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Concept in mathematical analysis
In mathematical analysis, the Dirichlet kernel, is the collection of periodic functions defined as D n ( x ) = ∑ k = − n n e i k x = ( 1 + 2 ∑ k = 1 n
Dirichlet_kernel
Integral of sin(x)/x from 0 to infinity
are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral
Dirichlet_integral
German mathematician (1805–1859)
theorem for the Fourier series, introduced the Dirichlet kernel and the Dirichlet integral. Dirichlet also studied the first boundary-value problem, for
Peter Gustav Lejeune Dirichlet
Peter_Gustav_Lejeune_Dirichlet
Family of functions in mathematics
_{s=-k}^{k}{\rm {e}}^{isx}} is the k {\displaystyle k} th order Dirichlet kernel. 2) The Fejér kernel F n ( x ) {\displaystyle F_{n}(x)} may also be written in
Fejér_kernel
{\displaystyle \theta \not \equiv 0{\pmod {2\pi }}.} A related function is the Dirichlet kernel: D n ( θ ) = 1 + 2 ∑ k = 1 n cos k θ = sin ( ( n + 1 2 ) θ ) sin
List of trigonometric identities
List_of_trigonometric_identities
Generalized function whose value is zero everywhere except at zero
In the terminology of Lang (1997), the Fejér kernel is a Dirac sequence, whereas the Dirichlet kernel is not. Reed & Simon 1980, Ch. II–III, VIII. Adams
Dirac_delta_function
Mathematical problem in classical harmonic analysis
D_{n}(t)={\frac {\sin((n+{\frac {1}{2}})t)}{\sin(t/2)}}.} The Dirichlet kernel is not a positive kernel, and in fact, its norm diverges, namely ∫ | D n ( t )
Convergence_of_Fourier_series
Mathematical concept
kernel is an integral kernel, used for solving the two-dimensional Laplace equation, given Dirichlet boundary conditions on the unit disk. The kernel
Poisson_kernel
hyperbola method Dirichlet integral Dirichlet kernel (functional analysis, Fourier series) Dirichlet L-function Dirichlet principle Dirichlet problem (partial
List of things named after Peter Gustav Lejeune Dirichlet
List_of_things_named_after_Peter_Gustav_Lejeune_Dirichlet
Fundamental solution to the heat equation, given boundary values
\end{cases}}} To derive a formal expression for the heat kernel on an arbitrary domain, consider the Dirichlet problem in a connected domain (or manifold with
Heat_kernel
Mathematical form
functions) and functional analysis, Dirichlet forms generalize the Laplacian (the mathematical operator on scalar fields). Dirichlet forms can be defined on any
Dirichlet_form
Problem of solving a partial differential equation subject to prescribed boundary values
using the Poisson kernel was known to Dirichlet (judging by his 1850 paper submitted to the Prussian academy). Lord Kelvin and Dirichlet suggested a solution
Dirichlet_problem
Periodic distribution ("function") of "point-mass" Dirac delta sampling
is periodic, it can be represented as a Fourier series based on the Dirichlet kernel: Ш T ( t ) = 1 T ∑ n = − ∞ ∞ e i 2 π n t / T . {\displaystyle \operatorname
Dirac_comb
Decomposition of periodic functions
continuous, it is not differentiable. ATS theorem Carleson's theorem Dirichlet kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier
Fourier_series
Mathematical theorem about the Fourier series
s n ( f , x ) {\displaystyle s_{n}(f,x)} may be written using the Dirichlet Kernel as s n ( f , x ) = 1 2 π ∫ − π π f ( x − t ) D n ( t ) d t {\displaystyle
Fejér's_theorem
Topics referred to by the same term
functions Dn, a Coxeter–Dynkin diagram Dn, a dihedral group Dn, a Dirichlet kernel Decinewton (symbol dN), an SI unit of force Diametre Nominal, the European
DN
Summability method in physics
be understood as eigenvalues of the heat kernel. In mathematics, such a sum is known as a generalized Dirichlet series; its use for averaging is known as
Zeta_function_regularization
Function in discrete mathematics
