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Wigner And Racah Coefficients For Su3, J. P. Draayer, Yoshimi Akiyama Jan 1973

Wigner And Racah Coefficients For Su3, J. P. Draayer, Yoshimi Akiyama

Faculty Publications

A general yet simple and hence practical algorithm for calculating SU 3 ⊃ SU2 × U1 Wigner coefficients is formulated. The resolution of the outer multiplicity follows the prescription given by Biedenharn and Louck. It is shown that SU3 Racah coefficients can be obtained as a solution to a set of simultaneous equations with unknown coefficients given as a by-product of the initial steps in the SU3 ⊃ SU2 × U1 Wigner coefficient construction algorithm. A general expression for evaluating SU3 ⊃ R3 Wigner coefficients as a sum over a simple subset of the corresponding SU3 ⊃ SU2 × U1 …

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Differential And Stochastic Equations In Abstract Wiener Space, Hui Hsiung Kuo Jan 1973

Differential And Stochastic Equations In Abstract Wiener Space, Hui Hsiung Kuo

Faculty Publications

This paper studies the differential equation ( ∂ ∂t) u(t, x) = 1 2trace A(t, x) D2u(t, x) A*(t, x) + 〈σ(t, x), Du(t, x)〉 - V(x) u(t, x), u(0, x) = φ(x) in infinite dimensional space. A Kac's type representation of solution in terms of function space integral is proved. Kac's method is modified to work nicely regardless of the dimensionality. © 1973.

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On The Stochastic Maximum Principle In Banach Space, Hui Hsiung Kuo Jan 1973

On The Stochastic Maximum Principle In Banach Space, Hui Hsiung Kuo

Faculty Publications

No abstract provided.

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Stochastic Integrals In Abstruct Wiener Space Ii: Regularity Properties, Hui Hsiung Kuo Jan 1973

Stochastic Integrals In Abstruct Wiener Space Ii: Regularity Properties, Hui Hsiung Kuo

Faculty Publications

No abstract provided.

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Intrinsic Topologies In Topological Lattices And Semilattices, Jimmie D. Lawson Jan 1973

Intrinsic Topologies In Topological Lattices And Semilattices, Jimmie D. Lawson

Faculty Publications

This paper demonstrates that the topology of a compact topological lattice or semilattice can be defined intrinsically, i.e., in terms of the algebraic structure. Properties of various intrinsic topologies are explored. © 1973 Pacific Journal of Mathematics.

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On The Transition From Shell Structure To Collective Behavior. A Simplified Shell-Model Study, K. T. Hecht, J. B. Mcgrory, J. P. Draayer Dec 1972

On The Transition From Shell Structure To Collective Behavior. A Simplified Shell-Model Study, K. T. Hecht, J. B. Mcgrory, J. P. Draayer

Faculty Publications

To study the feasibility of carrying out shell-model calculations in nuclei with active protons and neutrons in different major shells, the following simple idealized model has been studied: (i) Proton and neutron configurations are chosen to be (f 5 2p 3 2p 1 2)np and (g 7 2d 5 2d 3 2s 1 2)nn, so that results for the separate proton and neutron basis states to be used in any approximation scheme can be compared with the results for exact shell-model calculations, (ii) The proton and neutron single-particle energies for these active shells are separately taken to be degenerate. (iii) …

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On Improved Wkb (Uniform Asymptotic) Quantum Conditions, Dunham Corrections, The Langer Modification, And Rkr Potentials, Russell T. Pack Dec 1972

On Improved Wkb (Uniform Asymptotic) Quantum Conditions, Dunham Corrections, The Langer Modification, And Rkr Potentials, Russell T. Pack

Faculty Publications

An improvement to the WKB quantum condition for the rotation-vibration levels of diatomic molecules, known empirically to give RKR potentials of increased accuracy and to account for the Dunham correction Y00, is derived using uniform asymptotic methods. The role of the Langer transformation in this problem is also discussed.

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Stochastic Integro-Differential Equations Of Volterra Type, William J. Padgett, Chris P. Tsokos Dec 1972

Stochastic Integro-Differential Equations Of Volterra Type, William J. Padgett, Chris P. Tsokos

Faculty Publications

No abstract provided.

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Nonnegative Matrices Whose Inverses Are M-Matrices, Thomas L. Markham Dec 1972

Nonnegative Matrices Whose Inverses Are M-Matrices, Thomas L. Markham

Faculty Publications

A characterization of a class of totally nonnegative matrices whose inverses are M-matrices is given. It is then shown that if A is nonnegative of order n and A^-1 is an M-matrix, then the almost principal minors of A of all orders are nonnegative.

