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A Lone Ranger, Two Smoking Barrels and the Dirty Dozen: Confirming the harmonious nature (convergence) of the alternating harmonic series and some serious series stuff
(City University of New York, 2026) Kashyap, Ravi
This study provides a proof of the convergence of the alternating harmonic series. The alternating harmonic series could be termed the more harmonious sibling of the harmonic series, which is divergent. As a byproduct of this proof - and the associated technique - we arrive at the convergence of a few other series and related results. All the main results are stated as propositions and corollaries, complete with proofs that are simple yet formal. In addition, we create a custom program - code - to numerically illustrate the convergence of one of the series. This serves as an example of how to approach series calculations using computational tools. We verify the convergence of all the series using mathematical software. Our findings confirm the convergence of the alternating harmonic series and several related series. To complement the mathematical content, we have given a compilation of several techniques that can aid in disseminating this knowledge across appropriate audiences. We discuss challenges with respect to mathematics education and provide some pedagogical prescriptions - for the classroom, or other educational settings - to approach the topics we have presented. Our suggestions can help ease the anxiety of participants - who tend to get uneasy when engaging with mathematical material - while performing symbolic manipulations. Despite the simplicity of our proofs - and our belief that these results are surely known - we were surprised that we could not find these results easily elsewhere. This indicates that an unintended consequence of the many advances in mathematics - and related knowledge creation - might be that some knowledge could either be getting lost or just becoming harder to find, which is the equivalent of getting lost in many cases. We outline a potential solution to mitigate this unwanted outcome.
Between empire, periphery, and the United States of America: The local and international origins of the Melbourne Social Survey (1941–1943)
(Taylor & Francis, 2021) Arnott, Georgina; Greenhalgh, Charlotte
This article sets out to test competing characterisations of early Australian social research through an explication of the origins of Australia’s first major social survey, the Melbourne Social Survey (1941–1943), and its historical retelling. It asks to what extent international social survey models, figures, intellectual approaches and finances shaped the survey, and what this reveals about the degree to which early Australian social research was defined by its position of global marginality. This article finds that histories of the survey have overestimated the influence of British survey models and intellectual traditions by paying disproportionate attention to its director from 1941, Wilfred Prest. It argues that a much more powerful inspiration for the social survey, and a new social research direction at Melbourne, can be seen in a trip to the United States of America taken by University of Melbourne Dean of Commerce, Douglas Copland, in 1926 and 1927. Planners of the Melbourne Social Survey were sure it would be ‘of major social significance’. Today, the story of the survey and its historical representation illuminates shifting forces that shaped early Australian social research, and contributes to ongoing debate about the way twentieth-century social science knowledge has been circulated globally.
The survey and the state: Governments and early social research in New Zealand and Australia, 1930s–40s
(Taylor & Francis, 2020) Arnott, Georgina; Greenhalgh, Charlotte
© Editorial Board, Australian Historical Studies 2020. This article tells the story of two pioneering social surveys designed to extend international developments in quantitative social research into the Antipodes: the 1937–38 survey of living standards in rural New Zealand and the University of Melbourne's 1941–43 urban survey of 7,609 households. Archival material associated with these surveys illuminates the influence of governments on the topics, methods and publication of survey results and the tensions their involvement caused for academic researchers. Caught between the strategic interests of funders and the higher ideals of social science, social researchers struggled to deliver significant findings about local populations.
Ko te reo te mauri o te mana Māori: Reclaiming mātauranga, identity and the future of our people
(Te Pua Wānanga ki te Ao | Faculty of Māori and Indigenous Studies, University of Waikato, 2026) Maxwell, Te Kahautu
This lecture offers a glimpse into research into te reo Māori, tikanga Māori, mātauranga Māori and kapa haka. It presents te reo as the root of tikanga, tikanga as the foundation of mātauranga Māori, and kapa haka as the vehicle through which this knowledge is brought to life. More than a language, te reo is the mauri through which all people can understand the Māori worldview and deepen their appreciation of Aotearoa, the ancestral homeland, Māori have shared with all who now call it home. Through kapa haka, whakapapa, histories, values, belief systems, iwitanga and ancestral knowledge are expressed, revitalised and transmitted, connecting the hunga mate with te hunga mate and carrying Māoritanga, identity, knowledge and aspirations forward for future generations. “He uri nō te Raupatu, he toa nō te Rauora!” (Te Arikinui Kuini Ngā Wai hono i te pō, 2026).
