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in subjects: "Integrals"

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One and two electron integrals over Cartesian Gaussian functions

A formalism is developed which allows overlap, kinetic energy, potential energy and electron repulsion integrals over cartesian Gaussian functions to be expressed in a very compact form involving easily computed auxiliary functions. Similar formulas involving the same auxiliary functions are given for the common charge moments, electric-field operators, and spin-interaction operators. Recursion relations are given for the auxiliary functions which make possible the use of Gaussian functions of … more

Date: January 1, 1976

Creator: McMurchie, L. E. & Davidson, E. R.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Digital simulation and modeling of nonlinear stochastic systems

Digitally generated solutions of nonlinear stochastic systems are not unique, but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to … more

Date: January 1, 1980

Creator: Richardson, J. M. & Rowland, J. R.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Change in the particle action due to magnetic field perturbations in the SSC

The motion of a particle in the linear lattice of the SSC is stable, that is, the Courant-Synder invariant (W/sub 0/) remains exactly constant and the betatron phase (psi) increase by (2..pi nu..) for every revolution around the circumference. However, when magnetic field perturbations are present around the ring, this mode of describing the motion is no longer valid. One can then still speak of action-angle variables (W,phi) which in the limit of zero perturbation reduce to the linear betatron… more

Date: June 1, 1986

Creator: Herrera, J.C.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Gauge invariant actions for string models

String models of unified interactions are elegant sets of Feynman rules for the scattering of gravitons, gauge bosons, and a host of massive excitations. The purpose of these lectures is to describe the progress towards a nonperturbative formulation of the theory. Such a formulation should make the geometrical meaning of string theory manifest and explain the many ''miracles'' exhibited by the string Feynman rules. There are some new results on gauge invariant observables, on the cosmological c… more

Date: June 1, 1986

Creator: Banks, T.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Inherent limitations and current status of the unresolved resonance treatment

The two general methods for representing the behavior of the unresolved resonances and the limitations of these methods are discussed. Possible solutions to the problem are considered. 17 references. (WHK)

Date: January 1, 1984

Creator: Hwang, R.N.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Relationship of field components and the matched dispersion function in Arc achromats

The general integral condition connecting the field, its derivative and the resulting eta function derived for any lattice is applied to the achromats of the SLC Arcs. This condition can be combined with the non-dispersive condition to give a simple parameterization of second-order achromats constructed of combined function magnets.

Date: August 28, 1986

Creator: Fieguth, T.; Kheifets, S. & Murray, J. J.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Neutron cross sections for /sup 152/Gd and /sup 153/Gd

Cross section data is tabulated for /sup 152/Gd and /sup 153/Gd. Resonance data is given for /sup 152/Gd. Both reported and revised measurements are presented for cross sections and resonance parameters. Recommendations for further cross section and resonance research for these two isotopes are made. (DWL). 15 ref., 3 tabs.

Date: January 1, 1986

Creator: Holden, Norman E.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Automatic multirate methods for ordinary differential equations. [Adaptive time steps]

A study is made of the application of integration methods in which different step sizes are used for different members of a system of equations. Such methods can result in savings if the cost of derivative evaluation is high or if a system is sparse; however, the estimation and control of errors is very difficult and can lead to high overheads. Three approaches are discussed, and it is shown that the least intuitive is the most promising. 2 figures.

Date: January 1, 1980

Creator: Gear, C.W.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Inelastic Strong Interactions at High Energies. [Cross Sections, Field Theory]

A method permitting the calculation of inclusive and semi-inclusive cross sections at high energies starting from an arbitrary field theory was worked out. The method relies on a functional integral representation of the generating functional of inclusive cross sections and on the use of semiclassical methods. The inclusive cross section is proportional to the absolute square of the Fourier transform of a special soliton solution of the classical field equations in zeroth order semi-classical a… more

Date: October 20, 1977

Creator: Suranyi, P.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Calculation of the probability of overlapping one family of nuclear levels with resonances of an independent family

