multiple issues orphan March 2010 notability March 2010 Kernel relocation may refer to the Linux feature in which a Linux kernelkernel can be compiled to be bootable at a variety of different memory address es, instead of a fixed address, used in connection with kexec for crash recovery. ref http kernelnewbies.org Linux 2 6 20 head 3c215483506a27123005168c491eea0f2e5549dd ref References reflist DEFAULTSORT Kernel Relocation Category Linux kernel linux stub ... more details
In telecommunication , the term security kernel has the following meanings In computer and communications security , the central part of a computer or communications system computer hardware hardware , firmware , and software that implements the basic security procedures for controlling Access control access to system resources. A self contained usually small collection of key security related statements that a works as a part of an operating system to prevent unauthorized access to, or use of, the system and b contains criteria that must be met before specified programs can be accessed. Hardware, firmware, and software elements of a trusted computing base that implement the reference monitor concept. References FS1037C National Information Systems Security Glossary Category Computing terminology ... more details
Windows kernel may refer to architecture of Windows 9x Windows 9x kernel , used in Windows 95, 98 and ME Architecture of Windows NT Windows NT kernel , used in all Windows NT systems including Windows 2000, XP, Vista and 7 disambig ... more details
Refimprove date June 2007 Infobox Cultivar name Ashmead s Kernel image Ashmead s Kernel.JPG Ashmead s Kernel cultivar Ashmead s Kernel origin Gloucester , England , 18th Century Ashmead s Kernel is a ploidy triploid ref name Grin Observation Data cultivar of apple . Traditionally Ashmead s Kernel was thought to be diploid but a poor pollinator. Origin Ashmead s Kernel is often reported as having been raised by Dr Ashmead in Gloucester, England in the 18th century. However Christine Leighton of the Gloucestershire Orchard Group suggests he may have been William Ashmead. a lawyer who died in 1782. ref name Leighton Description This dessert apple is of medium size, on average 83mm ref name Grin Observation Data in diameter on vigorous rootstock and has a flat round shape. The base colour of the apple is greenish yellow, yet has a dull russet colour all over sometimes there are brownish red stripes. Ashmead s Kernel makes a good apple juice because of its sweet sharp flavour. Culture Produces an upright spreading tree, that generally crops well, though on exposed sites it can be irregular. It is a cultivar that is susceptible to bitter pit , and fire blight . The fruit is generally picked in late October ref name Grin Observation Data for use between December and February. References Reflist colwidth 30em refs ref name Leighton Leighton, Christine, History of Ashmead s Kernel http www.gloucestershireorchardgroup.org.uk varieties apples ashmeads kernel history ref ref name Grin Observation Data USDA, ARS, National Genetic Resources Program. GRIN . http www.ars grin.gov cgi bin npgs acc obs.pl?1018745 ref Smith, M. W. G., National Apple Register of the United Kingdom Apples DEFAULTSORT Ashmead s Kernel Apple Category Apple cultivars ... more details
refimprove date May 2012 The term kernel has two separate meanings in statistics . In Bayesian statistics In statistics, especially in Bayesian statistics , the kernel of a probability density function ... ignored during the calculations, and only the kernel considered. At the end, the form of the kernel ... distributions, the kernel can be written in closed form, but not the normalization constant. An example ... 1 sqrt 2 pi sigma 2 e frac x mu 2 2 sigma 2 math and the associated kernel is math p x mu, sigma 2 ... variable math x math . In non parametric statistics In non parametric statistics, a kernel is a weighting function used in non parametric estimation techniques. Kernels are used in kernel density estimation to estimate random variable s density function s, or in kernel regression to estimate the conditional ... varying intensity for a point process . Commonly, kernel widths must also be specified when running a non parametric estimation. Definition A kernel is a non negative real valued function real valued ... math K u K u mbox for all values of u ,. math The first requirement ensures that the method of kernel ... of the corresponding distribution is equal to that of the sample used. If K is a kernel ... to select a scale that is appropriate for the data. Kernel functions in common use Several types of kernel functions are commonly used uniform, triangle, Epanechnikov, quartic biweight , tricube, triweight ... style has the problem that the maths is cut off gallery Caption Commonly used Kernel Functions style background white Image Kernel uniform.svg Uniform br math K u frac 1 2 1 u leq1 math Image Kernel triangle.svg Triangle br math K u 1 u 1 u leq1 math Image Kernel epanechnikov.svg V. A. Epanechnikov Epanechnikov br math K u frac 3 4 1 u 2 1 u leq1 math Image Kernel quartic.svg Quartic br math K u frac 15 16 1 u 2 2 1 u leq1 math Image Kernel triweight.svg Triweight br math K u frac 35 32 1 u 2 3 1 u leq1 math Image Kernel exponential.svg Normal distribution Gaussian br math K u frac 1 sqrt 2 ... more details
