Search

We study the isoperimetric problem on $\mathbb{R}^1$ with a prescribed density function $f$ that affects how area and perimeter are measured. We examine density functions that are symmetric, radially increasing, and satisfy two additional conditions: they have a point of zero density (at the origin), and they satisfy a "log-concavity" requirement $\left[ \log f \right]'' \leq 0$. Under these conditions, we find that isoperimetric $n$-bubbles satisfy a regular structure and can be identified for arbitrary $n$. This generalizes recent work done on the density function $|x|^p$, and stands in contrast to log-convex density functions which have no such regular structure.

We study the isoperimetric problem on $\mathbb{R}^1$ with a prescribed density function $f(x) = |x|$. Under these conditions, we find that isoperimetric $3$-bubble and $4$-bubble results satisfy a regular structure. As our regions increase in size, the intervals that form them alternate back-and-forth across the origin, with the smaller regions closer to the origin. This expands on previously known observations about the single- and double-bubble results on $\mathbb{R}$ with density $|x|^p$., Comment: 1 figure. arXiv admin note: text overlap with arXiv:2201.01808

In this paper we show the existence of a closed, embedded $\lambda$-hypersurfaces $\Sigma \subset \mathbb{R}^{2n}$. The hypersurface is diffeomorhic to $\mathbb{S}^{n-1} \times \mathbb{S}^{n-1} \times \mathbb{S}^1$ and exhibits $SO(n) \times SO(n)$ symmetry. Our approach uses a "shooting method" similar to the approach used by McGrath in constructing a generalized self-shrinking torus solution to mean curvature flow. The result generalizes the $\lambda$-torus found by Cheng and Wei., Comment: 11 pages

We report radio SETI observations on a large number of known exoplanets and other nearby star systems using the Allen Telescope Array (ATA). Observations were made over about 19000 hours from May 2009 to Dec 2015. This search focused on narrow-band radio signals from a set totaling 9293 stars, including 2015 exoplanet stars and Kepler objects of interest and an additional 65 whose planets may be close to their Habitable Zone. The ATA observations were made using multiple synthesized beams and an anticoincidence filter to help identify terrestrial radio interference. Stars were observed over frequencies from 1- 9 GHz in multiple bands that avoid strong terrestrial communication frequencies. Data were processed in near-real time for narrow-band (0.7- 100 Hz) continuous and pulsed signals, with transmitter/receiver relative accelerations from -0.3 to 0.3 m/s^2. A total of 1.9 x 10^8 unique signals requiring immediate follow-up were detected in observations covering more than 8 x 10^6 star-MHz. We detected no persistent signals from extraterrestrial technology exceeding our frequency-dependent sensitivity threshold of 180 - 310 x 10^-26 W / m^2., Comment: 225 pages including very long table, 9 figures, 7 tables, resubmitted to Astrophysical Journal

We study stable smooth solutions to the isoperimetric type problem for a Gaussian weight on Euclidean Space. That is, we study hypersurfaces $\Sigma^n \subset \mathbb R^{n+1}$ that are second order stable critical points of compact variations that minimize Gaussian weighted area and preserve Gaussian weighted volume. We show that such $\Sigma$ satisfy a curvature condition, and derive the Jacobi operator $L$ for the second variation of such $\Sigma$. Our first main result is that for non-planar $\Sigma$, bounds on the index of $L$, acting on volume preserving variations, gives us that $\Sigma$ splits off a linear space. A corollary of this result is that hyperplanes are the only stable smooth complete solutions to this Gaussian isoperimetric type problem, and that there are no hypersurfaces of index one. Finally, we show that for the case of $\Sigma^2 \subset \mathbb R^3$, there is a gradient decay estimate depending on bounds for the curvature condition and an appropriate area growth bound. This shows that, in the limit as $R \to \infty$, stable $(\Sigma, \partial\Sigma) \subset (B_{2R}(0), \partial B_{2R}(0))$ with good area growth bounds approach hyperplanes., Comment: 20 pages

On February 29, 2008, Gov. Bobby Jindal presented the Louisiana Legislature with a proposed budget allocating $10 million for a school choice initiative that would enable parents in New Orleans to send their children to the school of their choice, including private schools, with state-funded scholarships. Leaders of the public school establishment went on record to oppose the initiative, spreading fear that providing parents more educational options would take away from public schools. But, as this report demonstrates, Louisiana has a rich history of offering a wide array of choices, including private and religious options, through public programs, including in education. These choices add to--rather than subtract from--the opportunities available to its citizens. In this paper, the authors include more detail about Louisiana's choice-based programs. These profiles include short descriptions of each program, when the programs were established and data on the number of participants and dollars expended or allocated (when available). The first set of current programs described are those funded solely or primarily by the state. The second includes programs funded by the federal government but directed by state and local agencies. Not included are programs administered and funded solely or in large part by the federal government, such as Pell grants and housing vouchers. Thus, the programs described in this paper actually undercount the broad scope of services received by Louisianans through choice-based programs. (Contains 52 endnotes.)

