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1990

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Full-Text Articles in Physics

An Alternative Proof Of Some Relations Between Hydrogenic Matrix Elements, R. A. Swainson, Gordon W. F. Drake Jan 1990

An Alternative Proof Of Some Relations Between Hydrogenic Matrix Elements, R. A. Swainson, Gordon W. F. Drake

Physics Publications

A relationship between certain integrals of the product of two Laguerre polynomials is obtained. It is shown how this relationship, together with two known Hankel transforms, allows for an alternative derivation of some relations between matrix elements of r k for hydrogenic ions. A further relation, involving matrix elements of logarithmic functions, is obtained in a similar manner. © 1990 IOP Publishing Ltd.

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Expectation Values Of Rp For Arbitrary Hydrogenic States, Gordon W. F. Drake, R. A. Swainson Jan 1990

Expectation Values Of Rp For Arbitrary Hydrogenic States, Gordon W. F. Drake, R. A. Swainson

Physics Publications

Expectation values of rP for an arbitrary nl hydrogenic state are expressed in terms of state-independent coefficients that are determined by a simple recursion relation. Explicit results are given for negative P down to -16 and, by an algebraic transformation, for positive P up to 13. Closed-form expressions are obtained for the coefficients of the two highest-order terms in l multiplying each power of n. The result is an asymptotic expression valid for each P and sufficiently large l. © 1990 The American Physical Society.

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Bethe Logarithms For Hydrogen Up To N=20, And Approximations For Two-Electron Atoms, Gordon W. F. Drake, R. A. Swainson Jan 1990

Bethe Logarithms For Hydrogen Up To N=20, And Approximations For Two-Electron Atoms, Gordon W. F. Drake, R. A. Swainson

Physics Publications

Bethe logarithms accurate to 14 or 15 places to the right of the decimal are tabulated for all states of hydrogen up to n=20. Approximation methods for Rydberg states of two-electron atoms are discussed. © 1990 The American Physical Society.

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All-Electronic Peierls Instability In The Infinite-U Mean-Field Theory For The Hubbard Model, S. E. Barnes Jan 1990

All-Electronic Peierls Instability In The Infinite-U Mean-Field Theory For The Hubbard Model, S. E. Barnes

Physics Articles and Papers

It is shown, for a small hole doping relative to half filling, that the large-U limit of the Hubbard model (or J=0 limit of the t-J model) exhibits an all-electron Peierls instability towards a state with a charge-density wave. The resulting gap in the spinon spectrum renders the model an insulator.

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Spin-Disordered Ground State For A Nearly Half-Filled Hubbard Model, S. E. Barnes Jan 1990

Spin-Disordered Ground State For A Nearly Half-Filled Hubbard Model, S. E. Barnes

Physics Articles and Papers

Following Nagaoka, the ground state of the large-U nearly half-filled Hubbard model is ‘‘ferromagnetic.’’ However, because of the anisotropic exchange energy JA, the physical Nagaoka ground state is nondegenerate and comprises a totally disordered spin state, i.e., a linear combination of all possible spin arrangements. For this ground state the susceptibility is Pauli-like but of a magnitude associated with a narrow band of width ∼JA while the holons, i.e., the charge excitations, correspond to spinless fermions with a band of width 2zt. Associated with the spinon sector are very poorly defined spin waves, i.e., bosons, with a …

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Iron Compounds In Brazilian Pre-Columbian Pigments Identified By 57Fe Mossbauer Spectroscopy And X-Ray Powder Diffraction, F. F.T. De Araujo, M. A.B. De Araujo, R. B. Frankel, G. C. Papaefthymiou, V. W. Vieira Jan 1990

Iron Compounds In Brazilian Pre-Columbian Pigments Identified By 57Fe Mossbauer Spectroscopy And X-Ray Powder Diffraction, F. F.T. De Araujo, M. A.B. De Araujo, R. B. Frankel, G. C. Papaefthymiou, V. W. Vieira

Physics

Mossbauer spectroscopy and X-ray powder diffraction have been used to identify iron compounds in pre-Columbian pigments, probably used for art decorating, collected from the oldest archaeological site of Early Man presently known in American at Sao Raimundo Nonato, in Northeastern Brazil. The iron compounds were identified as being alpha-Fe203 (haematite) with full Morin transition supressed and small particles of alpha-FeOOH (goethite).

