kernel
American Heritage Dictionary:
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ker·nel
(kûr'nəl) 
n.
n.
- A grain or seed, as of a cereal grass, enclosed in a husk.
- The inner, usually edible seed of a nut or fruit stone.
- The most material and central part; the core: "that hard kernel of gaiety that never breaks" (Evelyn Waugh).
[Middle English, from Old English cyrnel.]
kerneled ker'neled adj.
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The nucleus of an operating system. It is the closest part to the machine level and may activate the hardware directly or interface to another software layer that drives the hardware. The kernel orchestrates the entire operation of the computer by slicing time for each system function and each application as well as managing all the computer's resources. It typically resides in memory at all times. See microkernel, monolithic kernel, kernel space and kernel panic.
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Roget's Thesaurus:
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kernel
noun
- A fertilized plant ovule capable of germinating: pip, pit2, seed. See start/end.
- A source of further growth and development: bud1, embryo, germ, nucleus, seed, spark1. See start/end.
- The most central and material part: core, essence, gist, heart, marrow, meat, nub, pith, quintessence, root1, soul, spirit, stuff, substance. Law gravamen. See be.
Word Tutor:
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kernel
IN BRIEF: A seed.
Can you put the kernel back in the nut or the broken egg in its shell?
— zaadz.com.
Tutor's tip: The officers nicknamed the "colonel" (military rank between lieutenant colonel and brigadier general) "kernel" (part of an ear of corn) for his penchant to eat corn at every meal.
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Whole grains and the meats of nuts and stone fruit pips or pits.
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categories related to 'kernel'
- Botany and Plant Parts - kernel: grain or seed, esp. inside fruit
- Plants and Plant Parts - kernel: grain or seed, esp. inside fruit
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Kernel (mathematics)
In mathematics, the word kernel has several meanings.
Kernels of mappings
Kernel may mean a subset associated with a mapping, which measures how far it is from being injective or being a monomorphism:
- The kernel of a mapping is the set of elements that map to the zero element (such as zero or zero vector), as in kernel of a linear operator and kernel of a matrix. In this context, kernel is often called nullspace.
- More generally, the kernel in algebra is the set of elements that map to the neutral element. Here, the mapping is assumed to be a homomorphism, that is, it preserves algebraic operations, and, in particular, maps neutral element to neutral element. The kernel is then the set of all elements that the mapping cannot distinguish from the neutral element.
- The kernel in category theory is a generalization of this concept to morphisms rather than mappings between sets.
- In set theory, the kernel of a function is the set of all pairs of elements that the function cannot distinguish, that is, they map to the same value. This is a generalization of the kernel concept above to the case when there is no neutral element.
- In set theory, the difference kernel or binary equalizer is the set of all elements where the values of two functions coincide.
Kernels of transforms
Kernel may also mean a function which serves as parameter for some class of functional mappings:
- In integral calculus, the kernel (also called integral kernel or kernel function) is a function of two variables that defines an integral transform, such as the function k in
- In partial differential equations, when the solution of the equation for the right-hand side f can be written as Tf above, the kernel becomes the Green's function. The heat kernel is the Green's function of the heat equation.
- In the case when the integral kernel depends only on the difference between its arguments, it becomes a convolution kernel, as in
- In statistics, a kernel is a weighting function used in kernel density estimation to estimate the probability density function of a random variable.
- In probability theory and statistics, a stochastic kernel is the transition function of a stochastic process. In a discrete time process with continuous probability distributions, it is the same thing as the kernel of the integral operator that advances the probability density function.
- Kernel trick is a technique to write a nonlinear operator as a linear one in a space of higher dimension.
- In operator theory, a positive definite kernel is a generalization of a positive-definite matrix.
- The kernel in a reproducing kernel Hilbert space.
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This disambiguation page lists mathematics articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article. |
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Translations:
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Kernel
Nederlands (Dutch)
pit, kern, korrel
Deutsch (German)
n. - Kern, Korn
v. - Körner bilden
Ελληνική (Greek)
n. - ψίχα κουκουτσιού, κουκούτσι, πυρήνας, μόνιμο τμήμα λειτουργίας Η/Υ ή προγράμματος, (μτφ.) πεμπτουσία, ουσία
v. - περικλείω σε κέλυφος
Italiano (Italian)
nocciolo, nucleo
Português (Portuguese)
n. - semente (f), parte comestível de uma noz, grão (m) de cereal, cerne (m), parte (f) essencial
Русский (Russian)
зерно, ядро, суть
Español (Spanish)
n. - núcleo, meollo, pipa, pepita, grano, médula, almendra, semilla
v. tr. - encerrar, granar
Svenska (Swedish)
n. - kärna, (vete)korn
v. - hårdna till kärna
中文（简体）(Chinese (Simplified))
仁, 核心, 要点, 粒, 子
中文（繁體）(Chinese (Traditional))
n. - 仁, 核心, 要點, 粒, 子
日本語 (Japanese)
n. - 仁, 粒, 核心, 要点
العربيه (Arabic)
(الاسم) جوهر الشي, النواة, لب النواة (فعل) يكون أو يغلف اللب
עברית (Hebrew)
n. - גלעין, גרעין, זרע, עיקר, החלק האכיל של פרי או אגוז
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