Results Of Brown Research Articles

Classification of Toeplitz operators on hardy spaces of bounded domains in the plane

We construct an orthonormal basis for the class of square integrable functions on bounded domains in the plane in terms of the classical kernel functions in potential theory. Then we generalize the results of Brown and Halmos about algebraic properties of Toeplitz operators and Laurent operators on the unit disc to general bounded domains. This is a complete classification of Laurent operators and Toeplitz operators for bounded domains.

EXCITATION OF GRAVITY WAVES BY FINGERING CONVECTION, AND THE FORMATION OF COMPOSITIONAL STAIRCASES IN STELLAR INTERIORS

Fingering convection (or thermohaline convection) is a weak yet important kind of mixing that occurs in stably-stratified stellar radiation zones in the presence of an inverse mean-molecular-weight gradient. Brown et al. (2013) recently proposed a new model for mixing by fingering convection, which contains no free parameter, and was found to fit the results of direct numerical simulations in almost all cases. Notably, however, they found that mixing was substantially enhanced above their predicted values in the few cases where large-scale gravity waves, followed by thermo-compositional layering, grew spontaneously from the fingering convection. This effect is well-known in the oceanographic context, and is attributed to the excitation of the so-called "collective instability". In this work, we build on the results of Brown et al. (2013) and of Traxler et al. (2011b) to determine the conditions under which the collective instability may be expected. We find that it is only relevant in stellar regions which have a relatively large Prandtl number (the ratio of the kinematic viscosity to the thermal diffusivity), $O(10^{-3})$ or larger. This implies that the collective instability cannot occur in main sequence stars, where the Prandtl number is always much smaller than this (except in the outer layers of surface convection zones where fingering is irrelevant anyway). It could in principle be excited in regions of high electron degeneracy, during He core flash, or in the interiors of white dwarfs. We discuss the implications of our findings for these objects, both from a theoretical and from an observational point of view.

Every operator has almost-invariant subspaces

We show that any bounded operator T on a separable, reflexive, infinite-dimensional Banach space X admits a rank-one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we show that the same is true for operators which have non-eigenvalues in the boundary of their spectrum. In the Hilbert space, our methods produce perturbations that are also small in norm, improving on an old result of Brown and Pearcy.

Determination of Fundamental Properties of an M31 Globular Cluster from Main-Sequence Photometry

ABSTRACTM31 globular cluster B379 is the first extragalactic cluster whose age was determined by main-sequence photometry. In the main-sequence photometric method, the age of a cluster is obtained by fitting its color-magnitude diagram (CMD) with stellar evolutionary models. However, different stellar evolutionary models use different parameters of stellar evolution, such as range of stellar masses, different opacities and equations of state, and different recipes, and so on. So, it is interesting to check whether different stellar evolutionary models can give consistent results for the same cluster. Brown et al. constrained the age of B379 by comparing its CMD with isochrones of the 2006 VandenBerg models. Using SSP models of Bruzual & Charlot and its multiphotometry, ZMa et al. independently determined the age of B379, which is in good agreement with the determination of Brown et al. The models of Bruzual & Charlot are calculated based on the Padova evolutionary tracks. It is necessary to check whether the age of B379 as determined based on the Padova evolutionary tracks is in agreement with the determination of Brown et al.. In this article, we redetermine the age of B379 using isochrones of the Padova stellar evolutionary models. In addition, the metal abundance, the distance modulus, and the reddening value for B379 are reported. The results obtained are consistent with the previous determinations, which include the age obtained by Brown et al. This article thus confirms the consistency of the age scale of B379 between the Padova isochrones and the 2006 VandenBerg isochrones; i.e., the comparison between the results of Brown et al. and Ma et al. is meaningful. The results reported in this article of values found for B379 are: metallicity [M/H] = log(Z/Z⊙) = -0.325, age τ = 11.0 ± 1.5 Gyr, reddening E(B - V) = 0.08, and distance modulus (m - M)0 = 24.44 ± 0.10.

Is “Absorb Knowledge” An Improper Collocation?

