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Topic: Eulerian integral

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	QNS Results (Site not responding. Last check: 2007-11-01)
		Stationary Eulerian velocity measurements were made at locations spanning the entire test section of the fully developed turbulent water channel used for experimentation.
		Measurements were also taken in the moving Eulerian reference frame where the traverse and measuring volume were moved at the mean speed of the flow to obtain RMS velocities as well as integral scales of the fluid.
		Integral scales were also influenced by gravity, namely by the reduction of measured fluid integral scales in the p-L reference frame.
	www.tuftl.tufts.edu /Users2/TUFTL/htmlpages/Jim_Lda/data.html (526 words)

	Infinitesimal Calculus - LoveToKnow 1911
		The processes of the integral calculus consist largely in transformations of the functions to be integrated into such forms that they can be recognized as differential coefficients of functions which have previously been differ entiated.
		For example, the rule (ii.) for a sum leads to the result that the integral of a sum of a finite number of terms is the sum of the integrals of the several terms.
		Conversely, indefinite integrals are indeterminate to the extent of an additive constant.
	www.1911encyclopedia.org /Infinitesimal_Calculus (17087 words)

	MAXIMA - Online Information article about MAXIMA
		When a change of Integrals variables is made, the limits of integration with respect to the new variable must be such that the domain of and Multiple integration is the same as before.
		When the former integral is taken between assigned limits it represents the volume contained between the surface and two planes which cut the axis of x at right angles.
		The latter integral is to be understood as a line integral taken along the curve, and it represents the area of the portion of the curved surface which is contained between two planes at right angles to the axis of x.
	encyclopedia.jrank.org /MAR_MEC/MAXIMA.html (5569 words)

	Lagrangian particle velocity correlation (Site not responding. Last check: 2007-11-01)
		Therefore, the Lagrangian particle velocity correlation is the same as the fluid's Eulerian velocity correlation.
		This is similar to the transition from Lagrangian to Eulerian correlations for small particles as a function of increasing inertia (Reeks 1977; Pismen and Nir 1978).
		Therefore, the velocity correlation along the length of the fibre is approximated as the fluid Eulerian spatial velocity correlation, with the corresponding Eulerian integral length scale.
	api.mech.ubc.ca /research/turb/turb_jfm_html/node12.html (341 words)

	Kenneth Meyer - Integral manifolds of the restricted three-body problem
		We compute the homology of the integral manifolds of the restricted three-body problem--planar and spatial, unregularized and regularized.
		There are five positive critical values of the Jacobi constant: one is due to a critical point at infinity, another is due to the Lagrangian critical points, and three are due to the Eulerian critical points.
		These computations show that at each critical value the integral manifolds undergo a bifurcation in their topology.
	www.cms.math.ca /Events/winter99/abstracts/node26.html?nomenu=1 (231 words)

	[No title]
		The basic idea of the ALE (Arbitrary Lagrangian Eulerian) approach is to write the evolution equations in a reference frame that is moving at some grid velocity (with respect to the fixed lab frame).
		See the integral form at http://www.csar.uiuc.edu/F_bcs/sld011.htm The familiar Eulerian differential form of the fluid equations is derived by considering a finite volume and then taking the limit as the volume shrinks to infinitesimal size.
		One may obtain a differential form for the fluid equations for a moving reference frame, but the finite volume formulation is simpler and guarantees global mass, momentum, and energy conservation.
	www.csar.uiuc.edu /SITeam/SIT_041499.htm (934 words)

	Randolph-Macon College Mathematics Department
		Topics include graph theory (including Eulerian and Hamiltonian circuits, scheduling, and graph coloring); notions of scaling in one, two, and three dimensions; basic functions (linear, power, polynomial, rational, exponential, and logarithmic).
		131 - Calculus I - This is a course in differential and integral calculus.
		Technology will be used to explain the definition of the definite integral, to obtain numerical approximations of definite integrals, to examine the graphs of functions, and to check computations of integrals and derivatives.
	www.rmc.edu /directory/academics/math/courses.asp (2710 words)