The Allen Telescope Array (ATA) is a cm-wave interferometer in California, comprising 42 antenna elements with 6-m diameter dishes. We characterize the antenna optical accuracy using two-antenna interferometry and radio holography. The distortion of each telescope relative to the average is small, with RMS differences of 1 percent of beam peak value. Holography provides images of dish illumination pattern, allowing characterization of as-built mirror surfaces. The ATA dishes can experience mm-scale distortions across -2 meter lengths due to mounting stresses or solar radiation. Experimental RMS errors are 0.7 mm at night and 3 mm under worst case solar illumination. For frequencies 4, 10, and 15 GHz, the nighttime values indicate sensitivity losses of 1, 10 and 20 percent, respectively. The ATA.s exceptional wide-bandwidth permits observations over a continuous range 0.5 to 11.2 GHz, and future retrofits may increase this range to 15 GHz. Beam patterns show a slowly varying focus frequency dependence. We probe the antenna optical gain and beam pattern stability as a function of focus and observation frequency, concluding that ATA can produce high fidelity images over a decade of simultaneous observation frequencies. In the day, the antenna sensitivity and pointing accuracy are affected. We find that at frequencies greater than 5 GHz, daytime observations greater than 5 GHz will suffer some sensitivity loss and it may be necessary to make antenna pointing corrections on a 1 to 2 hourly basis., Comment: 19 pages, 23 figures, 3 tables, Authors indicated by an double dagger ({\ddag}) are affiliated with the SETI Institute, Mountain View, CA 95070. Authors indicated by a section break ({\S}) are affiliated with the Hat Creek Radio Observatory and/or the Radio Astronomy Laboratory, both affiliated with the University of California Berkeley, Berkeley CA

In 2002, the Tennessee Department of Education asked the Appalachia Educational Laboratory (AEL) at Edvantia, Inc. to develop content for online professional development that would help meet the goals of the state's Reading First Program. In response, laboratory staff developed and subsequently delivered Assessment and Intervention in a Comprehensive Literacy Classroom, a five-module course delivered over 16 weeks. The course was designed to help K-3 teachers, K-12 special education teachers, and building-level administrators incorporate formal and informal assessments into their reading instruction and use the results of those assessments to guide instruction. The course was organized and delivered in five modules that covered the following topics: (1) a conceptual model of a comprehensive literacy classroom in which all children can learn to read by the end of the third grade; (2) the five essential elements of reading instruction; (3) the Tennessee assessment system and the four types of assessments (screening, diagnosis, outcome, and progress monitoring); (4) assessment instruments, implementation steps, and practice opportunities; and (5) use of assessment data to guide planning, grouping for instruction, and selection of instructional strategies. (Contains 9 tables and 1 figure.) [This report was written with assistance from Miguel Martinez.]

In spring 2004, more than 1,200 teachers and principals in Tennessee participated in online professional development as part of the state?s Reading First grant. The opportunity also allowed the state to investigate the possibility of using online professional development to help teachers meet high-quality teacher requirements. Staff at the Appalachia Educational Laboratory (AEL) relied on internally developed instructional design standards and John Keller?s ARCS model of motivational design to develop and deliver the online professional development. An evaluation was completed by The CNA Corporation. Gains shown from pre- to posttest scores indicate that the training allowed participants to make significant gains in content knowledge. Three sources of participant feedback indicate high levels of satisfaction with the content of the training modules.

The Pi GHz Sky Survey (PiGSS) is a key project of the Allen Telescope Array. PiGSS is a 3.1 GHz survey of radio continuum emission in the extragalactic sky with an emphasis on synoptic observations that measure the static and time-variable properties of the sky. During the 2.5-year campaign, PiGSS will twice observe ~250,000 radio sources in the 10,000 deg^2 region of the sky with b > 30 deg to an rms sensitivity of ~1 mJy. Additionally, sub-regions of the sky will be observed multiple times to characterize variability on time scales of days to years. We present here observations of a 10 deg^2 region in the Bootes constellation overlapping the NOAO Deep Wide Field Survey field. The PiGSS image was constructed from 75 daily observations distributed over a 4-month period and has an rms flux density between 200 and 250 microJy. This represents a deeper image by a factor of 4 to 8 than we will achieve over the entire 10,000 deg^2. We provide flux densities, source sizes, and spectral indices for the 425 sources detected in the image. We identify ~100$ new flat spectrum radio sources; we project that when completed PiGSS will identify 10^4 flat spectrum sources. We identify one source that is a possible transient radio source. This survey provides new limits on faint radio transients and variables with characteristic durations of months., Comment: Accepted for publication in ApJ; revision submitted with extraneous figure removed