a sinc-like function (specifically, X k {\displaystyle X_{k}} is a Dirichlet kernel) ∑ j ∈ Z exp ( − π c N ⋅ ( n + N ⋅ j ) 2 ) {\displaystyle \sum _{j\in
Discrete_Fourier_transform
Pair of polynomial sequences
arccos x {\displaystyle \theta =\arccos x} . They coincide with the Dirichlet kernel. In the airfoil literature V n ( x ) {\displaystyle V_{n}(x)} and W
Chebyshev_polynomials
Family of functions
|t|>\delta } . The Fejér kernel The Poisson kernel (continuous index) The Landau kernel The Dirichlet kernel is not a summability kernel, since it fails the
Summability_kernel
Type of operator in Fourier analysis
in the form Tf = f∗K for some distribution K, known as the convolution kernel of T. In this view, translation by an amount x0 is convolution with a Dirac
Multiplier_(Fourier_analysis)
partial sums, which Dirichlet transformed into a particular Dirichlet integral involving what is now called the Dirichlet kernel. This paper introduced
List of publications in mathematics
List_of_publications_in_mathematics
Interpolation with trigonometric polynomials
is obviously involved. A much simpler approach is to consider the Dirichlet kernel D ( x , N ) = 1 N + 2 N ∑ k = 1 ( N − 1 ) / 2 cos ( k x ) = sin
Trigonometric_interpolation
Overlap–save method Sigma approximation Dirichlet kernel — convolving any function with the Dirichlet kernel yields its trigonometric interpolant Gibbs
List of numerical analysis topics
List_of_numerical_analysis_topics
Mapping involving integration between function spaces
two variables, that is called the kernel or nucleus of the transform. Some kernels have an associated inverse kernel K − 1 ( u , t ) {\displaystyle K^{-1}(u
Integral_transform
}^{1}(1-t^{2})^{n}\,dt\leq (n+1)(1-\delta ^{2})^{n}} Poisson kernel Fejér kernel Dirichlet kernel Terras, Audrey (May 25, 2009). "Lecture 8. Dirac and Weierstrass"
Landau_kernel
Theorem stating that pointwise boundedness implies uniform boundedness
dt,} where D N {\displaystyle D_{N}} is the N {\displaystyle N} -th Dirichlet kernel. Fix x ∈ T {\displaystyle x\in \mathbb {T} } and consider the convergence
Uniform_boundedness_principle
Second-order partial differential equation
{C} } , the solution of the Dirichlet problem with continuous boundary data f {\displaystyle f} is given by the Poisson kernel formula u ( r e i θ ) = 1
Laplace's_equation
Overview of and topical guide to trigonometry
generating functions in combinatorics, see Alternating permutation. Dirichlet kernel Euler's formula Exact trigonometric values Exponential sum Trigonometric
Outline_of_trigonometry
Laplace transform Discrete Hartley transform List of transforms Dirichlet kernel Fejér kernel Convolution theorem Least-squares spectral analysis List of
List of Fourier analysis topics
List_of_Fourier_analysis_topics
Trigonometric function Trigonometric polynomial Exponential sum Dirichlet kernel Fejér kernel Gibbs phenomenon Parseval's identity Parseval's theorem Weyl
List of harmonic analysis topics
List_of_harmonic_analysis_topics
Integral expressing the amount of overlap of one function as it is shifted over another
scattering media Convolution power Convolution quotient Deconvolution Dirichlet convolution List of convolutions of probability distributions LTI system
Convolution
{\mathcal {D}}(\Omega )} (named after Peter Gustav Lejeune Dirichlet), is the reproducing kernel Hilbert space of holomorphic functions, contained within
Dirichlet_space
Set of machine learning methods
Multiple kernel learning refers to a set of machine learning methods that use a predefined set of kernels and learn an optimal linear or non-linear combination
Multiple_kernel_learning
Image classification model
different themes. Probabilistic latent semantic analysis (pLSA) and latent Dirichlet allocation (LDA) are two popular topic models from text domains to tackle
