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Cosmological Dynamics Of A Phantom Field, Parampreet Singh, M. Sami, Naresh Dadhich Jan 2003

Cosmological Dynamics Of A Phantom Field, Parampreet Singh, M. Sami, Naresh Dadhich

Faculty Publications

We study the general features of a dynamics of a phantom field in the cosmological context. In the case of an inverse coshyperbolic potential, we demonstrate that the phantom field can successfully drive the observed current accelerated expansion of the Universe with the equation of state parameter wφ< - 1. The de Sitter universe turns out to be the late time attractor of the model. The main features of the dynamics are independent of the initial conditions and the parameters of the model. The model fits the supernova data very well, allowing for - 2.4

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Action Principle Formulation For The Motion Of Extended Bodies In General Relativity, Jeeva Anandan, Naresh Dadhich, Parampreet Singh Jan 2003

Action Principle Formulation For The Motion Of Extended Bodies In General Relativity, Jeeva Anandan, Naresh Dadhich, Parampreet Singh

Faculty Publications

We present an action principle formulation for the study of the motion or an extended body in general relativity in the limit of a weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order coupling to the gravitational field. In particular, a new force due to the octupole moment is obtained. The action also yields the gravitationally induced phase shifts in quantum interference experiments due to the coupling of all multipole moments. ©2003 The American Physical Society.

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Proposal To Determine The Spectrum Of Pairing Glue In High-Temperature Superconductors, I. Vekhter, C. M. Varma Jan 2003

Proposal To Determine The Spectrum Of Pairing Glue In High-Temperature Superconductors, I. Vekhter, C. M. Varma

Faculty Publications

We propose a method for an analysis of the angle-resolved photoemission data in two-dimensional anisotropic superconductors which directly yields the spectral function of the bosons mediating Cooper pairing. The method includes a self-consistency check for the validity of the approximations made in the analysis. We explicitly describe the experimental data needed for implementing the proposed procedure. © 2003 The American Physical Society.

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Tail States In Clean Superconductors With Magnetic Impurities, A. V. Shytov, I. Vekhter, I. A. Gruzberg, A. V. Balatsky Jan 2003

Tail States In Clean Superconductors With Magnetic Impurities, A. V. Shytov, I. Vekhter, I. A. Gruzberg, A. V. Balatsky

Faculty Publications

We analyze the behavior of the density of states in a singlet [Formula presented]-wave superconductor with weak magnetic impurities in the clean limit. By using the method of optimal fluctuation and treating the order parameter self-consistently we show that the density of states is finite everywhere in the superconducting gap, and that it varies as [Formula presented] near the mean field gap edge [Formula presented] in a [Formula presented]-dimensional superconductor. In contrast to most studied cases the optimal fluctuation is strongly anisotropic. © 2003 The American Physical Society.

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Avoided Antiferromagnetic Order And Quantum Critical Point In [Formula Presented], A. Bianchi, R. Movshovich, I. Vekhter, P. G. Pagliuso, J. L. Sarrao Jan 2003

Avoided Antiferromagnetic Order And Quantum Critical Point In [Formula Presented], A. Bianchi, R. Movshovich, I. Vekhter, P. G. Pagliuso, J. L. Sarrao

Faculty Publications

We measured the specific heat and resistivity of heavy fermion [Formula presented] between the superconducting critical field [Formula presented] and 9 T, with the field in the [001] direction, and at temperatures down to 50 mK. At 5 T the data show a non-Fermi liquid (NFL) behavior down to the lowest temperatures. At the field above 8 T the data exhibit a crossover from the Fermi liquid to a non-Fermi liquid behavior. We analyzed the scaling properties of the specific heat and compared both the resistivity and the specific heat with the predictions of a spin-fluctuation theory. Our analysis leads …

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Tail States In Superconductors With Weak Magnetic Impurities, I. Vekhter, A. V. Shytov, I. A. Gruzberg, A. V. Balatsky Jan 2003

Tail States In Superconductors With Weak Magnetic Impurities, I. Vekhter, A. V. Shytov, I. A. Gruzberg, A. V. Balatsky

Faculty Publications

We analyze the behavior of the density of states in a singlet s-wave superconductor with weak magnetic impurities in the clean limit by using the method of optimal fluctuation. We show that the density of states varies as In N(E) ∝ |E - Δ|(7-d)/4 near the mean field gap edge Δ0 in a d-dimensional superconductor. The optimal fluctuation in d > 1 is strongly anisotropic. We compare the density of states with that obtained in other recent approaches. © 2002 Elsevier Science B.V. All rights reserved.