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Differential, Partial Cross Sections For Electron Excitation Of The Sodium 3p State, Xianming Han, G. W. Schwinn, A. Gallagher Jan 1990

Differential, Partial Cross Sections For Electron Excitation Of The Sodium 3p State, Xianming Han, G. W. Schwinn, A. Gallagher

Scholarship and Professional Work - LAS

Using a powerful laser-based experimental method, the cross section for electron excitation of Na(3S) atoms to the Na(3P) state has been decomposed into partial components with respect to changes in the spin and angular momentum of the atomic electron, and these partial cross sections are further reduced to their differential character with respect to the electron scattering angle. Partial, differential cross sections are reported for electron collision energies from threshold 2.1 to 3.6 eV, and compared to available calculations.

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Methyl Reorientation In Methylphenanthrenes. Ii. Solid-State Proton Spin-Lattice Relaxation In The 1-Ch3, 9-Ch3, And 1-Cd3, 9-Ch3 Systems, F B. Mallory, C. W. Mallory, K. G. Conn, Peter A. Beckmann Jan 1990

Methyl Reorientation In Methylphenanthrenes. Ii. Solid-State Proton Spin-Lattice Relaxation In The 1-Ch3, 9-Ch3, And 1-Cd3, 9-Ch3 Systems, F B. Mallory, C. W. Mallory, K. G. Conn, Peter A. Beckmann

Physics Faculty Research and Scholarship

We report proton Zeeman relaxation rates R as a function of temperature T at 8.5 and 53 MHz in polycrystalline 1,9-dimethylphenanthrene (1,9-DMP) and l-trideuteriomethyl-9-methylphenanthrene (1, 9-DMP[1-d3]). The data are interpreted using a Davidson-Cole spectral density for intramolecular reorientation and the implications of this are discussed. R vs T−1data for 1,9-DMP[1-d3] are used to determine the parameters that characterize the reorientation of the 9-methyl group. By assuming that the parameters characterizing the dynamics of the 9-methyl group are the same in 1,9-DMP and 1,9-DMP[1-d3], we subtract out the R vs T−1 contribution of the 9-methyl group in 1,9-DMP to …

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Mirrorless Optical Bistability In A Nonlinear Absorbing Dielectric Film, Kevin L. Stokes, Ashok Puri Jan 1990

Mirrorless Optical Bistability In A Nonlinear Absorbing Dielectric Film, Kevin L. Stokes, Ashok Puri

Physics Faculty Publications

The optical transmissivity of a mirrorless, nonlinear, absorbing dielectric thin film is investigated numerically. The dielectric function in the film region is dependent on the intensity of the electromagnetic field. Multivalued solutions of transmissivity as a function of incident power are calculated for the steady-state wave equation. The numerical solution is applied to two different model dielectric functions. As the absorption parameter is increased, larger values of incident intensity are required to switch the systems between stable output states. Also, the peak values of transmissivity are reduced as the absorption is increased.

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Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall Jan 1990

Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall

Collected Faculty and Staff Scholarship

Feynman’s path integral formulation of quantum mechanics is used to study the correlated electronic states of Na4–Na6. Two types of simulations are performed: in the first, the nuclei are allowed to move at finite temperature in order to find the most stable geometries. In agreement with previous calculations, we find that planar structures are the most stable and that there is significant vibrational amplitude at finite temperatures, indicating that the Born–Oppenheimer surface is relatively flat. In the second type of simulation, the nuclei are held fixed at symmetric and asymmetric geometries and the correlated electron density is found. Our results …

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Molecular View Of The Interfacial Adhesion In Aluminum‐Silicon Carbide Metal‐Matrix Composites, B. K. Rao, Puru Jena Jan 1990

Molecular View Of The Interfacial Adhesion In Aluminum‐Silicon Carbide Metal‐Matrix Composites, B. K. Rao, Puru Jena

Physics Publications

The binding energies, electron charge transfer,bond lengths, and core level shifts of Al‐Al, Al‐Si, Al‐C, and Si‐C dimers have been calculated self‐consistently using the linear combination of atomic orbitals‐molecular orbital theory. The exchange interactions are treated using the unrestricted Hartree–Fock theory and correlation corrections are included through the Möller–Plesset perturbation scheme up to fourth order. The results are used to understand the nature and strength of bonding at the interface of Al and SiC crystals. The strong bonding of Al‐C dimers compared to Al‐Al and Al‐Si is shown to be responsible for the aluminumcarbide formation at the interface. The charge …

