Burapha Science Journal

Toxicity of Glufosinate-Ammonium Herbicide in Giant Freshwater Prawn (Macrbrachium rosenbergii)

Butsayamat Wongchan — 2025-09-09

Background and Objectives : Nowadays, the Thailand export agricultural product was intensively expanded. Therefore, Thailand agricultural sector expels the promotion in chemical using trends in agricultural system. By these economic forces, farmers have encountered large-scale farming production sufficiently for increase consumer demands such agrochemicals using such as chemical fertilizers and herbicides is an important factor for farmers relying on. Herbicides are widely used not only to increase crop yields but also to control weed growth and dissipation that hinders nutrient needs for crop. So far, high volume of herbicide imports value is an evidence reflecting the remains agrochemicals farming system in contribution to the environmental pollution and crisis via inappropriate and excessive usage. Thereby the improper chemicals practice and usage arising from overuse or runoff into nearby ecosystems leads to the herbicide accumulation in environments such as soil, water, and even the air that causes the long-term contamination. Aquatic animals Inevitably affects to this risk by exposure to herbicide–contaminated environments. Aquatic animal health is damaged by herbicide effect in either immediate toxicity or long-term accumulation in animal tissue. Although the concentration of herbicides detected in aquatic animals remains in safety range for consuming, the long-period exposure of such chemicals bring into health risk, especially the human diet made from these aquatic animals. Glufosinate ammonium is herbicide disrupting cell structure and function of plants, but has no effect in aquatic invertebrates. This study aimed to investigate the short-term toxicological effects of glufosinate ammonium on the giant freshwater prawn (Macrobrachium rosenbergii), a commercially and ecologically important species in Thailand. However, limited data about the response to its glufosinate ammonium exposure in this species was little studied. Therefore, the objective of this research is to examine the physiological and biochemical effects of this herbicide on M. rosenbergii. The changes in tissues and blood cells were observed including characterizing the acetylcholinesterase (AChE) expression using the Western blot technique in the nervous system. This key enzyme acts as a valuable biomarker for neurotoxicity in aquatic organisms. Thereby determining the alteration in both cellular and molecular responses, this study provides better understanding pathophysiological effect on post-exposure herbicides of aquatic animals in contribution to threatening human health risk via the contaminated food consuming.

Methodology : Glufosinate ammonium toxicity was assessed in this study for determining its effect on cumulative mortality rate in relation to acetylcholinesterase (AChE) expression as well as the physiological response after glufosinate ammonium exposure was investigated by measuring the total hemocytes and histopathological alteration in muscular and intestinal tissue. After glufosinate ammonium exposure to healthy giant freshwater prawns at effective concentrations from 0 (control), 250, 300, 350, 400, and 450 µL/L, respectively. For simulating possible duration time and exposure levels in nature this experimented duration time were performed at 24, 48, 72, and 96 hours.Moreover, the responsive biochemical function in protein expression profile and AChE expression by using western blot analysis was determined for neurotoxic damage AChE acting as a biomarker.

Main Results : The study for glufosinate ammonium toxicity revealed an increased mortality of post-exposure of M. rosenbergii in time and concentration dependent manner that evidenced on the increased cumulative mortality.Western blot analysis demonstrated the significantly decrease in AChE expression while increased exposure time. AChE was detected at molecular weight of approximately 71 kilodaltons (kDa) in hemolymph. The awkwardly decreased in AChE expression in glufosinate ammonium-exposed prawns revealed its neuronal disruptive effect on neuromuscular function. For histopathological examination, the exposed prawns displayed the structural damage of hemocytes in multiple cell types, including large granular hemocytes (LGH), small granular hemocytes (SGH), and hyaline-type cells (H-type). Evidence on irregular cell boundaries, disrupted cell membranes and cytoplasmic disintegration suggested the herbicide effect on to the immunity compromises. For histological study, swelling and degeneration of muscular tissue was shown, thereby its direct effect on muscle structure and function. Similarly, after exposure pathological changes was shown in prawn intestinal tissues such as lumen dilation and fusion of microvilli, thereby reducing nutrient absorption and hindering digestion efficiency. Therefore, much longer exposure time with an effective concentration of glufosinate-ammonium, the growth and health was retarded by the persistent changes at vital structure of the exposed prawns.

