Functions are the core of algebra, and the teaching of function concepts is also the main task of high school mathematics Students' learning of functions and their concepts shifts from understanding specific quantitative relationships to understanding abstract quantitative relationships The monotonicity of functions, as the property of the first function that students learn in high school, lays a certain foundation for learning function related knowledge in the future.

This study introduces a novel Groundwater Flooding Risk Assessment (GFRA) model to evaluate risks associated with groundwater flooding (GF), a globally significant hazard often overshadowed by surface water flooding. GFRA utilizes a conditional probability function considering critical factors, including topography, ground slope, and land use-recharge to generate a risk assessment map. Additionally, the study evaluates the return period of GF events (GFRP) by fitting annual maxima of groundwater levels to probability distribution functions (PDFs). Approximately 57% of the pilot area falls within high and critical GF risk categories, encompassing residential and recreational areas. Urban sectors in the north and east, containing private buildings, public centers, and industrial structures, exhibit high risk, while developing areas and agricultural lands show low to moderate risk. This serves as an early warning for urban development policies. The Generalized Extreme Value (GEV) distribution effectively captures groundwater level fluctuations. According to the GFRP model, about 21% of the area, predominantly in the city’s northeast, has over 50% probability of GF exceedance (1 to 2-year return period). Urban outskirts show higher return values (> 10 years). The model’s predictions align with recorded flood events (90% correspondence). This approach offers valuable insights into GF threats for vulnerable locations and aids proactive planning and management to enhance urban resilience and sustainability.

Since 2022, global geopolitical conflicts have intensified, and there has been a notable increase in the international community’s demand for currency diversification. This has created a new opportunity for the internationalization of the Renminbi (RMB). This paper examines the factors influencing the internationalization of the RMB, with a particular focus on its role as a unit of account, medium of exchange and store of value. These functions are considered in conjunction with the digital technological innovation represented by e-CNY. The methodology employed is based on the vector autoregression (VAR) model, Granger causality test and variance decomposition analysis. The Granger causality test indicates that digital technology innovation is not the primary driver of RMB internationalization at this juncture. The impulse response analysis and variance decomposition analysis revealed that the impact and direction of influence exerted by the various factors on RMB internationalization exhibit considerable discrepancies.

Catastrophes, like earthquakes, bring sudden and severe damage, causing fatalities, injuries, and property loss. This often triggers a rapid increase in insurance claims. These claims can encompass various types, such as life insurance claims for deaths, health insurance claims for injuries, and general insurance claims for property damage. For insurers offering multiple types of coverage, this surge in claims can pose a risk of financial losses or bankruptcy. One option for insurers is to transfer some of these risks to reinsurance companies. Reinsurance companies will assess the potential losses due to a catastrophe event, then issue catastrophe reinsurance contracts to insurance companies. This study aims to construct a valuation model for catastrophe reinsurance contracts that can cover claim losses arising from two types of insurance products. Valuation in this study is done using the Fundamental Theorem of Asset Pricing, which is the expected present value of the number of claims that occur during the reinsurance coverage period. The number of catastrophe events during the reinsurance coverage period is assumed to follow a Poisson process. Each impact of a catastrophe event, such as the number of fatalities and injuries that cause claims, is represented as random variables, and modeled using Peaks Over Threshold (POT). This study uses Clayton, Gumbel, and Frank copulas to describe various dependence characteristics between random variables. The parameters of the POT model and copula are estimated using Inference Functions for Margins method. After estimating the model parameters, Monte Carlo simulations are performed to obtain numerical solutions for the expected value of catastrophe reinsurance based on the Fundamental Theorem of Asset Pricing. The expected reinsurance value based on Monte Carlo simulations using Indonesian earthquake data from 1979–2021 is Rp 10,296,819,838.