Collocation is practically very tough to Chinese English learners. The main reason lies in the fact that English and Chinese belong to two distinct language systems. And the deep reason is that learners tend to develop different metaphorical concept in accordance with distinct ways of thinking in Chinese. The paper, taking “absorb knowledge” as an example, intend to explore how to present the potential collocation patterns of “knowledge”in the learner’s dictionary for Chinese learners, based on a series of search results of BROWN and LOB as well as CLEC, by comparing the usual combinational patterns of “knowledge”of Chinese learners and English native speakers.

Brown measures of sets of commuting operators in a type II 1 factor

Using the spectral subspaces obtained in [U. Haagerup, H. Schultz, Invariant subspaces of operators in a general II 1-factor, preprint, 2005], Brown's results (cf. [L.G. Brown, Lidskii's theorem in the type II case, in: H. Araki, E. Effros (Eds.), Geometric Methods in Operator Algebras, Kyoto, 1983, in: Pitman Res. Notes Math. Ser., vol. 123, Longman Sci. Tech., 1986, pp. 1–35]) on the Brown measure of an operator in a type II 1 factor ( M , τ ) are generalized to finite sets of commuting operators in M . It is shown that whenever T 1 , … , T n ∈ M are mutually commuting operators, there exists one and only one compactly supported Borel probability measure μ T 1 , … , T n on B ( C n ) such that for all α 1 , … , α n ∈ C , τ ( log | α 1 T 1 + ⋯ + α n T n − 1 | ) = ∫ C n log | α 1 z 1 + ⋯ + α n z n − 1 | d μ T 1 , … , T n ( z 1 , … , z n ) . Moreover, for every polynomial q in n commuting variables, μ q ( T 1 , … , T n ) is the push-forward measure of μ T 1 , … , T n via the map q : C n → C . In addition it is shown that, as in [U. Haagerup, H. Schultz, Invariant subspaces of operators in a general II 1-factor, preprint, 2005], for every Borel set B ⊆ C n there is a maximal closed T 1 - , … , T n -invariant subspace K affiliated with M , such that μ T 1 | K , … , T n | K is concentrated on B. Moreover, τ ( P K ) = μ T 1 , … , T n ( B ) . This generalizes the main result from [U. Haagerup, H. Schultz, Invariant subspaces of operators in a general II 1-factor, preprint, 2005] to n-tuples of commuting operators in M .

LAMPREYS FEEL THE PRESSURE

It's a tough life for a river lamprey. Not only do these primitive fish have to swim upstream from the sea to the freshwater streams where they spawn and then die, they also have to cope with changes in water composition along the way. Because they are immersed in water, any change in the environment's saltiness affects lampreys' body fluid volume. In salty surroundings the fish lose water by osmosis, while splashing in a freshwater stream has the opposite effect. Now a study by Anne Brown has shed light on how lampreys achieve this tricky balance (p. 223).Most fish cope with changes in the environment's saltiness using the renin-angiotensin system, a protein network that regulates body fluid volume in virtually all vertebrates. When blood volume drops, renin triggers production of the active form of angiotensin. Angiotensin counteracts body fluid decreases by constricting blood vessels and encouraging the animal to drink. Until recently, lamprey osmotic regulation was a mystery, as they did not appear to have a renin-angiotensin system. When the system was finally discovered in lampreys, Brown was determined to find out how it responds to changes in body fluid volume and osmotic pressure.Studying river lampreys in the UK is problematic as they are a protected species, but the Ringkøbing Fjord in Denmark provided an excellent source of experimental creatures. To see how the animals responded to changes in body fluid volume, Brown removed up to 40% of the lampreys' blood. She found that the renin-angiotensin system became activated, and circulating active angiotensin levels rapidly doubled. When she injected lampreys with extra blood-like fluid, angiotensin levels dropped. Intriguingly, she found that salty fluid injections did not affect angiotensin levels. This suggests that the effects of increased body fluid volume are counteracted to some extent by increased saltiness.Brown also tested the effects of changing the environment's saltiness. Since the fjord's saltiness lies between freshwater and seawater, Brown could see how these migrating lampreys respond to osmotic pressure changes simply by moving the lampreys from saltwater to freshwater and vice versa. When she moved fish from freshwater to seawater, their angiotensin levels increased,but the reverse move caused angiotensin to drop. So the lamprey's renin-angiotensin system responds to both changes in volume and osmotic pressure, similar to the systems in bony fish like trout.Brown suspects that volume detectors within the fish may regulate the lamprey renin-angiotensin system, and that osmotic receptors (detecting saltiness) modulate the volume detectors' effects. But while most vertebrates have a kidney-based renin supply, renin-releasing cells have not yet been found in the lamprey kidney. The location of the lamprey's renin-producing cells remains a mystery for now.Since lampreys are primitive animals, Brown's results show that the renin-angiotensin system is an ancient and highly conserved blood volume regulation mechanism. After her adventures with lampreys in Danish fjords,Brown plans to study the renin-angiotensin system in the even more primitive hagfish. `Studying the hagfish would give us deeper insights into the origin of this system,' suggests Brown, `by taking us one step further back in evolutionary history.'