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Effect Of Size And Dimensionality On The Magnetic Moment Of Transition Metals, Feng Liu, S. N. Khanna, P. Jena Jan 1990

Effect Of Size And Dimensionality On The Magnetic Moment Of Transition Metals, Feng Liu, S. N. Khanna, P. Jena

Physics Publications

The effect of size and dimensionality on the magnetic moments of Fe, Co, and Ni have been studied theoretically by confining the atoms to various structural forms such as chains, surfaces, and thin films. The size of these systems is controlled by limiting the number of atoms. A new first‐principles theory is developed that enables us to study the electron spin density of states and moments of atoms in clusters containing two to a few thousand atoms. The theory is based upon the elementary principles governing the tight binding and linear combination of atomic orbitals formulations. It contains no adjustable …

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Instrument Matrix Of The Four-Detector Photopolarimeter: Physical Meaning Of Its Rows And Columns And Constraints On Its Elements, R. M.A. Azzam Jan 1990

Instrument Matrix Of The Four-Detector Photopolarimeter: Physical Meaning Of Its Rows And Columns And Constraints On Its Elements, R. M.A. Azzam

Electrical Engineering Faculty Publications

The four-detector photopolarimeter (FDP) is an arrangement of four photodetectors for measuring the state of polarization of light. The output current vector I of the FDP is related to the input Stokes vector S by I = AS, where A is the instrument matrix. The rows of A can be viewed as projection operators that determine the output currents of the detectors. This leads to the recognition of four special totally polarized input states, each of which maximizes the output of one detector. The associated four orthogonal states produce minimum signals. Because each detector is absorptive and its output is …

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Specific-Heat Study Of The Anomalous Quantum Limit Of (Tmtsf)2clo4, Nathanael A. Fortune, J. S. Brooks, M. J. Graf, G. Montambaux, L. Y. Chiang, Jos A.A.J. Perenboom, D. Althof Jan 1990

Specific-Heat Study Of The Anomalous Quantum Limit Of (Tmtsf)2clo4, Nathanael A. Fortune, J. S. Brooks, M. J. Graf, G. Montambaux, L. Y. Chiang, Jos A.A.J. Perenboom, D. Althof

Physics: Faculty Publications

We report calorimetric measurements of the organic conductor (TMTSF)2ClO4 in the quantum limit. In addition to the field-induced spin-density-wave (FISDW) phases, we have measured the magnetic-field-dependent specific heat associated with the recently discovered reentrant phase. In terms of a semiempirical model, we find that the reentrant transition is second order, but that the electronic density of states is greatly reduced in the reentrant phase. We also observe a specific-heat signal corresponding to the anomalous fast oscillations which are known to coexist with the FISDW phases.

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Theoretical Intensity-Dependent Response Of Nonlinear Periodic Structures, Paul A. Gohman, Gust Bambakidis, Robert J. Spry Jan 1990

Theoretical Intensity-Dependent Response Of Nonlinear Periodic Structures, Paul A. Gohman, Gust Bambakidis, Robert J. Spry

Physics Faculty Publications

We have modeled the response of a nonlinear periodic structure by means of the Abelés 2×2 matrix method. Our structure differs from the usual rejection‐band filter designs, in that we have chosen the filter elements to be index matched in the absence of radiation, providing a rejection band that both grows and shifts as a function of incident intensity. The intensity output function of the model not only directly demonstrates optical bistability, but also limiting, switching, self‐pulsing, and chaos.

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In Situ Hall-Effect System For Real-Time Electron-Irradiation Studies, B. S. Ziebro, David C. Look, Joseph W. Hemsky, J. Rice Jan 1990

In Situ Hall-Effect System For Real-Time Electron-Irradiation Studies, B. S. Ziebro, David C. Look, Joseph W. Hemsky, J. Rice

Physics Faculty Publications

A unique system capable of taking in situ Hall‐effect measurements during electron irradiation has been developed. The key element is a small, powerful rare‐earth magnet. Measurements can be taken while the electron beam is on, resulting in a considerable time savings and eliminating problems associated with mounting and demounting the sample. High resolution electron concentration and mobility versus fluence data are quickly and easily obtained, making possible detailed defect production rate studies as functions of energy and flux.