Bag-of-words model in computer vision
Bag-of-words_model_in_computer_vision
Topics referred to by the same term
theorem Dirichlet convolution Infimal convolution Logarithmic convolution Vandermonde convolution Convolution, in digital image processing, with a Kernel (image
Convolution_(disambiguation)
Overview of and topical guide to machine learning
model Kernel adaptive filter Kernel density estimation Kernel eigenvoice Kernel embedding of distributions Kernel method Kernel perceptron Kernel random
Outline_of_machine_learning
differential equation Poisson differential operator Dirichlet–Poisson problem Discrete Poisson equation Poisson kernel Poisson integral formula Poisson–Jensen formula
List of things named after Siméon Denis Poisson
List_of_things_named_after_Siméon_Denis_Poisson
Green's function for Laplacian
fact can be used to prove existence and uniqueness of solutions to the Dirichlet problem for the Poisson equation in suitably regular domains, and for
Newtonian_potential
Differential operator in mathematics
Laplacian can be defined wherever the Dirichlet energy functional makes sense, which is the theory of Dirichlet forms. For spaces with additional structure
Laplace_operator
American mathematician (1916–2002)
no. 1 (1945), pp. 113–119. (LINK) "A geometric construction of the Dirichlet kernel". Trans. N. Y. Acad. Sci., Volume 36, Issue 7 (1974), Series II, pp
Howard_Levi
Machine kernels basing on Bayesian inference and another approach to establish hierarchical clustering. Tiao, George (1965). "The inverted Dirichlet distribution
Inverted Dirichlet distribution
Inverted_Dirichlet_distribution
spaces", Encyclopedia of Mathematics, EMS Press. Bergman kernel Banach space Hilbert space Reproducing kernel Hilbert space Hardy space Dirichlet space
Bergman_space
Concept in statistical mechanics
meanings of the word "distribution"). Given a domain Ω⊆Rn, consider the Dirichlet inner product ⟨ f , g ⟩ := ∫ Ω ( D f ( x ) , D g ( x ) ) d x {\displaystyle
Gaussian_free_field
Method in statistics
\ldots ,f(x_{n})} to set the kernel hyperparameters using, for example, maximum likelihood estimation. The estimation of kernel hyperparameters introduces
Bayesian_quadrature
Non-self-adjoint compact operator used to solve boundary value problems for the Laplacian
follows: Interior Dirichlet problem: ∆u = 0 in Ω, u = f on ∂Ω Interior Neumann problem: ∆u = 0 in Ω, ∂n− u = f on ∂Ω Exterior Dirichlet problem: ∆u = 0
Neumann–Poincaré_operator
American mathematician (born 1931)
Hypercontractivity and logarithmic Sobolev inequalities for the Clifford Dirichlet form. Duke Math. J. 42 (1975), no. 3, 383–396. Gross, Leonard: Existence
Leonard_Gross
which case one has to prescribe suitable boundary conditions, such as Dirichlet or Neumann boundary conditions. More generally one can define Z ( P ,
Minakshisundaram–Pleijel zeta function
Minakshisundaram–Pleijel_zeta_function
and, in the proof of the theorem for the Fourier series, the Dirichlet kernel and Dirichlet integral. He also introduces a general modern concept for a
1829_in_science
Theorem about Diophantine approximations
theorem is a result about Diophantine approximations that generalizes Dirichlet's approximation theorem to multiple variables. The Kronecker approximation
Kronecker's_theorem
Infinite series summing alternating 1 and -1 terms
limits of the Dirichlet, Fejér, and Poisson kernels, respectively. Multiplying the terms of Grandi's series by 1/nz yields the Dirichlet series η ( z )
Grandi's_series
Chinese-American mathematician (born 1949)
their new "conformal invariant", which is a min-max quantity based on the Dirichlet energy. The main work of their article is devoted to relating their conformal
Shing-Tung_Yau
Branch of number theory