Multivariate dispersive ordering of epoch times of nonhomogeneous Poisson processes

In this paper we find conditions under which the epoch times of two nonhomogeneous Poisson processes are ordered in the multivariate dispersive order. Some consequences and examples of this result are given. These results extend a recent result of Brown and Shanthikumar (1998).

Noncommutative Pressure and the Variational Principle in Cuntz–Krieger-type C*-Algebras

Let a be a self-adjoint element of an exact C*-algebra A and θ:A→A a contractive completely positive map. We define a notion of dynamical pressure Pθ(a) which adopts Voiculescu's approximation approach to noncommutative entropy and extends the Voiculescu–Brown topological entropy and Neshveyev and Størmer unital-nuclear pressure. A variational inequality bounding Pθ(a) below by the free energies hσ(θ)+σ(a) with respect to the Sauvageot–Thouvenot entropy hσ(θ) is established in two stages via the introduction of a local state approximation entropy, whose associated free energies function as an intermediate term. Pimsner C*-algebras furnish a framework for investigating the variational principle, which asserts the equality of Pθ(a) with the supremum of the free energies over all θ -invariant states. In one direction we extend Brown's result on the constancy of the Voiculescu–Brown entropy upon passing to the crossed product, and in another we show that the pressure of a self-adjoint element over the Markov subshift underlying the canonical map on the Cuntz–Krieger algebra OA is equal to its classical pressure. The latter result is extended to a more general setting comprising an expanded class of Cuntz–Krieger-type Pimsner algebras, leading to the variational principle for self-adjoint elements in a diagonal subalgebra. Equilibrium states are constructed from KMS states under certain conditions in the case of Cuntz–Krieger algebras.

A counterexample to questions on the integrality property of virtual signature

Wall (1961), defined the virtual Euler Characteristic χ(Γ) of an arbitrary group Γ of finite homological type as χ(Γ)=χ(Γ′)/[Γ:Γ′]∈Q, where Γ′ is any torsion free subgroup of finite index in Γ. Analogous to virtual Euler Characteristic, we define the Virtual signature of an oriented virtual Poincare Duality group, a rational number. We show that two of Ken Brown's results on questions regarding the integrality property of virtual Euler Characteristics when formulated in the Virtual signature case is false.

New results of some existence theorems on nonlinear boundary value problems

With the use of the homeomorphism theory and fixed point theory, the existence and uniqueness of solutions to boundary value problems are investigated. Two basic theorems are obtained without the boundness condition, which generalizes results of Brown. When our results are applied to the existence and uniqueness of periodic solutions for nonlinear perturbed conservative systems (Newtonian equations of motion), the existence and uniquenes of the solution are obtained. The results in this note seem less restrictive than those of the former papers we have seen. Meanwhile, as far as we know, it seems that applying the homeomorphism theory to the research of this kind of problem is new.

On cyclicity in weighted Dirichlet spaces

We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0 < α < 1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.

How to derive flux control coefficients from the rate equations of classical enzyme kinetics.