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The Effects Of An Individualized Instruction Workshop And Its Related Follow-Up Program On The Attitudes And Behavior Of Selected Elementary Teachers And Their Students: Final Report, Helen Dell, Warren Kallenbach Nov 1972

The Effects Of An Individualized Instruction Workshop And Its Related Follow-Up Program On The Attitudes And Behavior Of Selected Elementary Teachers And Their Students: Final Report, Helen Dell, Warren Kallenbach

Faculty Publications

The effects of an individualized instruction workshop and its related follow-up program on the attitudes and behavior of selected elementary teachers and their students were discussed in this report. Participants were teachers in a four-day workshop on individualizing instruction. The workshop included training in classroom procedures, managing physical facilities, utilizing human resources, and developing techniques for encouraging students to be self-managing. Evaluation methods, questionnaires and observation indicated a favorable change in teacher behavior. The effects of the inservice program for teachers indicated little or no affect on student attitude and independent work habits. (Appendixes of related program material and a …

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Magnetic And Thermometric Properties Of Na3[Ce(C7h3no4)3] ·15h2o In The Millikelvin Range, Richard A. Webb, J. C. Wheatley Oct 1972

Magnetic And Thermometric Properties Of Na3[Ce(C7h3no4)3] ·15h2o In The Millikelvin Range, Richard A. Webb, J. C. Wheatley

Faculty Publications

Measurements of the 16-Hz susceptibility of a powdered Na3[Ce(C7H3NO4)3] · 15H2O (CDP) sample, in the shape of a right-circular cylinder with diameter equal to height, have been made as a function of the Johnson noise temperature TJ of a resistor in the range 2 to 20 mK. Pure liquid 3He was used for thermal contact between the CDP and the noise thermometer in a demagnetization cell. The results are compared with similar data for cerium magnesium nitrate (CMN). CDP appears, like CMN, to have an anomalously …

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X-Ray Diffraction Studies On Liquids At Very High Pressures Along The Melting Curve Ii. Sodium, Keith H. Brown, J. Dean Barnett Sep 1972

X-Ray Diffraction Studies On Liquids At Very High Pressures Along The Melting Curve Ii. Sodium, Keith H. Brown, J. Dean Barnett

Faculty Publications

Coherent x-ray diffraction patterns for liquid Na have been extracted from measured patterns at 0.5, 7.5, 17, and 43 kbar along the melting curve. The experimentally determined liquid structure factor and resulting radial distribution function are given at each pressure. The position of the principal x-ray intensity peak is reproducible to within 0.5% and shows shifts of the order of 12%. The resulting nearest neighbor distance in the radial distribution function also shifts 12% but is reproducible only to approximately 2%. The distribution functions obtained at points along the melting curve suggest a simple dimensional compression or scaling; however, a …

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X-Ray Diffraction Studies On Liquids At Very High Pressures Along The Melting Curve. I. Methods And Techniques, Keith H. Brown, J. Dean Barnett Sep 1972

X-Ray Diffraction Studies On Liquids At Very High Pressures Along The Melting Curve. I. Methods And Techniques, Keith H. Brown, J. Dean Barnett

Faculty Publications

A technique using the tetrahedral anvil high-pressure x-ray system has been developed to extract coherent x-ray intensity patterns of liquids near melting from measured scattering curves in the presence of high-background counts. Radial distribution functions for liquids along the melting curve to pressures of at least 50 kbar can be obtained. At each pressure scattering curves are recorded for the liquid and solid on opposite sides of the melting curve and a subtraction is made to eliminate background and incoherent scattering. Theoretical estimates of the thermal diffuse scattering from the solid are added to the appropriately corrected difference patterns to …

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Life - By Luck Or God?, C. Mervyn Maxwell Aug 1972

Life - By Luck Or God?, C. Mervyn Maxwell

Faculty Publications

No abstract provided.

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Β-Delayed Proton Decay Of 9c, David D. Allred, John E. Esterl, J. C. Hardy, R. G. Sextro, Joseph Cerny Jul 1972

Β-Delayed Proton Decay Of 9c, David D. Allred, John E. Esterl, J. C. Hardy, R. G. Sextro, Joseph Cerny

Faculty Publications

The delayed-proton spectrum following the β decay of 9C (t1/2=126.5±1.0 msec) was found to consist primarily of a continuum extending from 13 to 1.5 MeV, the latter being the lowest energy observed. In addition to the previously observed peaks at 9.28 and 12.30 MeV (C.M.), possible peaks between 3 and 7 MeV have been tentatively identified.

