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Following Cayley, MacMahon, and Sylvester, define a non-unitary partition to be an integer partition with no part equal to one, and let $\nu(n)$ denote the number of non-unitary partitions of size $n$. In a 2021 paper, the sixth author proved a formula to compute $p(n)$ by enumerating only non-unitary partitions of size $n$, and recorded a number of conjectures regarding the growth of $\nu(n)$ as $n\to \infty$. Here we refine and prove some of these conjectures. For example, we prove $p(n) \sim \nu(n)\sqrt{n/\zeta(2)}$ as $n\to \infty$, and give Ramanujan-like congruences between $p(n)$ and $\nu(n)$ such as $p(5n)\equiv \nu(5n)\ (\operatorname{mod} 5)$., Comment: 9 pages, to appear in The Journal of the Ramanujan Mathematical Society

Many industries are now investing heavily in data science and automation to replace manual tasks and/or to help with decision making, especially in the realm of leveraging computer vision to automate many monitoring, inspection, and surveillance tasks. This has resulted in the emergence of the 'data scientist' who is conversant in statistical thinking, machine learning (ML), computer vision, and computer programming. However, as ML becomes more accessible to the general public and more aspects of ML become automated, applications leveraging computer vision are increasingly being created by non-experts with less opportunity for regulatory oversight. This points to the overall need for more educated responsibility for these lay-users of usable ML tools in order to mitigate potentially unethical ramifications. In this paper, we undertake a SWOT analysis to study the strengths, weaknesses, opportunities, and threats of building usable ML tools for mass adoption for important areas leveraging ML such as computer vision. The paper proposes a set of data science literacy criteria for educating and supporting lay-users in the responsible development and deployment of ML applications., Comment: 4 pages

Performance prediction or forecasting sporting outcomes involves a great deal of insight into the particular area one is dealing with, and a considerable amount of intuition about the factors that bear on such outcomes and performances. The mathematical Theory of Evidence offers representation formalisms which grant experts a high degree of freedom when expressing their subjective beliefs in the context of decision-making situations like performance prediction. Furthermore, this reasoning framework incorporates a powerful mechanism to systematically pool the decisions made by individual subject matter experts. The idea behind such a combination of knowledge is to improve the competence (quality) of the overall decision-making process. This paper reports on a performance prediction experiment carried out during the European Football Championship in 1996. Relying on the knowledge of four predictors, Evidence Theory was used to forecast the final scores of all 31 matches. The results of this empirical study are very encouraging., Comment: Appears in Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI1997)

A study was made: (1) to determine whether children allowed to choose the difficulty levels of their arithmetic problems in a Computer Assisted Instruction (CAI) task would show greater engagement in learning than children who were not given a choice, (2) to discover possible patterns in the choices made, and (3) to determine the relationship of locus of control (LOC) attributions to engagement in the task. The subjects were 4th and 5th grade students, mostly Mexican-Americans, in a low-income school. Pairs of subjects were matched on age, sex, and initial achievement level in math. Subjects in both conditions used a modified form of the Math Drill and Practice program by Suppes, et al, 1974. Task specific attention or inattention and locus of control were measured. Among the major finds were: (1) that the choice group was significantly higher in engagement, (2) for both groups, engagement decreased significantly over a 15 day period; and (3) distinctive choice patterns did occur. The findings also showed that children will choose problems that result in poor academic performance; if performance in choice situations is to be improved, training methods that use information about children's unique patterns of choices should be designed. (Author/WCM)

The two purposes of this literature review are to provide the Research Triangle Institute staff a thorough grounding in the migrant education literature, and to furnish theoretical and/or empirical bases for the meaning and refinement of variables and parameters for a study design development. Examined analytically are the characteristics of migrant culture and migrant children in order to identify and define their educational and social needs. Facts emerging from the classification and processing of materials are: the information is diverse and primarily descriptive, publishing dates are mostly between 1970 and 1972, very few studies are based on objective research, and few studies deal with migrants from specific ethnic groups. However, this review does provide a profile of migrant life and a summary of educational programs that have been described to date. Reviewed in depth are the following categories: background characteristics of migrant culture, characteristics of migrant children as related to educational programs and achievement levels, general descriptions of education and noneducation migrant programs, characteristics of Elementary Secondary Education Act (ESEA) Title I migrant programs, and evaluations of the Migrant Student Record Transfer System (MSRTS). Further studies are recommended. (AN)

Drawing from site visits to 10 community colleges located in New York (New York), Miami (Florida), Cleveland (Ohio), Jacksonville (Florida), Kansas City (Missouri), Dallas (Texas), Los Angeles (California), Denver (Colorado), Pittsburgh (Pennsylvania), and Detroit (Michigan), this report traces the efforts of inner-city community colleges to provide education, training, and urban survival skills to new immigrants, high school dropouts, homeless, and socially and economically disadvantaged, as well as to large numbers of traditional students. Part 1 of the report presents a position statement by the Commission on Urban Community Colleges of the American Association of Community and Junior Colleges concerning the role of urban community colleges. Part 2 offers introductory information on the purpose of the study and on the campuses that were visited. Part 3 offers brief descriptions of each college's efforts to establish partnerships with the community, build articulated and cooperative programs with schools and universities, and establish partnerships with business and industry. This section also highlights the colleges' role in the education and training of nontraditional students, in providing community services, and in serving as a home for community-based organizations and activities. In part 4, conclusions stress that: (1) the colleges' commitment to the central city in the face of extremely challenging odds appears to be firm; (2) urban community college leaders are firm in their belief that quality education is not and should not be sacrificed in the name of programs related to meeting social needs; (3) enrollment declines of the early and mid-1980's appear to have been reversed; (4) campus leadership continues to struggle with the issues of social change and higher education; and (5) there appears to be no national consensus on the multiple missions and roles of the central city campus and its special programs that reach out to the community. In conclusion, part 5 offers seven recommendations. (JMC)