Conclusions : The health burden of giant freshwater prawns (Macrobrachium rosenbergii) is caused by the toxic effect of glufosinate ammonium exposure, leading to a high morbidity rate in a concentration- and time exposure-dependent manner. At a high dose and with increased time of exposure, glufosinate ammonium exerted its effect by causing a decline in AChE activity in relation to decreased acetylcholinesterase (AChE) expression. At the biochemical and histological levels in glufosinate ammonium–exposed prawns, hemocyte morphological abnormalities and tissue structural damage caused by disturbed AChE activity were observed. From these results, AChE is determined as a sensitive biomarker for effectively patrolling herbicide contamination in aquatic ecosystems.

Necessary and Sufficient Conditions for the Concurrent Point of Cevians with Area-Bisecting and Perimeter-Bisecting Properties in a Given Triangle

Somkid Intep — 2025-10-08

Background and Objectives : The problem of fairly dividing a pizza between two individuals such that both receive equal quantities has been a long-standing topic of mathematical interest. This has led to a range of studies involving various geometric shapes and principles to ensure equal division not only in terms of area but also in terms of boundary length (or crust). In 1994, Carter and Wagon demonstrated that a circular pizza could be equally divided into eight slices using four straight lines intersecting at any point, such that each of the resulting eight angles measures 45 degrees. This slicing method ensured each person received equal portions when slices were alternately distributed. Later in 2015, Nicollier extended this idea to equilateral triangular pizzas, introducing a division using six lines—three connecting an arbitrary interior point to the triangle’s vertices, and three drawn perpendicularly from that point to each side. By distributing these sections alternately, both individuals received equal areas and crust lengths. Further developments by Embacher and Humenberger in 2019 explored the division of acute or non-equilateral triangles into six smaller triangles from a chosen internal point. Their findings revealed that the area is equally divided when alternating regions are shaded black and white, but only if the point lies on the Stammler hyperbola—an important geometric curve containing the incenter, circumcenter, and excenter of the triangle. In 2020, Humenberger focused on unequal-sided triangular pizzas and proposed that crust bisection is guaranteed when the dividing point lies on a line connecting the incenter and circumcenter. For achieving area bisection, however, he utilized Cevians—line segments from each vertex to the opposite side intersecting at a common internal point—finding that equality in area occurs only if the intersection point lies along the triangle’s medians. Building upon this rich context, the current research aims to identify the necessary and sufficient conditions for a point within a triangle such that the Cevians intersecting at that point divide both the area and the perimeter of the triangle equally. While prior studies examined these two properties individually, this study focuses on their concurrent realization using only Cevians, which introduces a unique constraint that deepens the geometric inquiry.

Methodology : The investigation began with a conjecture formed through dynamic geometry software (GSP), which allowed for visual experimentation and hypothesis testing. Once a conjecture was formed, the authors pursued a rigorous mathematical proof using classical geometric theorems—chiefly, Ceva’s Theorem, which provides conditions for concurrency of Cevians in a triangle.

Key definitions were employed for precision:

A Cevian is a line segment drawn from a vertex of a triangle to the opposite side.
A median is a Cevian that intersects the opposite side at its midpoint.
The main median refers to the median corresponding to the triangle’s axis of symmetry in an isosceles triangle.
A point of Cevian concurrency is called a concurrent point.
A centroid is the common point of intersection of all three medians of a triangle.