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Review Of Hall Effect And Magnetoresistance Measurements In Gaas Materials And Devices, David C. Look Jan 1990

Review Of Hall Effect And Magnetoresistance Measurements In Gaas Materials And Devices, David C. Look

Physics Faculty Publications

The use of magnetic fields in the electrical characterization of semiconductor materials is familiar to everyone in the form of Hall‐effect measurements. However, there is another magnetic‐field‐based phenomenon, magnetoresistance (MR), which is highly useful but not nearly so familiar to the majority of workers. One of the unique features of MR measurements is their applicability to common device structures, in particular, field‐effect transistors (FETs) and contact‐resistance patterns. We will show how channel mobility information can be extracted from the MR data in metal‐semiconductor FETs (MESFETs) and modulation‐doped heterostructure FETs (MODFETs), and also how the material under ohmic contacts can be …

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Transition Probabilities And Franck-Condon Factors For The Second Negative Band System Of O2+, Jane L. Fox, Alexander Dalgarno Jan 1990

Transition Probabilities And Franck-Condon Factors For The Second Negative Band System Of O2+, Jane L. Fox, Alexander Dalgarno

Physics Faculty Publications

Transition probabilities for the second negative band system of O2+ are computed using the dipole transition moment presented by Wetmore et al. [1984]. Vibrational levels υ″ = 0 − 54 of the X²Πg ground state and υ′ = 0 − 33 of the excited A²Πu state are included. Franck-Condon factors for ionization-excitation of O2 (X³Σg−; υ = 0 − 25) to O2+(A²Πu;υ′ = 0 − 33) are also presented.

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A Signature Of Auroral Precipitation In The Nightside Ionosphere Of Venus, Jane L. Fox, H. A. Taylor Jr. Jan 1990

A Signature Of Auroral Precipitation In The Nightside Ionosphere Of Venus, Jane L. Fox, H. A. Taylor Jr.

Physics Faculty Publications

We show here that the densities of mass-28 ions measured by the Pioneer Venus Orbiter ion mass spectrometer (OIMS) on the nightside of Venus are highly variable and show little correlation with the values of the O+ densities. We have determined the total production rates of mass-28 ions in the chemical equilibrium region and find that this production rate cannot be explained by known chemical production reactions. We propose that the “excess” production is due to precipitation of electrons into the nightside thermosphere.

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Rotational Effects In The Continuous Vacuum-Ultraviolet Fluorescence Spectrum Of H2 Associated With Spontaneous Dissociation, H. Schmoranzer, T. Noll, E. Roueff, H. Abgrall, Ronald James Bieniek Jan 1990

Rotational Effects In The Continuous Vacuum-Ultraviolet Fluorescence Spectrum Of H2 Associated With Spontaneous Dissociation, H. Schmoranzer, T. Noll, E. Roueff, H. Abgrall, Ronald James Bieniek

Physics Faculty Research & Creative Works

The effects of rotational-vibrational interaction, and of rotational coupling between the B 2p u+1 and C 2p u1 electronic states, on the B X fluorescence continuum of H2 associated with spontaneous dissociation were investigated spectroscopically using monochromatized synchrotron radiation for selective excitation of rovibronic states. The rotational shifts and perturbations in the modulated continua intensities observed agree well with close-coupling and Jeffreys-Wentzel-Kromers-Brillouin (JWKB) calculations also performed and are explained in terms of nonadiabatic coupling effects and rainbow-interference structures. A straightforward experimental technique is described to detect mixed electronic states. © 1990 The American Physical Society.