Lejeune Dirichlet's work was what led him to his later study of algebraic number fields and ideals. In 1863, he published Lejeune Dirichlet's lectures
Algebraic_number_theory
German mathematician (1877–1938)
inequality Landau–Ramanujan constant Landau's problem on the Dirichlet eta function Landau kernel Endmund Landau (1895). "Zur relativen Wertbemessung der Turnierresultate"
Edmund_Landau
Functions in mathematics
are determined by their singularities and boundary conditions (such as Dirichlet boundary conditions or Neumann boundary conditions). On regions without
Harmonic_function
American mathematician
Heins, from Brown University with thesis Method for the Solution of the Dirichlet Problem for Certain Types of Domains. In the early 1940s, he worked as
Bernard_Epstein
Partial differential equation describing the evolution of temperature in a region
,0)=g(\mathbf {x} )&\mathbf {x} \in \Omega \end{cases}}} with either Dirichlet or Neumann boundary data. A Green's function always exists, but unless
Heat_equation
used in the theory of partial differential equations for solving the Dirichlet and Neumann boundary value problems for the Laplacian in a bounded domain
Sobolev spaces for planar domains
Sobolev_spaces_for_planar_domains
Swedish mathematician
contributed to the development of the theory of Bergman spaces and spaces of Dirichlet series. After 2010, Hedenmalm became interested in complex normal random
Hakan_Hedenmalm
Product of the prime factors of an integer
multiples of rad ( n ) {\displaystyle \operatorname {rad} (n)} . The Dirichlet series is ∏ p ( 1 + p 1 − s 1 − p − s ) = ∑ n = 1 ∞ rad ( n ) n s {\displaystyle
Radical_of_an_integer
of harmonic functions that arises from the solution of the classical Dirichlet problem. In probability theory, the harmonic measure of a subset of the
Harmonic_measure
Mathematical operation
transform. This integral transform is closely connected to the theory of Dirichlet series, and is often used in number theory, mathematical statistics, and
Mellin_transform
Type of vector space in math
differential equations. An example is the Poisson equation −Δu = g with Dirichlet boundary conditions in a bounded domain Ω in R2. The weak formulation
Hilbert_space
Mathematical theorem
extent, the Dirichlet principle is valid under the hypothesis that Riemann was working with. However, in order to be valid, the Dirichlet principle needs
Riemann_mapping_theorem
Statistical concept
weights are typically viewed as a K-dimensional random vector drawn from a Dirichlet distribution (the conjugate prior of the categorical distribution), and
Mixture_model
distribution Kernel density estimation Kernel Fisher discriminant analysis Kernel methods Kernel principal component analysis Kernel regression Kernel smoother
List_of_statistics_articles
Infinite sum
Like the zeta function, Dirichlet series in general play an important role in analytic number theory. Generally a Dirichlet series converges if the real
Series_(mathematics)
Method of solution to differential equations
0 or Poisson's equation ∇2φ(x) = −ρ(x), subject to either Neumann or Dirichlet boundary conditions. In other words, we can solve for φ(x) everywhere
Green's_function
Branch of mathematical analysis
non-singular kernels provide distinct mechanisms for modeling anomalous diffusion. The Atangana–Baleanu–Caputo (ABC) operator, with its Mittag-Leffler kernel, yields
Fractional_calculus
French mathematician and physicist (1781–1840)
kernel. Thanks to the works of Dirichlet and Hermann Schwarz, the Poisson kernel is now typically presented in the context of solving the Dirichlet problem
Siméon_Denis_Poisson
Method for analyzing semantic data
not a proper generative model for new documents. Latent Dirichlet allocation – adds a Dirichlet prior on the per-document topic distribution Higher-order
