On recursions for coefficients of mock theta functions

We use a generalized Lambert series identity due to the first author to present q-series proofs of recent results of Imamoglu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions. Additionally, we discuss an application of this identity to other mock theta functions.Comment: 21 pages, to appear in Research in Number Theor

Variations of Andrews-Beck type congruences

We prove three variations of recent results due to Andrews on congruences for $NT(m,k,n)$, the total number of parts in the partitions of $n$ with rank congruent to $m$ modulo $k$. We also conjecture new congruences and relations for $NT(m,k,n)$ and for a related crank-type function.Comment: 15 pages, typos corrected, to appear in the Journal of Mathematical Analysis and Application

The Effectiveness of Greenhouse Gas Abatement Strategies for the Dairy Industry in South-Western Victoria, Australia

In Australia, the dairy industry generates 8.9 million tonnes of carbon dioxide equivalents (t CO2e) per year (Christie et al. 2011). Most greenhouse gas (GHG) emissions from the dairy sector are high global warming potential gases such as methane (CH4) from enteric fermentation and nitrous oxide (N2O) from cattle urine and nitrogen (N) based fertilizers, contributing to climate change issues. Several GHG abatement options are available to dairy farmers, including increasing diet quality, feeding oils and reducing replacement rates (Eckard et al. 2010), but little assessment of their effectiveness has been carried out at a farm system level. The two objectives of this study were: first, to quantify GHG emissions from pasture-based dairy production systems in southwestern Victoria; second, to identify GHG abatement strategies and examining their effects on reducing farm emissions

catena-Poly[[[bis­[4-(1H-1,3,7,8-tetra­azacyclo­penta­[l]phenanthren-2-yl)phenol-κ2 N 7,N 8]manganese(II)]-μ-naphthalene-1,4-dicarboxyl­ato-κ2 O 1:O 4] naphthalene-1,4-dicarboxylic acid hemisolvate monohydrate]

The 1,4-dicarboxyl­ate dianions in the title compound, [Mn(C12H6O4)(C19H12N4O)2]·0.5C12H8O4·H2O, bond to two 4-(1H-1,3,7,8-tetra­azacyclo­penta­[l]phenanthren-2-yl)phenol-chelated Mn atoms to form a chain that features the metal atom in an octa­hedral coordination geometry. Adjacent chains inter­act with the uncoordinated water mol­ecules to form a three-dimensional network. The naphthalene-1,4-dicarboxylic acid solvent mol­ecule, which is disordered about a centre of inversion, occupies the space within the network but is not bonded to the network. One NH group is disordered equally over two positions

Unleashing Cognitive Synergy in Large Language Models: A Task-Solving Agent through Multi-Persona Self-Collaboration

Human intelligence thrives on the concept of cognitive synergy, where collaboration and information integration among different cognitive processes yield superior outcomes compared to individual cognitive processes in isolation. Although Large Language Models (LLMs) have demonstrated promising performance as general task-solving agents, they still struggle with tasks that require intensive domain knowledge and complex reasoning. In this work, we propose Solo Performance Prompting (SPP), which transforms a single LLM into a cognitive synergist by engaging in multi-turn self-collaboration with multiple personas. A cognitive synergist refers to an intelligent agent that collaborates with multiple minds, combining their individual strengths and knowledge, to enhance problem-solving and overall performance in complex tasks. By dynamically identifying and simulating different personas based on task inputs, SPP unleashes the potential of cognitive synergy in LLMs. We have discovered that assigning multiple, fine-grained personas in LLMs elicits better problem-solving abilities compared to using a single or fixed number of personas. We evaluate SPP on three challenging tasks: Trivia Creative Writing, Codenames Collaborative, and Logic Grid Puzzle, encompassing both knowledge-intensive and reasoning-intensive types. Unlike previous works, such as Chain-of-Thought, that solely enhance the reasoning abilities in LLMs, SPP effectively elicits internal knowledge acquisition abilities, reduces hallucination, and maintains strong reasoning capabilities. Code, data, and prompts can be found at: https://github.com/MikeWangWZHL/Solo-Performance-Prompting.git.Comment: work in progres

Flux density measurements for 32 pulsars in the 20 cm band

Flux density measurements provide fundamental observational parameters that describe a pulsar. In the current pulsar catalogue, 27% of radio pulsars have no flux density measurement in the 20 cm observing band. Here, we present the first measurements of the flux densities in this band for 32 pulsars observed using the Parkes radio telescope and provide updated pulse profiles for these pulsars. We have used both archival and new observations to make these measurements. Various schemes exist for measuring flux densities. We show how the flux densities measured vary between these methods and how the presence of radio-frequency-interference will bias flux density measurementsComment: Accepted by RA