Infobox Newspaper name The Kentucky Kernel image caption type Daily student newspaper format Broadsheet foundation 1915 ceased publication price Free owners University of Kentucky publisher editor language political circulation 17,000 daily headquarters 026 Grehan Journalism Building br Lexington, Kentucky 40506 0042 ISSN None oclc 13363397 website http kykernel.com kykernel.com The Kentucky Kernel is the daily student newspaper of the University of Kentucky . The Kernel is distributed free on and around the University of Kentucky campus. It claims a circulation of 17,000 and readership of more than 30,000. Its sole source of revenue is advertising . It is issued during the weekdays during the spring and fall semesters and weekly during the summer term, roughly 150 days in the calendar year. It is one of the largest circulating newspapers in Kentucky. History The Kentucky Kernel was preceded by several student newspapers, with the earliest dating to 1892. From 1908 to 1915, the University of Kentucky s student newspaper was called The Idea , but it became the Kentucky Kernel following a naming contest in 1915. The first issue produced under the Kernel name was published September 16 ... in 1966. In 1972, the Kernel formally established its editorial and financial independence from the University of Kentucky administration. Operations and alumni The Kernel operates out of the Grehan ... of its first faculty members. Several prominent journalists worked at the Kernel while they were ... South Africa correspondent Michael Wines. The writer Bobbie Ann Mason also worked at the Kernel . The famous The Walt Disney Company Disney writer and illustrator Don Rosa worked for the Kernel from 1969 to 1973. The Pertwillaby Papers were first printed in the Kernel , which inspired many of Rosa ... spawned a panel discussion on diversity. Awards In 2006 and 2008, the Kernel won the National ... University of Kentucky Student Newspapers of the SEC DEFAULTSORT Kentucky Kernel, The Category Student ... more details
The VA Kernel is a set of programs, developed by the Department of Veterans Affairs of the United States Government, which provide an operating system and MUMPS implementation independent abstraction to the VistA Hospital Information System. These programs called routines in MUMPS are the only programs which are expected to not be written in ANSI Standard MUMPS. The MUMPS language used in the kernel is amazingly simple, consisting of a single language MUMPS , a single data type string , a single data storage mechanism global arrays stored on disk , 19 commands and 22 functions. MUMPS is a symbolic language with linguistic roots closer to LISP than Fortran or Cobol . Because of this simple software layer, the VistA software architecture has been able to adapt to changing hardware environments over the decades with only the minimum amount of software changes at higher levels of abstraction. The CHCS system and the RPMS system have a Kernel as well, which provides a similar degree of support to those systems as the VA Kernel does to VistA . The VA Kernel provides abstractions for Menu Management MenuMan Electronic mail, group conferencing, transaction processing MailMan Login and Access Security Task scheduling and Batch processing Input Output devices Protocol and Event processing Date processing and manipulation Mathematical and common library functions References http blip.tv file 405389 Video Interview of Tom Munnecke on the design of the kernel Category Free software operating systems ... more details
Inappropriate tone date January 2011 For machine learning algorithms, the kernel trick is a way of mapping observations from a general set S into an inner product space V equipped with its natural norm , without ever having to compute the mapping explicitly, in the hope that the observations will gain meaningful linear structure in V . linear classifier Linear classifications in V are equivalent to generic classifications in S . The trick to avoid the explicit mapping is to use learning algorithms that only require dot products between the vectors in V , and choose the mapping such that these high dimensional dot products can be computed within the original space, by means of a kernel function ... product in usually a different space . K is often referred to as a kernel mathematics kernel or a kernel function . The word kernel is used in different ways throughout mathematics. If one is lucky ... the kernel trick. Given a finite observation set S , one can simply select the measure math mu T T math ... c sub n sub cf. positive definite kernel . Some algorithms that depend on arbitrary relationships ... also use it to justify the meanings and properties of existing algorithms. The kernel trick was first ... journal Automation and Remote Control volume 25 pages 821 837 ref Theoretically, a kernel matrix ... K is a Mercer kernel, K can still be referred to a kernel . Suppose K is any square matrix ... analysis Commonly used kernels in such algorithms include the polynomial kernel, representing a mapping ... order versus lower order terms in the polynomial. For the case math d 2 math of the quadratic kernel ... 