A divisibility property of binomial coefficients viewed as an elementary sieve

The triangular array of binomial coefficients 012301111212131331… is said to have undergone a j-shift if the r-th row of the triangle is shifted rj units to the right (r=0,1,2,…). Mann and Shanks have proved that in a 2-shifted array a column number c>1 is prime if and only if every entry in the c-th column is divisible by its row number. Extensions of this result to j-shifted arrays where j>2 are considered in this paper. Moreover, an analog of the criterion of Mann and Shanks [2] is given which is valid for arbitrary arithmetic progressions

Silver Praised, Assailed

Letters to the editor of the Memphis, Tenn. Commercial Appeal regarding James Silver\u27s pro-integration views; one letter is supportive, the rest are critical; Source: Commercial Appeal (Memphis, Tenn.)https://egrove.olemiss.edu/jws_clip/1012/thumbnail.jp

Haptic-Multimodal Flight Control System Update

The rapidly advancing capabilities of autonomous aircraft suggest a future where many of the responsibilities of today s pilot transition to the vehicle, transforming the pilot s job into something akin to driving a car or simply being a passenger. Notionally, this transition will reduce the specialized skills, training, and attention required of the human user while improving safety and performance. However, our experience with highly automated aircraft highlights many challenges to this transition including: lack of automation resilience; adverse human-automation interaction under stress; and the difficulty of developing certification standards and methods of compliance for complex systems performing critical functions traditionally performed by the pilot (e.g., sense and avoid vs. see and avoid). Recognizing these opportunities and realities, researchers at NASA Langley are developing a haptic-multimodal flight control (HFC) system concept that can serve as a bridge between today s state of the art aircraft that are highly automated but have little autonomy and can only be operated safely by highly trained experts (i.e., pilots) to a future in which non-experts (e.g., drivers) can safely and reliably use autonomous aircraft to perform a variety of missions. This paper reviews the motivation and theoretical basis of the HFC system, describes its current state of development, and presents results from two pilot-in-the-loop simulation studies. These preliminary studies suggest the HFC reshapes human-automation interaction in a way well-suited to revolutionary ease-of-use

Piloted Evaluation of the H-Mode, a Variable Autonomy Control System, in Motion-Based Simulation

As aircraft become able to autonomously respond to a range of situations with performance surpassing human operators, we are compelled to look for new methods that help understand their use and guide the design of new, more effective forms of automation and interaction. The "H-mode" is one such method and is based on the metaphor of a well-trained horse. The concept allows the pilot to manage a broad range of control automation functionality, from augmented manual control to FMS-like coupling and automation initiated actions, using a common interface system and easily learned set of interaction skills. The interface leverages familiar manual control interfaces (e.g., the control stick) and flight displays through the addition of contextually dependent haptic-multimodal elements. The concept is relevant to manned and remotely piloted vehicles. This paper provides an overview of the H-mode concept followed by a presentation of the results from a recent evaluation conducted in a motion-based simulator. The evaluation focused on assessing the overall usability and flying qualities of the concept with an emphasis on the effects of turbulence and cockpit motion. Because the H-mode results in interactions between traditional flying qualities and management of higher-level flight path automation, these effects are of particular interest. The results indicate that the concept may provide a useful complement or replacement to conventional interfaces, and retains the usefulness in the presence of turbulence and motion

Extension of a theorem of Cauchy and Jacobi

AbstractLet q and p be prime with q = a2 + b2 ≡ 1 (mod 4), a ≡ 1 (mod 4), and p = qf + 1. In the nineteenth century Cauchy (Mém. Inst. France 17 (1840), 249–768) and Jacobi (J. für Math. 30 (1846), 166–182) generalized the work of earlier authors, who had determined certain binomial coefficients (mod p) (see H. J. S. Smith, “Report on the Theory of Numbers,” Chelsea, 1964), by determining two products of factorials given by Πk kf! (mod p = qf + 1) where k runs through the quadratic residues and the quadratic non-residues (mod q), respectively. These determinations are given in terms of parameters in representations of ph or of 4ph by binary quadratic forms. A remarkable feature of these results is the fact that the exponent h coincides with the class number of the related quadratic field. In this paper C. R. Mathews' (Invent. Math. 54 (1979), 23–52) recent explicit evaluation of the quartic Gauss sum is used to determine four products of factorials (mod p = qf + 1, q ≡ 5 (mod 8) > 5), given by Πk kf! where k runs through the quartic residues (mod q) and the three cosets which may be formed with respect to this subgroup. These determinations appear to be considerably more difficult. They are given in terms of parameters in representations of 16ph by quaternary quadratic forms. Stickelberger's theorem is required to determine the exponent h which is shown to be closely related to the class number of the imaginary quartic field Q(i√2q + 2a√q), q = a2 + b2 ≡ 5 (mod 8), a odd

Prevalence of Inherited Hemoglobin Disorders and Relationships with Anemia and Micronutrient Status among Children in Yaoundé and Douala, Cameroon.