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On The Mechanism Of Low-Temperature Termolecular Atomic Recombination, Russell T. Pack, Richard L. Snow, Wesley D. Smith Jan 1972

On The Mechanism Of Low-Temperature Termolecular Atomic Recombination, Russell T. Pack, Richard L. Snow, Wesley D. Smith

Faculty Publications

A simple theory of gas-phase termolecular atomic recombination kinetics is presented which treats the bound-complex (BC) mechanism in a fashion which parallels the Roberts, Bernstein, and Curtiss resonance theory of the energy-transfer (ET) mechanism. The ET rate constant has a low temperature maximum, but the BC rate constant does not. The contributions of the two mechanisms to the low-temperature recombination of hydrogen atoms, with He, Ar, and H2 as third bodies, are estimated and compared. The presence (absence) of a low-temperature maximum in the observable total rate constant is determined by absence (presence) of bound vibrational levels of the hydrogen-third …

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Isopiestic Studies Of Some Aqueous Electrolyte Solutions At 80°C, John T. Moore Jan 1972

Isopiestic Studies Of Some Aqueous Electrolyte Solutions At 80°C, John T. Moore

Faculty Publications

No abstract provided.

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Stochastic Integrals In Abstract Wiener Space, Hui Hsiung Kuo Jan 1972

Stochastic Integrals In Abstract Wiener Space, Hui Hsiung Kuo

Faculty Publications

Let W(t, ω) be the Wiener process on an abstract Wiener space (i, H, B) corresponding to the canonical normal distributions on H. Stochastic integrals (formula presented) and (formula presented) are defined for non-anticipating transformations f with values in B(B, B) such that (x(t, ω) — I)(B) B* and C with values in H. Suppose (formula presented), where u is a non-anticipating transformation with values in H. Let fit, x be a continuous function on R x B, continuously twice differentiable in the indirections with D2 f(t, x) e H) for the x variable and once differentiable for the t …

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Greater Than Your Greatest Need, C. Mervyn Maxwell Aug 1971

Greater Than Your Greatest Need, C. Mervyn Maxwell

Faculty Publications

No abstract provided.

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High-Pressure Equation Of State For Nacl, Kcl, And Cscl, Daniel L. Decker Jul 1971

High-Pressure Equation Of State For Nacl, Kcl, And Cscl, Daniel L. Decker

Faculty Publications

A calculation of the equation of state for NaCl from a Mie-Grüneisen equation was repeated using more accurate values of the zero-pressure compressibility. It was also extended to KCl and CsCl. An analysis of this approach to pressure calibration indicates that it will yield pressures with about the same accuracy as can be presently achieved by experimental measurements above 25 kbar, and thus furnishes a temporary practical pressure scale.

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Lamb-Mössbauer Factor Of Sodium Ferrocyanide, Daniel L. Decker, L. E. Lortz Feb 1971

Lamb-Mössbauer Factor Of Sodium Ferrocyanide, Daniel L. Decker, L. E. Lortz

Faculty Publications

Using a set of commercially prepared sodium ferrocyanide absorbers enriched to 91.2% Fe57 the Lamb-Mössbauer factor was measured to be 0.28±0.03. The thickness of Fe57 for these absorbers was measured using x-ray absorption techniques and was found to be considerably smaller than that advertised by the manufacturer even after correcting for the size of the ferrocyanide particles in the absorbers.

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A Variable Coeficient Of Restitution Experiment On A Linear Air Track, R. Gruebel, James C. Dennis, L. Choate Jan 1971

A Variable Coeficient Of Restitution Experiment On A Linear Air Track, R. Gruebel, James C. Dennis, L. Choate

Faculty Publications

A system consisting of two pendula attached to an air cart is mathematically analyzed, and the coefficient of restitution is shown to pass through a deep minimum. The solution to the small angle equation of motion is transcendental and provides an exercise in graphical methods for the beginning mechanics student.

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High-Pressure Phase Studies On Sodium–Potassium Alloys, D. Ray Anderson, J. Bevan Ott, Rex J. Goates, H. Tracy Hall Jan 1971

High-Pressure Phase Studies On Sodium–Potassium Alloys, D. Ray Anderson, J. Bevan Ott, Rex J. Goates, H. Tracy Hall

Faculty Publications

The solid–liquid phase diagrams were investigated to 60 kbar for elemental sodium, potassium, and various sodium–potassium alloys. The data for Na and K are in general agreement with those of earlier workers. In the alloy system the temperatures of both the peritectic and eutectic halts increase as the pressure increases, but with different slopes, so that the two invariant points merge at approximately 35 kbar. Above this pressure, two halts are again observed. One increases with increasing pressure, and the other decreases with increasing pressure up to 55 kbar, where it abruptly starts increasing again. Melting points for samples in …

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Distribution List: Science Steering Group Final Report, Douglas E. Jones Jr. Mar 1970

Distribution List: Science Steering Group Final Report, Douglas E. Jones Jr.

Faculty Publications

List of the Mariner Venus Mercury Science Instrument teams.