Probabilistic latent semantic analysis
Probabilistic_latent_semantic_analysis
employs the double layer potentials from the potential theory as its basis/kernel functions. Like the method of fundamental solutions (MFS), the numerical
Regularized_meshless_method
Oscillatory error in Fourier series
value of the original function at the discontinuity) as a consequence of Dirichlet's theorem. The quantity ∫ 0 π sin t t d t = ( 1.851937051982 … ) =
Gibbs_phenomenon
American mathematician (1943–2024)
this flow, proving an analogous result to Eells and Sampson's for the Dirichlet condition and Neumann condition.[H75] The analytic nature of the problem
Richard_S._Hamilton
Automated recognition of patterns and regularities in data
empirical observations – using e.g., the Beta- (conjugate prior) and Dirichlet-distributions. The Bayesian approach facilitates a seamless intermixing
Pattern_recognition
Construct for Hermitian matrices
principle Min-max theorem Rayleigh's quotient in vibrations analysis Dirichlet eigenvalue Also known as the Rayleigh–Ritz ratio; named after Walther
Rayleigh_quotient
Infinite series that is not convergent
type is known as a generalized Dirichlet series; in applications to physics, this is known as the method of heat-kernel regularization. Abelian means are
Divergent_series
Differential equation that is linear with respect to the unknown function
the equation, such as Ly(x) = b(x) or Ly = b. The kernel of a linear differential operator is its kernel as a linear mapping, that is the vector space of
Linear_differential_equation
penalty". arXiv:1209.0368 [math.OC]. Blei, D., Ng, A., and Jordan, M. Latent dirichlet allocation. J. Mach. Learn. Res., 3:993–1022, 2003. Bengio, Y. "Learning
Structured sparsity regularization
Structured_sparsity_regularization
Orientation-preserving mapping class group of the torus
65. ISBN 9780821839850. Apostol, Tom M. (1990). Modular Functions and Dirichlet Series in Number Theory (2nd ed.). New York: Springer. ch. 2. ISBN 0-387-97127-0
Modular_group
Classification of Artificial Neural Networks (ANNs)
many other forms. Convolutional neural networks (CNN): a FNN that uses kernels and regularization to evade problems in prior generations of NNs. They
Types of artificial neural networks
Types_of_artificial_neural_networks
Calculation of complex statistical distributions
sampling over nonparametric Bayesian models such as those involving the Dirichlet process or Chinese restaurant process, where the number of mixing
Markov_chain_Monte_Carlo
Vector space of functions in mathematics
L^{2}\!(\Omega ),} is compact. This fact plays a role in the study of the Dirichlet problem, and in the fact that there exists an orthonormal basis of L 2
Sobolev_space
x , y ) {\displaystyle p(t,x,y)} of Brownian motion is the minimal heat kernel of the heat equation. Interpreting the paths of Brownian motion as characteristic
Stochastic analysis on manifolds
Stochastic_analysis_on_manifolds
Type of statistical analysis
nonparametric hierarchical Bayesian models, such as models based on the Dirichlet process, which allow the number of latent variables to grow as necessary
Nonparametric_statistics
Concept in mathematical group theory
_{1}*\chi _{2}](g)=\chi _{1}(g)\chi _{2}(g)} . This group is connected to Dirichlet characters and Fourier analysis. The characters discussed in this section
Character_theory
Spline function
{\displaystyle B_{i,n,{\textbf {norm}}}} can be written as Carlson's Dirichlet average R k {\displaystyle R_{k}} , which in turn can be solved exactly
B-spline
Fourier transform of the probability density function
when X is the discrete random variable that is always 0, it becomes the Dirichlet integral. Inversion formulas for multivariate distributions are available