Information on the etiology of anemia is necessary to design effective anemia control programs. Our objective was to measure the prevalence of inherited hemoglobin disorders (IHD) in a representative sample of children in urban Cameroon, and examine the relationships between IHD and anemia. In a cluster survey of children 12-59 months of age (n = 291) in Yaoundé and Douala, we assessed hemoglobin (Hb), malaria infection, and plasma indicators of inflammation and micronutrient status. Hb S was detected by HPLC, and α⁺thalassemia (3.7 kb deletions) by PCR. Anemia (Hb < 110 g/L), inflammation, and malaria were present in 45%, 46%, and 8% of children. A total of 13.7% of children had HbAS, 1.6% had HbSS, and 30.6% and 3.1% had heterozygous and homozygous α⁺thalassemia. The prevalence of anemia was greater among HbAS compared to HbAA children (60.3 vs. 42.0%, p = 0.038), although mean Hb concentrations did not differ, p = 0.38). Hb and anemia prevalence did not differ among children with or without single gene deletion α⁺thalassemia. In multi-variable models, anemia was independently predicted by HbAS, HbSS, malaria, iron deficiency (ID; inflammation-adjusted ferritin <12 µg/L), higher C-reactive protein, lower plasma folate, and younger age. Elevated soluble transferrin receptor concentration (>8.3 mg/L) was associated with younger age, malaria, greater mean reticulocyte counts, inflammation, HbSS genotype, and ID. IHD are prevalent but contribute modestly to anemia among children in urban Cameroon

A Diagnostic System for Studying Energy Partitioning and Assessing the Response of the Ionosphere during HAARP Modification Experiments

This research program focused on the construction of several key radio wave diagnostics in support of the HF Active Auroral Ionospheric Research Program (HAARP). Project activities led to the design, development, and fabrication of a variety of hardware units and to the development of several menu-driven software packages for data acquisition and analysis. The principal instrumentation includes an HF (28 MHz) radar system, a VHF (50 MHz) radar system, and a high-speed radar processor consisting of three separable processing units. The processor system supports the HF and VHF radars and is capable of acquiring very detailed data with large incoherent scatter radars. In addition, a tunable HF receiver system having high dynamic range was developed primarily for measurements of stimulated electromagnetic emissions (SEE). A separate processor unit was constructed for the SEE receiver. Finally, a large amount of support instrumentation was developed to accommodate complex field experiments. Overall, the HAARP diagnostics are powerful tools for studying diverse ionospheric modification phenomena. They are also flexible enough to support a host of other missions beyond the scope of HAARP. Many new research programs have been initiated by applying the HAARP diagnostics to studies of natural atmospheric processes

Architecture from textiles in motion

Wind is one important concern when it comes to its impact on textile structures within architecture. One method to limit wind-caused displacements is to heavily pre-stress the structures. We discuss an alternative approach, in which wind is seen as a positive design parameter for architectural textiles. We explore how one could work with the shape and internal structure of the textile to design architectural structures which become kinetic volumes when airflow is applied. The implications of such a design approach are formulated based on a two-day workshop at the conference Advances in Architectural Geometry (AAG) 2018. The explorations embraced digital and physical simulations of textile behaviors arising from the presence of wind. Smart textiles, whose structures can be changed using heat, were employed to explore how the geometrical expressions of textiles under wind load can be affected through local internal textile property changes. The ambition was to investigate the possibility of dynamically altering the 3-dimensionality of the textiles by reshaping them in real-time using airflow. The main conclusion from the workshop is that the dialogue between the digital and physical simulations seems to play an important role in supporting and enhancing the process of designing the geometrical expressions of textiles subjected to dynamic influence. A combination of the digital and the physical design tools enables the creation of a unique workflow to generate architectural design typologies that would have been difficult to develop if such complementary design tools have not been employed

Application of the H-Mode, a Design and Interaction Concept for Highly Automated Vehicles, to Aircraft

Driven by increased safety, efficiency, and airspace capacity, automation is playing an increasing role in aircraft operations. As aircraft become increasingly able to autonomously respond to a range of situations with performance surpassing human operators, we are compelled to look for new methods that help us understand their use and guide their design using new forms of automation and interaction. We propose a novel design metaphor to aid the conceptualization, design, and operation of highly-automated aircraft. Design metaphors transfer meaning from common experiences to less familiar applications or functions. A notable example is the "Desktop metaphor" for manipulating files on a computer. This paper describes a metaphor for highly automated vehicles known as the H-metaphor and a specific embodiment of the metaphor known as the H-mode as applied to aircraft. The fundamentals of the H-metaphor are reviewed followed by an overview of an exploratory usability study investigating human-automation interaction issues for a simple H-mode implementation. The envisioned application of the H-mode concept to aircraft is then described as are two planned evaluations