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From Laser-Induced Line Narrowing To Electromagnetically Induced Transparency: Closed System Analysis, H. Lee, Y. Rostovtsev, C. J. Bednar, A. Javan Jan 2003

From Laser-Induced Line Narrowing To Electromagnetically Induced Transparency: Closed System Analysis, H. Lee, Y. Rostovtsev, C. J. Bednar, A. Javan

Faculty Publications

The laser-induced line-narrowing effect, discovered more than thirty years ago, can also be applied to recent studies in high resolution spectroscopy based on electromagnetically induced transparency. In this paper we first present a general form of the transmission width of electromagnetically induced transparency in a homogeneously broadened medium. We then analyze a Doppler broadened medium by using a lorentzian function as the atomic velocity distribution. The dependence of the transmission linewidth on the driving field intensity is discussed and compared to the laser-induced line-narrowing effect. This dependence can be characterized by a parameter which can be regarded as "the degree …

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Zymogram With Remazol Brilliant Blue-Labeled Micrococcus Lysodeikticus Cells For The Detection Of Lysozymes: Example Of A New Lysozyme Activity In Formosan Termite Defense Secretions, Markus Hardt, Youzhong Guo, Gregg Henderson, Roger A. Laine Jan 2003

Zymogram With Remazol Brilliant Blue-Labeled Micrococcus Lysodeikticus Cells For The Detection Of Lysozymes: Example Of A New Lysozyme Activity In Formosan Termite Defense Secretions, Markus Hardt, Youzhong Guo, Gregg Henderson, Roger A. Laine

Faculty Publications

No abstract provided.

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Incremented Alkyl Derivatives Enhance Collision Induced Glycosidic Bond Cleavage In Mass Spectrometry Of Disaccharides, Sanford Mendonca, Richard B. Cole, Junhua Zhu, Yang Cai, Alfred D. French, Glenn P. Johnson, Roger A. Laine Jan 2003

Incremented Alkyl Derivatives Enhance Collision Induced Glycosidic Bond Cleavage In Mass Spectrometry Of Disaccharides, Sanford Mendonca, Richard B. Cole, Junhua Zhu, Yang Cai, Alfred D. French, Glenn P. Johnson, Roger A. Laine

Faculty Publications

Electrospray ionization and collision induced dissociation on a triple quadrupole mass spectrometer were used to determine the effect of spatial crowding of incremented alkyl groups of two anomeric pairs of peralkylated (methyl to pentyl) disaccharides (maltose/cellobiose and isomaltose/gentiobiose). Protonated molecules were generated which underwent extensive fragmentation under low energy conditions. For both the 1 → 4 and 1 → 6 α and β isomers, at comparable collision energies the methyl derivative exhibited the least fragmentation followed by ethyl, propyl, butyl, and pentyl. Collision energy is converted to rotational-vibrational modes in competition with bond cleavage, as represented by the slope of …

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Diesel Exhaust Particles Exert Acute Effects On Airway Inflammation And Function In Murine Allergen Provocation Models, Minqi Hao, Stephania Comier, Meiying Wang, James J. Lee, Andre Nel Jan 2003

Diesel Exhaust Particles Exert Acute Effects On Airway Inflammation And Function In Murine Allergen Provocation Models, Minqi Hao, Stephania Comier, Meiying Wang, James J. Lee, Andre Nel

Faculty Publications

Background: Epidemiologic studies show that sudden surges in ambient particulate matter (PM) levels can trigger acute asthma exacerbations. Although diesel exhaust particles (DEPs) act as an adjuvant for allergic sensitization, this is a delayed response and does not explain acute PM effects on airway hyperreactivity (AHR). Objective: Our aim was to determine the acute effects of DEPs on AHR using a mouse model. Methods: Three protocols were developed, 2 of which require OVA sensitization, whereas the third was OVA independent. In the mild sensitization protocol BALB/c mice receive intraperitoneal OVA without alum and are then challenged with aerosolized OVA with …