We present the Allen Telescope Array Twenty-centimeter Survey (ATATS), a multi-epoch (12 visits), 690 square degree radio image and catalog at 1.4GHz. The survey is designed to detect rare, very bright transients as well as to verify the capabilities of the ATA to form large mosaics. The combined image using data from all 12 ATATS epochs has RMS noise sigma = 3.94mJy / beam and dynamic range 180, with a circular beam of 150 arcsec FWHM. It contains 4408 sources to a limiting sensitivity of S = 20 mJy / beam. We compare the catalog generated from this 12-epoch combined image to the NRAO VLA Sky Survey (NVSS), a legacy survey at the same frequency, and find that we can measure source positions to better than ~20 arcsec. For sources above the ATATS completeness limit, the median flux density is 97% of the median value for matched NVSS sources, indicative of an accurate overall flux calibration. We examine the effects of source confusion due to the effects of differing resolution between ATATS and NVSS on our ability to compare flux densities. We detect no transients at flux densities greater than 40 mJy in comparison with NVSS, and place a 2-sigma upper limit on the transient rate for such sources of 0.004 per square degree. These results suggest that the > 1 Jy transients reported by Matsumura et al. (2009) may not be true transients, but rather variable sources at their flux density threshold., Comment: 41 pages, 19 figures, ApJ accepted; corrected minor typo in Table 1

Collective teacher efficacy refers to teacher perceptions that they constitute an effective instructional team, capable of bringing about learning in students. Previous research demonstrates that a school staff with a strong sense of collective efficacy is likely to generate high student achievement. This study of 2,170 teachers in 141 elementary schools used structural equation modeling to examine the antecedents of collective teacher efficacy. The study found that prior student achievement in grade 6 mathematics predicted collective teacher efficacy, as predicted by social cognition theory. The study also found that school processes that promoted teacher ownership in school directions (shared school goals, school-wide decision making, fit of plan with school needs, and empowering principal leadership) exerted an even stronger influence on collective teacher efficacy than prior student achievement. School cohesions and support contributed to collective teacher efficacy but only in domains in which the school had control over its direction. (Contains 66 references.) (Author/SM)

The first 42 elements of the Allen Telescope Array (ATA-42) are beginning to deliver data at the Hat Creek Radio Observatory in Northern California. Scientists and engineers are actively exploiting all of the flexibility designed into this innovative instrument for simultaneously conducting surveys of the astrophysical sky and conducting searches for distant technological civilizations. This paper summarizes the design elements of the ATA, the cost savings made possible by the use of COTS components, and the cost/performance trades that eventually enabled this first snapshot radio camera. The fundamental scientific program of this new telescope is varied and exciting; some of the first astronomical results will be discussed., Comment: Special Issue of Proceedings of the IEEE: "Advances in Radio Telescopes", Baars,J. Thompson,R., D'Addario, L., eds, 2009, in press

The Institute for the Advancement of Emerging Technologies in Education (IAETE) at AEL recently explored the potential benefits and limitations of traditional print-based textbooks and many e-book alternatives. Having considered these media, IAETE created prototype interactive textbook pages that retain the salient aspects of print media while providing access to unlimited electronic resources. While the prototype appears to be a standard textbook, imperceptible digital watermarks embedded in the graphics act as convenient conduits to electronic access of dynamic content, assessments, applications, and communication tools. IAETE is exploring digital watermarking as an alternative to delivering electronic instructional media. This report covers the following topics: (1) traditional textbooks; (2) electronic books (e-books); (3) issues influencing e-book development; (4) alternatives for electronic publishing of textbooks, including handheld devices, customized printing, and Web-based delivery; (5) the interactive textbook; and usability study and group interview results. PowerPoint print-outs from a presentation on digital watermarking are attached. (Contains 21 references.) (MES)