	Abstracts 2000
		Unsteady bore diffraction patterns generated by a bore wave impinging on a cylindrical pier and those generated by a bore wave passing through a contraction-expansion channel are simulated using a high resolution upwind scheme of the Godunov type on a boundary conforming grid.
		The two dimensional shallow water equations are formulated in integral finite volume form in such a way that no explicit transformation to curvilinear coordinates is needed.
		Integral models of merging behavior are cumbersome because of the need to sum the momentum of individual jets during the merging process.
	www.iahr.org /publications/JHR/bdy_JHRabs2000.htm (7232 words)

	3.3 Finite Volume Dynamical Core
		The physically correct way of approximating the integral (3.374) must be ``upwind'', in the sense that it is integrated along the backward trajectory of the cell edges.
		The surface pressure is needed for the physical parameterizations and to define the reference Eulerian coordinate for the mapping procedure (to be described in section 3.3.5).
		in the Eulerian coordinate system are obtained by integrating analytically the sub-grid distributions, in the vertical direction, from model top to the surface, layer by layer.
	www.ccsm.ucar.edu /models/atm-cam/docs/description/node13.html (3744 words)

	Sensible Calculus V.A
		The problem of solving differential equations was investigated using graphical tools (tangent fields and integral curves), numerical tools (Euler's method for estimating the values of solutions with initial conditions- a numerical integration) and, for a more limited family of differential equations, symbolically (indefinite integrals).
		As the number of summands increases the estimating sums approach a single number which can be interpreted in the two distinct models using the function P to describe either the velocity of a moving object or the graph of a function bounding of a planar region.
		The notion of the definite integral has continued to grow further even in the 20th century, demonstrating the vitality of the concept in an ever expanding world of mathematical studies.
	www.humboldt.edu /~mef2/book/ch5/VA/CH5A.html (3475 words)

	Course objectives
		explain what the Eulerian and Lagrangian perspectives are and how they relate to the laws of motion, the fluid, and the governing equations, 2.
		derive the both integral and differential forms of the Eulerian equation for the transport of a property, given its governing law, 3.
		derive of the Eulerian expression for the substantial derivative, and derive the Reynolds transport theorem, 5.
	www.aoe.vt.edu /~devenpor/aoe5104/objectives.html (1368 words)

	ANGEO - Abstracts
		It reveals that the horizontal wind variance, the Eulerian integral scales, the frequency range of turbulence and the turbulent kinetic energy dissipation rate are affected by the surface roughness.
		In the vicinity of the ground surface, the horizontal wind variance logarithmically increases with height, directly in relation to the friction velocity and the roughness length scale.
		It was found that the time integral scale (and subsequently the length integral scale) increased with the surface roughness and decreased with the anemometer height.
	www.copernicus.org /EGU/annales/21/2119.htm (296 words)

	Adrien-Marie Legendre
		The third volume (1816) contains the very elaborate and now well-known tables of the elliptic integrals which were calculated by Legendre himself, with an account of the mode of their construction.
		The second volume (1817) relates to the Eulerian integrals, and to various integrals and series, developments, mechanical problems, etc., connected with the integral calculus; this volume contains also a numerical table of the values of the gamma function.
		The latter portion of the second volume of the Traité des Fonctions Elliptiques (1826) is also devoted to the Eulerian integrals, the table being reproduced.
	www.nndb.com /people/891/000093612 (1750 words)

	SHARED-MEMORY PARALLEL VECTOR IMPLEMENTATION OF THE IMMERSED BOUNDARY METHOD FOR THE COMPUTATION OF BLOOD FLOW IN THE ... (Site not responding. Last check: 2007-11-01)
		Equation 3 represents the force of the fibers on the fluid as a continuous sum (integral) of point forces applied at the locations of the fiber points.
		The first is that the Eulerian (fluid) lattice has to be accessed in an unstructured way: there is no constant stride through memory.
		The first pair of loops is vectorized over the 64 Eulerian points with which a Lagrangian point interacts, but the second pair of loops is vectorized over the different Lagrangian points.
	math.nyu.edu /~mcqueen/Public/papers/psc/PSC_19971216/PSC.19971216.html (6682 words)