1, ldots, sqrt 2c x n, c rangle math The kernel trick here lies in working in an math n 2 n 1 math ... space using only math n 1 math multiplications. References references See also Kernel methods Integral transform s Hilbert space , specifically reproducing kernel Hilbert space Mercer kernel Category Kernel methods for machine learning de Kernel Maschinelles Lernen fr Kernel trick ... more details
In the mathematics mathematical study of several complex variables , the Szeg kernel is an integral kernel that gives rise to a reproducing kernel on a natural Hilbert space of holomorphic function s. It is named for its discoverer, the Hungarian mathematician G bor Szeg . Let &Omega be a bounded domain in C sup n sub with C sup 2 sup boundary, and let A &Omega denote the set of all holomorphic functions in &Omega that are continuous on math overline Omega math . Define the Hardy space H sup 2 sup &Omega to be the closure in L sup 2 sup &Omega of the restrictions of elements of A &Omega to the boundary. The Poisson integral implies that each element &fnof of H sup 2 sup &Omega extends to a holomorphic function P&fnof in &Omega . Furthermore, for each z &isin &Omega , the map math f mapsto Pf z math defines a continuous linear functional on H sup 2 sup &Omega . By the Riesz representation theorem , this linear functional is represented by a kernel k sub z sub , which is to say math Pf z int partial Omega f zeta overline k z zeta ,d sigma zeta . math The Szeg kernel is defined by math S z, zeta overline k z zeta , quad z in Omega, zeta in partial Omega. math Like its close cousin, the Bergman kernel , the Szeg kernel is holomorphic in z . In fact, if &phi sub i sub is an orthonormal basis of H sup 2 sup &Omega consisting entirely of the restrictions of functions in A &Omega , then a Riesz Fischer theorem argument shows that math S z, zeta sum i 1 infty phi i z overline phi i zeta . math References Citation last1 Krantz first1 Steven G. authorlink Steven Krantz title Function Theory of Several Complex Variables publisher American Mathematical Society location Providence, R.I. isbn 978 0 8218 2724 6 year 2002 mathanalysis stub Category Complex analysis Category Several complex variables ... more details
In universe date October 2008 Infobox character name Kernel Fleck image caption creator Darren Shan alias ... Mage powers br li Creating windows using panels of light br li Mental scrying Cornelius Kernel Fleck ... series. He is one of the three main characters in the series. Kernel is mentioned in Slawter ... biography Early life Kernel Fleck had magical abilities as a child he constantly saw strange ... it to his parents and teachers, he was assumed to be crazy and consequently ignored. As a result, Kernel had no friends and was lonely throughout his childhood. He even contemplated suicide. As Kernel ... master s universe, Kernel successfully transformed one of Lord Loss demon servants, Artery character ... . Kernel s parents, disturbed by the coming of Art, moved into a village to start a new life. A year ... of humans, who slaughtered dozens of schoolchildren and stole Art from Kernel. Following the demon back to its own universe, Kernel encounters the magician fantasy magician Beranabus character Beranabus ... to get back his brother, Kernel joins the Disciples. After a long pursuit they arrive in the realm ... Kernel. After another long struggle, within Lord Loss magical chess board, Kernel finds that he ... Gash for which Beranabus is searching is actually Kernel himself. With Beranabus Kernel is next ... Universe, Kernel only looks around 16 17 years old. This version of Kernel has grown into a warrior ... Universe, Kernel is so infuriated by Grubbs lack of courage that he sends him back to the human universe. When Kernel and Beranabus join him again two days later in Demonata time scale and seven ... and plan an attack on the Demonata to send them back to their own universe. Unknown to Kernel until ... with Demonata and blooded human carcasses. Kernel follows Beranabus off their helicopter and charges ... Bec MacConn Bec s soul is trapped. Together they create a shield around themselves, Kernel and Beranabus. Kernel is pulled into the connection and the three of them chant in unison and destroy the entire ... more details