Successfully integrating technology does not result from isolating and focusing solely on technology issues but rather from infusing technology into the overall school culture. Chris Dede (1998) suggests that effective integration of new and emerging technologies requires simultaneous innovations in pedagogy, curriculum, assessment, and school organization. These competing demands compound the difficulties of effectively integrating technology into daily practice. Ritchie (1996) described these needs in the form of eight variables that impact technology adoption and implementation in classrooms. Of these, a lack of administrative support is identified as the most crucial. Without administrative support, other variables such as inadequate professional development or lack of funds are more likely to impede the effective use of technology in schools. This review is organized from the perspective of the school leader. Topics discussed in detail in this review include: vision, planning, community relationships, tools and media, integration, professional development, access, support, accountability, and ethical and legal issues. All contribute significantly to the effective use of technology to support teaching, learning, and school management. A concluding section presents a summary of key findings in each of the topic areas. (Contains 181 references.) (AEF)

This paper draws on chaos theory to examine the potential of change within a living community. It focuses on secondary-school change in order to consider the divergent paths and the unexpected cultural adaptations that emerged when a Canadian school district required its secondary schools to revise their organizational models. Department heads were replaced by facilitators, and schools were encouraged to develop site-based models that were program based. To record the nature of the changes, annual survey data were collected beginning in 1995. It became quickly apparent that no grand plan for change was in place, although it was assumed that the school-restructuring teams would create the best possible organizational structures for their schools. Reformers discovered that, because past structures were deeply embedded in the secondary school cultures, restructuring would require a reculturing of stakeholders. Effective change arose when participants supported constantly evolving and emerging organizational values, involved stakeholders in making the decisions in a collaborative manner, and rethought the functions of the organizations more in terms of processes as opposed to isolated tasks. The metaphor of a living organization proved important in grasping the program's development because it emphasized the need of continual organizational learning and the importance of collaborative interaction. (Contains 21 references.) (RJM)

This study investigated techniques for supporting college students' self-regulation within a core course in child development. The course incorporated Web-based instructional elements as ancillary instruction. Regularly scheduled class meetings occurred approximately twice weekly, highlighting various presentation methods to illustrate materials offered through both the Web page and supplemental materials. The course incorporated ideas gained through a review of the literature on self-regulation and metacognition. Nine self-regulation strategies were the focus for development of the Web page (e.g., keeping records and monitoring, reviewing notes, and seeking teacher assistance). The Web site included structured activities to encourage self-directed learning, a self-assessment inventory of self-regulatory learning skills, and additional tools for planning, monitoring, and evaluating learning. Data were collected on whether students desired support for additional strategies, whether their self-regulation strategies changed over the semester, and what strategies were most effective. Overall, students wanted the site to include the capacity to monitor grades online, a goal checklist, and elaborate feedback in testing situations. Students' self-efficacy and self-regulation increased and anxiety decreased over time. The most effective learning strategies were reviewing notes, keeping records, and self-evaluating. (Contains 24 references, 5 figures, and 5 tables.) (SM)

A closer look at what actually occurs in classrooms forces observers to realize that to integrate technology effectively into teaching and learning, teachers must address many challenges and demonstrate more than superficial knowledge about technology and its use. To assess one element of the technology integration issue, a regional survey of teachers' software selection and use was conducted. The spring 1999 survey was designed to provide insight into the types of software and frequency of software use in classrooms across Kentucky, Tennessee, Virginia, and West Virginia and to identify issues for further research and technical assistance in the region. Key findings revealed that of those responding to the survey: 83.6% indicated they never use software in their teaching; productivity tools and research tools were the most frequently used software; curriculum software and instructional simulations were the least utilized software; and drill-and-practice software was utilized daily by 9.5% of respondents. The type of software use by subject area is also outlined. Implications for action are discussed. Contains 16 references.) (AEF)

This research investigated the impact of combining two approaches to inservice teacher education (action research and train the trainer) on teacher attitudes and practices. The inservice developed assessment approaches aligned with cooperative learning instructional approaches. Teachers were introduced to a model of collaborative assessment aimed at improving students' abilities to self-evaluate. A team of five university and school/district personnel conducted a series of three inservice sessions over 4 months. Teams of teachers from several schools were paired, with two teachers attending the first full-day inservice as trainers, working back at the school with their partners (trainees), then attending the second and third inservice sessions together. The effects of the inservice were measured in a pre-post design which examined the impact of the inservice design on personal teaching efficacy, general teaching efficacy, commitment to authentic practices, and commitment to traditional testing practices. Data were also collected on how teachers used the four stages in the study model for teaching self-evaluation. Researchers found significant pre-post changes. Use of self-evaluation procedures increased substantially, commitment to authentic assessment practices increased, commitment to traditional assessment practices declined, and personal teaching efficacy scores were higher. The action-research-enhanced train-the-trainer approach facilitated teachers' movement toward student assessment practices congruent with the ideals of the cooperative learning/teaching practices. This approach also succeeded in enhancing teachers' beliefs about their competence. (Contains 48 references.) (SM)