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Closed Form Solution for the Wave Equation This paper documents both the development of a closed form solution for the one-dimensional wave equation as it is applied to piles and its comparison to numerical solutions of the same problem. The comparison shows variations between the closed form solution and the numerical methods that, although not egregious, are also not consistent from case to case. Closed form solutions were either abandoned entirely or applied on a limited basis or in an ancillary way to other techniques. www.vulcanhammer.net /wave/isa.php   (1352 words)

Closed-form solution   (Site not responding. Last check: 2007-10-21) The classic example involves the two roots of a quadratic equation, which can be expressed in closed form in terms of addition and subtraction, multiplication and division, and square root extraction. When no closed-form solutions exist – as is the case for fifth-order or higher polynomial equations, for example – such equations have to be solved numerically, typically by using some root-finding algorithm. For example, many cumulative distribution functions cannot be expressed in closed form, unless one considers special functions such as the error function or Gamma function to be well-known. www.sciencedaily.com /encyclopedia/closed_form_solution   (267 words)

Closed-Form Maximum Likelihood Estimates of Nearest Neighbor Spatial Dependence In turn, this leads to a closed form solution for the maximum likelihood estimates of the spatially autoregressive and mixed regressive spatially autoregressive models. In fact, we obtain a closed form not just for the log-determinant of the nearest neighbor adjacency matrix but also the log-determinant of any linear combination of the odd powers of this matrix. One could imagine the heavy line represents a closed border, for example, and economic activity on each side is correlated, but that the economic activities of each side are independent of the other side due to lack of trade. www.spatial-statistics.com /pace_manuscripts/closest_neighbors/html/nearest_neighbor.html   (5728 words)

Closed Form Solution for the Wave Equation In this paper the closed form solution for the damped wave equation will first be stated and related to an actual pile driven into the soil. A solution to this equation which involves the solution of the semi-infinite pile using Laplace transform for the first part of the impact followed by a Fourier series solution for the remainder. The rationale for the use of closed form solutions as opposed to the numerical ones is set forth. www.wingnet.net /~jfwnctm/wave/isa.htm   (1887 words)

Macroapproach Closed-Form Series Solution for Orthotropic Plates   (Site not responding. Last check: 2007-10-21) The objective of this study is to present the derivations in closed-form series for moments and deflections of thin orthotropic plates with general edge beams (boundaries) under arbitrary out-of-plane loading. The displacement solutions for the major components of the system (plate and beam) or macroelements are obtained by first solving for the unknown interactive forces and moments at the beam or nodal line locations after satisfying displacement compatibility along nodal lines. The major advantage of this technique is the development of a solution algorithm in the form of summation equations, leading to fast converging closed-form series solutions. www.pubs.asce.org /WWWdisplay.cgi?9500585   (211 words)

Maybe this Explains the Economic Cycle... best Closed-Form Solution   (Site not responding. Last check: 2007-10-21) A Closed Form Solution to Blind Equalization A Closed Form Solution to Blind Equalization In some recent papers new algorithms for blind adaptive equalization were proposed. Image charges revisited: a closed form solution Image charges revisited: a closed form solution We demonstrate that the corrections to the classical Kelvin image theory due to finite electron screening length $\lambda$, recently discussed by... Closed-Form Solution -- from MathWorld Closed-Form Solution -- from MathWorld An equation is said to be a closed-form solution if it solves a given problem in terms of functions and mathematical operations from a given generally accepted set. ascot.pl /th/Fourier3/Closed-Form-Solution.htm   (525 words)

Isotropic Capacitance Since most real-world problems don't have any exact, closed-form mathematical solution, (at least that we've yet been able to find) we are forced to either work with approximations or go with computer-based numerical solutions. But looking for a closed-form solution, we often end up having to assume away reality in order to make the problem simple enough to be solvable. If someone really really needed a close prediction of the capacitance in a real-world situation, they'd need to apply something like the Method of Moments on a decent computer with a good matrix inversion routine that can handle some hefty sized matrices in something less than the expected lifetime of the universe. www.pupman.com /listarchives/1996/may/msg00110.html   (1126 words)

Question Corner -- Finding the Ratio from the Sum of a Geometric Series Closed-form solutions are more of a rarity than one might think, and not as important as one might think. Solutions by radicals of polynomials of degree <= 4 were known by the 1500's (the degree 2 case being the familiar quadratic formula). There are general solutions of quintic equations involving other functions like hypergeometric functions, but from a practical point of view that doesn't matter too much since the only way to evaluate them is by numerical calculations anyway. www.math.toronto.edu /mathnet/questionCorner/sumtoratio.html   (956 words)