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Movement And Spatial Population Structure Of A Prairie Planthopper, James T. Cronin Jan 2003

Movement And Spatial Population Structure Of A Prairie Planthopper, James T. Cronin

Faculty Publications

The transfer of organisms among patches is a key process influencing the spatial structure and regional dynamics of a population; yet, detailed experimental studies of animal movement among patches are uncommon. I performed a series of mark-recapture studies to quantify the movement of a planthopper, Prokelisia crocea (Hemiptera: Delphacidae), among discrete patches of its host plant, prairie cordgrass (Spartina pectinata). Results from these dispersal studies were used to predict the natural distributions and to characterize the spatial population structure of P. crocea. Planthopper emigration loss per patch increased linearly with the density of female conspecifics and was nonlinearly related to …

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A Genome-Wide Scan For Body Mass Index Among Nigerian Families, Adebowale Adeyemo, Amy Luke, Richard Cooper, Xiaodong Wu, Bamidele Tayo, Xiaofeng Zhu, Charles Rotimi, Nourdine Bouzekri, Ryk Ward Jan 2003

A Genome-Wide Scan For Body Mass Index Among Nigerian Families, Adebowale Adeyemo, Amy Luke, Richard Cooper, Xiaodong Wu, Bamidele Tayo, Xiaofeng Zhu, Charles Rotimi, Nourdine Bouzekri, Ryk Ward

Faculty Publications

Objective: Interest in mapping genetic variants that are associated with obesity remains high because of the increasing prevalence of obesity and its complications worldwide. Data on genetic determinants of obesity in African populations are rare. Research Methods and Procedures: We have undertaken a genome-wide scan for body mass index (BMI) in 182 Nigerian families that included 769 individuals. Results: The prevalence of obesity was only 5%, yet polygenic heritability for BMI was in the expected range (0.46 ± 0.07). Tandem repeat markers (402) were typed across the genome with an average map density of 9 cM. Pedigree-based analysis using a …

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Erratum: A Genome-Wide Scan For Obesity In African-Americans (Diabetes (2002) 51 (541-544), X. Zhu, R. S. Cooper, A. Luke, G. Chen, X. Wu, D. Kan, A. Chakravarti, A. Weder Jan 2003

Erratum: A Genome-Wide Scan For Obesity In African-Americans (Diabetes (2002) 51 (541-544), X. Zhu, R. S. Cooper, A. Luke, G. Chen, X. Wu, D. Kan, A. Chakravarti, A. Weder

Faculty Publications

No abstract provided.

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Functionality Of Palm Oil As A Stabilizer In Peanut Butter, K. J. Aryana, A. V.A. Resurreccion, M. S. Chinnan, L. R. Beuchat Jan 2003

Functionality Of Palm Oil As A Stabilizer In Peanut Butter, K. J. Aryana, A. V.A. Resurreccion, M. S. Chinnan, L. R. Beuchat

Faculty Publications

Studies have shown that palm oil is an effective stabilizer in peanut butter. The objective of our investigation was to better define the role of palm oil as a stabilizer. Peanut butters without and with palm oil added at concentrations of 1.5, 2.0, and 2.5% (w/w of peanuts), and Fix-X™ (hydrogenated rapeseed and cottonseed oils as commercial control) were stored at 0, 21, 30, and 45°C for 23 wk. Palm oil improved the oil holding capacity (OHC) of peanut butters, but had no effect on their adhesiveness and hardness characteristics. The unstabilized and palm oil-stabilized peanut butters were not as …

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Influence Of Agronomic Hosts On The Susceptibility Of Helicoverpa Zea (Boddie) (Lepidoptera: Noctuidae) To Genetically Engineered And Non-Engineered Cottons, J. Gore, B. R. Leonard, R. H. Jones Jan 2003

Influence Of Agronomic Hosts On The Susceptibility Of Helicoverpa Zea (Boddie) (Lepidoptera: Noctuidae) To Genetically Engineered And Non-Engineered Cottons, J. Gore, B. R. Leonard, R. H. Jones