The motions of grinding media and powder in an attritor canister were studied by means of filming the agitated charge and frame-by-frame scrutiny of the footage. In conjunction with auxiliary experiments, this permitted semiquantitative analysis of the milling action. In particular, the mill can be divided into several regions characterized by different balances between direct impacts and rolling/sliding of the grinding media. Simple calculations suggest that impacts are more capable of effecting mechanical alloying (MA) than are rolling or sliding events in an attritor. Powder circulation within an operating mill was also investigated. Based on the results and the accompanying analysis, concepts for improved attritor design are presented.

Two programs have been developed to compute the dimensional and property changes that occur with repetitive impacts during the mechanical alloying process. The more sophisticated of the programs also maintains a running count of the fractions of particles present and from this calculates a population distribution. The programs predict powder particle size and shape changes in accord with the accepted stages of powder development during mechanical alloying of ductile species. They also predict hardness and lamellar thickness changes with processing, again with reasonable agreement with experimental results. These predictions offer support of the model (and thereby give insight into the possible 'actual' happenings of mechanical alloying) and hence allow refinement and calibration of the myriad aspects of the model. They also provide a vehicle for establishing control over the dimensions and properties of the output powders used for consolidation, thereby facilitating optimization of the consolidation process.

The study examined the effects of training 209 regular class elementary school students and their 12 emotionally disturbed classmates about handicapping conditions. Investigated were normal students' attitudes toward emotionally disturbed students, and the self esteem of emotionally disturbed students. Data gathered prior to and at the conclusion of the training program were obtained in classes containing mainstreamed emotionally disturbed students. Classes were randomly divided into a treatment and control group. Statistical analysis of questionnaire results using the analysis of covariance indicated that elementary students within the treatment group showed increased positive attitudes toward the handicapped and increased acceptance of mainstreamed emotionally disturbed students. (Author)

Simulator studies of the deep-stall problem encountered with modern airplanes are discussed. The results indicate that the basic deep-stall tendencies produced by aerodynamic characteristics are augmented by operational considerations. Because of control difficulties to be anticipated in the deep stall, it is desirable that adequate safeguards be provided against inadvertent penetrations.

A power-off landing technique, applicable to aircraft of configurations presently being considered for manned re-entry vehicles, has been developed and flight tested at Ames Research Center. The flight tests used two configurations of an airplane for which the values of maximum lift-drag ratios were 4.0 and 2.8. Twenty-four idle-power approaches were made to an 8000-foot runway with touchdown point and airspeed accuracies of +/-600 feet and +/-10 knots, respectively. The landing pattern used was designed to provide an explicitly defined flight path for the pilot and, yet, to require no external guidance other than the pilot's view from the cockpit. The initial phase of the approach pattern is a constant high-speed descent from altitude aimed at a ground reference point short of the runway threshold. At a specified altitude and speed, a constant g pull-out is made to a shallow flight path along which the air-plane decelerates to the touchdown point. Repeatability and safety are inherent because of the reduced number of variables requiring pilot judgment, and because of the fact that a missed approach is evident at speeds and altitudes suitable for safe ejection. The accuracy and repeatability of the pattern are indicated by the measured results. The proposed pattern appears to be particularly suitable for configurations having unusual drag variations with speed in the lower speed regime, since the pilot is not required to control speed in the latter portions of the pattern.

Carrier landing-approach studies of a tailless delta-wing fighter airplane disclosed that approach speeds were limited by ability to control altitude and lateral-directional characteristics. More detailed flight studies of the handling-qualities characteristics of the airplane in the carrier-approach configuration documented a number of factors that contributed to the adverse comments on the lateral-directional characteristics. These were: (1) the tendency of the airplane to roll around the highly inclined longitudinal axis, so that significant sideslip angles developed in the roll as a result only of kinematic effects; (2) reduction of the rolling response to the ailerons because of the large dihedral effect in conjunction with the kinematically developed sideslip angles; and (3) the onset of rudder lock at moderate angles of sideslip at the lowest speeds with wing tanks installed. The first two of the factors listed are inseparably identified with this type of configuration which is being considered for many of the newer designs and may, therefore, represent a problem which will be encountered frequently in the future. The results are of added significance in the demonstration of a typical situation in which extraneous factors occupy so much of the pilot's attention that his capability of coping with the problems of precise flight-path control is reduced, and he accordingly demands a greater speed margin above the stall to allow for airspeed fluctuations.

Writers and books viewed as having particular value in planning for gifted education in the year 2000 are identified, including works on identifying the gifted, accelerated early development, behavioral and learning characteristics, aesthetics, core gifted curriculum, literature studies, ethics, philosophy, and mathematical and scientific thinking. (MSE)