A recent report by Brown and Cooper demonstrated the usefulness of calculating "flux control coefficients" for each of the rate constants involved in the assumed kinetic mechanism of a single enzyme. The calculations of Brown and Cooper involved numerical differentiation. The present article substantiates this report by showing that the numerical results of Brown and Cooper can also be obtained in an explicit form. The analytical equations given establish the relationship between rigorously specified overall rate processes and "elementary rate constants," both being defined by the rate equations of classical enzyme kinetics. It is shown that analytical flux control coefficients can be obtained for all types of rate processes considered in classical enzyme kinetics, including, "initial rates," equilibrium exchange reactions, and reactions at limiting levels of substrate (and/or product) saturation. By restricting the discussion to strictly consecutive (ordered, unbranched, linear) mechanisms, the line of reasoning can be presented in a relatively simple form. The main conclusions are the following: (a) It is advantageous to carry out the analysis in terms of paired (conjugated) control coefficients. (b) Flux control analysis of "elementary rate constants" does not require any extra kinetic argument. (c) Neither the immediate aim nor the results of the presented type of analysis are directly relevant to theories of metabolic control. On the contrary, the type of control analysis considered completes classical enzyme kinetics with a new facet. (d) For illustrating its usefulness, the concept of flux control coefficients is applied to the problem of optimization of enzyme activity.

Habakkuk (review)

Book Reviews 135 to her "judging" Israel. Instead he assigns the role of leader to the less than impressive Barak: apparently "even a bad male leader is better than a good female leader" (p. 81). Josephus does not actually portray Jephthah 's daughter negatively, but neither does he give much attention to her story. He depicts her as dutiful toward her father and her country, and he subtly shapes this depiction to make it suit his particular audience (for example, by echoing the Greek story of Iphegenia, who was devoted to Artemis in exchange for her father's victory over the Trojans). Josephus adds the apologetic note that God did not approve ofJephthah's act, and that it was illegal according to the Jewish scriptures. In recounting the story of Hannah, Josephus omits any reference to the taunting of Peninnah, leaving the reader to infer that her vexation was due solely to her frantic obsession with having a child. He emphasizes Hannah's subordination to Elkanah, and he omits any reference to her nursing of Samuel. Josephus's expanded depiction of the witch of Endor, on the other hand, greatly magnifies her positive traits. In his account the witch exemplifies the Roman ideals of clementia and humanitas. Josephus even describes her slaughter of her fatted calf for Samuel in terms echoing Nathan's parable of the poor man and the ewe (2 Sam 12:1-14). He adds a lengthy epilogue in which he commends her virtues and encourages others to emulate her example. Brown suggests that Josephus depicts the witch so positively in an attempt to appeal to his educated pagan audience, "for which the occult was fashionable," and whose members "would have seen no incongruity in a necromancer being of such exemplary character" (p. 204). Brown reads the texts carefully, and ably correlates the data she uncovers with knowledge from other sources of this era. Some readers may find the book a bit repetitive (with numerous summaries and conclusions, perhaps reflecting the work's origin as a dissertation), but others will welcome these clear restatements of Brown's results. Brown has made a perceptive' and interesting contribution to our knowledge of attitudes toward women in the biblical world. Susan R. Garrett Yale Divinity School Habakkuk, by Robert D. Haak. ieiden: E. J. Brill, 1992. 177 pp. $57.25. This book is a revision of Haak's Ph.D. dissertation (University of Chicago Divinity School, G. W. Ahlstrom [advisor]). Firmly rooted in the 136 SHOFAR Spring 1994 Vol. 12, No.3 historical-critical approach, Haak searches for an understanding of the historical (original) message of Habakkuk. Since such a message is fully intelligible only in the context of the historical situation in which it was created, Haak also studies the social and historical circumstances of the late monarchic period, which is, according to Haak, the time of Habakkuk's message. Haak first discusses the state of the masoretic text of Habakkuk and compares it especially with ancient Hebrew texts and Greek versions. His goal here is to develop general guidelines for the reconstruction of the original text of Habakkuk. Haak's conclusions are similar to those ofD. N. Freedman and others who maintain the general priority of the consonantal masoretic text (hereafter MT), but not necessarily that of the vocalization tradition attested in the MT. Haak next approaches the issue of the genre of the prophecy of Habakkuk. He concludes that the prophecy should be characterized as a complaint, and that the woe oracles (2:6-19) and the psalm (3:2-19) are expanded sections that are integral to the complaint. Haak then presents a translation of his proposed late monarchic text of the prophecy of Habakkuk. He also provides a comprehensive set of notes (pp. 29-106) that explain the textual and interpretive decisions reflected in the translation. It is impossible to summarize in a few lines the many discussions presented there. It is worth noting, however, that Haak's translation of the reconstructed original text strongly disagrees in numerous instances with the "usual" English translations of Habakkuk. Haak then moves to discussion of the political and social history of the late monarchic period in order to...

