Root counting in product homotopy method

Product Homotopy method is used to solve dense multivariate polynomial systems for finding all isolated solutions (real or complex). There are two stages in the computation of Homotopy method which are root counting and root finding. This study focuses on root counting which involves the computation of multi-homogeneous Bézout number (MHBN). This value determines the number of solution path in the second stage. Homogenization of partition each gives its own MHBN. Therefore, it is crucial to have minimum MHBN. The computation of minimum MHBN using local search method, fission and assembly method and genetic algorithm had become intractable when the system size gets larger. Hence, this study applied recent heuristic method, Tabu Search. Other than that, the computation of estimating MHBN is of exponential time. For large size system, the usage of row expansion with memory becomes impossible, hence, this study focus on implementing General Random Path algorithm (GRPA). This study implements Tabu search method and GRPA into several systems of different sizes. Tabu search is effective since the global minimum is obtained instead of the local minimum. Other than that, the number of visited partition is much smaller compared with the previous method. Although GRPA gives estimated value, it helps for large size system. We implement two accuracy level in the computation and in the result, the N=1000 gives more accurate result. Hence, GRPA is important when it comes to solve estimated MHBN for large size system

A comparative flood frequency analysis of high-flow between annual maximum and partial duration series at Sungai Langat Basin

Flood frequency analysis should consider small and frequent floods. Despite the complexities in partial duration series implementation, it can give a better flood estimation in a way that it does not exclude any significant high flow events, even if it is not the highest event of the year. This study employs the streamflow data recorded at Kajang station, Sungai Langat, Malaysia over a 36-year period spanning from 1978 to 2013. The paper attempts to conduct flood frequency analysis using two approaches, annual maximum and partial duration series. The optimal threshold value is selected to be 48.7 m3/s, where the dispersion index stabilizes at around 1, DI = 1. The results have shown that generalized extreme value (GEV) distribution describes the annual maximum data while the lognormal (LN3) and generalized Pareto (GPA) distribution is chosen as the best fit distribution at Kajang station for a partial duration series. There is a slight difference between estimated streamflow magnitude when using GPA and LN3 for selected return periods, while a considerable difference was observed when using annual maximum at a higher return period. As a conclusion, PDS gives more relevant magnitude estimation rather than AMS. Flood frequency plays an important role in understanding the nature and magnitude of high flow, which in turn can assist relevant agencies in the design of hydrological structures and reduce flood impacts

Long term trend analysis of upstream and middle-stream river in Langat Basin, Selangor, Malaysia

The present study investigates the trend in long term monthly streamflow of Sungai Lui (upstream) and Sungai Kajang (middle-stream) of the Sungai Langat Basin located in Selangor, Malaysia. The Mann-Kendall (MK) and Innovative Trend Method (ITM) tests were utilized to assess the trends at the two stations. The trend free pre-whitening (TFPW) and variance correction (VC) tests were used to assess the effects of serial correlation on the established trend, and Sen’s slope estimator was used to assess the magnitude of streamflow. Based on Sen’s Slope estimator results, the trend magnitude for Lui station is very small compared to the Kajang station. The Kajang station shows the highest increase in trend magnitude for November. The results of TFPW and VC trend tests showed that the most significant increasing trend of months occurred at Kajang station, while the less increasing significant trend of months occurred at Lui station. It can be concluded that similar trend results were obtained when the modified Mann-Kendall and ITM were applied to the same data for Sungai Lui and Sungai Kajang. The study found that there is a significant difference in terms of trend and magnitud between upstream and middle-stream

Trend and Linearity Analysis of Meteorological Parameters in Peninsular Malaysia

Climate change has often led to severe impact on the environment. This study aimed to investigate the monthly trends and linearity of meteorological parameters at four locations during the period from 1970 to 2016. These locations represent the south, north, east, and west of Peninsular Malaysia. The meteorological parameters used were monthly total precipitation (mm) and monthly average temperature (°C). To illustrate the methodology, the Mann–Kendall (MK) trend test and a non-parametric regression model were used. The MK trend test did not indicate significant trends in precipitation, but indicated a trend in temperature for all locations. The Sen value gives the amount of fluctuation of precipitation and temperature for every year. The results of the linearity test exhibited a linear trend for precipitation and temperature for most of the months throughout the study period. Thus, this study gives insights into the monthly trends of meteorological parameters, especially in Peninsular Malaysia