Calculations of the resonance integrals of particular isotopes in a mixture of isotopes show that the overlapping of the resonances of one isotope by resonances of other isotopes affects the final values of effective cross sections. The same effect might adversely influence those nondestructive techniques which assay fissile materials on the basis of resonance effects. Of relevance for these applications is the knowledge of the probability of overlapping resonances of a family of nuclear levels… more

Date: January 1, 1982

Creator: Difilippo, F. C.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Automatic detection and treatment of oscillatory and/or stiff ordinary differential equations

The next generation of ODE software can be expected to detect special problems and to adapt to their needs. The low-cost, automatic detection of oscillatory behavior, the determination of its period, and methods for its subsequent efficient integration are addressed here, along with stiffness detection. In the first phase, the method for oscillatory problems discussed examines the output of any integrator to determine if the output is nearly periodic. At the point this answer is positive, the s… more

Date: June 1, 1980

Creator: Gear, C. W.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

The Mean Integral

The purpose of this paper is to examine properties of the mean integral. The mean integral is compared with the regular integral. If [a;b] is an interval, f is quasicontinuous on [a;b] and g has bounded variation on [a;b], then the man integral of f with respect to g exists on [a;b]. The following theorem is proved. If [a*;b*] and [a;b] each is an interval and h is a function from [a*;b*] into R, then the following two statements are equivalent: 1) If f is a function from [a;b] into [a*;b*], gi… more

Date: December 1985

Creator: Spear, Donald W.

Item Type: Thesis or Dissertation

Partner: UNT Libraries

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DEMOLISHING A COLD-WAR-ERA FUEL STORAGE BASIN SUPERSTRUCTURE LADEN WITH ASBESTOS

The K East (KE) Basin facilities are located near the north end of the Hanford Site's 100 K area. The facilities were built in 1950 as part of the KE Reactor complex and constructed within 400 meters of the Columbia River, which is the largest river in the Pacific Northwest and by volume the fourth largest river in the United States. The basin, located adjacent to the reactor, was used for the underwater storage of irradiated nuclear fuel discharged from the reactor. The basin was covered by a … more

Date: November 25, 2008

Creator: ER, LLOYD; TK, ORGILL & EB, DAGAN

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Experimental computation with oscillatory integrals

A previous study by one of the present authors, together with D. Borwein and I. Leonard [8], studied the asymptotic behavior of the p-norm of the sinc function: sinc(x) = (sin x)/x and along the way looked at closed forms for integer values of p. In this study we address these integrals with the tools of experimental mathematics, namely by computing their numerical values to high precision, both as a challenge in itself, and also in an attempt to recognize the numerical values as closed-form co… more

Date: June 26, 2009

Creator: Bailey, David H. & Borwein, Jonathan M.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Function, J(x,y), occurring in problems of solute transport with non-equilibrium interphase mass transfer

The function, J(x,y), which has appeared frequently in analytical solutions of a variety of technical problems, is described and its applications briefly reviewed. Two detailed examples of applications are given. Tabulations of functions related to J(x,y) are listed, and relationships of J(x,y) to these functions are stated. Methods of computation of J(x,y), suitable for use with digital computers, are described.

Date: July 1, 1981

Creator: Carnahan, C. L.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Monte Carlo Renormalization Group: a review

The logic and the methods of Monte Carlo Renormalization Group (MCRG) are reviewed. A status report of results for 4-dimensional lattice gauge theories derived using MCRG is presented. Existing methods for calculating the improved action are reviewed and evaluated. The Gupta-Cordery improved MCRG method is described and compared with the standard one. 71 refs., 8 figs.