Faculty Publications

Field and laboratory studies evaluated the influence of selected crop hosts on Helicoverpa zea (Boddie) population dynamics in relation to genetically engineered Bt (Bollgard) and non-Bt cottons. Host specific H. zea colonies were initiated with a colony originally collected from sweet corn. The colony was allowed to complete one generation on meridic diet then split into cohorts and allowed to complete one generation on field corn, grain sorghum, soybean, cotton, or meridic diet in individual 29.5 ml plastic cups. During the first part of the study, larval developmental times, pupal weights, and survival were measured. H. zea survival was higher …

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Terpene-Induced Morphological Changes To Exoskeleton Of Formosan Subterranean Termites (Isoptera: Rhinotermitidae): Toxic Effects Of Cis-Nerol, Betty C.R. Zhu, Gregg Henderson, Huixin Fei, Xiao Ying, Roger A. Laine Jan 2003

Terpene-Induced Morphological Changes To Exoskeleton Of Formosan Subterranean Termites (Isoptera: Rhinotermitidae): Toxic Effects Of Cis-Nerol, Betty C.R. Zhu, Gregg Henderson, Huixin Fei, Xiao Ying, Roger A. Laine

Faculty Publications

The terpenoid, cis-nerol was found to be highly toxic to the Formosan subterranean termite, Coptotermes formosanus Shiraki. Morphological abnormalities were observed in the exoskeleton including the spiracles and trichoid sensilla using scanning electron microscopy after exposure of termites to cis-nerol for 2 h. Proteins were found in a water-soluble fraction collected from the whole termite body exposed to cis-nerol for 60 min. It appears that terpenoids cause damage to cell membranes resulting in a significant loss of proteins.

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A Representation Theorem For Recovering Contraction Relations Satisfying Wci, Zhaohui Zhu, Bin Li, Xi'an Xiao, Shifu Chen, Wujia Zhu Jan 2003

A Representation Theorem For Recovering Contraction Relations Satisfying Wci, Zhaohui Zhu, Bin Li, Xi'an Xiao, Shifu Chen, Wujia Zhu

Faculty Publications

A notion of an image structure associated with the canonical epistemic state is introduced. Based on it, we get a representation result for recovering contraction inference relations satisfying the condition weak conjunctive inclusion (wci) in terms of F-standard epistemic AGM states. In effect, this result establishes a representation theorem for belief contraction functions satisfying AGM postulates (k-1) - (k-7), and Rott's (wci) and (k-8c), and hence generalizes Rott's corresponding result in the finite framework. © 2002 Elsevier Science B.V. All rights reserved.

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Comparison Of Three Primary Aggregator Databases, Kelly D. Blessinger, Maureen Olle Jan 2003

Comparison Of Three Primary Aggregator Databases, Kelly D. Blessinger, Maureen Olle

Faculty Publications

This article explores the results of a study conducted by Louisiana State University Libraries to determine the strengths and weaknesses of three aggregator databases: EBSCO Academic Search Premier, Gale Expanded Academic ASAP, and ProQuest Research Library Core. Main ideas discussed are title coverage, full-text availability, and search features. It is hoped that this article will aid institutions in determining the acquisition of an aggregator database that best meets their institutional needs.

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Deterrents To Participation In Parenting Education, Debora C. Johnson, Betty C. Harrison, Michael F. Burnett, Peter Emerson Jan 2003

Deterrents To Participation In Parenting Education, Debora C. Johnson, Betty C. Harrison, Michael F. Burnett, Peter Emerson

Faculty Publications

The purpose of this study was to determine the deterrents to participation by adults in parenting education programs. The objectives were (a) to describe parents with children in selected day care facilities on selected sociodemographic characteristics, (b) to determine factors that deterred those parents from participating in parenting education, and (c) to determine if there was a relationship between selected sociodemographic characteristics and the parents' participation in parenting education programs. A simple random sample of parents was drawn from the accessible population. Factor analysis revealed five factors that deterred this population from participating in parenting education: Lack of Confidence, Lack …

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Packing Cycles In Graphs, Ii, Guoli Ding, Zhenzhen Xu, Wenan Zang Jan 2003

Packing Cycles In Graphs, Ii, Guoli Ding, Zhenzhen Xu, Wenan Zang

Faculty Publications

A graph G packs if for every induced subgraph H of G, the maximum number of vertex-disjoint cycles in H is equal to the minimum number of vertices whose deletion from H results in a forest. The purpose of this paper is to characterize all graphs that pack. © 2002 Elsevier Science (USA). All rights reserved.

