
	Where results make sense

Topic: Weakly harmonic

Related Topics

Harmonic function

Partial differential equation

Heat equation

	Harmonic function - Wikipedia, the free encyclopedia
		Indeed a function is harmonic if and only if it is weakly harmonic.
		The set of harmonic functions on a given open set U can be seen as the kernel of the Laplace operator Î” and is therefore a vector space over R : sums, differences and scalar multiples of harmonic functions are again harmonic.
		The harmonic functions satisfy the following maximum principle : if K is any compact subset of U, then f, restricted to K, attains its maximum and minimum on the boundary of K ; there are no local maxima or minima, except if f is constant.
	en.wikipedia.org /wiki/Harmonic_function (373 words)

	Harmonic function (Site not responding. Last check: 2007-11-05)
		The real and imaginary part of any holomorphic function yield harmonic functions on 'R' Conversely there is an operator taking a harmonic function u on a region in 'R' to its harmonic conjugate'' ''v, for which u+iv is a holomorphic function; here v is well-defined up to a real constant.
		Harmonic Function Theory and Mathematica Performs symbolic manipulation of expressions that arise in the study of harmonic functions.
		Harmonic Psychology Harmonic Psychology unfolds the laws of human psychological harmony on both intra- and interpersonal levels.
	www.serebella.com /encyclopedia/article-Harmonic_function.html (653 words)

	Harmonic (Site not responding. Last check: 2007-11-05)
		Harmonic In sine wave, it is an integral multiple of the frequency of the wave.
		Harmonic analysis Harmonic analysis is the branch of harmonics", hence the name "harmonic analysis." In the past two cen...
		Harmonic divisor number A harmonic divisor number, or Ore number, is a number whose divisors, averaged in a perfect nu...
	www.brainyencyclopedia.com /topics/harmonic.html (308 words)

	Mathematics Faculty • Jie Qing (Site not responding. Last check: 2007-11-05)
		Jie Qing is interested in nonlinear analysis, harmonic analysis, and partial differential equations (systems) with applications to differential geometry, complex geometry and mathematical physics.
		He continues his research on the study of the Ginzburg-Landau problem and continues to be involved in the study of the geometry of conformally covariant differential operators on 4-manifolds.
		Lecture notes in the proceeding of the second workshop of non-linear functional analysis and its applications in PDE at ICTP of Italy in 1997.
	www.math.ucsc.edu /Faculty/Qing.html (242 words)

	Harmonic motion \| TutorGig.co.uk Encyclopedia (Site not responding. Last check: 2007-11-05)
		Complex harmonic motion is the superposition &mdash linear combination &mdash of several simultaneous simple harmonic motion s.
		Damped harmonic motion is similar to simple harmonic motion, i.e the period is constant and the frequency is equal to 1 Period.
		A harmonic spectrum is a spectrum with harmonic s whose frequency frequencies are whole number multiples of the fundamental.
	www.tutorgig.co.uk /encyclopedia/sencyclo.jsp?keywords=Harmonic+motion (426 words)

	Journal Abstract (Site not responding. Last check: 2007-11-05)
		Weakly electric fish emit an electric communication signal that is controlled by a highly specialized neural circuit.
		The amplitude of the second harmonic was relatively high at both low and high temperatures and relatively low at intermediate temperatures.
		The amplitude of the third harmonic increased monotonically with temperature.
	www.trincoll.edu /~kdunlap/abstracts/temperature.html (243 words)

	Harmonic \| TutorGig.co.uk Encyclopedia (Site not responding. Last check: 2007-11-05)
		In mathematics, a function math f math is weakly harmonic in a domain D if math int D f Delta g 0 math...
		In mathematics, the harmonic mean is one of several methods of calculating an average.
		Harmonic analysis is the branch of mathematics which studies the representation of functions or signals...
	www.tutorgig.co.uk /encyclopedia/sencyclo.jsp?keywords=Harmonic (438 words)

