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Note on the Numerical Evaluation of Integrals of the Form anti l*SUB infinity/*SUP infinity/ f(x) *phi/(x) dx, with Particular Reference to the Determination of the Expectation of a Function of a Normally Distributed Random Variable

Description: This note is concerned with the numerical integration of the integrals of the form anti l*SUB infinity/*SUP infinity/ f(x) *phi/(x) dx is "smooth."
Date: September 1, 1953
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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VARI Solution of Simultaneous, First-Order, Ordinary, Differential Equations

Description: VARI solves on the IBM-650 a system of simultaneous, first-order, ordinary, differential equations. The program was written so that a large number of calculations could be done in a reasonable length of time. The program permits the consideration of the production of the isotope by absorption and/or decay of one or more of any of the other isotopes in the chain.
Date: March 15, 1960
Creator: Kerr, B. A.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Non-Linear Bunch Motion at Transition

Description: A summary of the dynamic behavior of the proton bunches in the Brookhaven Alternating Gradient Synchrotron (AGS) has been given previously. In these reports, the usual linearization of the differential equations involved has been made and the theory was restricted to well bunched beams. The linearized approach is no longer valid at transition where the actual phase angle of the bunch can differ appreciably for a short time from the stable phase angle Φ₀. In this report the non-linearity of the … more
Date: December 4, 1961
Creator: Hahn, Harald
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Remarks on the Double Dispersion Approach to the Bethe-Salpeter Equation

Description: The following remarks are made on the applicability of the double dispersion approach to the Beth-Salpeter equation introduced previously. 1) Any invariant solution of the Bethe-Salpeter equation in ladder approximation satisfies the double dispersion representation when the total energy-momentum is space-lake. 2) There are some exceptional invariant solutions which are not given by the previous method in the equal-mass case, but the existence of such solutions is very unlikely in the unequal-m… more
Date: August 7, 1962
Creator: Nakanishi, Noboru
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Error Estimates for Some Unstable Continuation Problems

Description: The purpose of this paper is to give a method of approximating u(x,y) by bounded solutions of the elliptic equation when the given data, F(x), f₁(y), and f₂(y), are known only to within a given error. A priori error estimates for the approximation will be given. Since the method involves the solution of a linear programming problem, a posteriori estimates of the error will also be obtained.
Date: 1962
Creator: Cannon, J. R.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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LMFR Progress Letter for April 1954

Description: Summary of miscellaneous updates related to the project. This includes information on the following. Simplified equations for modeling reactor conditions. Solubility tests involving thorium, bismuth, and protactinium. various other measurements and tests involving thorium, uranium, protactinium, bismuth, aluminum, and various other salts.
Date: May 21, 1954
Creator: Miles, F. T.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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The Development of Compression Waves in an Adiabatic Two-Fluid Model of a Collision-Free Plasma

Description: "A generalized discontinuous solution was found for the adiabatic two- fluid equations in the steady state: it covers the case of strong shocks and enables a complete account to be made of the steady state solutions of these equations. By considering a piston problem using numerical methods, time dependent solutions of the equations were also found; these rapidly steepened and converged to the discontinuous steady state solutions whenever these existed."
Date: unknown
Creator: Morton, K. W.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Propagation of Long Wavelength Disturbances in a Plasma

Description: "The long wavelength modes of excitation of a two component plasma in a steady magnetic field are examined. Two linearized Boltzmann equations are given with collision terms which are coupled through the difference in temperatures and difference in velocities of the two gases. A formal means of classification of phenomena is described in terms of the nature of the roots about k = 0. Two types of behavior are uncovered: MHD, magnetohydrodynamics, which include finite phase speed phenomena near k… more
Date: unknown
Creator: Liboff, Richard L.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Difference Schemes With High Order of Accuracy for Solving Hyperbolic Equations

Description: "The limitation of the speed and memory of calculating machines places an upper bound on the number of meshpoints that may be used in a finite difference calculation. This means that in problems involving many independent variables (and for present-day machines, three is many) the mesh employed is necessarily coarse. Therefore in order to get reasonably accurate final results one must employ highly accurate difference approximations. The purpose of this paper is to set up and analyze such diffe… more
Date: unknown
Creator: Lax, Peter D. & Wendroff, Burton
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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The Canonical Theory of Motion of a Charged Particle in a Slowly Varying Electromagnetic Field

Description: "The canonical theory of motion of a charged particle in a slowly varying, static electromagnetic field is formulated. The Hamiltonian is written down explicitly in terms of the coordinates of the gyration and the drift. The method of approach is analogous to that of the canonical formalism with subsidiary condition as used in theories of collective motion in many-body systems, such as the motion of the center of gravity. In the lowest order of the perturbation, it is shown that the Hamiltonian… more
Date: unknown
Creator: Taniuti, Tosiya
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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The Quantum Mechanical Scattering Problem II: Multi-Channel Scattering

Description: "The study of the single channel scattering problem was extended to include the multi-channel case. The scattering problem was formulated in a mathematically rigorous way which reflects the time-independent point of view but is not limited by any dependence on a configuration space representation. Wave operators were defined by an integral representation. When the conditions necessary for the time-dependent formulation are valid these wave operators will be identical to those defined by the asy… more
Date: Date unknown.
Creator: Jordon, Thomas F.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Hamiltonian Dynamics of Relativistic Particles