Main Results : This research focuses on investigating the geometric conditions associated with the concurrency point of Cevians in a given triangle that simultaneously induces two notable properties: first, that the concurrency point partitions the triangle into six smaller subregions of equal geometric relevance; and second, that this point serves as both an area-bisecting and a perimeter-bisecting point of the triangle. The findings of the study lead to the identification of a fundamental geometric characterization. The necessary and sufficient condition for the concurrency point of the Cevians to possess both the area-bisecting and the perimeter-bisecting properties can be precisely formulated as follows: in the case of an isosceles triangle, the concurrency point must lie on the main median, whereas in the case of a scalene triangle, the concurrency point must coincide with the centroid of the triangle. These conclusions establish a clear distinction between symmetric and asymmetric triangular configurations and highlight the unique and significant role of the centroid in a scalene triangle. The validity of these results has been rigorously established through proofs constructed by employing Ceva’s theorem, in conjunction with proportional reasoning concerning both triangular areas and the segment lengths determined by the Cevians. This methodological framework not only ensures the logical soundness of the arguments but also demonstrates the deep interrelationship between classical Ceva-type concurrency conditions and the division properties of both the area and the perimeter of triangles. The outcomes of this investigation contribute to the broader understanding of triangle geometry by providing a comprehensive condition that unifies two fundamental partitioning properties within a single concurrency framework.

Conclusions : The study offers a nuanced extension to prior works (Humenberger, 2020) by merging two types of fairness criteria (area and boundary) under a single geometric constraint—the concurrency of Cevians. In summary, the research contributes a precise characterization of geometric conditions under which a triangle can be equally divided—both in area and crust—via intersecting Cevians. The central conclusion is that:

For isosceles triangles, the point of concurrency must lie on the main median.
For scalene triangles, the point must be the centroid.

This result advances our understanding of fair division in geometric terms, with potential applications not only in recreational mathematics (e.g., pizza problems) but also in educational settings where concepts like medians, centroids, and Cevians are introduced.

Assessment of Lipase Inhibitory Efficiency, Total Phenolic Content and Antioxidant Activity of Spirogyra sp. Extract from Closed-Circulation Cultivation System

Rawinipa Srimoon — 2025-10-20

Background and Objectives : Obesity is a lipid homeostasis dysfunction and hyperlipidemia condition, leading to the occurrence of the other chronic diseases such as cardiovascular disease, diabetes and hypertension. The enzyme which is importance in lipid digestion is lipase. Inhibition of lipase enzyme decreases the digestion and the absorption of lipid to the cells, causing in lower level of the lipid in blood. The studies of many natural lipase inhibitors may help the reduction of synthetic drug which causes long-term adverse side effects. Thus, the objectives of this research were to assess the lipase inhibitory efficiency, total phenolic content and antioxidant activity in Spirogyra sp. extract. Spirogyra sp. was the green-fresh water macroalgae with high nutrition values and antioxidants content such as phenolic and flavonoids compounds. But the phytochemicals containing in algae were variation because of the different aquatic habitat of algae. It made the unstable quality and productivity of algae from natural sources. In this study, Spirogyra sp. sample was cultivated from closed-circulating system, which the culture conditions were controlled for both productivity and quality of algae. Moreover, algae were non-contaminated from any toxic substances because there was the water treatment process both before and after cultivation. There has been no previous study on the assessment of lipase inhibitory efficiency, total phenolic content and antioxidant activity in Spirogyra sp., which was cultivated in the closed-circulation cultivation system.

Methodology : Spirogyra sp. sample was cultured in 1,000 L closed-circulating raceway pond type in transparent acrylic roof greenhouse. Water treatment was done using precipitation method coupled with the aerator before and after each cultivation cycle. Algae sample was picked, washed, dried at 50^OC for 2 days and blended. Dried powder sample was macerated with 70% ethanol at a ratio of dried powder : solvent was 1:5 weight by volume for 48 h, and evaporated to produce the crude extract. Afterthat, crude extract was determined the lipase inhibitory efficiency by measuring the rate of oleic acid released from triolein breakdown by pancreatic lipase enzyme, compared with the drug named Xenical (standard Orlistat). Total phenolic content was performed using Folin–Ciocalteu phenol reagent method. The antioxidant activity was conducted using the DPPH radical scavenging activity method. The enzyme inhibition kinetic was evaluated using the Lineweaver-Burg plot derived from the Michaelis-Menten equation. The relationship between lipase inhibition efficiency and, total phenolic content and DPPH antioxidant activity was also investigated using Pearson correlation coefficient.