	Weakly (Site not responding. Last check: 2007-11-05)
		Formally, a cardinal κ is weakly compact homogeneous for...
		Weakly harmonic In continuous and for all with harmonic function.
		Weakly hyper-Woodin cardinal In iff for every set S there exists a normal measure U on κ such that the set {&lambd...
	www.brainyencyclopedia.com /topics/weakly.html (60 words)

	DXing Medium Wave Harmonics
		Harmonics should not be confused with images, which are generated internally in a receiver, and are usually received plus or minus 910 kHz or 1000 kHz of a frequency, depending on the receiver, or receiver mixing products that cause exceptionally strong stations to appear where they don't belong.
		Harmonics may seem like a free way for a small AM station to become an international broadcaster, but AM stations don't want to intentionally transmit harmonics, as any power that goes into a harmonic frequency is not being used for their fundamental frequency, which means a less powerful signal for their main audience.
		Usually that's the case as the harmonic is likely coming from several hundred miles away and there are probably other AM stations on the fundamental that are closer to you, and those are the ones you're going to hear on the fundamental frequency.
	donmoore.tripod.com /genbroad/harmonics.htm (3392 words)

	Harmonic function (Site not responding. Last check: 2007-11-05)
		Indeed a function is harmonic and only if it is weakly harmonic.
		The set of harmonic functions on a open set U can be seen as the kernel of the Laplace operator Δ and therefore a vector space over R : sums differences and scalar multiples of functions are again harmonic.
		The harmonic functions satisfy the following maximum principle : if K is any compact subset of U then f restricted to K attains its maximum and minimum on boundary of K ; there are no local maxima or except if f is constant.
	www.freeglossary.com /Harmonic_function (578 words)

	Harmonic motion in TutorGig Encyclopedia (Site not responding. Last check: 2007-11-05)
		Harmonic tremor describes a continuous rhythmic earthquakes in the Earth s upper lithosphere that can be detected by a seismograph and is often preceded or accompanied by a volcanic eruptions.
		In mathematics, the harmonic conjugate of a harmonic function harmonic real valued function of two variables u x, y, is a function v x, y such that v is harmonic and u and v satisfy the Cauchy Riemann..
		A Pinch harmonic is a guitar technique in which the nail or thumb slightly catches the string after it is picked...
	www.tutorgig.com /es/Harmonic+motion (1006 words)

	research (Site not responding. Last check: 2007-11-05)
		Before this, I investigated the quasi-invariance of weakly analytic measures with values in some dual space X*.
		My results are submitted in a paper:“ Decomposition and quasi-invariance of weakly analytic vector-valued measures”.
		In the future, I plan to study harmonic approximation (with B. Kelly).
	www.nlu.edu /~mathweb/research.html (220 words)

	Resume of Charles F. Dunkl (Site not responding. Last check: 2007-11-05)
		Operators and harmonic analysis on the sphere, Trans.
		Weakly almost periodic functionals carried by hypercosets, Trans.
		Harmonic polynomials and peak sets on reflection groups, Geometriae Ded.
	www.math.virginia.edu /~cfd5z/mypapers.html (863 words)

	Mathematics
		Indeed, we prove that a weakly periodic ring with commuting nilpotents, such that the set of potent elements form an ideal of R, is a subdirect sum of finite fields and nil commutative rings.
		Variations in harmonic amplitudes of one-dimensional signals, which are locally almost periodic, are analyzed over finite length records by single Fourier series.
		Univalent harmonic mappiand a conjecture of J.C.C. Nitsche
	www.aub.edu.lb /~webpubof/research/23report/as/math.htm (2576 words)

	Citebase - A Weakly Nonlinear Analysis of Impulsively-Forced Faraday Waves
		The exact impulsive-forcing results, in the linear and weakly nonlinear regimes, are compared with numerical results for sinusoidal and multifrequency forcing.
		The familiar situation of alternating subharmonic and harmonic resonance tongues emerges for unequally-spaced impulses.
		As the capillary parameter is varied, one finds a parameter region of wave amplitude suppression, which is due to a familiar 1:2 spatio-temporal resonance between the subharmonic mode of instability and a damped harmonic mode.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:nlin/0502025 (627 words)

