An annotated bibliography for comparative prime number theory

The goal of this annotated bibliography is to record every publication on the topic of comparative prime number theory together with a summary of its results. We use a unified system of notation for the quantities being studied and for the hypotheses under which results are obtained. We encourage feedback on this manuscript (see the end of Section~1 for details).Comment: 98 pages; supersedes "Comparative prime number theory: A survey" (arXiv:1202.3408

Tracing river chemistry in space and time : dissolved inorganic constituents of the Fraser River, Canada

Author Posting. © The Author(s), 2013. This is the author's version of the work. It is posted here by permission of Elsevier for personal use, not for redistribution. The definitive version was published in Geochimica et Cosmochimica Acta 124 (2014): 283-308, doi:10.1016/j.gca.2013.09.006.The Fraser River basin in southwestern Canada bears unique geologic and climatic features which make it an ideal setting for investigating the origins, transformations and delivery to the coast of dissolved riverine loads under relatively pristine conditions. We present results from sampling campaigns over three years which demonstrate the lithologic and hydrologic controls on fluxes and isotope compositions of major dissolved inorganic runoff constituents (dissolved nutrients, major and trace elements, 87Sr/86Sr, δD). A time series record near the Fraser mouth allows us to generate new estimates of discharge-weighted concentrations and fluxes, and an overall chemical weathering rate of 32 t km-2 y-1. The seasonal variations in dissolved inorganic species are driven by changes in hydrology, which vary in timing across the basin. The time series record of dissolved 87Sr/86Sr is of particular interest, as a consistent shift between higher (“more radiogenic”) values during spring and summer and less radiogenic values in fall and winter demonstrates the seasonal variability in source contributions throughout the basin. This seasonal shift is also quite large (0.709 – 0.714), with a discharge-weighted annual average of 0.7120 (2 s.d. = 0.0003). We present a mixing model which predicts the seasonal evolution of dissolved 87Sr/86Sr based on tributary compositions and water discharge. This model highlights the importance of chemical weathering fluxes from the old sedimentary bedrock of headwater drainage regions, despite their relatively small contribution to the total water flux.This work was supported by the WHOI Academic Programs Office and MIT PAOC Houghton Fund to BMV, a WHOI Arctic Research Initiative grant to ZAW, NSF-ETBC grant OCE-0851015 to BPE and TIE, and NSF grant EAR-1226818 to BPE

Expressions 1992

https://openspace.dmacc.edu/expressions/1014/thumbnail.jp

Counting integers with restrictions on their prime factors

In this thesis, we examine two problems that, on the surface, seem like pure group theory problems, but turn out to both be problems concerning counting integers with restrictions on their prime factors. Fixing an odd prime number q and a finite abelian q-group H=ℤqᵅ₁×ℤqᵅ₂×⋯×ℤqᵅʲ, our first aim is to find a counting function, D(H,x), for the number of integers n up to x such that H is the Sylow q-subgroup of (ℤ/nℤ)×. In Chapter 2, we prove that D(H,x)∼ K_H x(log log x)ʲ/(log x)⁻¹/⁽q⁻¹⁾, where K_H is a constant depending on H. The second problem that we examine in this thesis concerns counting the number of n up to x for which (ℤ/nℤ)× is cyclic and for which (ℤ/nℤ)× is maximally non-cyclic, where (ℤ/nℤ)× is said to be maximally non-cyclic if each of its invariant factors is squarefree. In Chapter 3, we prove that the number of n up to x such that (ℤ/nℤ)× is cyclic is asymptotic to (3/2)x/log x and that the number of n up to x such that (ℤ/nℤ)× is maximally non-cyclic is asymptotic to C_f x/(log x)¹⁻ξ, where ξ is Artin's constant and C_f is the convergent product, C_f=(15/14Γ(ξ)) limₓ→∞ (∏_p≤ₓ\\{p-₁ square-free} (1+(1/p)+(1/p²)) ∏_p≤ₓ (1-(1/p))^ξ). It turns out that both of these problems can be reduced to problems of counting integers with restrictions on their prime factors. This allows the problems to be addressed by classical techniques of analytic number theory.Mathematics, Department ofGraduat

Selective Mutism: A Three Tiered Approach to Prevention and Intervention

Selective mutism is a rare anxiety disorder that prevents a child from speaking at school or other community settings, and can be detrimental to a child’s social development. School psychologists can play an important role in the prevention and treatment of selective mutism. As an advocate for students, school psychologists can work with teachers, parent caregivers, speech pathologists, and other support staff toward helping children who may develop or have selective mutism. The purpose of this article is to present school-based prevention and intervention approaches within a three-tiered approach that may reduce the incidence and severity of selective mutism. We present theories and research on the etiology and prevalence of the disorder, followed by a review of intervention methods and research at each tier. Based on the theoretical and research literature base, we conclude that early intervention may result in the prevention and amelioration of many occurrences of selective mutism

\u3ci\u3eDrosophila\u3c/i\u3e Muller F Elements Maintain a Distinct Set of Genomic Properties Over 40 Million Years of Evolution

The Muller F element (4.2 Mb, ~80 protein-coding genes) is an unusual autosome of Drosophila melanogaster; it is mostly heterochromatic with a low recombination rate. To investigate how these properties impact the evolution of repeats and genes, we manually improved the sequence and annotated the genes on the D. erecta, D. mojavensis, and D. grimshawi F elements and euchromatic domains from the Muller D element. We find that F elements have greater transposon density (25–50%) than euchromatic reference regions (3–11%). Among the F elements, D. grimshawi has the lowest transposon density (particularly DINE-1: 2% vs. 11–27%). F element genes have larger coding spans, more coding exons, larger introns, and lower codon bias. Comparison of the Effective Number of Codons with the Codon Adaptation Index shows that, in contrast to the other species, codon bias in D. grimshawi F element genes can be attributed primarily to selection instead of mutational biases, suggesting that density and types of transposons affect the degree of local heterochromatin formation. F element genes have lower estimated DNA melting temperatures than D element genes, potentially facilitating transcription through heterochromatin. Most F element genes (~90%) have remained on that element, but the F element has smaller syntenic blocks than genome averages (3.4–3.6 vs. 8.4–8.8 genes per block), indicating greater rates of inversion despite lower rates of recombination. Overall, the F element has maintained characteristics that are distinct from other autosomes in the Drosophila lineage, illuminating the constraints imposed by a heterochromatic milieu

Students' participation in collaborative research should be recognised

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