In linear algebra , the kernel or null space also nullspace of a matrix mathematics matrix A is the set mathematics set of all vectors x for which Ax 0 . The kernel of a matrix with n columns is a Euclidean subspace linear subspace of n dimensional Euclidean space . ref name textbooks Linear algebra, as discussed in this article, is a very well established mathematical discipline for which there are many sources. Almost all of the material in this article can be found in Lay 2005, Meyer 2001, and Strang 2005. ref The dimension vector space dimension of the null space of A is called the nullity of A . If viewed as a linear transformation , the null space of a matrix is precisely the kernel of the mapping i.e. the set of vectors that map to zero . For this reason, the kernel of a linear transformation between abstract vector space s is sometimes referred to as the null space of the transformation . Definition The kernel of an m × n matrix A is the set math mbox N mathbf A mbox Null mathbf A mbox Ker mathbf A left textbf x in mathbb C n mathbf A textbf x textbf 0 right text , math ref This equation uses set builder notation . ref where 0 denotes the zero vector with m components. The matrix equation Ax 0 is equivalent to a homogeneous system ... associated to the matrix A . Null space of a transformation main kernel linear operator If V and W are vector space s, the null space or kernel mathematics kernel of a linear transformation T ... v textbf 0 right text . math If we represent the linear transformation by a matrix, then the kernel ... s i varepsilon, math where math varepsilon math is the machine epsilon of the computer, that is, the smallest number such that in the floating point arithmetics of the computer, math 1 , , varepsilon ... the null space of A . See also Matrix mathematics Kernel algebra Euclidean subspace System of linear ... Space of a Matrix linear algebra DEFAULTSORT Kernel Matrix Category Linear algebra Category Matrices ... more details
The realized kernel RK is an estimator of volatility. The estimator is typically computed with high frequency return data, such as second by second returns. Unlike the realized variance , the realized kernel is a robust estimator of volatility, in the sense that the realized kernel estimates the appropriate volatility quantity, even when the returns are contaminated with noise. ref Cite journal last Barndorff Nielsen first Ole E. last2 Hansen first2 Peter Reinhard last3 Lunde first3 Asger last4 Shephard first4 Neil authorlink Ole Barndorff Nielsen authorlink2 Peter Reinhard Hansen authorlink4 Neil Shephard year 2008 month November title Designing realised kernels to measure the ex post variation of equity prices in the presence of noise pages 1481 1536 doi 10.3982 ECTA6495 url http www.econometricsociety.org abstract.asp?ref 0012 9682&vid 76&iid 6&aid 9&s 9999 accessdate quote journal Econometrica volume 76 ref See also Realized variance Notes Reflist Category Mathematical finance ... more details
In mathematics, the Mehler kernel is the heat kernel of the Hamiltonian of the harmonic oscillator . harvs txt last Mehler authorlink Gustav Ferdinand Mehler year 1866 gave an explicit formula for it called Mehler s formula . The Kibble Slepian formula generalizes Mehler s formula to higher dimensions. The Mehler kernel &phi x , y , t is a solution to math frac partial varphi partial t frac partial 2 varphi partial x 2 x 2 varphi math Mehler s kernel is math frac exp coth 2t x 2 y 2 2 text cosech 2t xy sqrt 2 pi sinh 2t math By a simple transformation this is, apart from a multiplying factor, the bivariate Gaussian probability density given by math frac 1 2 pi sqrt 1 rho 2 exp frac x 2 y 2 2 rho xy 1 rho 2 math It can be written as an infinite series involving the one dimensional probability densities and Hermite polynomials of x and y see the link to Slepian . References Citation last1 Grigor yan first1 Alexander title Heat kernel and analysis on manifolds url http books.google.com books?id X7QQcVa2EWsC publisher American Mathematical Society location Providence, R.I. series AMS IP Studies in Advanced Mathematics isbn 978 0 8218 4935 4 mr 2569498 year 2009 volume 47 Citation last1 Mehler first1 F. G. title Ueber die Entwicklung einer Function von beliebig vielen Variabeln nach Laplaceschen Functionen h herer Ordnung url http resolver.sub.uni goettingen.de purl?GDZPPN002152975 language German id ERAM 066.1720cj year 1866 journal Journal f r Reine und Angewandte Mathematik issn 0075 4102 issue 66 pages 161 176 Category Parabolic partial differential equations ... more details