Main Results : The results showed that lipase inhibition efficiency increased with increasing the extract concentration (p0.05). The inhibitory efficiency of Spirogyra sp. extract and the anti-obesity drug named Xenical at the same concentration of 40 mg/mL were 23.81±0.97% and 85.71±2.33 %, respectively, and the IC₅₀ value (the 50% lipase inhibition concentration) were 90.91±1.83 and 16.67±1.87 mg/mL, respectively. In comparison, the percentage of lipase inhibition of Xenical was 3.59 times higher than that of Spirogyra sp. extract while the IC₅₀ value of Xenical was 5.45 times lower than that of the extract. The lower IC₅₀ value showed the higher enzyme inhibition. Although the enzyme inhibitory efficiency of Spirogyra sp. extract was lower than Xenical, it is still counted that Spirogyra sp. extract had the lipase inhibition power. The behavior of lipase inhibition of Spirogyra sp. extract was non-competitive manner, with consideration to V_max, K_m, K_i and K_i' values derived from the Lineweaver-Burg plot. The V_max values (maximum reaction rate) were significantly decreased (p0.05), the K_m values (Michaelis-Menten constant) were significantly unchanged (p>0.005) and the K_i value was more than the K_i' value (Inhibition constant). This inhibition behavior meant that the inhibitor bound to both enzyme or enzyme-substrate complex at the allosteric sites, resulting in the decrease of the enzyme activity. In addition, the total phenolic content of Spirogyra sp. extracts was 36.65±0.25 mg gallic acid/g extract and the DPPH antioxidant activity was 3.13±0.03 mg Trolox/g extract. The percentage of DPPH radical scavenging was 70.30±0.64. Pearson correlation coefficient showed that the percentage of lipase inhibition was strong correlation with total phenolic content (r=0.8224), and moderate correlation with DPPH radical scavenging activity (r=0.7145) of the extract. It indicated that phenolic compounds and antioxidant activity in the extract play an important role in the efficiency of lipase inhibition. Generally, natural extract that contained high content of phenolic and flavonoid compounds, and high antioxidant activity, also showed the high lipase inhibition efficiency.

Conclusions : The results of this research provided that the extract of Spirogyra sp. cultivated in closed-circulating system, which the culture conditions were controlled for both quantity and quality of algae, was potential used as a lipase inhibitor. The extract had high content of total phenolic and antioxidant activity, influenced on the lipase enzyme inhibition capacity. Therefore, Spirogyra sp. extract has the potential development to the heathy product. However, this study was the assessment of lipase inhibitory potential of Spirogyra sp. extract only in test tube (in vitro), the studies on lipase inhibitors from natural extract should be done in cultured cells (in vitro) or a laboratory animal (in vivo) in order to confirm the exactly efficiency, possible side effects and the use safe of the extract.

The Optimal Harvesting Frequency for Production on a Number of Calanoid Copepod Parvocalanus crassirostris

Doungtip Oungern — 2025-10-28

Background and Objectives : Parvocalanus crassirostris is a calanoid copepod species of significant ecological and nutritional importance, widely recognized as a premium live feed for the larviculture of marine ornamental fish. Its naupliar stage is particularly small, highly digestible, and enriched with essential polyunsaturated fatty acids (PUFAs), including docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA), which play critical roles in enhancing larval growth, pigmentation, neural development, and survival rates. These nutritional qualities make P. crassirostris an optimal live diet for marine fish species with small mouth openings, such as butterflyfish and angelfish, which are otherwise challenging to rear. Distributed across tropical and subtropical waters—including coastal areas of Thailand and the Hawaiian Islands—this species has been the focus of intensive research aimed at improving culture techniques, optimizing production efficiency, and meeting the increasing demand for high-quality live feeds in aquaculture hatcheries.Despite its high potential, the continuous and efficient production of P. crassirostris remains challenging, mainly due to the delicate balance required between harvesting and population stability. Over-harvesting can severely deplete populations, while insufficient harvesting may lead to overcrowding, increased competition for resources, and reduced reproductive output. Previous studies have highlighted the importance of establishing optimal harvest intervals to maintain sustainable yields and prevent fluctuations in population dynamics. This study aimed to determine the most appropriate harvesting frequency for P. crassirostris, focusing on naupliar and copepodite stages, to develop guidelines applicable to commercial-scale production systems and ornamental fish hatcheries.