Exact weighted time fields: two-field form Emanating from the two-field form and using the Greens' formula for the equation (1.3) in a consistent manner yields Substituting the fundamental solution equation (3.97), into equation (1.22), we have the closed form solution of the equation (3.91) as In its present form, the time discretized operator, namely equation (3.103) pertains to Type 1 classification and is still the exact representation of the dynamic equations (3.91-3.92) or is termed as an exact integral operator [EIO]. www-users.cs.umn.edu /~xiangmin/arc/node41.html   (329 words)

Princeton Computer Science :: Technical Reports Form factors are used in computer graphics and radiative heat transfer to describe the fraction of diffusely refledted light or radiation leaving one surface and arriving at another. However, the important case of the form factor between two polygons in three space has had no known closed form solution. We give a closed form solution for the case of general (planar, convex, or concave, possibly containing holes) polygons. www.cs.princeton.edu /research/techreps/TR-404-93   (96 words)

Computer Vision and Robotics Laboratory, Beckman Institute, UIUC The authors present a closed-form solution to motion and structure parameters from line correspondences through three monocular perspective views. The uniqueness of the solution is established, and necessary and sufficient conditions for degenerate spatial line configurations are given. Simulations have shown that the errors of the optimized estimates are close to the theoretical lower error bound. vision.ai.uiuc.edu /abstracts/pub1_2_1_a0392wha.htm   (129 words)

Closed form solution to a alternating binomial sum Closed form solution to a alternating binomial sum Hey Everyone, I've been trying to figure out the closed form solution to this sum, but have failed so far. Closed form solution to a alternating binomial sum, Thomas Paine www.usenet.com /newsgroups/sci.math/msg15352.html   (91 words)

Analogue Design For Teletubbys   (Site not responding. Last check: 2007-10-21) This paper derives a closed form solution for the Widlar current mirror. This paper shows that the solution can be expressed in closed form using relatively well known mathematical functions. Is the closed form solution for I2 in terms of the Lambert W Function. www.anasoft.co.uk /EE/widlarlambert/widlarlambert.html   (278 words)

A Closed Form Solution to the Reconstruction and (ResearchIndex)   (Site not responding. Last check: 2007-10-21) A Closed Form Solution to the Reconstruction and (ResearchIndex) A Closed Form Solution to the Reconstruction and (2003) The well known thereotical foundation for multi-view geometry is extended in light of this to solve the problems of triangulation and forming multi-view matching constraints for degree d apparent contours. citeseer.ist.psu.edu /668471.html   (335 words)

Re: Closed-Form pricing formula A function has a closed form if it can be written exactly with a finite number of standard functions (powers, exponentials, sins, etc). Sometimes it has a closed form, as with the Black-Scholes formula for an equity option paying no dividends. Other times it has no closed form solution and must be evaluated with Monte Carlo simulation or some other means. www.contingencyanalysis.com /archive/archive99-4/00000269.htm   (160 words)

A Closed-Form Dynamic Elasticity Solution to the Fluid/Structure Interaction Problem of a Two-Layer Infinite ... Abstract: This report documents an exact closed-form solution to the problem of a two-layer viscoelastic solid infinite cylinder that is immersed in an infinite ideal inviscid fluid and contains an infinite ideal inviscid fluid within its diameter. The viscoelasticity is modeled with structural damping, which is incorporated by the use of a complex modulus of elasticity. Simulations of the transfer surfaces for the interior pressure field are performed for radial excitation P0 and longitudinal excitation Px applied to a single-layer cylinder for n = 0, 1, and 2. www.stormingmedia.us /84/8460/A846013.html   (339 words)

Numerical Solution, Closed-Form Solution A closed-form solution (or closed form expression) is any formula that can be evaluated in a finite number of standard operations. In this case, we were fortunate that [2] had a particularly simple form, which allowed us to find a closed-form solution for it. Closed form solutions and numerical solutions are similar in that they both can be evaluated with a finite number of standard operations. www.riskglossary.com /articles/closed_form_solution.htm   (698 words)

A closed form solution for the rapid shear of homogeneous turbulence in a rotating frame with and without stratification   (Site not responding. Last check: 2007-10-21) A closed-form solution for the evolution of one-point statistics is derived for the case of initially two-dimensional three-component (2D-3C) homogeneous turbulence deformed by rapid shear in a rotating frame. Except for small total shear, the analytical result is shown to be in good agreement with the numerical solution of the governing equations, linearized for rapid distortions, and solved for the more general initial case of 3D-3C isotropic homogeneous turbulence. Based on this agreement, we show that the closed-from solution provides insight into the stabilizing and destabilizing effects of frame rotation on homogeneous stratified shear flow, and provides a useful reference point for the one-point modeling of rotated and stratified shear flows. flux.aps.org /meetings/YR00/DFD00/abs/S1720008.html   (178 words)