In the mathematics mathematical study of heat conduction and diffusion , a heat kernel is the fundamental solution to the heat equation on a particular domain with appropriate boundary conditions . It is also one of the main tools in the study of the spectral theory spectrum of the Laplace operator , and is thus of some auxiliary importance throughout mathematical physics . The heat kernel represents the evolution of temperature in a region whose boundary is held fixed at a particular temperature typically zero , such that an initial unit of heat energy is placed at a point at time t 0. The most well known heat kernel is the heat kernel of d dimensional Euclidean space R sup d sup , which has the form math K t,x,y frac 1 4 pi t d 2 e x y 2 4t . math This solves the heat equation math K t t,x,y Delta x K t,x,y , math for all t 0 and x , y R sup d sup , with the initial condition math lim t downarrow 0 K t,x,y delta x y delta x y math where is a Dirac delta distribution and the limit is taken in the sense of distribution mathematics distributions . To wit ... and Jacobi theta function s. Nevertheless, the heat kernel for, say, the Dirichlet problem still ..., in these more general domains, the heat kernel for the Dirichlet problem is the solution of the initial ... kernel on an arbitrary domain. Consider the Dirichlet problem in a connected domain or manifold ... lambda 1 lambda 2 le lambda 3 le cdots, quad lambda n to infty. math The heat kernel has the following ... equation. However, convergence and regularity of the series are quite delicate. The heat kernel ... of T in the form math T e t Delta . math See also Heat kernel signature Minakshisundaram Pleijel zeta function Mehler kernel References Citation last1 Berline first1 Nicole last2 Getzler ... 4 year 1994 Citation last1 Grigor yan first1 Alexander title Heat kernel and analysis on manifolds url ... volume 47 DEFAULTSORT Heat Kernel Category Heat conduction Category Spectral theory Category Parabolic ... more details
In mathematics , the Fej r kernel is used to express the effect of Ces ro summation on Fourier series . It is a non negative kernel, giving rise to an approximate identity . Image Fej r kernel.svg thumb 400px Plot of several Fej r kernels The Fej r kernel is defined as math F n x frac 1 n sum k 0 n 1 D k x , math where math D k x sum s k k rm e isx math is the k th order Dirichlet kernel . It can also be written in a closed form as math F n x frac 1 n left frac sin frac n x 2 sin frac x 2 right 2 math , where this expression is defined. ref cite book title Banach Spaces of Analytic Functions last Hoffman first Kenneth year 1988 publisher Dover isbn 0 486 45874 1 page 17 pages 216 ref It is named after the Hungary Hungarian mathematician Lip t Fej r 1880&ndash 1959 . The important property of the Fej r kernel is math F n x ge 0 math . The convolution F sub n sub is positive for math f ge 0 math of period math 2 pi math it satisfies math 0 le f F n x frac 1 2 pi int pi pi f y F n x y ,dy, math and, by Young s inequality , math F n f L p pi, pi le f L p pi, pi math for every math 0 le p le infty math for continuous function math f math moreover, math f F n rightarrow f math for every math f in L p pi, pi math math 1 le p infty math for Continuous function topology continuous function math f math . Indeed, if math f math is continuous, then the convergence is uniform. See also Fej r s theorem Dirichlet kernel Gibbs phenomenon Charles Jean de la Vall e Poussin References references DEFAULTSORT Fejer Kernel Category Fourier series bg de Fej r Polynome fr Noyau de Fej r ja ru zh ... more details
Infobox software name Lively Kernel logo screenshot File Chromium5.0.375.99 showing lively kernel using gtk theme.png center 230px Lively demo caption Lively Kernel 0.9 example running in Chromium web ... The Lively Kernel is an open source web programming environment. It supports desktop style applications ... The Lively Kernel A Self supporting System on a Web Page ref ref http www.svgopen.org 2008 papers 93 The Lively Kernel Web Application Framework The Lively Kernel Application Framework ref Development ... Institute in Potsdam Babelsberg near Berlin. Overview The Lively Kernel is a graphical composition .... Shapes, widgets, windows, IDE all on a Web page The Lively Kernel uses a Morphic software Morphic ... like Adobe Flash simulations. The Lively Kernel achieves complex dynamic behavior without any ... of multiple green thread processes in JavaScript. Text and transformations The Lively Kernel includes ... in an offline composition program, but it is the built in dynamic behavior of text in the Lively Kernel .... Cross browser compatibility The Lively Kernel depends on browser support for JavaScript and SVG ... one HTML implementation to another. Except for one small initial file, the Lively Kernel code base is entirely free of tests for which client browser is being used. As of 2011, Lively Kernel runs best ... implementation of the Lively Kernel in which the kernel parts are replaced by functionality offered ... retains the exceptionally interactive nature the liveliness of the Lively Kernel, e.g., by allowing ... http github.com rksm LivelyKernel Lively Kernel core repository at github http lively kernel.org development media LivelyKernel TechnicalOverview.pdf Lively Kernel Technical Overview http www.svgopen.org 2008 papers 93 The Lively Kernel Web Application Framework Lively Kernel Abstract http lively kernel.org list index.html Lively Kernel Mailing List http lively kernel.org repository lively wiki index.xhtml Lively Kernel Wiki http lively kernel.org repository lively wiki users Lively Kernel Wiki ... more details