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Multiplicative Renormalization And Generating Functions I, Nobuhiro Asai, Izumi Kubo, Hui Hsiung Kuo Jan 2003

Multiplicative Renormalization And Generating Functions I, Nobuhiro Asai, Izumi Kubo, Hui Hsiung Kuo

Faculty Publications

Let μ be a probability measure on the real line with finite moments of all orders. Apply the Gram-Schmidt orthogonalization process to the system {1, x, x2, . . ., xn, . . .} to get orthogonal polynomials Pn(x), n ≥ 0, which have leading coefficient 1 and satisfy (x-αn)Pn(x) = Pn+1(x) +ωnPn-1(x). In general it is almost impossible to use this process to compute the explicit form of these polynomials. In this paper we use the multiplicative renormalization to develop a new method for deriving generating functions for a large class of probability measures. From a generating function for …

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Optimization Of Resonances In Photonic Crystal Slabs, Robert P. Lipton, Stephen P. Shipman, Stephanos Venakides Jan 2003

Optimization Of Resonances In Photonic Crystal Slabs, Robert P. Lipton, Stephen P. Shipman, Stephanos Venakides

Faculty Publications

Variational methods are applied to the design of a two-dimensional lossless photonic crystal slab to optimize resonant scattering phenomena. The method is based on varying properties of the transmission coefficient that are connected to resonant behavior. Numerical studies are based on boundary-integral methods for crystals consisting of multiple scatterers. We present an example in which we modify a photonic crystal consisting of an array of dielectric rods in air so that a weak transmission anomaly is transformed into a sharp resonance.

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Tourmaline-Bearing Quartz Veins In The Baraboo Quartzite, Wisconsin: Occurrence And Significance Of Foitite And "Oxy-Foitite", L. Gordon Medaris, John H. Fournelle, Darrell J. Henry Jan 2003

Tourmaline-Bearing Quartz Veins In The Baraboo Quartzite, Wisconsin: Occurrence And Significance Of Foitite And "Oxy-Foitite", L. Gordon Medaris, John H. Fournelle, Darrell J. Henry

Faculty Publications

The alkali-deficient tourmaline, foitite [□(Fe2+2Al Al6Si6O18(BO3)3(OH 3(OH)], and associated hematite occur in quartz veins that cut the geon 17 Baraboo Quartzite in south-central Wisconsin. The bluish green prismatic crystals of tourmaline are chemically zoned from core to rim, with the cores being very aluminous, highly alkali-deficient and, in one sample, relatively magnesian. Electron-microprobe analyses demonstrate that the tourmaline has a prevailing alkali-deficient in the X site, which ranges from 49 to 87%, with a mean of 73%, making this the most alkali-deficient tourmaline reported to date. In one sample, high contents of Al (up to 7.7 Al apfu) and high …

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Binary Black Hole Initial Data For Numerical General Relativity Based On Post-Newtonian Data, Wolfgang Tichy, Bernd Brügmann, Manuela Campanelli, Peter Diener Jan 2003

Binary Black Hole Initial Data For Numerical General Relativity Based On Post-Newtonian Data, Wolfgang Tichy, Bernd Brügmann, Manuela Campanelli, Peter Diener

Faculty Publications

With the goal of taking a step toward the construction of astrophysically realistic initial data for numerical simulations of black holes, we for the first time derive a family of fully general relativistic initial data based on post-2-Newtonian expansions of the 3-metric and extrinsic curvature without spin. It is expected that such initial data provide a direct connection with the early inspiral phase of the binary system. We discuss a straightforward numerical implementation, which is based on a generalized puncture method. Furthermore, we suggest a method to address some of the inherent ambiguity in mapping post-Newtonian data onto a solution …

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Gauge Conditions For Long-Term Numerical Black Hole Evolutions Without Excision, Miguel Alcubierre, Bernd Brügmann, Peter Diener, Michael Koppitz, Denis Pollney, Edward Seidel, Ryoji Takahashi Jan 2003

Gauge Conditions For Long-Term Numerical Black Hole Evolutions Without Excision, Miguel Alcubierre, Bernd Brügmann, Peter Diener, Michael Koppitz, Denis Pollney, Edward Seidel, Ryoji Takahashi

Faculty Publications

Numerical relativity has faced the problem that standard 3+1 simulations of black hole spacetimes without singularity excision and with singularity avoiding lapse and vanishing shift fail early on due to the so-called slice stretching. We discuss lapse and shift conditions for the nonexcision case that effectively cure slice stretching and allow run times of [Formula Presented] and more. © 2003 The American Physical Society.

