘crag’ (Old Norse fjall, fell).English, German, and Jewish (Ashkenazic) : metonymic occupational name for a furrier, from Middle English fell, Middle High German vel, or German Fell or Yiddish fel, all of which mean ‘skin’, ‘hide’, or ‘pelt’. Yiddish fel refers to untanned hide, in contrast to pelts ‘tanned hide’ (see Pilcher).
Boy/Male
Australian, French, Swedish
Handsome Friend; God Promise; Beautiful
Female
English
Variant spelling of English Belle, BELL means "beautiful."Â
Male
Welsh
Variant spelling of Welsh Bel, BELI means "shining."
Male
English
Short form of English unisex Kelly, KELL means "bright-headed."
Surname or Lastname
English and German
English and German : from a Germanic personal name, either a short form of compound names such as Billard, or else a byname Bill(a), from Old English bil ‘sword’, ‘halberd’ (or a Continental cognate). (Bill as a short form of William was not used until the 17th century.)English : metonymic occupational name for a maker of pruning hooks and similar implements, from Middle English bill, from Old English bil ‘sword’, with the meaning shifted to a more peaceful agricultural application (see Biller 5).
Surname or Lastname
English
English : nickname for a strong, aggressive, bull-like man, from Middle English bul(l)e, bol(l)e. Occasionally, the name may denote a keeper of a bull. Compare Bulman.German (mainly northern) : from a byname for a cattle breeder, keeper, or dealer. Compare South German Ochs.South German : nickname for a short fat man, a variant of Bolle, or a nickname for a man with the physical characteristics of a bull.
Female
English
Pet form of English Eleanor, NELL means "foreign; the other."
Girl/Female
Christian & English(British/American/Australian)
Beautiful
Girl/Female
British, English, French, German, Netherlands, Romanian
Form of Beli
Girl/Female
Czechoslovakian American English French German Latin Spanish
White.
Surname or Lastname
English
English : topographic name for someone who lived near a spring or stream, Middle English well(e) (Old English well(a)).German : from a short form of the personal names Wallo, Walilo.German : nickname from Middle High German wël ‘round’.
Surname or Lastname
English and Scottish
English and Scottish : variant spelling of Beal.Ninian Beall, a Scottish Royalist, emigrated to Calvert co., MD, in about 1650, after King Charles I was beheaded.
Girl/Female
Japanese
Ball; bell.
Male
English
Variant spelling of English Abel, ABELL means "vanity," i.e. "transitory."
Boy/Male
French English
Handsome.
Male
Hebrew
(בֶּלַע) Hebrew name BELA means "destruction." In the bible, this is the name of several characters, including a king of Edom.
Boy/Male
British, English, Hindu, Indian
From Bell; Stomach
Male
English
Pet form of English William, BILL means "will-helmet."
BELL POLYNOMIALS
BELL POLYNOMIALS
Girl/Female
Tamil
Wavy, Night
Surname or Lastname
English
English : probably a habitational name from Lamplugh in Cumbria, an ancient Celtic name meaning ‘bare valley’, from nant ‘valley’ + bluch ‘bare’.
Male
Japanese
(三郎) Japanese name SABURO means "third son."Â
Surname or Lastname
English and Scottish
English and Scottish : origin uncertain; perhaps a nickname for a foster parent, from Middle English foden ‘to nurse or nourish’.
Boy/Male
Hindu, Indian, Malaysian
Smart
Girl/Female
French American German
Nobility. French form of the Old German Adalheidis, a compound of 'athal' (noble) and 'haida'...
Female
English
Anglicized form of Hebrew Ritspah, RIZPAH means "hot coal" or "pavement." In the bible, this is the name of one of King Saul's concubines.
Girl/Female
Muslim
Unbelievable flower
Surname or Lastname
Irish
Irish : reduced Anglicized form of Gaelic Ó hEachthighearna ‘descendant of Eachthighearna’, a personal name meaning ‘lord of horses’, from each ‘horse’ + tighearna ‘master’, ‘lord’. This name is most common in southwestern Ireland.Irish : Anglicized form of Gaelic Ó hUidhrÃn (see Herron).English : variant of Heron 1.English : topographic name for someone who lived by a bend in a river or in a recess in a hill, both of which are meanings of Middle English herne (Old English hyrne). It may also be a habitational name from any of the various places, such as Herne in Kent and Hurn in Dorset, which are named with the Old English word. Its exact original sense and its etymology are not clear; it may be a derivative of horn ‘horn’.English : habitational name from Herne in Bedfordshire, so called from the dative plural (originally used after a preposition) of Old English hær ‘stone’.
Boy/Male
Tamil
Lord Ganesh
BELL POLYNOMIALS
BELL POLYNOMIALS
BELL POLYNOMIALS
BELL POLYNOMIALS
BELL POLYNOMIALS
v. t.
To form or wind into a ball; as, to ball cotton.
n.
The strikes of the bell which mark the time; or the time so designated.
a.
Expanding at the mouth; as, a bell-mouthed gun.
n.
A hollow perforated sphere of metal containing a loose ball which causes it to sound when moved.
v. t.
To put a bell upon; as, to bell the cat.
v. i.
To develop bells or corollas; to take the form of a bell; to blossom; as, hops bell.
n.
Any paper, containing a statement of particulars; as, a bill of charges or expenditures; a weekly bill of mortality; a bill of fare, etc.
a.
Of or pertaining to a bull; resembling a bull; male; large; fierce.
n.
Anything that resembles a belt, or that encircles or crosses like a belt; a strip or stripe; as, a belt of trees; a belt of sand.
n.
Alt. of Sancte bell
n.
A cell; a house.
v. t.
To pour forth, as from a well.
n.
Anything in the form of a bell, as the cup or corol of a flower.
a.
Hung with a bell or bells.
a.
Having the shape of a wide-mouthed bell; campanulate.
v. t.
To charge or enter in a bill; as, to bill goods.
v. t.
To endeavor to raise the market price of; as, to bull railroad bonds; to bull stocks; to bull Lake Shore; to endeavor to raise prices in; as, to bull the market. See 1st Bull, n., 4.
n.
See Sanctus bell, under Sanctus.
n.
The bell, or boom, of the bittern
v. t.
To make bell-mouthed; as, to bell a tube.