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Machine learning methods using multiple input modalities
outperform traditional models like support vector machines and latent Dirichlet allocation in classification tasks and can predict missing data in multimodal
Multimodal_learning
Number, approximately 3.14
higher-dimensional Poincaré inequalities that provide best constants for the Dirichlet energy of an n-dimensional membrane. Specifically, π is the greatest constant
Pi
On the other hand, by studying Dirichlet L-series of characters of the group H0(E/F), one shows that the Dirichlet density of primes of k representing
Class_formation
Mathematical constant
deformed function ξ t {\displaystyle \xi _{t}} can be approximated by a Dirichlet series ζ t ( s ) = ∑ n = 1 ∞ exp ( t 4 log 2 n ) n − s , {\displaystyle
De_Bruijn–Newman_constant
American mathematician
Shapiro, Joel H. (1982). "Tangential boundary behavior of functions in Dirichlet-type spaces". Annals of Mathematics. 116 (2): 331–360. doi:10.2307/2007064
Alexander_Nagel
Research topic in computational geometry
with a blur kernel formed using the Laplace operator, geometric smoothing might be achieved by convolving a surface geometry with a blur kernel formed using
Geometry_processing
System where changes of output are not proportional to changes of input
principle. A good example of this is one-dimensional heat transport with Dirichlet boundary conditions, the solution of which can be written as a time-dependent
Nonlinear_system
Wiener process with reflecting spatial boundaries
boundary condition for the process absorption or killed Brownian motion, a Dirichlet boundary condition instantaneous reflection, as described above a Neumann
Reflected_Brownian_motion
Canadian mathematician
O. El-Fallah, K. Kellay, J. Mashreghi, T. Ransford, A Primer on the Dirichlet Space, Cambridge Tracts in Mathematics 203, Cambridge University Press
Javad_Mashreghi
Mathematical approximation of a function
Aguech, Rafik; Jedidi, Wissem (2015). "Completely monotone functions and kernels of the cut-off operator". p. 14. arXiv:1511.08345 [math.PR]. Hille & Phillips
Taylor_series
Algorithm used by recommender systems
probabilistic latent semantic analysis, multiple multiplicative factor, latent Dirichlet allocation and Markov decision process-based models. Through this approach
Collaborative_filtering
Matrix of second derivatives
plays an important role in Morse theory and catastrophe theory, because its kernel and eigenvalues allow classification of the critical points. The determinant
Hessian_matrix
DIRICHLET KERNEL
DIRICHLET KERNEL
Female
English
Anglicized form of Irish Gaelic Eithne, ETHNA means "kernel."
Female
Irish
Variant spelling of Irish Gaelic Eithne, AITHNEA means "kernel."
Surname or Lastname
Swedish
Swedish : ornamental name formed with the common surname suffix -ell. The first element is unexplained, possibly from a place-name.English, Scottish, and northern Irish : unexplained; possibly a respelling of Scottish Kerneil, a habitational name from Carneil in Carnock, Fife.
Female
Irish
Variant spelling of Irish Gaelic Eithne, AITHNE means "kernel."
Female
English
 Variant spelling of English Ethna, ETNA means "kernel." Compare with another form of Etna.
Girl/Female
Australian, Chinese, Christian, Danish, German, Irish
Kernel; Nut
Female
Irish
Variant spelling of Irish Gaelic Eithne, ETHNE means "kernel."
Girl/Female
Australian, Celtic, Christian, Irish
Graceful; Kernel
Female
English
(Hebrew ×¢Ö¶×“Ö°× Ö¸×”): Anglicized form of Irish Gaelic Eithne, EDNA means "kernel." Hebrew name meaning "delight, pleasure, rejuvenation." In the apocryphal Book of Tobit, this is the name of the mother of Sarah.Â
Girl/Female
Australian, Celtic, Christian, Irish
Kernel; Nut
Female
English
Anglicized form of Irish Gaelic Eithne, ENYA means "kernel."