Methodology : The experiment was designed using a completely randomized design (CRD). Four different harvesting strategies were tested: non-harvest (control), harvesting once every other day, harvesting once every third day, and harvesting once every fifth day. Each harvest involved the removal of 20% of the culture volume, after which the tank was replenished with filtered, sterilized seawater. Twelve units of 5-litre glass tanks were divided into 4 triplicate treatments, 3 replicates each. Copepods were sourced from stock cultures maintained at the Cha-am Research Station, Institute of Marine Science, Burapha University, and were acclimated under controlled laboratory conditions. The initial stocking density was 1.99±0.13 ind./ml^-1. In the current study, Cultures were fed daily with two microalgal species, including Isochrysis galbana & Chaetocerop sp. each at a concentration of 75,000 cells/ml^-1 to 1 time per day. The culture was maintained at room temperature, salinity of 28 ppt, and a photoperiod of 24:0 h light:dark cycle. Routine culture management included siphoning bottom sediments and performing 20% water exchanges every three days to maintain optimal water quality and reduce organic waste buildup. Population density, specific growth rate (SGR), and the proportion of developmental stages (nauplii, copepodite, and adult) were monitored every two days over a 21-day experimental period. Sampling was conducted by collecting 49 mL of water from each tank, which was preserved with 10% neutral buffered formalin prior to counting under a stereo microscope (Olympus SZ).

Main Results : The results showed that the optimal harvest frequency was every other day, yielding a total number of 6,170 copepods (60% of the production). Harvesting once every third day had an average copepod output of 2,527.78 (25%). Harvesting once every fifth day gave the lowest total output (1,511.11 copepods, 15%). In compared were consisting of the harvesting frequencies in this experiment there was no significant effect on copepod density during the production (P > 0.05). The results showed that responded copepods by increasing the maximum copepod density was (mean±SE) 3.33±0.33, 4.53±0.82, 3.43±0.23, 3.22±0.39 ind./mL^-1 at 4-6 daysbefore increasing density to below 1 ind./mL^-1 (mean±SE) 0.31±0.08, 0.36±0.09, 0.33±0.07, 0.24±0.04 ind./mL^-1 at 14 days, respectively. P. crassirostris showed no significant (P>0.05) in the specific population growth rate (mean±SE) 0.06±0.125, 0.14±0.14, 0.21±0.11, 0.002±0.14 day^-1. The proportion of copepods in adult stage (36.19%, 59.04%, 71.76% and 28.11% respectively), copepodite (9.57%, 20.16%, 14.51% and 13.11% respectively), and nauplii (54.24%, 20.28%, 13.76% and 58.78% respectively) did not show statistical differences between treatments. These results suggest that harvesting frequency does not disrupt age structure or recruitment dynamics within the population, provided that harvesting is conducted in moderate volumes.

Conclusions : Harvesting P. crassirostris every other day proved to be the most effective strategy for maximizing yield while maintaining population stability. This schedule ensures regular availability of nauplii and copepodites at peak nutritional value, which is essential for larval fish culture. Less frequent harvesting (every three or five days) resulted in lower yields and less efficient population turnover. These findings agree with previous studies on calanoid copepods, which highlighted that frequent but moderate harvesting supports culture performance, reduces density-related stress, and promotes reproduction.Harvesting every other day provides an optimal balance between sustainable biomass production and stable population dynamics, making it suitable for hatcheries requiring a steady supply of high-quality live feed. Non-harvest strategies may be useful for maintaining broodstock populations for future scaling. Moreover, this study underscores the potential of semi-recirculating or intensive culture systems to further enhance production efficiency, reduce operational costs, and meet the growing demand for sustainable aquaculture feeds. The insights gained here offer practical guidelines for improving P. crassirostris culture, ensuring reliable, cost-effective live feed supply chains for marine ornamental fish hatcheries and other aquaculture industries.