In potential theory , the Poisson kernel is an integral kernel , used for solving the two dimensional Laplace equation , given Dirichlet boundary condition s on the unit disc . The kernel can be understood as the derivative of the Green s function for the Laplace equation. It is named for Sim on Poisson . The Poisson kernel is important in complex analysis because its integral against a function defined on the unit circle &mdash the Poisson integral &mdash gives the extension of a function defined on the unit circle to a harmonic function on the unit disk. By definition, harmonic functions are solutions to Laplace s equation, and, in two dimensions, harmonic functions are equivalent to meromorphic function s. Thus, the two dimensional Dirichlet problem is essentially the same problem as that of finding ... kernels On the unit disc In the complex plane, the Poisson kernel for the unit disc is given by math ..., the Poisson kernel is commonly used to demonstrate the equivalence of the Hardy space s on the unit disk, and the unit circle. In the study of Fourier series the Poisson kernel arises ... kernel harv Katznelson 1976 On the upper half plane The unit disk may be conformal map conformally ... of a harmonic function is also harmonic, the Poisson kernel carries over to the upper half plane. In this case ... x t f t dt math for math y 0 math . The kernel itself is given by math P y x frac y x 2 y 2 . math Given ... For the ball of radius r, math B r math , in R sup n sup , the Poisson kernel takes the form ... half space An expression for the Poisson kernel of an upper half space can also be obtained. Denote ... space is the set defined by math H n 1 t mathbf x in mathbf R n 1 mid t 0 . math The Poisson kernel ... 1 2 pi n 1 2 . math The Poisson kernel for the upper half space appears naturally as the Fourier transform of the Abel kernel math K t, xi e 2 pi t xi math in which t assumes the role of an auxiliary ... 0 691 08078 X . MathWorld urlname PoissonKernel title Poisson Kernel citation author2 link Neil Trudinger ... more details
Kernel Holding S.A. is a leading diversified and integrated agri business company operating in Ukraine . ref http www.kernel.ua en ref The company operate in farming , origination, handling and international marketing of grain , and in the production, refining, bottling and marketing of bulk and bottled vegetable oil both on the international market and domestically. ref http www.kernel.ua en our company ref Infobox Company company name Kernel Holding S.A. company logo company type Public company Public foundation location Kiev , Ukraine area served key people industry Agriculture products num employees revenue decrease United States dollar US 1.02 1000000000 number billion small 2010 small ref name finres10 cite web author Kernel Holding S.A. date 3 June 2010 url http www.kernel.ua media uploads library 11 03 Consolidated Financial Statements for the Year Ended 30 June 2010.pdf title Consolidated Financial Statements for the Year Ended 30 June 2010 work kernel.ua publisher Kernel Holding S.A. accessdate 14 July 2011 ref operating income increase US 167 million small 2010 small ref name finres10 net income increase US 152 million small 2010 small ref name finres10 assets increase US 1.1 billion small 2010 small ref name finres10 equity increase US 605 million small 2010 small ref name finres10 slogan homepage http www.kernel.ua References Reflist Ukraine company stub Category Economy of Ukraine Category Companies of Ukraine Category Companies based in Kiev ... more details
In the mathematics mathematical study of several complex variables , the Bergman kernel , named after Stefan Bergman , is a reproducing kernel for the Hilbert space of all square integrable holomorphic function s on a domain D in C sup n sup . In detail, let Lp space L sup 2 sup D be the Hilbert space of square integrable functions on D , and let L sup 2, h sup D denote the subspace consisting of holomorphic functions in D that is, math L 2,h D L 2 D cap H D math where H D is the space of holomorphic functions in D . Then L sup 2, h sup D is a Hilbert space it is a closed set closed linear subspace of L sup 2 sup D , and therefore complete metric space complete in its own right. This follows from the fundamental estimate, that for a holomorphic square integrable function &fnof in D NumBlk math sup z in K f z le C K f L 2 D math EquationRef 1 for every compact set compact subset K of D . Thus convergence of a sequence of holomorphic functions in L sup 2 sup D implies also compact convergence , and so the limit function is also holomorphic. Another consequence of EquationRef 1 is that, for each z &isin D , the evaluation math operatorname ev z f mapsto f z math is a continuous linear functional on L sup 2, h sup D . By the Riesz representation theorem , this functional can be represented as the inner product with an element of L sup 2, h sup D , which is to say that math operatorname ev z f int D f zeta overline eta z zeta ,d mu zeta . math The Bergman kernel K is defined by math K z, zeta overline eta z zeta . math The kernel K z ,&zeta holomorphic in z and antiholomorphic in &zeta , and satisfies math f z int D K z, zeta f zeta ,d mu zeta . math See also Bergman metric Bergman space Szeg kernel References Citation last1 Krantz first1 Steven G. authorlink Steven Krantz title Function Theory of Several Complex Variables publisher American Mathematical Society location Providence, R.I. isbn 978 0 8218 2724 6 year 2002 . springer title Bergman kernel function ... more details