Girl/Female
Assamese, Christian, French, Gaelic, Indian, Marathi, Sanskrit, Swedish
The Zodiac Sign of Capricorn; Kernel
Surname or Lastname
Irish
Irish : reduced form of McCarron.German, Dutch, and Jewish (Ashkenazic) : from Middle High German kerne ‘kernel’, ‘seed’, ‘pip’; Middle Dutch kern(e), keerne; German Kern or Yiddish kern ‘grain’, hence a metonymic occupational name for a farmer, or a nickname for a small person. As a Jewish surname, it is mainly ornamental.English : probably a metonymic occupational name for a maker or user of hand mills, from Old English cweorn ‘hand mill’, or a habitational name for someone from Kern in the Isle of Wight, named from this word.
Female
Irish
(pronounced ee-na) Irish Gaelic name derived from the word eithne, EITHNE means "kernel." Edna, Ena, Enya, Ethna and Etna are Anglicized forms.
Female
English
Anglicized form of Irish Gaelic Eithne, ENA means "kernel."
DIRICHLET KERNEL
DIRICHLET KERNEL
Female
Scandinavian
Scandinavian form of Old Norse Hildr, HILDE means "battle." Compare with masculine Hilde.
Boy/Male
Polish
Fair-haired.
Boy/Male
Arabic, Biblical, Hebrew
Song; Singer; Vine
Boy/Male
Muslim
Khair Udeen | خیر یودین
The good of the faith
Surname or Lastname
English and Irish
English and Irish : variant spelling of Mayberry.
Male
English
Anglicized form of Hebrew Asar'el, ASAREEL means "whom God has bound (by a vow)."
Boy/Male
American, Anglo, Australian, British, English
From the Hedged Forest
Surname or Lastname
English
English : habitational name from any of several places in Hampshire and Wiltshire named with Chute, from Celtic cēd ‘wood’. Compare Welsh coed.Americanized form of German Schütt, a variant of Schütte (see Schutte).
Female
Cornish
, emerald.
Girl/Female
Anglo, Australian, British, Czechoslovakian, Danish, English, French, German, Italian, Spanish, Swedish
Joyous; Prosperity; Battle; Spoils of War; Strife for Wealth; Prosperous in War; Fortune
DIRICHLET KERNEL
DIRICHLET KERNEL
DIRICHLET KERNEL
DIRICHLET KERNEL
DIRICHLET KERNEL
n.
A single seed or grain; as, a kernel of corn.
n.
The shell or hard external covering in which the kernel of a nut is inclosed.
v. t.
To beat out grain from, as straw or husks; to beat the straw or husk of (grain) with a flail; to beat off, as the kernels of grain; as, to thrash wheat, rye, or oats; to thrash over the old straw.
v. i.
To harden or ripen into kernels; to produce kernels.
v. t.
To separate the kernels of (an ear of Indian corn, wheat, oats, etc.) from the cob, ear, or husk.
p. pr. & vb. n.
of Kernel
n.
The woody, thick skin inclosing the kernel of a walnut.
a.
Having a kernel.
n.
The central, substantial or essential part of anything; the gist; the core; as, the kernel of an argument.
v. t.
The outer covering of anything, particularly of a nut or of grain; the outer skin of a kernel; the husk.
a.
Alt. of Kernelled
n.
An American tree of the genus Carya, of which there are several species. The shagbark is the C. alba, and has a very rough bark; it affords the hickory nut of the markets. The pignut, or brown hickory, is the C. glabra. The swamp hickory is C. amara, having a nut whose shell is very thin and the kernel bitter.
n.
The essential part of a seed; all that is within the seed walls; the edible substance contained in the shell of a nut; hence, anything included in a shell, husk, or integument; as, the kernel of a nut. See Illust. of Endocarp.
a.
Full of kernels; resembling kernels; of the nature of kernels.
imp. & p. p.
of Kernel