Atmospheric Precipitable Water Estimation from Long-Term Ground-Based Meteorological Data using Artificial Neural Network Model

Sattra Sirikaew — 2025-10-29

Background and Objectives: Water is one of the constituents of the atmosphere, being abundant at the surface and in small quantities in the stratosphere. Generally, atmospheric water vapor exists in solid, liquid, and gaseous states. The gaseous state known as water vapor is important to the physical, chemical, and various processes that occur in the atmosphere, such as its ability to absorb solar radiation transmitted to the earth, its ability to absorb infrared radiation emitted from the earth, its role in the size and composition of hygroscopic aerosol particles, affecting the optical properties of aerosols, and being naturally occurring greenhouse gas, and etc. Furthermore, atmospheric water vapor is vital for the formation of cloud and rain, as it can remove dissolved gases and aerosols from the atmosphere. It is also important for energy transformation processes in the atmosphere between continents and oceans for regional or climate-sensitive radiation balance. Therefore, the amount of atmospheric water vapor is a key variable for hydrology, ecosystem, climate, and global climate change. Thus, it is necessary to monitor, measure and study the changes in the amount of atmospheric water. Atmospheric water content can be expressed in several forms, such as absolute humidity, relative humidity, specific humidity, mass mixing ratio, volume mixing ratio, and total precipitable water in the atmospheric column, and etc. These quantities are derived from direct measurements using instruments or indirect methods employing models or calculations from other variables. Currently, instruments for measuring atmospheric water content remain expensive, leading to limited and discontinuous measurement coverage. Consequently, the objective of this study is to estimate monthly average atmospheric water from long-term ground-based meteorological data using Artificial Neural Network (ANN).

Methodology: The study area was defined as three locations with continuous measurement of atmospheric water and ground-based meteorological data: the northern meteorological center, Chiang Mai province (18.98N, 98.98E); the northeastern meteorological center (lower part), Ubon Ratchathani province (15.25N, 104.87E); and the southern-east coast meteorological center, Songkhla province (7.20N, 100.60E). The data utilized for the study, covering the period 2008 – 2024, include: (1) Monthly average TPW measured by ground-based sunphotometer of the Aerosol Robotic Network (AERONET), National Aeronautics and Space Administration (NASA); (2) daily average ground-level ambient air temperature measured by the Thai Meteorological Department (TMD); (3) daily average ground-level ambient air relative humidity measured by the TMD; (4) monthly average saturated water vapor pressure calculated from the Improved Magnus Formula using monthly average ground-level ambient air temperatures and relative humidity; and (5) month of the year (as an ordinal variable). The daily average ground-level ambient air temperature and relative humidity with more than or equal to 15 days/month were averaged to be used as the monthly average of that month, while months with less than 15 days/month of such data were not considered. The relationship between input and output variables and between input variables were then analyzed using the Pearson correlation coefficient (or Pearson product-moment correlation coefficient, r) via Python programming language through Google Colaboratory. Data from 2008 – 2021 were used for model development and data from 2022 – 2024 for model testing using the WEKA software. Finally, the model performance was evaluated with the Mean Bias Error (MBE), Root Mean Squared Error (RMSE), and coefficient of determination (R²) in Microsoft Excel.