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Rayleigh Hysteresis Shape: Its Relationship To Displacement Distance Of A Single Domain Wall In 50% Ni–Fe, R. C. Woodbury, M. R. Hunt Mar 1970

Rayleigh Hysteresis Shape: Its Relationship To Displacement Distance Of A Single Domain Wall In 50% Ni–Fe, R. C. Woodbury, M. R. Hunt

Faculty Publications

The need to measure the displacement distance of domain walls from equilibrium for very weak alternating fields (H ≪ coercive force) in bulk magnetic material has prompted a study of the possible use of the opening of the Rayleigh hysteresis loop to indicate the amount of wall displacement. This paper contains (1) a review of the theoretical relationship between hysteresis shape and the displacement distance of a domain wall, based upon defect-energy models of Rodbell and Bean, and Baldwin; and (2) an experimental approach which provides a measure of the wall displacements versus hysteresis shape for 50% Ni–Fe tape. Discrepancies …

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Asymptotic Evaluation Of Wkb Matrix Elements. Ii. Use Of Langer's Uniform Asymptotic Wavefunctions, Wesley D. Smith, Russell T. Pack Feb 1970

Asymptotic Evaluation Of Wkb Matrix Elements. Ii. Use Of Langer's Uniform Asymptotic Wavefunctions, Wesley D. Smith, Russell T. Pack

Faculty Publications

An improvement in a previous procedure for the analytic asymptotic evaluation of integrals arising in the quantum-mechanical theory of inelastic molecular collisions is presented. The integrals are evaluated using Langer's uniform asymptotic wavefunctions and the higher-order saddle-point or steepest-descents method. It is found that the Langer functions give no better results than WKB functions, but the higher-order steepest-descents corrections produce a marked improvement. The result is a simple method for evaluating a large class of integrals with an error of 0.1%-2.1%.

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Proposed Thermodynamic Pressure Scale For An Absolute High-Pressure Calibration, Daniel L. Decker, J. Dean Barnett Feb 1970

Proposed Thermodynamic Pressure Scale For An Absolute High-Pressure Calibration, Daniel L. Decker, J. Dean Barnett

Faculty Publications

The field of high pressure has developed rapidly over the past few years to a point where relatively sophisticated experiments are being attempted. In many experiments it is no longer sufficient to qualitatively estimate the pressure or to base conclusions on experimental results tied to an empirical pressure parameter. One desires to accurately know the pressure dependence of physical quantities related to a true thermodynamic scale.

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Su(4) ⊃ Su(2) ⊗ Su(2) Projection Techniques, J. P. Draayer Jan 1970

Su(4) ⊃ Su(2) ⊗ Su(2) Projection Techniques, J. P. Draayer

Faculty Publications

The twofold multiplicity problem associated with the Wigner supermultiplet reduction SU(4) ⊃ SU(2) ⊗ SU(2) is resolved by spin-isospin projection techniques analogous to the angular momentum projection technique introduced by Elliott to resolve the SU(3) ⊃ R(3) multiplicity problem. The projection quantum numbers, which furnish either an integer or half-integer characterization of the multiplicity, are assigned according to an (sT)-multiplicity formula derived from a consideration of the symmetry properties of spin-isospin degeneracy diagrams. An expression is obtained for the coefficients which relate the SU(4) ⊃ SU(2) ⊗ SU(2) projected basis states to states labeled according to the natural U(4) ⊃ …

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Lattices With No Interval Homomorphisms, J. D. Lawson Jan 1970

Lattices With No Interval Homomorphisms, J. D. Lawson

Faculty Publications

This paper arose from the following analogous questions: (1) Does a distributive topological lattice on a continuum admit sufficiently many continuous lattice homomorphisms onto the unit interval to separate points, and (2) does a topological semilattice on a continuum admit sufficiently many continuous semilattice homomorphisms onto the unit interval to separate points? Earlier investigations of topological lattices and semilattices have provided partial positive solutions. However, examples of an infinite-dimensional distributive lattice and a one-dimensional semilattice which admit only trivial homomorphisms into the interval are presented in this paper. © 1970 Pacific Journal of Mathematics.

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The Geomorphology Of The Glacial Valley Cross Section, William L. Graf Jan 1970

The Geomorphology Of The Glacial Valley Cross Section, William L. Graf

Faculty Publications

Several alpine valley systems in the southeastern Beartooth Mountains, Montana and Wyoming, have been examined using techniques similar to methods of stream system analysis. The general equation y = a x**b is the most adequate mathematical model for the cross valley profile; b values range between 1.5 and 2.0, indicating a parabolic form. As intensity of erosion increases in the glacial valley system, the b value also increases, indicating relatively deeper and narrower valley cross sections. The law of stream numbers, the law of stream lengths, and the bifurcation ratio, derived from fluvial geomorphology, are also applicable in glacial geomorphology.

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