Covariants of binary sextics and vector-valued Siegel modular forms of genus two

We extend Igusa’s description of the relation between invariants of binary sextics and Siegel modular forms of degree 2 to a relation between covariants and vector-valued Siegel modular forms of degree 2. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree 2

The Prevention of the Ice Hazard on Airplanes

A review of various methods to prevent ice formation and adhesion to aircraft surfaces is given. It was concluded that the adhesion of ice to a surface may be reduced somewhat by the application of certain waxes and varnishes. In the experiments described, the varnishes containing calcium stearate and calcium oleate gave the best results. In wind tunnel tests, the adhesion was further reduced by the application of these waxes and varnishes to a thin, heat insulating layer of rubber. The adhesion of ice is greatly reduced when the surface consists of a vehicle which carries an oil in sufficient quantity so that the surface of the vehicle is self lubricating. Ice may be removed from wings, struts, wires and other parts of an airplane during flight by the inflation of properly constructed pneumatic rubber members, providing that these members have been previously treated with a suitable low adhesion oil

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon

Comparison of uniform perturbation solutions and numerical solutions for some potential flows past slender bodies

Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention

Cusps of Hilbert modular varieties

Motivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifold M to be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that every Sol 3-manifold is diffeomorphic to a cusp cross-section of a (generalized) Hilbert modular surface. We also deduce an obstruction to geometric bounding in this setting. Consequently, there exist Sol 3-manifolds that cannot arise as a cusp cross-section of a 1-cusped nonsingular Hilbert modular surface.Comment: To appear in Mathematical Proceedings Cambridge Philosophical Societ

All in with Google Slides: Virtual engagement and formative assessment in introductory sign language linguistics

My goals as an instructor are to be transparent and approachable and to cultivate a community of learners. The transition to virtual instruction in Sign Language Structure and Usage presented significant challenges. I wondered how students could engage effectively with me, with each other, and with course content; how students could identify what they understood and on what they needed further instruction. To address these questions, I went all in with Google Slides to build engaging, searchable, self-paced slide presentations with built-in formative assessments. COVID-19 inspired this shift in slide creation, but I envision using these slides going forward because they are more equitable and more inclusive. If studentsare not able to come to class for any reason, they can review videos and complete selfassessments, just as they would in class. Anecdotal remarks suggest this approach appeals to a wider range of students and learning styles, but further study should explicitly examine student perceptions of this slide format. Other faculty in my college have recently expressed interest in adopting this style of presentation in their owncourses

Addressing Reality: A Model for Learner Driven and Standards-Based Internships for Educational Leadership Programs

In many professions, internships apply classroom learning to the actual professional setting with the guidance of mentors. Internships, as a component of education for educational leaders has been roundly criticized. This paper describes the research and design process employed as an internship experience for a new Master’s degree program in educational leadership. The result is a flexible, site, and intern specific internship model applying principles of heutagogy as interns learn about Complex Adaptive Systems within schools. Unexpected positive outcomes for interns and the schools they serve are discussed

Ecology and conservation of marine turtles in Kenya

Conservation requires comprehensive data about the target species or ecosystem. For marine turtles, obtaining such data can be challenging due to their migratory and cryptic nature, as well as their long and complex life histories. This hampers our ability to assess fundamental parameters such as population size and reproductive output, and to design adequate spatial conservation measures. In this thesis, I aim to comprehensively synthesize the available information regarding marine turtles along the African continental east coast and address several of the identified knowledge gaps with multiple long- term data sets from Watamu, Kenya, that were collected by a grassroots community-based organisation. More specifically, in Chapter 1, I combine results from a systematic literature review with perspectives from Kenya, Tanzania, Mozambique, South Africa and the Western Indian Ocean (WIO) region, provided by marine turtle experts, to create a comprehensive assessment of the biology and conservation of marine turtles along the African continental east coast. I highlight the importance of this sub-region as foraging and nesting grounds, identify knowledge gaps and threats to turtles, and discuss strengths and impediments in turtle conservation. In Chapter 2, I analyse turtle nesting data collected at Watamu between 2000 and 2020 and show promising signs of recovery for green (Chelonia mydas) and olive ridley turtle (Lepidochelys olivacea) nesting. I also present information crucial to the conservation of turtle populations in the WIO. Following this, in Chapter 3, I present the first empirical data on estimated green turtle primary sex ratios in Kenya. The analysis I present demonstrates balanced sex ratios are achieved in clutches that incubate in-situ and that the conservation intervention of clutch relocation induces a female-biased sex ratio. Lastly, in Chapter 4, I examine the data from an incentive-based bycatch mortality mitigation program that has been in operation in Watamu since 1998. I provide insights into small-scale fisheries turtle bycatch and show the importance of coastal areas as foraging grounds for juvenile green and hawksbill turtles (Eretmochelys imbricata). In conclusion, this thesis has identified and addressed fundamental knowledge gaps about marine turtles along the African continental east coast and Kenya, whilst demonstrating the potential of community-based conservation in achieving conservation outcomes and bolstering ecological knowledge

Non semi-simple sl(2) quantum invariants, spin case

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order $2r$ where $r>1$ is odd or congruent to $2$ modulo $4$. In this paper we consider the remaining cases where $r$ is congruent to zero modulo $4$ and produce invariants of $3$-manifolds with colored links, equipped with generalized spin structure. For a given $3$-manifold $M$, the relevant generalized spin structures are (non canonically) parametrized by $H^1(M;\mathbb C/2\mathbb Z)$.Comment: 13 pages, 16 figure