Main Results: The analysis of the relationship between the input variables (monthly average ground-level ambient air temperature, monthly average ground-level ambient air relative humidity, monthly average saturated water vapor pressure, and month of the year (as an ordinal variable) and the output variables (monthly average TPW) showed that the Pearson correlation coefficients at Chiang Mai, Ubon Ratchathani, and Songkhla stations were in the range of 0.36 – 0.64, 0.29 – 0.52, and 0.17 – 0.44, respectively. This result showed that the input and output variables were a weak to moderate positive relationship. Moreover, the relationship between input variables also were a weak to moderate positive and negative relationship. The results of ANN model derived from these relationship levels showed that each station had 2 hidden layers. The number of nodes in the hidden layers were 5 and 2 for Chiang Mai, 8 and 5 for Ubon Ratchathani, and 8 and 5 for Songkhla. The results of the model performance evaluation of these stations found that the model can estimate the monthly average atmospheric water content with accuracy of MBE values of -0.89%, -1.23%, and 1.04%, respectively, RMSE values of 4.21%, 4.85%, and 5.34%, respectively, and R² values of 0.98, 0.95, and 0.81, respectively.

Conclusions: From the atmospheric water content estimation using the ANN model, it was found that the overall MBE, RMSE, and R² were -0.39%, 4.83%, and 0.95, respectively. The results of the study showed that, despite low to moderate correlation between variables, the utilization of long-term data allows the proposed model to estimate the monthly average atmospheric water content with high level of accuracy compared to other similar studies (in terms of location and variables).

Utilizing Auxiliary Information to Develop an Exponential Ratio-type Estimator under the Problem of Non-Response in Sample Surveys

Napattchan Dansawad — 2025-11-04

Background and Objectives: In survey sampling, the estimation of population parameters, such as the mean (Mean), proportion (Proportion), variance (Variance), or total (Total), based on sampling methods often faces limitations in the precision of estimators. This is especially true when the sample size is limited due to various factors, such as budget, time, or the resources required for data collection. These factors directly affect the resulting estimators, leading to high variance and an inability to accurately reflect the true values of the population parameters. To mitigate these limitations, most researchers have developed approaches using auxiliary variables to construct or extend the estimators of interest. An auxiliary variable is information or a characteristic of a variable that researchers believe is correlated with the study variable and can be accessed easily or at a low cost. The integration of auxiliary variables into parameter estimation not only reduces bias and variance of the estimators but also increases the efficiency of the estimators under study compared to traditional estimation methods. Therefore, the study of the role of auxiliary variables in the development of estimators is important both theoretically and practically, including applications, as researchers can use the benefits of auxiliary variables in constructing estimators across various fields, including demography, economics, agriculture, industry, and social sciences, all of which may face limitations in resources and data completeness. Moreover, considering the relationship between auxiliary variables and the study variable helps to understand the characteristics of the population in greater depth and can be used to improve survey planning and resource allocation efficiently. This aligns with research that aims to use information from auxiliary variables to develop exponential ratio-type estimators under the presence of non-response in sample surveys, which is important for increasing the accuracy and reliability of survey estimators. Additionally, an in-depth study of auxiliary variables helps to ensure that survey design is appropriate and can reduce measurement errors throughout all stages of the survey process.

Methodology: This research studies certain key properties of the newly proposed estimators, which were developed from the estimators introduced by Rao (1986) and Singh et al. (2009), such as mean squared error (MSE) and minimum mean squared error (MMSE). The efficiency of the proposed estimators will be compared with other related estimators theoretically, through applications to real data, and via simulation studies. The study comprises three components: 1) Theoretical comparison: The conditions under which the proposed estimators perform better than other related estimators will be presented. 2) Comparison using real data: Real data collected by Khare & Sinha (2010) and Yadav et al. (2019) will be used to compare the efficiency of the proposed estimators with other estimators, using percentage relative efficiency (PRE) as the criterion. 3) Comparison using simulation: A bivariate normal population (X,Y) will be generated using the R program, where the study variable Y has a mean of 150 and variance of 5, and the auxiliary variable X has a mean of 180 and variance of 10 (when Y=114.10+.02X ) while 25% of the total observations are considered as non-respondents. The population size is set to 1,000, and correlation coefficients () are set at 0.2, 0.5, and 0.8, respectively. Samples of the study variable Y and auxiliary variable X will be drawn from the simulated population using a two-phase sampling design, with sample sizes of 20 and 120, respectively. The efficiency of the studied estimators will be compared using percentage relative efficiency (PRE). This simulation helps researchers to understand the behavior of the estimators under different scenarios in detail and enhances the reliability of the study findings.