Study on the formation mechanisms of core–shell structures and their influence on the properties of Ni-Co-Al-Ti-based high-entropy intermetallic
(The University of Waikato, 2026) Liu, Junqi; Yang, Fei
The advancement of aerospace technology imposes increasingly stringent requirements on the mechanical properties of structural materials at both room and elevated temperatures. Intermetallic compounds have attracted considerable attention due to their excellent specific strength and high-temperature performance. However, their engineering applications are persistently constrained by issues such as room-temperature brittleness or insufficient high-temperature strength. Inspired by the concept of high-entropy design, this study employs a sublattice high-entropy alloying strategy to improve the mechanical properties of conventional intermetallic compounds, developing Ni-Co-Al-Ti-based high-entropy intermetallics with a core–shell structure that exhibit favorable room-temperature ductility. Through further compositional tuning, the core–shell structure evolves toward multi-scale characteristics, achieving synergistic enhancement of strength and ductility. This work reveals the formation mechanism of the multi-scale core–shell structure and its influence on room-temperature mechanical properties, while also elucidating the strengthening–ductilization mechanism of the multi-scale core–shell structured high-entropy intermetallics. In addition, the mechanical properties over a wide temperature range are investigated, revealing the embrittlement at intermediate temperature and an anomalous yield effect, along with the corresponding microscopic mechanisms. First, through thermodynamic and solidification analyses, the effect of Co addition on the Ni(75-x)CoxAl8.33Si8.33Ti8.34 series alloys is studied. The results show that Co addition favors the stable formation of an L12/FCC dual-phase structure. Further microstructural characterization reveals that, at a Co content of 25 at.%, a dual-phase core–shell structure consisting of ordered L12 cores and disordered FCC shells forms within the grains. Based on these observations, the mechanism by which Co addition promotes the formation of the core–shell structure is analyzed. On the one hand, Co addition induces the formation of the FCC phase and promotes the precipitation of the L12 phase, providing the phase-structural basis for the core–shell structure. On the other hand, it maintains a low L12/FCC interfacial energy, supplying an stable interfacial condition for core–shell formation. Mechanical testing indicates that the formation of this structure effectively improves the room-temperature ductility of the alloy. The Ni25Co25Al8.33Si8.33Ti8.34 alloy exhibits a yield strength of approximately 450 MPa, an ultimate tensile strength of about 650 MPa, and a plastic elongation of roughly 10%. Building upon the alloy in which the core–shell structure has already been established, compositional adjustments are performed to promote the development of the core–shell structure toward multi-scale features. The addition of Ta induces the formation of a dual-scale core–shell structure with micron- and submicron- scale in the Ni50Co25Al7Ti7Ta1.5Cr9.5 alloy, effectively enhancing the room-temperature strength. This alloy shows a yield strength of about 800 MPa, an ultimate tensile strength of approximately 1000 MPa, and a plastic strain of about 8%. Further increasing the Al/Ti ratio promotes the formation of a multi-scale core–shell structure comprising micron-scale, submicron-scale, and nanoscale in the Ni50Co25AlxTi(14-x)Ta1.5Cr9.5 alloys, achieving a synergistic improvement in room-temperature strength and ductility. Among them, the Ni50Co25Al9Ti5Ta1.5Cr9.5 alloy exhibits a yield strength of approximately 1000 MPa, an ultimate tensile strength of about 1250 MPa, and a plastic strain of roughly 12.5%. The formation mechanism of the multi-scale core–shell structure can be summarized as follows: Ta addition exacerbates compositional segregation at grain boundaries, inducing the formation of micron-scale core–shell structure. Meanwhile, an increased Al/Ti ratio enhances the sluggish diffusion effect, promoting the precipitation of submicron-scale and nanoscale core–shell structures. Furthermore, Ni50Co25Al9Ti5Ta1.5Cr9.5 alloy with multi-scale core–shell structure is selected as the research object. The evolution of dislocation substructures during room-temperature deformation was systematically characterized, revealing that the room-temperature deformation mechanism of this alloy is synergistically governed by superlattice intrinsic/extrinsic stacking faults, stacking faults, Lomer-Cottrell locks, dislocation forests, and dislocation walls.. On this basis, combined with theoretical calculations, the strengthening–ductilization mechanism is thoroughly elucidated. The results indicate that the high strength of the alloy mainly originates from precipitation strengthening arising from the high-volume-fraction ordered L12 cores and hetero-deformation-induced strengthening caused by the multi-scale core–shell structure, while the favorable ductility is attributed to continuous (FCC+nanoscale L12) dislocation motion channels and hetero-deformation-induced strain hardening. In addition, the highly coherent core–shell interfaces and serrated grain boundaries jointly promote cooperative deformation, enabling the material to achieve an excellent combination of strength and ductility at room temperature. Subsequently, the microstructural stability and mechanical properties of the Ni50Co25Al9Ti5Ta1.5Cr9.5 alloy at 800 ℃ are investigated, revealing a good thermal stability and relatively high yield strength, but with almost zero plastic elongation. Vacuum comparative tensile tests indicate that this intermediate-temperature embrittlement originates from grain-boundary weakening caused by oxygen penetration and stress concentration induced by grain-boundary sliding. By increasing the Cr content to 20 at.%, discontinuous α-Cr phases and small-scale core–shell structures are induced to form at grain boundaries, which effectively hinder oxygen diffusion and restore the 800 ℃ plastic elongation to about 5%, thereby mitigating the embrittlement issue at intermediate temperature. In addition, the mechanical properties of the high-Cr alloy over a wide temperature range from 25 to 1000 ℃ are evaluated. The results show that the yield strength first increases and then decreases with rising temperature, reaching a peak value of about 920 MPa at 800 ℃, exhibiting a clear anomalous yield effect. TEM characterization reveals that this effect is attributable to the transition of the deformation mechanism to anti-phase boundary shearing at elevated temperatures, as well as the formation of Kear-Wilsdorf locks and Lomer-Cottrell locks.