In mathematics , a Fredholm kernel is a certain type of a kernel integral operator kernel on a Banach space , associated with nuclear operator s on the Banach space. They are an abstraction of the idea of the Fredholm integral equation and the Fredholm operator , and are one of the objects of study in Fredholm theory . Fredholm kernels are named in honour of Erik Ivar Fredholm . Much of the abstract theory of Fredholm kernels was developed by Alexander Grothendieck and published in 1955. Definition Let B be an arbitrary Banach space , and let B sup sup be its dual, that is, the space of bounded linear functional s on B . The tensor product math B otimes B math has a complete space completion under the norm math Vert X Vert pi inf sum i Vert e i Vert Vert e i Vert math where the infimum is taken over all finite representations math X sum i e i e i in B otimes B math The completion, under this norm, is often denoted as math B widehat , otimes , pi B math and is called the topological tensor product projective topological tensor product . The elements of this space are called Fredholm kernels . Properties Every Fredholm kernel has a representation in the form math X sum i lambda i e i otimes e i math with math e i in B math and math e i in B math such that math Vert e i Vert Vert e i Vert 1 math and math sum i vert lambda i vert infty. , math Associated with each such kernel is a linear operator math mathcal L X B to B math which has the canonical representation math mathcal L X f sum i lambda i e i f otimes e i. , math Associated with every Fredholm kernel is a trace, defined as math mbox tr X sum i lambda i e i e i . , math p summable kernels A Fredholm kernel is said to be p summable if math sum i vert lambda i vert p infty math A Fredholm kernel is said to be of order q .... France volume 84 pages 319 84 year 1956 springer id f f041440 title Fredholm kernel author B.V. Khvedelidze ... Kernel as n Becomes Infinite journal Proc. Natl. Acad. Sci. U.S.A. volume 18 issue 11 pages ... more details
A kernel smoother is a statistics statistical technique for estimating a real valued function mathematics function math f X , , left X in mathbb R p right math by using its noisy observations, when non parametric statistics no parametric model for this function is known. The estimated function is smooth, and the level of smoothness is set by a single parameter. This technique is most appropriate for low dimensional p 3 data visualization purposes. Actually, the kernel smoother represents the set of irregular data points as a smooth line or surface. Definitions Let math K h lambda X 0 ,X math be a kernel defined by math K h lambda X 0 ,X D left frac left X X 0 right h lambda X 0 right math where math X,X 0 in mathbb R p math math left cdot right math is the Euclidean norm math h lambda X 0 math is a parameter kernel radius D t typically is a positive real valued function, which value is decreasing or not increasing for the increasing distance between the X and X sub 0 sub . Popular Kernel statistics kernels used for smoothing include V. A. Epanechnikov Epanechnikov Tri cube Gaussian function Gaussian Let math hat Y X mathbb R p to mathbb R math be a continuous function of X . For each math X 0 in mathbb R p math , the Nadaraya Watson kernel weighted average smooth Y X estimation is defined by math hat Y X 0 frac sum limits i 1 N K h lambda X 0 ,X i Y X i sum limits i 1 N K h lambda X 0 ,X i math where N is the number of observed points Y X sub i sub are the observations at X sub i sub points. In the following sections, we describe some particular cases of kernel smoothers ... to X sub 0 sub points denoted by red . The result is not smooth enough. Kernel average smoother The idea of the kernel average smoother is the following. For each data point X sub 0 sub , choose a constant distance size &lambda kernel radius, or window width for p 1 dimension , and compute ... 0 end align math See also Kernel statistics Kernel methods Kernel density estimation Kernel regression ... more details