	Citebase - Two-frequency forced Faraday waves: Weakly damped modes and pattern selection
		The superlattice pattern is synchronous with the forcing, spatially periodic on a large hexagonal lattice, and exhibits small-scale triangular structure.
		Here we use the spatial and temporal symmetries of the problem to argue that weakly damped harmonic waves may be critical to understanding the stabilization of this pattern in the Faraday system.
		Analytic stability theory for Faraday waves and the obervation of the harmonic surface response.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:nlin/0002041 (726 words)

	Flexibility of Duplex DNA on the Submicrosecond Timescale -- Okonogi et al. 77 (6): 3256 -- Biophysical Journal
		The weakly bending rod model of DNA dynamics relates the mean square amplitudes of oscillation to the force constant for bending
		weakly bending rod model is valid for the dynamics as a function
		We used the weighted, weakly bending rod theory to obtain an optimized persistence length that uses all of the data shown
	www.biophysj.org /cgi/content/full/77/6/3256 (5080 words)

	Wash U Graduate Program : Faculty Research Projects
		Applications to regularity theory for the "d-bar" operator on weakly pseudoconvex domains using the language of invariant metrics; automorphism groups of weakly pseudoconvex domains.
		Aspects of harmonic analysis: atomic, molecular, and maximal characterizations of Hardy spaces; spaces generated by blocks, a generalization of atomic theory.
		Harmonic analysis and operator theory: in particular, real and complex interpolation of Banach spaces and quasi-Banach spaces.
	www.math.wustl.edu /gradprog/projects.html (595 words)

	Harmonic Maps, Conservation Laws, and Moving Frames by Frederic Helein, ISBN 0521811600 And An Alphabestiary
		Harmonic Maps, Conservation Laws, and Moving Frames by Frederic Helein, ISBN 0521811600 And An Alphabestiary
		A presentation of "exotic" functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results.
		The importance of conservation laws is stressed and the concept of a "Coulomb moving frame" is explained in detail.
	www.pastaconcerto.com /laws.htm (215 words)

	Encyclopedia of Laser Physics and Technology - parametric amplifiers, periodic poling, phase matching, photodiodes, ...
		The combination of high bandwidth (tens of GHz) and high photocurrents (tens of mA) is achieved in velocity-matched photodetectors, containing several small-area photodetectors, which are weakly coupled to an optical waveguide and deliver their photocurrents into a common RF waveguide structure.
		The quantum efficiency of a photodiode is the fraction of the incident (or absorbed) photons which contribute to the photocurrent.
		Recently, high harmonic generation allowed for the first time the formation of single attosecond pulses or attosecond pulse trains, with pulse durations of a few hundred attoseconds.
	www.rp-photonics.com /encyclopedia_p.html (9561 words)

	inoceramid overview
		Because of the basically elliptical shape of many inoceramids, relatively few harmonics are required to describe their outlines and most of the same information of interest (i.e., the variance) resides in the first three or four harmonics (i.e., first 12 - 16 coefficients, Crampton unpublished data).
		Alternatively, one can sum the variance for successive harmonics and compare this sum to the total variance of the Fourier series based upon the maximum possible number of harmonics (equal to half the number of points on the digitized outline).
		Posterior auricle small relative to shell size, subtriangular, weakly to moderately defined, separated from disc by slightly to moderately concave auricular sulcus on dorsoposterior flank of umbo, or the flank of the first divaricating fold on the disc.
	www.fuhrmann-hilbrecht.de /Heinz/geology/InoIntro/InoIntro.html (11782 words)

	Welcome to Adobe GoLive 6
		Abstract: Traditionally, an important tool to study harmonic functions in $R^2$ is to identify $R^2$ as $C$ and identify harmonic functions as real parts of analyic functions.
		As an example, the homotopy type of the identity component in the space of maps on the 2-sphere has been fully determined, whereas the case of the homotopy type of the component of constant maps is still an open problem.
		The theory applies to the harmonic maps equations for maps to negatively-curved manifolds, and allows to count algebraical number of solutions for these and similar equations.
	www.maths.warwick.ac.uk /research/2002_2003/taheri/abstract.html (1421 words)