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Structure Of End States For A Haldane Spin Chain, M. Kenzelmann, G. Xu, I. A. Zaliznyak, C. Broholm, J. F. Ditusa, G. Aeppli, T. Ito, K. Oka, H. Takagi Jan 2003

Structure Of End States For A Haldane Spin Chain, M. Kenzelmann, G. Xu, I. A. Zaliznyak, C. Broholm, J. F. Ditusa, G. Aeppli, T. Ito, K. Oka, H. Takagi

Faculty Publications

Inelastic neutron scattering was used to probe edge states in a quantum spin liquid. The experiment was performed on finite length antiferromagnetic spin-1 chains in [Formula presented]. At finite fields, there is a Zeeman resonance below the Haldane gap. The wave-vector dependence of its intensity provides direct evidence for staggered magnetization at chain ends, which decays exponentially towards the bulk [[Formula presented] at [Formula presented]]. Continuum contributions to the chain-end spectrum indicate interchain segment interactions. We also observe a finite size blueshift of the Haldane gap. © 2003 The American Physical Society.

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Design-Dependent Loads In Topology Optimization, Blaise Bourdin, Antonin Chambolle Jan 2003

Design-Dependent Loads In Topology Optimization, Blaise Bourdin, Antonin Chambolle

Faculty Publications

We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S, which is the total work of the pressure and internal forces at the equilibrium displacement. In order to prevent …

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Decoherence In A Driven Three-Level System, A. R.P. Rau, Weichang Zhao Jan 2003

Decoherence In A Driven Three-Level System, A. R.P. Rau, Weichang Zhao

Faculty Publications

Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics, are handled through master equations for the density matrix. Master equations such as the Lindblad equation preserve the trace of this matrix. Viewing them as first-order time-dependent operator equations for the elements of the density matrix, a unitary integration procedure can be adapted to solve for these elements. A simple model for decoherence preserves the Hermiticity of the density matrix. A single, classical Riccati equation is the only one requiring numerical handling to obtain a full solution of the quantum evolution. The procedure is general, valid …

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Detectability Of Gravitational Waves From Sn 1987a, Giovanni Santostasi, Warren Johnson, Juhan Frank Jan 2003

Detectability Of Gravitational Waves From Sn 1987a, Giovanni Santostasi, Warren Johnson, Juhan Frank

Faculty Publications

We discuss the potential for the detection of gravitational waves from a rapidly spinning neutron star produced by supernova (SN) 1987A, taking the parameters claimed by Middleditch et al. at face value. Assuming that the dominant mechanism for spin-down is gravitational waves emitted by a freely precessing neutron star, it is possible to constrain the wobble angle, the effective moment of inertia of the precessing crust, and the crust cracking stress limit. Our analysis suggests that if the interpretation of the Middleditch data is correct, the compact remnant of SN 1987A may well provide a predictable source of gravitational waves …

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Galaxy Formation In Triaxial Halos: Black Hole-Bulge-Dark Halo Correlation, Amr A. El-Zant, Isaac Shlosman, Mitchell C. Begelman, Juhan Frank Jan 2003

Galaxy Formation In Triaxial Halos: Black Hole-Bulge-Dark Halo Correlation, Amr A. El-Zant, Isaac Shlosman, Mitchell C. Begelman, Juhan Frank

Faculty Publications

The masses of supermassive black holes (SBHs) show correlations with bulge properties in disk and elliptical galaxies. We study the formation of galactic structure within flat-core, mildly triaxial halos and show that these correlations can be understood within the framework of a baryonic component modifying the orbital structure in the underlying potential. In particular, we find that terminal properties of bulges and their central SBHs are constrained by the destruction of box orbits in the harmonic cores of dark halos and the emergence of progressively less eccentric loop orbits there. SBH masses, M •, should exhibit a tighter correlation with …

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