On the deleted squares of lens spaces

The configuration space $F_2 (M)$ of ordered pairs of distinct points in a manifold $M$, also known as the deleted square of $M$, is not a homotopy invariant of $M$: Longoni and Salvatore produced examples of homotopy equivalent lens spaces $M$ and $N$ of dimension three for which $F_2 (M)$ and $F_2 (N)$ are not homotopy equivalent. In this paper, we study the natural question whether two arbitrary $3$-dimensional lens spaces $M$ and $N$ must be homeomorphic in order for $F_2 (M)$ and $F_2 (N)$ to be homotopy equivalent. Among our tools are the Cheeger--Simons differential characters of deleted squares and the Massey products of their universal covers.Comment: 27 pages, 10 figure

An Alternative Derivation of the Nimbus 7 Total Solar Irradiance Variations

Nimbus 7 solar irradiance values have been made available to the scientific community through the open literature (e.g., Hickey et al., 1988) and through NASA data centers. A comparison of these measurements to the Solar Maximum Mission/Active Cavity Radiometer Irradiance Monitor (SSM/ACRIM) time series indicated differences which might be caused in part by the method of converting the Nimbus 7 raw data counts to solar irradiance values. In an effort to see if the derivation of the solar irradiance could be improved, the raw counts were extracted from the tapes and analyzed to see how a new algorithm could be constructed. The basic form of the calibration remains the same as in the previous solar irradiance derivations. However, the input values to the equation differ from what was used before. In particular, improved values of the Earth-sun distance are incorporated and new temperature sensitivities were derived. Several problems with the instrument were uncovered which previously had not been noticed. The sun did not appear to cross the center of field of the radiometer but was systematically off by 1.5 to 2.5 degrees. The analog to digital convertor changed its properties in July 1980. The gain of the electronics apparently increased by 0.03 percent in September 1987. Applying these and other changes in the processing, the day to day variations appear much more like the SMM observations. In fact, the Nimbus 7 observations are sufficiently stable that a problem with the SSM observations in the spin mode period of 1981 to 1984 can be detected when the two time series are compared

Computation and analyses of averaged monthly zonal albedos at the top of the atmosphere using Nimbus-7 ERB observed data

The Nimbus-7 ERB experiment measures the Earth's albedo from a satellite in a fixed Sun synchronous orbit. The data is obtained at a fixed time of the day for each latitude observed. For Earth Radiation Budget studies it is normally assumed that the observed scene is invariant during the day and that the albedo varies only with the solar zenith angle. This paper presents a technique for computing mean zonal albedos as a function of the albedo (A sub s) of cloud free atmosphere, the albedo (A sub c) of cloudy atmosphere and of the cloud fractions. The values of A sub s and A sub c are obtained from radiation transfer theory and climatological values of the surface and cloud albedos. The albedos are a function of the solar zenith angle, latitude and solar declination. The cloud fractions are measured from the Nimbus-7 ERB albedos. The present study shows the importance of taking into account latitude variations in surface types and in cloud cover

Advertising and Collusion in Retails Markets

We consider non-price advertising by retail firms that are privately informed as to their respective production costs. We first analyze a static model. We construct an advertising equilibrium, in which informed consumers use an advertising search rule whereby they buy from the highest-advertising firm. Consumers are rational in using the advertising search rule, since the lowest-cost firm advertises the most and also selects the lowest price. Even though the advertising equilibrium facilitates productive efficiency, we establish conditions under which firms enjoy higher expected profit when advertising is banned. Consumer welfare falls in this case, however. We next analyze a dynamic model in which privately informed firms interact repeatedly. In this setting, firms may achieve a collusive equilibrium in which they limit the use of advertising, and we establish conditions under which optimal collusion entails pooling at zero advertising. More generally, full or partial pooling is observed in optimal collusion. In summary, non-price advertising can promote product efficiency and raise consumer welfare; however, firms often have incentive to diminish advertising competition, whether through regulatory restrictions or collusion.non-price advertising, retail firms, advertising equilibrium

Advertising and Collusion in Retail Markets

We consider non-price advertising by retail firms that are privately informed as to their respective production costs. We first analyze a static model. We construct an advertising equilibrium, in which informed consumers use an advertising search rule whereby they buy from the highest-advertising firm. Consumers are rational in using the advertising search rule, since the lowest-cost firm advertises the most and also selects the lowest price. Even though the advertising equilibrium facilitates productive efficiency, we establish conditions under which firms enjoy higher expected profit when advertising is banned. Consumer welfare falls in this case, however.We next analyze a dynamic model in which privately informed firms interact repeatedly. In this setting, firms may achieve a collusive equilibrium in which they limit the use of advertising, and we establish conditions under which optimal collusion entails pooling at zero advertising. More generally, full or partial pooling is observed in optimal collusion. In summary, non-price advertising can promote product efficiency and raise consumer welfare; however, firms often have incentive to diminish advertising competition, whether through regulatory restrictions or collusion.

