title: On square values of the product of the Euler totient and sum of divisors functions

authors: Broughan, Kevin A.

subjects: Euler function

abstract: If n is a positive integer such that ϕ(n)σ(n) = m² for some positive integer m, then m≤n. We put m = n - a and we study the positive integers a arising in this way.

text: On square values of the product of the Euler totient and sum of divisors functions If n is a positive integer such that ϕ(n)σ(n) = m² for some positive integer m, then m≤n. We put m = n - a and we study the positive integers a arising in this way.

year: 2012

title: Dynamic Nonlinear Resistance Model for a Power MOSFET in an Oscillatory RLC Circuit

authors: Raju, S

abstract: This paper presents the development of a new Matlab mosfet model specifically designed for RLC circuits. The key contribution is the formulation of a novel equation that accurately captures the device behavior across subthreshold, above-threshold regions and at threshold point, addressing limitations in existing models. The developed model treats the mosfet as a variable resistance element, with the resistance changing dynamically at each instant, enabling the solution of differential equations governing the RLC circuit. Curve fitting and refinement were conducted based on experimental results, leading to a close match between the simulations and experimental data. The model was tested with triangle, sinusoidal and quadrilateral gate voltages, and the simulation results show good match with the experimental data, demonstrating the model's accuracy. It provides a straightforward way to predict performance, making it easier to refine and optimize the design gate voltage before physical implementation. This work provides a solid foundation for mosfet modeling in oscillatory RLC circuits, which can be applied to a wide range of power electronics applications.

text: Dynamic Nonlinear Resistance Model for a Power MOSFET in an Oscillatory RLC Circuit This paper presents the development of a new Matlab mosfet model specifically designed for RLC circuits. The key contribution is the formulation of a novel equation that accurately captures the device behavior across subthreshold, above-threshold regions and at threshold point, addressing limitations in existing models. The developed model treats the mosfet as a variable resistance element, with the resistance changing dynamically at each instant, enabling the solution of differential equations governing the RLC circuit. Curve fitting and refinement were conducted based on experimental results, leading to a close match between the simulations and experimental data. The model was tested with triangle, sinusoidal and quadrilateral gate voltages, and the simulation results show good match with the experimental data, demonstrating the model's accuracy. It provides a straightforward way to predict performance, making it easier to refine and optimize the design gate voltage before physical implementation. This work provides a solid foundation for mosfet modeling in oscillatory RLC circuits, which can be applied to a wide range of power electronics applications.

year: 2025

title: Mental health of people of diverse genders and sexualities in Aotearoa/New Zealand: Findings from the New Zealand Mental Health Monitor

authors: Tan, Kyle K. H.

subjects: Science & Technology

abstract: Issues addressed: To examine mental health inequities, and social exclusion and isolation and protective factor differences between people of diverse genders and sexualities (lesbian/gay, bisexual, gender diverse, and takatāpui) and cisgender and heterosexual people in Aotearoa/New Zealand.  Methods: We employed data from the pooled probability sample of 2016 and 2018 New Zealand Mental Health Monitor. The sample comprised of 2,938 people at least 15 years old, of which 93 had diverse gender and sexuality identities. Generalised linear models were used to test for differences in mental health (current and lifetime mental distress, depression, anxiety, self-harm and suicide), social exclusion and isolation, and friend and family support for people of diverse genders and sexualities. We also conducted exploratory linear regression analyses to examine whether mental health difficulties were associated with social exclusion and isolation and friend/family support.  Results: People of diverse genders and sexualities had high rates of mental health difficulties across all variables we examined. For example, people identifying as diverse genders and sexualities had three times the risk of considering self-harm and suicide than their cisgender and heterosexual counterparts (22% vs 5%; RR = 3.12). People of diverse genders and sexualities also scored an average of 6.08 points higher on the 27-point PHQ-9 depression scale when they had experienced social isolation, and 4.01 points higher when they experienced social exclusion. Conclusion: Our results are consistent with current literature on the large mental health inequities faced by people of diverse genders and sexualities.  So what?: Policy makers and healthcare providers in Aotearoa/New Zealand should consider the negative mental health consequences of social exclusion and isolation for people of diverse genders and sexualities.

text: Mental health of people of diverse genders and sexualities in Aotearoa/New Zealand: Findings from the New Zealand Mental Health Monitor Issues addressed: To examine mental health inequities, and social exclusion and isolation and protective factor differences between people of diverse genders and sexualities (lesbian/gay, bisexual, gender diverse, and takatāpui) and cisgender and heterosexual people in Aotearoa/New Zealand.  Methods: We employed data from the pooled probability sample of 2016 and 2018 New Zealand Mental Health Monitor. The sample comprised of 2,938 people at least 15 years old, of which 93 had diverse gender and sexuality identities. Generalised linear models were used to test for differences in mental health (current and lifetime mental distress, depression, anxiety, self-harm and suicide), social exclusion and isolation, and friend and family support for people of diverse genders and sexualities. We also conducted exploratory linear regression analyses to examine whether mental health difficulties were associated with social exclusion and isolation and friend/family support.  Results: People of diverse genders and sexualities had high rates of mental health difficulties across all variables we examined. For example, people identifying as diverse genders and sexualities had three times the risk of considering self-harm and suicide than their cisgender and heterosexual counterparts (22% vs 5%; RR = 3.12). People of diverse genders and sexualities also scored an average of 6.08 points higher on the 27-point PHQ-9 depression scale when they had experienced social isolation, and 4.01 points higher when they experienced social exclusion. Conclusion: Our results are consistent with current literature on the large mental health inequities faced by people of diverse genders and sexualities.  So what?: Policy makers and healthcare providers in Aotearoa/New Zealand should consider the negative mental health consequences of social exclusion and isolation for people of diverse genders and sexualities.

year: 2021-10-03