Date: January 1, 1985

Creator: Gupta, R.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Aspects of the dynamics of heavy-quark systems

The analysis of bound states composed of heavy quarks and antiquarks has provided a window into the structure of the strong interactions. These systems contain our best evidence that the quarks from which the hadrons are built are ordinary fermions which obey the Dirac equation and which couple to electromagnetism just as electrons do. However, the heavy-quark systems which have been studied to date, the systems of c- anti c and b- anti b bound states, seem to be bound by forces which bear no o… more

Date: December 1, 1983

Creator: Peskin, M.E.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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ENDF/B-5 fission product cross section evaluations

Cross section evaluations were made for the 196 fission product nuclides on the ENDF/B-5 data files. Most of the evaluations involve updating the capture cross sections of the important absorbers for fast and thermal reactor systems. This included updating thermal values, resonance integrals, resonance parameter sets, and fast capture cross sections. For the fast capture results generalized least-squares calculations were made with the computer code FERRET. Input for these cross section adjustm… more

Date: December 1, 1979

Creator: Schenter, R. E. & England, T. R.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Chiral transition in lattice gauge theories with Higgs and fermions

Analytic and numerical studies of the lattice gauge theories with both Higgs and fermion fields are reported. A chiral transition is found in a wide class of such theories, both abelian and non-abelian. This transition separates each phase diagram into two regions, one with spontaneous chiral symmetry breaking and the other with explicit chiral symmetry. The transition is second order where probed. In models where Yukawa couplings are present, there exists a critical value of this coupling belo… more

Date: January 1, 1987

Creator: Lee, I-Hsiu

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Renormalizing the strong-coupling expansion for quantum field theory: present status

Progress made in determining the renormalized strong coupling expansion in quantum field theory is reviewed. Consideration restricted is to lambda phi/sup 4/ field theory in d dimensions. The starting point is the lattice version of the path integral representation for the Green's functions. The unrenormalized strong coupling expansion on the lattice is determined first. This is a series in a dimensionless parameter, x. A simple set of graphical rules for determining the Green's functions of th… more

Date: January 1, 1980

Creator: Cooper, F.; Sharp, D.; Bender, C. M.; Guralnik, G. S. & Roskies, R.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Computation of magnetic coordinates and action-angle variables

We have developed a new algorithm for calculating magnetic surfaces and coordinates for a given three-dimensional magnetic field. The algorithm serves also to solve the equivalent problem of computing invariant tori and action-angle variables for a one-dimensional time-dependent numerically specified Hamiltonian (or a two-dimensional time-independent Hamiltonian). Our approach combines features of both iterative and trajectory following methods. This allows us to overcome the inefficiency of tr… more

Date: October 4, 1989

Creator: Reiman, A.H. & Pomphrey, N.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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A Warning on Fission Resonance Intergrals -- Caveat Utor!

Abstract: A common error is made in defining the resonance integral in most tabulations and handbooks. Although it has a minor effect on the capture resonance integral and on the fission resonance integral for the fissile nuclides, it leads to gross errors in the fission resonance integral for the fertile nuclides. The errors in the fission resonance integral for fertile nuclides of the elements from thorium through curium in the ENDF/B-V library will be presented. Let the user beware.

Date: 1989~

Creator: Holden, Norman E.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Hydrogen scattering cross section, /sup 1/H(n,n)/sup 1/H. [Above 100 keV, review]

The status of the hydrogen scattering cross section is reviewed with particular emphasis on standards applications. The ENDF/B-V evaluation is described in detail and compared with experimental data. 58 references.

Date: July 1, 1979

Creator: Stewart, L.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Ultraviolet divergences and supersymmetric theories

This article is closely related to the one by Ferrara in these same Proceedings. It deals with what is perhaps the most fascinating property of supersymmetric theories, their improved ultraviolet behavior. My aim here is to present a survey of the state of the art as of August, 1984, and a somewhat more detailed discussion of the breakdown of the superspace power-counting beyond N = 2 superfields. A method is also described for simplifying divergence calculations that uses the locality of subtr… more

Date: September 1, 1984

Creator: Sagnotti, A.

Item Type: Article

Partner: UNT Libraries Government Documents Department