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On The Linearization Stability Of The Conformally (Anti-) Self-Dual Einstein Equations, Charles G. Torre Jan 1990

On The Linearization Stability Of The Conformally (Anti-) Self-Dual Einstein Equations, Charles G. Torre

All Physics Faculty Publications

The Einstein equations with a cosmological constant, when restricted to Euclidean space‐times with anti‐self‐dual Weyl tensor, can be replaced by a quadratic condition on the curvature of an SU(2) (spin) connection. As has been shown elsewhere, when the cosmological constant is positive and the space‐time is compact, the moduli space of gauge‐inequivalent solutions to this equation is discrete, i.e., zero dimensional; when the cosmological constant is negative, the dimension of the moduli space is essentially controlled by the Atiyah–Singer index theorem provided the field equations are linearization stable. It is shown that linearization instability occurs whenever the unperturbed geometry possesses …

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A Study Of The Hydration Properties Of Selected Laser Dye Aerosols Including Continuous-Flow Parallel Plate And Alternating-Gradient Thermal Diffusion Cloud Chamber Measurements In The High Supersaturation Regime, Donald E. Hagen, Max B. Trueblood, Darryl J. Alofs Jan 1990

A Study Of The Hydration Properties Of Selected Laser Dye Aerosols Including Continuous-Flow Parallel Plate And Alternating-Gradient Thermal Diffusion Cloud Chamber Measurements In The High Supersaturation Regime, Donald E. Hagen, Max B. Trueblood, Darryl J. Alofs

Mechanical and Aerospace Engineering Faculty Research & Creative Works

The Hydration Behavior of Aerosols made Up of Various Fluorescent Dyes when Exposed to Water Saturation or Supersaturated Conditions Has Been Studied. Critical Supersaturation Spectra Are Reported. the Dyes Are Found to Behave as High Molecular Weight Ionic Compounds that Obey Kohler Theory. their Relevant Kohler Parameters Are Measured. This Study Makes Use of and Compares Results from the Isothermal Hazecontinuous-Flowand Alternating-Gradient Thermal Diffusion Cloud Chambers. the Ability of the Continuous-Flow Thermal Diffusion Chamber to Operate Correctly at High Supersaturations is Shown. © 1990 Elsevier Science Publishing Co., Inc.

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Measurement Of Magnetic Fluctuations By O-X Mode Conversion, L. L. Vahala, G. Vahala, N. Bretz Jan 1990

Measurement Of Magnetic Fluctuations By O-X Mode Conversion, L. L. Vahala, G. Vahala, N. Bretz

Electrical & Computer Engineering Faculty Publications

The possibility of measuring magnetic fluctuations in a fusion plasma is considered by examining the O→X mode conversion. Under certain conditions and with good angular resolution, this mode conversion can be attributed to the presence of magnetic fluctuations even though the level of these fluctuations is much lower than that of density fluctuations. Some nonideal effects such as mode polarization mismatch at the plasma edge are also discussed.

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Application Of The Results Of Carbon Pellet Modeling To The Problem Of Plasma Penetration, L. L. Vahala, A. G. El Cashlan, G. A. Gerdin, P. B. Parks Jan 1990

Application Of The Results Of Carbon Pellet Modeling To The Problem Of Plasma Penetration, L. L. Vahala, A. G. El Cashlan, G. A. Gerdin, P. B. Parks

Electrical & Computer Engineering Faculty Publications

The assumptions of the evaporation model for low-Z pellets interacting with magnetic fusion plasmas developed by Parks are tested. These assumptions are that the vapor density profile in the region adjacent to the pellet surface falls off with radial distance as r-α , where 5 <α<6, and that the ionization time for the transition between charge states זf (i.e., for r < ~3 sonic radii). The first assumption is tested by solving a two-parameter eigenvalue problem for the evaporation cloud in the region interior to the sonic radius; the results are found to be consistent with the low-Z evaporation model. The second assumption, that זzi «זf, is tested at the sonic radius using the results from atomic physics and the low-Z evaporation model. It is found that indeed זzi «זf for plasmas with parameters close to thermonuclear conditions (e.g. CIT), but not for those of smaller Tokamaks such as …

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Influence Of Copper Doping On The Performance Of Optically Controlled Gaas Switches, St. T. Ko, V. K. Lakdawala, K. H. Schoenbach, M. S. Mazzola Jan 1990

Influence Of Copper Doping On The Performance Of Optically Controlled Gaas Switches, St. T. Ko, V. K. Lakdawala, K. H. Schoenbach, M. S. Mazzola

Electrical & Computer Engineering Faculty Publications

The influence of the copper concentration in silicon-doped gallium arsenide on the photoionization and photoquenching of charge carriers was studied both experimentally and theoretically. The studies indicate that the compensation ratio (NCu/NSi) is an important parameter for the GaAs:Si:Cu switch systems with regard to the turn-on and turn-off performance. The optimum copper concentration for the use of GaAs:Si:Cu as an optically controlled closing and opening switch is determined.