A Fredholm operator approach to Morita equivalence

Given C∗-algebras A and B and an imprimitivity A-B-bimodule X, we construct an explicit isomorphism X∗:Ki(A) → Ki(B) where Ki denote the complexK-theory functors for i = 0, 1. Our techniques do not require separability nor existence of countable approximate identities. We thus extend, to general C∗-algebras, the result of Brown, Green and Rieffel according to which strongly Morita equivalent C∗-algebras have isomorphic K-groups. The method employed includes a study of Fredholm operators on Hilbert modules.

Faculty and student perceptions of effective clinical teachers

This extension study was conducted to (1) identify which characteristics of the effective clinical teacher are deemed most important by nursing students and faculty; (2) determine whether previous findings remain valid (are transferable); and (3) investigate whether the perception of effective teaching behavior shifts as students advance toward graduation. The research tool, a two-part questionnaire developed by Brown, was circulated among students and instructors at a university college of nursing in southwestern Ohio. The first section listed 20 characteristics of teachers to be rated, using a Likert-type scale, from "of most importance" to "of no importance." The second section required subjects to select and rank in order the five most important characteristics from the list of 20. Descriptive analysis was applied to the data, and findings were compared with those of Brown. The study suggests that both faculty and students favor articulate, knowledgeable clinical instructors who are "objective and fair" in student evaluation. There is a high degree of similarity between the responses of faculty and students, but differences emerge. Both value skills involving the student-faculty relationship over skills centering on the professional or personal attributes of the instructor. However, faculty respondents appear to place a higher value on instructor interest in patients, and students are more concerned with communication-related attributes. Faculty members place a greater value on showing interest in patients than do students. The results, when compared with Brown's findings, appear largely transferable, but significant differences appear. For example, faculty members ranked characteristics dealing with the clinical instructor's relationship with students to be more important than those dealing with professional competence--the opposite of Brown's results. This study shows the need for nursing institutions to implement programs to foster and to promote uniformly identified effective clinical teaching characteristics. Given the special challenges of clinical nursing education, graduate programs should also seek to teach the skills identified as most effective, and persons with the skills perceived as effective should be urged to enter clinical instruction and should be rewarded for success in this important area.

On subsets of abelian groups with no 3-term arithmetic progression

A short proof of the following result of Brown and Buhler is given: For any ϵ > 0 there exists n 0 = n 0( ϵ) such that if A is an abelian group of odd order | A| > n 0 and B ⊆ A with | B| > ϵ| A|, then B must contain three distinct elements x, y, z satisfying x + y = 2 z.

REMARKS ON UNIVERSAL COEFFICIENT THEOREMS FOR GENERALIZED HOMOLOGY THEORIES

Abstract New proofs of universal coefficient theorems for generalized homology theories (cf. ∮ 2, ∮ 3) including L. G. Brown's result, relating Brown-Douglas-Fillmore's Ext (X) with complex K-theory are presented. They are all based on a theorem asserting the existence of a chain functor for a generalized homology theory (cf. ∮ 1), which was originally designed for the construction of strong homology theories on strong shape categories.

Reliability Bounds for Exponential Mixtures

We obtain some new reliability bounds for the class of life distributions which are exponential mixtures. It is shown that our bounds often improve on the usual DFR upper bound as well as those contained in the recent results of Shaked, Heyde and Leslie, Hall , and Brown. Simple sufficient conditions, under which such is the case, are developed. The main thrust of our findings is that our bounds are tighter for moderate to heavy departures from exponentiality. Among other results, it is shown that every DFR survival probability with a finite mean is stochastically strictly dominated by an exponential mixture. An application of our methods yields a new bound on the tail of the equilibrium distribution of a DFR renewal process, which can be tighter than the corresponding results of Brown.

The main problem of lunar theory solved by the method of Brown

Brown's method for solving the main problem of lunar theory has been adapted for the computation by machine with the help of an algebraic processor. Brown's results are first recovered and refined. The solution is then expanded to include most terms of order nine. The terms in the series for the longitude and latitude are listed with an accuracy of 0.000 01“ and of 0.000 001” for the parallax.