	Earliest Known Uses of Some of the Words of Mathematics (E) (Site not responding. Last check: 2007-11-01)
		This finite-dimensional case is used to motivate the treatment of differential equations and integral equations which involve infinite-dimensional spaces where the vector is now a function.
		He obtained an addition theorem for this integral and, therefore, demonstrated that the division of arcs of the lemniscate into n equal parts is an algebraic problem.
		Eulerian integral appears in 1825-26 in his Traité des Fonctions elliptiques et des Intégrales Eulériennes [James A. Landau].
	members.aol.com /jeff570/e.html (8741 words)

	Furman Mathematics: Course Descriptions (Site not responding. Last check: 2007-11-01)
		This course is an introduction to applications of the derivative and the theory and applications of the definite integral.
		Topics included are the trigonometric functions and their derivatives, applications of derivatives, antiderivatives, the definite integral and applications of the integral.
		The second course in the standard calculus sequence.Included are an introduction to the logarithmic and exponential functions, the applications of the definite integral, techniques of integration, indeterminate forms, improper integrals, numerical methods and infinite series.
	math.furman.edu /adviceinfo/descriptions.html (1306 words)

	PlanetMath: (Site not responding. Last check: 2007-11-01)
		estimating theorem of contour integral owned by pahio
		proof of estimating theorem of contour integral owned by cvalente
		Eulerian number (=natural log base) owned by akrowne
	planetmath.org /encyclopedia/E (2166 words)

	ZAIK preprints & publications
		We prove the NP-completeness of the planar edge-disjoint paths problem by showing the NP-completeness of the vertex disjoint paths problem for planar graphs with maximum vertex-degree three.
		Furthermore we present a counterexample to a conjugate of A. Frank mentioned in A. Seboe [Dual Integrality and Multicommodity Flows.
		This implies an answer to the long-standing question whether the edge-disjoint paths problem is polynomially solvable for Eulerian graphs.
	www.zpr.uni-koeln.de /~paper/preprints.html?preprint_session=d14663fe32ebb91610a06609aaa02d29&show=zpr91-098 (428 words)

	[No title]
		Eulerian approach is the preferred approach in most fluid dynamics applications.
		The effect of these approximations is that the right hand sides of the integral forms of u- v- and w- momentum equations (2.8, 2.9, 2.10) disappear, leaving us only with the left-hand side terms.
		Using this relationship to the surface integrals in the u-momentum equation, we get EMBED Equation.3 (2.13) The u-momentum equation thus becomes: EMBED Equation.3 (2.14) The only way this volume integral will be equal to zero for all arbitrary control volumes at all time levels is if the integrand is zero.
	www.ae.gatech.edu /people/lsankar/AE2020/ChapterII.doc (2229 words)

	Course Descriptions -- Ch10: 2001-2002 UVa Undergraduate Record
		The concepts of differential and integral calculus are developed and applied to the elementary functions of a single variable.
		Includes the concepts of differential and integral calculus, and applications to problems in geometry and elementary physics, including indeterminate forms and techniques of integration.
		An introduction to graph theory, including connectivity properties; and Eulerian and Hamiltonian graphs, spanning trees and shortest path problems.
	www.virginia.edu /registrar/records/01ugradrec/chapter10/uchap10-4.1.html (497 words)

	INP Toulouse Theses - Towards eulerian-eulerian large eddy simulation of reactive two-phase flows (Site not responding. Last check: 2007-11-01)
		This approach has been validated for the case of tracer particles with very low inertia that follow the carrier phase almost instantaneously due to their small response time compared with the microscale time scales of the carrier phase.
		Numerical simulations in the Eulerian framework are validated by comparison with simulations using Lagrangian particle tracking.
		Additionally coupling of the Eulerian transport equations for the particles to combustion models is tested.
	ethesis.inp-toulouse.fr /archive/00000131 (719 words)