Citations: A new closed-form solution for absolute orientation - Wang, Jepson (ResearchIndex)   (Site not responding. Last check: 2007-10-21) They proposed a novel closed form algorithm solving for the translation and rotation, which is claimed to be very robust in the presence of noise. Although closed form solutions are also presented for ideal motion problems by Aloimonos s group [1, 8] Huang s group [5, 15] and others [13, 16].... 3 General Correspondence Recovey A shortcoming of the closed form solution is that it is limited to ideal motion.... citeseer.ist.psu.edu /context/125070/0   (977 words)

Closed-Form Solution for the Timoshenko Beam Theory Using a Computer-Based Mathematical Package -- from Mathematica ... In many structures the structural joints may be far apart, and therefore many elements must be used if the inertia distributions are to be modelled accurately. The purpose of this study is to determine the influence of distributed rotary inertia and shear deformation on the motion of a mass-loaded clamped-free Timoshenko beam by means of an exact solution. The governing differential equations are solved, and the frequency results are presented graphically and are compared with those derived for a Euler-Bernoulli beam. library.wolfram.com /infocenter/Articles/1862   (179 words)

Re: Planet X: Messenger's CHOICE The solar system is a complex multibody system without > closed-form mathematical solution. A natural question to ask about > any complex dynamical system is how it will evolve in the long term, > and whether or not it is stable. Without a closed-form mathematical > solution, the answer does not simply pop out of the equations, as it > does for example with the two-body problem or certain classes of > three-body problem. www.zetatalk.com /usenet/use90520.htm   (695 words)

COMPUTER SCIENCE TECHNICAL REPORT ABSTRACTS   (Site not responding. Last check: 2007-10-21) Approximating general distributions by phase-type (PH) distributions is a popular technique in queueing analysis, since the Markovian property of PH distributions often allows analytical tractability. Since efficiency of the algorithm is of primary importance, we first define a particular subset of the PH distributions, which we refer to as EC distributions. Our solution is general in that it applies to any distribution whose first three moments can be matched by a PH distribution. reports-archive.adm.cs.cmu.edu /anon/2003/abstracts/03-114.html   (190 words)

m0000004.htm 2.3 Closed form solution of the estimated parameters Specifically, the roots equal the eigenvalues of the companion matrix associated with the polynomial (Horn and Johnson (1993, p. Thus, the maximum likelihood estimates have a closed-form solution in terms of the eigenvalues of a small matrix. www.spatial-statistics.com /spatial_statistical_manuscripts/MESS/html/m0000004.htm   (278 words)

Question Corner -- Finding the Ratio from the Sum of a Geometric Series The challenge is to solve for R. From the form of the first equation, we know that what we seek is one of the roots of a polynomial of degree N-1. The physical model that the algebra represents is: S is a distance to be spanned by N computational cells. From a purely intuitive view there ought to be a closed form generalized solution for R. But I have been unable to see my way to anything but an iterative numerical solution. www.math.toronto.edu /mathnet/plain/questionCorner/sumtoratio.html   (1004 words)

NSDL Metadata Record -- A Closed Form Solution for Inverse Kinematics of Robot Manipulator with Redundancy NSDL Metadata Record -- A Closed Form Solution for Inverse Kinematics of Robot Manipulator with Redundancy A closed form equation for inverse kinematics of manipulator with redundancy is derived, using the Lagrangian multiplier method. The proposed equation is proved to provide the exact equilibrium state for the resolved motion method. nsdl.org /mr/709499   (117 words)

Alongwind Response Estimation: Closed Form Solution   (Site not responding. Last check: 2007-10-21) The treatment of the problem presented in the paper leads to a closed form expression of the alongwind response. The remarkable simplicity and the very high precision of the proposed method is pointed out in general terms and illustrated by two examples. In conclusion, some prospects for possible future applications referred to this solution are outlined and briefly discussed. www.pubs.asce.org /WWWdisplay.cgi?8200035   (113 words)

Robotics Institute: A Closed-Form Solution to Nonrigid Shape and Motion Recovery This paper proves that the solutions obtained using only the rotation constraints are inherently ambiguous. The ambiguity arises from the fact that, the shape bases are not unique since their linear transformation is a new set of eligible bases. This paper proves that, under the weak-perspective projection model, once both the basis and the rotation constraints are imposed, we achieve a closed-form solution to the problem of non-rigid shape and motion recovery. www.ri.cmu.edu /pubs/pub_4495.html   (383 words)

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