Description: "The canonical (hamiltonlan) formulation of a relativistic dynamical theory is outlined, and the existence and explicit construction of general hamiltonian theories of relativiatic interacting particles are discussed. These hamiltonian theories are shown to contain certain elements of arbitrariness which are eliminated in manifestly coveriant formulations."
Date: March 2, 1961
Creator: Sudarshan, E.C.G.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Alternating Direction and Semi-Explicit Difference Methods for Parabolic Partial Differential Equations

Description: "The energy method is applied to study the stability of two types of difference approximations to parabolic partial differential equations, the alternating direction methods Douglas, Peaceman, and Rachford, and a new semi- explicit method. Each difference scheme is proved to be unconditionally stable. These results apply to parabolic equations with variable coefficients, defined in cylindrical domains with an essentially arbitrary bounded base."
Date: March 1, 1961
Creator: Lees, Milton
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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The Numerical Solution of a Parabolic System of Differential Equations Arising in Shallow Water Theory

Description: "A finite difference approximation to a non-linear set of parabolic differential equations arising in shallow water theory is given. These difference equations were used to determine the shape and rate of propagation of a hum of fluid down a channel of constant depth. The hump of fluid was found to spread instead of steepen, as is the case in the usual shallow water theory."
Date: October 15, 1960
Creator: Heller, Jack & Isaacson, Eugene
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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On the Generalized Overrelaxation Method for Operator Equations

Description: "In Householder, using Weissinger's identity , obtained the necessary and sufficient conditions for the c onvergence of the Seidel method for the solution of finite matrix equations of the form (D-S-S*-F)u = f. The same coniditions were also obtained by Krein and Prozorovakaya for an analog of the Seidel method for the operator equations of the form (D+S+S*)u = f in a Hilbert space. The purpose of this article is to extend the result of the above authors to the generalized overrelaxation iter… more
Date: June 14, 1962
Creator: Petryshyn, Wolodymyr V., 1929-
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Improved Method for Numerically Solving Multi-Group Reactor Equations

Description: "A method for solving multi-group reactor equations which arise in the diffusion approximation is outlined. Considerable work has been done on this problem at KAPL and ORNL. Their approach is to replace the differential equations by difference equations. Complications arise in this method where more than one slowing down medium is present since the fluxes are discontinuous at the interfaces. The primary purpose of this article is to develop an exact integral expression for the neutron flux w… more
Date: September 15, 1954
Creator: Lehman, G. W.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Closed Extensions of the Laplace Operator Determined by a General Class of Boundary Conditions

Description: This paper is concerned with the spectral theory of closed operators in Hilbert space determined by the Laplace operator and certain general boundary conditions. Using the method of J.W. Calkin, we treat the case of a bounded domain in E(m) with C(1,1) boundary, and, in addition, extend the method to cover the case for which the operator L in the boundary condition is not necessarily self-adjoint. It is shown that there exists an appropriate linear close of functions [formula] such that the ope… more
Date: December 1960
Creator: Badè, W. G. (William G.), 1924-2012 & Freeman, R. S.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Stability for inhomogeneous difference schemes

Description: Abstract. The Equivalence Theorem of P. Lax is extended to difference schemes for initial-value problems for linear inhomogeneous PDE with linear inhomogeneous boundary values and for boundary-value problems.
Date: July 13, 1960
Creator: Seidman, Thomas I.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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On the Stability of Certain Difference Schemes for Linear Parabolic PDE with Constant Coefficient

Description: Introduction. The von Neumann stability criterion is used to analyze the stability of three types of difference schemes for partial differential equations. It is shown that, contrary to the usual rule of thumb, there exist symmetric implicit schemes for a class of equations which are unstable for every mesh-ratio but that this cannot occur if (a) there are fewer than three "space" variables or (b) the difference expression is used to approximate the mixed derivative.
Date: June 1, 1960
Creator: Seidman, Thomas I.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Space-charge-based electrostatic plasma confinement involving relaxed plasma species

Description: In this article, a numerical study is reported on the equilibrium properties of a surface-emitted or edge-confined non-drifting plasma. A self-consistent finite-differences evaluation of the electrostatic potential is carried out for a non-neutral plasma that follows a Boltzmann density distribution.
Date: October 23, 2012
Creator: Pacheco, J. L.; Ordonez, Carlos A. & Weathers, Duncan L.
Item Type: Refine your search to only Article
Partner: UNT College of Arts and Sciences
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Electrostatic equilibria of non-neutral plasmas confined in a Penning trap with axially varying magnetic field

Description: This article describes a procedure for computing the electrostatic equilibria of non-neutral plasmas in a Penning trap with a nonuniform magnetic field by solving Poisson's equation using an iterative method. Plasma equilibria in a model Penning trap with high and low field regions are computed. The plasma is assumed to follow the Boltzmann density distribution along magnetic field lines.
Date: May 21, 2019
Creator: Lane, Ryan A. & Ordonez, Carlos A.
Item Type: Refine your search to only Article
Partner: UNT College of Science
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