	Julius Wihelm Richard Dedekind (Site not responding. Last check: 2007-11-01)
		There he was to receive a good understanding of basic mathematics studying differential and integral calculus, analytic geometry and the foundations of analysis.
		He did his doctoral work in 4 semesters under Gauss's supervision and submitted a thesis on the theory of Eulerian integrals.
		He attended courses by Dirichlet on the theory of numbers, on potential theory, on definite integrals, and on partial differential equations.
	www.stetson.edu /~efriedma/periodictable/html/Db.html (695 words)

	CSB\|SJU Academic Catalog 2000-2001 - MATH 300-Level Courses (Site not responding. Last check: 2007-11-01)
		Topics selected from Geometry of Rn, differentiation in Rn, vector-valued functions, optimization, multiple integrals, line and surface integrals, vector analysis and introduction to differential forms.
		Basic properties of graphs and digraphs, basic properties of trees and algorithms using spanning trees, graph coloring and related graphical parameters, Eulerian and Hamiltonian circuits and application to scheduling, coding, matchings and optimization problems.
		Topics selected from the following: mapping theorems and extremum problems, Riemann-Stieltjes integral, main theorems of integral calculus, complex analysis, functions defined by integrals, convergence theorems.
	www.csbsju.edu /catalog/2000-2001/academic_departments/mathematics/006.htm (559 words)

	Oxford University Press
		Integral representation and further properties of potential flow
		Investigation of integral equations of the second kind
		Regularization of integral equations of the second kind
	www.oup.com /ca/isbn/0-19-509320-8 (827 words)

	The Multiple Gamma and Related Functions Project
		Choi, C. Nash, Integral representations of the Kinkelin's constant A, Math.
		Nan-Ye, K.S. Williams, Values of the Riemann zeta function and integrals involving log (2 sinh oo2) and log (2sin oo2), Pacific journal of mathematics 168, no. 2 (1995) 271-290.
		Weisberger, Normalization of the path integral measure and the coupling constants for bosonic strings, Nuclear Phys.
	www.cs.cmu.edu /~adamchik/Barnes/bibliography.html (2891 words)

	Packing Odd Circuits in Eulerian Graphs - Geelen, Guenin (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		For nonnegative integral edge{weights w, we are interested in the linear program min(w t x : x(C) 1; for C 2 C; and x 0), which we denote by (P).
		Guenin proved that (P) has an optimal solution that is integral so long as (G; ) does not contain a minor isomorphic to odd{K 5.
		J.F. Geelen, B. Guenin, Packing odd-circuits in Eulerian graphs, Journal of Combinatorial Theory, Series B to appear.
	citeseer.ist.psu.edu /476271.html (546 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		The FVELLAM uses space-time finite volumes oriented along the streamlines of the flow field to solve an integral form of the solute-transport equation, thus combining local and global mass conservation with the advantages of Eulerian-Lagrangian characteristic methods.
		ELLAM solves integral equations and thus tracks mass associated with fluid volumes, so that it conserves mass locally and globally.
		The governing equation for this finite-volume approach is an integral form of the solute-transport equation, which is a statement of conservation of mass over the domain of integration.
	www-math.cudenver.edu /~trussell/modflow2001.proc.doc (3403 words)

	Stony Brook AMS - Downloadable Preprints, 1993
		With the aid of the compactness framework established in [CK1], we prove the convergence of the viscosity method, and the existence of global entropy solutions for the Cauchy problem with large initial data for canonical classes of the quadratic flux systems.
		The method uses a conservative Eulerian formulation of elasto-plasticity together with a higher-order Godunov finite difference method combined with tracking of material boundaries.
		The Eulerian approach avoids the problem of mesh distortion caused by a Lagrangian remap, and can be easily extended to the computation of flows in multiple space dimensions using operator splitting.
	www.ams.sunysb.edu /papers/papers93.html (2043 words)

	Introduction to the Gamma Function
		(x) (or the Eulerian integral of the second kind) is well defined and analytic for x > 0 (and more generally for complex numbers x with positive real part).
		The derivatives can be deduced by differentiating under the integral sign of (2)
		Definition 17 The beta function (or Eulerian integral of the first kind) is given by
	numbers.computation.free.fr /Constants/Miscellaneous/gammaFunction.html (1895 words)

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