	Introduction
		In many applications, an expansion of the HFB wave function in a large harmonic oscillator (HO) basis of spherical or axial symmetry provides a satisfactory level of accuracy.
		As a result, the calculated densities, especially in the pairing channel, are too small in the outer region and do not reflect correctly the pairing correlations of such nuclei.
		11 ], a new transformed harmonic oscillator (THO) basis, based on a unitary transformation of the spherical HO basis, was discussed.
	info.fuw.edu.pl /~dobaczew/tho23w/node1.html (679 words)

	C.V. of C. F. Dunkl
		Cube group invariant spherical harmonics and Krawtchouk polynomials, Math.
		An addition theorem for Heisenberg harmonics, Conference on Harmonic Analysis in Honor of Antoni Zygmund.
		Symmetric functions and B^N invariant spherical harmonics, J. Phys.A: Math.
	www.people.virginia.edu /~cfd5z/cfdpubs.html (950 words)

	Submultiple Generator (Site not responding. Last check: 2007-11-05)
		Now, if an oscillating triode, was weakly coupled from plate to grid so that it was more or less unstable, had its bias so arranged that the plate current was full of harmonics, the circuit would synchronize itself with another having the frequency of one of its harmonics.
		Thus suppose that this unstable oscillator was adjusted for about 10,000 cycles and that the 100,000-cycle power from a crystal oscillator was impressed on its plate; then the tenth harmonic of the unstable oscillator would synchronize exactly with the impressed 100,000-cycle power.
		Now, another unstable generator may have its plate circuit tuned for 1,000 cycles, and its bias adjusted to give a plate current rich in harmonics; then if the 10,000-cycle generator was coupled to its plate it would synchronize with the10,000-cycle power, by the action of its tenth harmonic.
	www.nuenergy.org /alt/submultiple_generator.htm (296 words)

	Publisher description for Library of Congress control number 2001043129 (Site not responding. Last check: 2007-11-05)
		The author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps.
		The reader is then presented with a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions.
		A self-contained presentation of 'exotic' functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results.
	www.loc.gov /catdir/description/cam022/2001043129.html (196 words)

	Math Graduate Student Seminar
		They have a number of intriguing properties: for instance, any weakly symmetric space is a real form of a complex spherical homogeneous space; then, the algebra of invariant differential operators of a weakly symmetric spaces is always commutative.
		Harmonic maps from a Riemann surface to a compact Lie group or symmetric space are of both physical and geometric interest.
		The harmonic map equations are then a reduction of the self-dual Yang-Mills equations, and thus physicists study harmonic maps of $\mathbb R^2$ and $\mathbb R^{1,1}$.
	www.math.princeton.edu /gradseminar (7562 words)

	Heneri Dzinotyiweyi - Mathematicians of the African Diaspora (Site not responding. Last check: 2007-11-05)
		(with A. van Rooij) Non-Archimedean harmonic analysis on topological semigroups II, $p$-adic functional analysis Lecture Notes in Pure and Appl.
		Uniformly continuous and weakly almost periodic functions on some topological semigroups, Proc.
		Almost convergent and weakly almost periodic functions on a semigroup, Trans.
	www.math.buffalo.edu /mad/PEEPS/dzinotyiweyi_heneri.html (197 words)

	SCEE Invited Talks (Site not responding. Last check: 2007-11-05)
		As phenomena at higher harmonics, due to power electronic supply or ferromagnetic saturation, have an increasing technical importance, transient or harmonic balanced FE (HBFEM) simulation is becoming more and more important [1].
		Several implementations rely upon a weakly coupled time-harmonic scheme [2] or a real-valued splitting of the system matrix [1].
		The scaling of the computation time with respect to the extension of the number of harmonics, is studied.
	www.scee-2000.uni-rostock.de /abstracts/de-gersem.html (389 words)

Try your search on: Qwika (all wikis)