Image Apricot seed and kernel.jpg thumb The kernel bottom and broken seed shell of an apricot An apricot kernel Prunus armeniaca , Armenian plum in Latin refers to the seed kernel of a species of Prunus , classified with the plum in the subgenus Prunus. It is known for containing amygdalin , a toxic cyanogenic glycoside . ref cite journal author Krashen, Stephen D. authorlink Stephen Krashen title Are Apricot Kernels Toxic? journal The Internet Journal of Health volume 9 issue 2 year 2009 url http www.ispub.com journal the internet journal of health volume 9 number 2 13 article are apricot kernels toxic.html issn 1528 8315 ref Seeds or kernels of the apricot grown in central Asia and around the Mediterranean region Mediterranean are so sweet that they may be substituted for almond s. The Italian liqueur amaretto and amaretti biscotti are flavored with extract of apricot kernels as well as almonds. Vegetable oil Oil pressed from these cultivars has been used as cooking oil . ref Wikipedia Article Apricots section kernel ref Apricot kernels can sometimes be strong tasting and bitter taste bitter . They feature in recipes for apricot jam , and Italian amaretto cookies and liqueur. Citation needed date February 2007 Taken in excess, they may produce symptoms of cyanide poisoning , including nausea , fever , rash , headaches , insomnia , increased thirst , weakness, lethargy , Anxiety nervousness , various aches and pains in joints and muscles, a drop in blood pressure . In 1993, the New York State Department of Agriculture and Markets tested the cyanide content of two nowrap 220 gram 8oz packages of apricot kernels that were imported from Pakistan which were being sold in health ... by apricot kernel ingestion journal Ann Emerg Med volume 32 issue 6 pages 742 4 year 1998 month December pmid 9832674 ref On average, an apricot kernel contains about 0.5 mg of cyanide. Image Apricot ... Apricot Kernel Category Prunus Category Edible nuts and seeds de Aprikosenkern fr Noyau d abricot ... more details
unref article date January 2009 In probability theory , a Markov kernel is a map that plays the role, in the general theory of Markov process es, that the transition matrix does in the theory of Markov processes with a finite state space. Formal definition Let math X, mathcal A math , math Y, mathcal B math be measurable space s. A Markov kernel with source math X, mathcal A math and target math Y, mathcal B math is a map math K math that associates to each point math x in X math a probability measure math K x math on math Y, mathcal B math such that, for every measurable set math B in mathcal B math , the map math x mapsto K x B math is measurable with respect to the math sigma math algebra math mathcal A math . br Let math mathcal P X, mathcal A math denote the set of all probability measures on the measurable space math X, mathcal A math . If math K math is a Markov kernel with source math X, mathcal A math and target math Y, mathcal B math then we can naturally associate to math K math a map math widehat K mathcal P X, mathcal A to mathcal P Y, mathcal B math defined as follows given math P math in math mathcal P X, mathcal A math , we set math widehat K P B int XK x B , mathrm dP x math , for all math B math in math mathcal B math . References citation first1 Heinz last1 Bauer title Probability Theory publisher de Gruyter year 1996 isbn 3 11 013935 9 36. Kernels and semigroups of kernels citation first1 R D last1 Reiss title A Course on Point Processes publisher Springer Verlag year 1993 isbn 0387979247 Category Stochastic processes ... more details
kastor is the first project of the Opaak educational trilogy which also includes kaneton and kayou . kastor is an introductory project to low level programming. The particularity of this project compared to other education oriented operating system kernels lies in the fact that it has been designed to be fun. Image Chichepong2.png thumb right 180px ChichePong. Objective The project consists for students to implement a simplistic monolithic kernel capable of running small arcade games . kastor does not require advanced features as for modern kernels . For instance, kastor is devoid of virtual memory and multitasking functionalities as unnecessary for the project s purpose. This way, the project can be programmed within a few weeks, making it very suitable as an introduction to low level programming. Games Image Yakanoid2.png thumb right 180px Yakanoid. Students are provided with ROM s of the arcade games having been developed with the kastor specific SDK . The game to be run is located on a specific file system referred to as the KFS. The kernel therefore extracts the ROM from the file system and runs it. Several games are provided for students to test their implementation including versions of Pong and Arcanoid among others. History The kastor project has been created in 2004 by Jean Pascal Billaud and Julien Quintard as an optional course at EPITA . However, at the time, the project was named k and was later renamed with the introduction of the Opaak educational trilogy. Besides, the initial form of the project was completely different, consisting for students in implementing parts of a monolithic kernel such as memory management, interruption handling etc. It was only later that Matthieu Bucchianeri and Renaud Voltz , taking over the teaching of the project, decided to introduce fun in order to make it easier to teach, leading to arcade emulation it is now. External links http kastor.opaak.org kastor official website http www.epita.fr EPITA official website Catego ... more details
Encyclopedia
top
