Central potential and examples of hidden algebra structure

We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrh\"odinger equations. Some relativistic counterparts of these problems are also discussed.Comment: 8 pages, latex, no figure

Factors Determining Transit Access by Car Owners: Implications for Intermodal Passenger Transportation Planning

Although walking is the dominant mode of transportation to transit facilities, there are strong variations by socio-demographics, geography, mode of public transit used and other factors. There is particularly a need to understand ways in which car owners who choose to use public transportation can be encouraged to carpool, walk or bicycle in the “first mile” and “last mile” of the transit trip, instead of driving. These considerations have implications for addressing cold start trips resulting from short drives to transit facilities, active transportation strategies that may benefit transit users who currently drive, and in deriving solutions for shared transportation such as bicycle-sharing and car-sharing programs. Using data collected in the Chicago Metropolitan Area, we investigate how the mode choice for the access trip to transit stations is related to costs, personal and household variables, trip characteristics, and neighborhood factors including crash frequencies, crime prevalence, neighborhood racial characteristics, population density, roadway density etc. for persons in car owning households. The results suggest that while much of the choice depends on personal and trip related variables, some neighborhood level factors as well as the provision of parking at transit stations have important relationships to mode choice that can influence built environment factors such as density and policy areas such as the provision and operation of transit parking facilities

The Angular Momentum Distribution within Halos in Different Dark Matter Models

We study the angular momentum profile of dark matter halos for a statistical sample drawn from a set of high-resolution cosmological simulations of $256^3$ particles. Two typical Cold Dark Matter (CDM) models have been analyzed, and the halos are selected to have at least $3\times 10^4$ particles in order to reliably measure the angular momentum profile. In contrast with the recent claims of Bullock et al., we find that the degree of misalignment of angular momentum within a halo is very high. About 50 percent of halos have more than 10 percent of halo mass in the mass of negative angular momentum $j$. After the mass of negative $j$ is excluded, the cumulative mass function $M(<j)$ follows approximately the universal function proposed by Bullock et al., though we still find a significant fraction of halos ($\sim 50$) which exhibit systematic deviations from the universal function. Our results, however, are broadly in good agreement with a recent work of van den Bosch et al.. We also study the angular momentum profile of halos in a Warm Dark Matter (WDM) model and a Self-Interacting Dark Matter (SIDM) model. We find that the angular momentum profile of halos in the WDM is statistically indistinguishable from that in the CDM model, but the angular momentum of halos in the SIDM is reduced by the self-interaction of dark matter.Comment: 23 pages, 10 figures, 2 tables. Revised version, added a new table, accepted for publication in MNRA

On Robin's criterion for the Riemann Hypothesis

Robin's criterion states that the Riemann Hypothesis (RH) is true if and only if Robin's inequality sum_{d|n}d=5041, where gamma denotes the Euler(-Mascheroni) constant. We show by elementary methods that if n>=37 does not satisfy Robin's criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that n must be divisible by a fifth power >1. As a consequence we infer that RH holds true if and only if every natural number divisible by a fifth power >1 satisfies Robin's inequality.Comment: 15 pages. Corrected version. In the first version in Theorem 5 (main result) it was falsely asserted that n must be superabundant, invalidating the proof. An alternative proof is provided in this version, some typos have been corrected, and the presentation has been improve

A numeric solution for metric-affine gravity and Einstein's gravitational theory with Proca matter

A special case of metric-affine gauge theory of gravity (MAG) is equivalent to general relativity with Proca matter as source. We study in detail a corresponding numeric solution of the Reissner-Nordstr"om type. It is static, spherically symmetric, and of electric type. In particular, this solution has no horizon, so it has a naked singularity as its origin.Comment: LaTeX2e, 20 pages, 22 figure

Developing Mathematical Learning Device Using Ttw (Think- Talk-Write) Strategy Assisted By Learning Cd To Foster Mathematical Communication

This research aims to produce mathematical learning device or tool using TTW strategy that is valid, practical, and effective. The developed device consists of syllabi, Learning Implementation Plan (RPP), Student Reading which is packaged in CD (BBS), and an evaluation tool. Receiver of treatment or Subjects are the eighth grade students of Muhammadiyah Junior High School in Purworejo. First experiment held in the class A of eighth grade students aimed to determine the legibility of device and the level of difficulty, distinguishing features, and reliability test learning outcomes. Second experiment conducted in class C of eighth grade students aimed to verify the practicality of the device and the effectiveness of learning using developed devices, whereas the class G is as control class. Results from 5 validations of the device are: the mean score of syllabi is 3.48; RPP is 3.79; BBS is 3.73; LKS is 3.73; assessment tool is 3.71 (on scale 1-4). Such results mean that validation criteria of the device is valid. The score of experiment results showed that the criteria of learning process is 3.80; the students’ response is 93.85%; the teacher’s score is 3.91, that means it’s a practical device. Learning using the devices results a classical learning mastery, and achievement test of an experimental class is better than the control class. Furthermore, student’s activity has a positive influence for achievement, so it’s the effective device. Key words: developed device, Think-Talk-Write (TTW), the mathematical learnin