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Oxidation-Reduction Behavior Of Undoped And Sr-Doped Lamno3: Defect Structure, Electrical Conductivity, And Thermoelectric Power, J. H. Kuo, Harlan U. Anderson, Don M. Sparlin Jan 1990

Oxidation-Reduction Behavior Of Undoped And Sr-Doped Lamno3: Defect Structure, Electrical Conductivity, And Thermoelectric Power, J. H. Kuo, Harlan U. Anderson, Don M. Sparlin

Materials Science and Engineering Faculty Research & Creative Works

Seebeck coefficient and electrical conductivity measurements were performed for undoped and Sr-doped LaMnO3 as a function of temperature and oxygen partial pressure. The results of electrical conductivity showed typical p-type behavior. As reduction proceeded, the electrical conductivity of these LaMnO3-based perovskites decreased with P 1 4O2. The analysis of the electrical conductivity data was performed by extending the defect model from a previous thermogravimetric (TG) study. The measured Seebeck coefficients were found to be positive except for the most reducing conditions when the decomposition into multiple phases occurred. The Heikes formula was adopted to interpret …

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Subshell Electron Capture In Collisions Of Fully Stripped Ions With He And H2 At Intermediate Energies, L. Meng, C. O. Reinhold, Ronald E. Olson Jan 1990

Subshell Electron Capture In Collisions Of Fully Stripped Ions With He And H2 At Intermediate Energies, L. Meng, C. O. Reinhold, Ronald E. Olson

Physics Faculty Research & Creative Works

Classical phase-space models of the hydrogen molecule and helium are utilized to study shell and subshell electron-capture processes in collisions of fully stripped ions on charge states from 1 to 15 with H2 and He at intermediate impact energies (20200 keV/amu). Autoionization after double electron capture is approximated and is found to be an important channel for high projectile charges. The resulting (n,l) distributions for proton impact of He and H2 as well as total capture cross sections are found to be in very good agreement with experimental data. l distributions for high projectile charges are also analyzed for …

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Improved Resolution Of A 6m Torodial Grating Monochromator, G. K. Wertheim, J. E. Rowe, D. Mark Riffe, N. V. Smith Jan 1990

Improved Resolution Of A 6m Torodial Grating Monochromator, G. K. Wertheim, J. E. Rowe, D. Mark Riffe, N. V. Smith

All Physics Faculty Publications

We report a modification of the AT&T Bell Laboratories 6m toroidal grating monochromator at the National Synchrotron Light Source at Brookhaven National Laboratory which provides greatly improved resolution at midrange without the use of a movable exit slit. This modification is based on detailed ray tracing calculation, using the precedures developed by Haber, Howells, and McKinney and Howells, modified to include the holographic correction terms to the focusing equations. To maintain the optimum resolution requires an exit slit assembly movable over a distance of ∼20 cm. However, we show that an additional fixed slit 16.8 cm closer to the grating …

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Cross Section, Robert Katz Jan 1990

Cross Section, Robert Katz

Robert Katz Publications

In radiobiology the term cross section is used in ways that depart from its original physical meaning. Some of these conceptual extensions represent significant distortions of the original concept. These distortions lead to the misinterpretation of experimental findings.

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Near-100% Production Of The Excited Be+ 1s22p Ion From Decay Of Be 1s2S22p, C. Denise Caldwell, Mark G. Flemming, Manfred O. Krause, Peter Van Der Meulen, Cheng Pan, Anthony F. Starace Jan 1990

Near-100% Production Of The Excited Be+ 1s22p Ion From Decay Of Be 1s2S22p, C. Denise Caldwell, Mark G. Flemming, Manfred O. Krause, Peter Van Der Meulen, Cheng Pan, Anthony F. Starace

Anthony F. Starace Publications

In examining the decay of photon-produced Be 1s2s2np(1P), n=2,3, we discovered that the vastly predominant decay mode is to the final excited ionic states Be+ 1s2np, rather than the ground state. For n=2, the 2p ion accounts for 95% of the total production, with Be+ 1s23p the other main contributor. For n=3, 3p is predominant, again with a very small fraction of 2s. The result for n=2 occurs as a consequence of the similarity between the 2s and …

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