Cloud types and the tropical Earth radiation budget, revised

Nimbus-7 cloud and Earth radiation budget data are compared in a study of the effects of clouds on the tropical radiation budget. The data consist of daily averages over fixed 500 sq km target areas, and the months of July 1979 and January 1980 were chosen to show the effect of seasonal changes. Six climate regions, consisting of 14 to 24 target areas each, were picked for intensive analysis because they exemplified the range in the tropical cloud/net radiation interactions. The normal analysis was to consider net radiation as the independent variable and examine how cloud cover, cloud type, albedo and emitted radiation varied with the net radiation. Two recurring themes keep repeating on a local, regional, and zonal basis: the net radiation is strongly influenced by the average cloud type and amount present, but most net radiation values could be produced by several combinations of cloud types and amount. The regions of highest net radiation (greater than 125 W/sq m) tend to have medium to heavy cloud cover. In these cases, thin medium altitude clouds predominate. Their cloud tops are normally too warm to be classified as cirrus by the Nimbus cloud algorithm. A common feature in the tropical oceans are large regions where the total regional cloud cover varies from 20 to 90 percent, but with little regional difference in the net radiation. The monsoon and rain areas are high net radiation regions

ELVIS: Exploring the Local Volume in Simulations

We introduce a set of high-resolution dissipationless simulations that model the Local Group (LG) in a cosmological context: Exploring the Local Volume in Simulations (ELVIS). The suite contains 48 Galaxy-size halos, each within high-resolution volumes that span 2-5 Mpc in size, and each resolving thousands of systems with masses below the atomic cooling limit. Half of the ELVIS galaxy halos are in paired configurations similar to the Milky Way (MW) and M31; the other half are isolated, mass-matched analogs. We find no difference in the abundance or kinematics of substructure within the virial radii of isolated versus paired hosts. On Mpc scales, however, LG-like pairs average almost twice as many companions and the velocity field is kinematically hotter and more complex. We present a refined abundance matching relation between stellar mass and halo mass that reproduces the observed satellite stellar mass functions of the MW and M31 down to the regime where incompleteness is an issue, $M_\star \sim 5\times 10^5 \, M_\odot$. Within a larger region spanning approximately 3 Mpc, the same relation predicts that there should be $\sim$ 1000 galaxies with $M_\star > 10^{3}\,M_\odot$ awaiting discovery. We show that up to 50% of halos within 1 Mpc of the MW or M31 could be systems that have previously been within the virial radius of either giant. By associating never-accreted halos with gas-rich dwarfs, we show that there are plausibly 50 undiscovered dwarf galaxies with HI masses $> 10^5\,M_\odot$ within the Local Volume. The radial velocity distribution of these predicted gas-rich dwarfs can be used to inform follow-up searches based on ultra-compact high-velocity clouds found in the ALFALFA survey.Comment: 22 pages, 19 figures, 3 tables; v2 -- accepted to MNRAS. Movies, images, and data are available at http://localgroup.ps.uci.edu/elvi

Solar Constant Data from Earth Radiation Budget Measurements

At present, solar total irradiance measurements are made from four satellites using electrically self calibrating pyrheliometers, as a part of the earth radiation budget measurement programs. The Earth Radiation Budget (ERB) mission onboard Nimbus-7 spacecraft (Nimbus/ERB) started solar total irradiance measurements in November 1978, and is still obtaining irradiance data on every orbit, daily. The Earth Radiation Budget Experiment (ERBE) solar monitors onboard Earth Radiation Budget Satellite (ERBS), NOAA-9 and NOAA-10 started solar total irradiance measurements in October 1984, January 1985, and October 1986, respectively. Our knowledge of solar total irradiance and its variability has grown remarkably during the past few years, as a result of the above measurements, and the high precision data obtained from Solar Maximum Mission/Active Cavity Radiometer Irradiance Monitor-1 (SMM/ACRIM-1). The results from a comparative study of the solar constant data available from the above missions are presented. The solar constant value derived from the sensors agree within the uncertainty associated with absolute pyrheliometers available at present. An attempt will be made to correlate the solar irradiance variability with other solar parameters. The measurements from Nimbus-7/ERB started November 1978, as the solar cycle 21 was increasing in activity. The solar luminosity reached a maximum in the spring of 1979. The irradiance then decreased slowly to a minimum which lasted from 1984 through 1986. The irradiance is presently increasing towards a new maximum. It appears that the solar constant value follow an eleven year cycle

THE INFLUENCE OF COLLECTIVE INSTRUCTIONAL LEADERSHIP ON TEACHER EFFICACY

In understanding leadership to be the single most important factor in shaping a school’s performance, and second highest factor influencing student achievement, it is a necessity for investigations to focus on what successful leaders do to have excelling schools. Research has alluded to the understanding that the principal can no longer serve as the sole instructional leader of a school. This need for collaboration within the organization places a weight on principals to incorporate others within the school decision-making process. This study examined how collective instructional leadership is currently influencing teacher efficacy in high performing central Kentucky elementary schools. Data were collected through individual principal interviews and focus-group interviews to gain perspectives about how collective instructional leadership is currently influencing teacher efficacy, individuals involved in collective instructional leadership, and actions leaders engage in to promote individual and collective teacher efficacy. The findings of this study identified themes to support a hypothesis around how collective instructional leadership is influencing teacher efficacy. Through the finding of this study a working model of collective instructional leadership was developed. Findings indicate the four working dimensions within the collective instructional leadership model will help raise both individual and collective teacher efficacy within schools