Main Results: From the comparison of the efficiency of the proposed estimators with other related estimators, in theory, applications to real data, and simulation studies, it was found that the proposed estimators perform better than other estimators when the conditions in Table 1 are satisfied. Moreover, the application to real data, as shown in Table 2, indicates that the proposed estimators have lower MSE than other estimators. When considering the efficiency of the estimators from PRE values, the proposed estimators have higher PRE than other studied estimators under the same conditions. In-depth analysis shows that the difference in PRE between the proposed estimators and other estimators tends to increase when the correlation between the study variable and the auxiliary variable is higher. For the comparison of the efficiency of estimators from the simulation study, it was found that when the correlation coefficient and sample size are the same, an increase in the relevant parameter leads to a decrease in PRE for all estimators. However, the proposed estimators remain the estimators with the highest PRE, confirming that the proposed estimators continue to perform better than other related estimators in all scenarios studied.

Conclusions: The study proposed an exponential ratio-type estimator for the population mean using information from auxiliary variables under two-phase sampling with non-response, developed from the estimators introduced by Rao (1986) and Singh et al. (2009). Results from the efficiency comparison between the proposed estimators and other related estimators, using theoretical analysis, real data applications, and simulation studies, consistently show that the newly proposed exponential ratio-type estimator for the population mean outperforms all other related estimators under the same datasets and scenarios. In conclusion, the estimators proposed in this study provide a useful and reliable tool for researchers and statisticians in quantitative surveys. They can be applied across various fields, particularly in situations involving non-response, as they enhance the accuracy of population parameter estimation and have been validated using both real and simulated data.

On the Diophantine Equation p^x+n^y=z^2 where p is an Odd Prime and n is a Non-Negative Integer with n≡7(mod 12) and gcd(n,p)=1

Vipawadee Moonchaisook — 2025-11-05

Background and Objectives : Diophantine equations, which seek integer solutions to polynomial equations, have long been a fundamental and extensively studied topic in number theory. Among these, exponential Diophantine equations, where variables appear as exponents, are particularly challenging due to their nonlinear nature and profound connections to classical conjectures such as Catalan’s Conjecture. This conjecture, proven by Mihailescu in 2004, states that the equation x^a- y^b = 1, where a, b, x and y are integers with min 1 has the unique positive integer solution (x, y, a, b) = (3 ,2, 2, 3). This study focuses on the exponential Diophantine equation p^x + n^y = z² where p is an odd prime, and n, x, y, z are non-negative integers. The primary objective is to determine all possible integer solutions of this equation under various conditions, with particular emphasis on modular restrictions imposed on the parameter n. The research investigates the interplay between the prime base p and the parameter n in determining the existence of solutions. Previous works have contributed foundational insights into related problems. Notably, Nagell (1948) proved the finiteness of solutions to the Lebesgue-Nagell equation x² + D = yⁿ, for fixed integers and Tijdeman (1976) extended these results using Baker’s theory of linear forms in logarithms to show the finiteness of positive integer solutions to exponential Diophantine equations of the form a^x + b^y = c, for fixed integers a, b, c . While these studies have illuminated important aspects of the problem, a comprehensive understanding of solutions under specific modular constraints on remains incomplete. Therefore, this research conducts a detailed analysis of the equation under the modular condition n 7(mod 12). This is achieved by employing classical number theory tools such as the theory of quadratic residues and the Legendre symbol to rigorously restrict the possible solution values. The methodology involves transforming the equation into forms amenable to modular arithmetic analysis and factorization, with the goal of establishing necessary and sufficient conditions for the existence of non-negative integer solutions. Analyzing these constraints will allow a complete characterization of all possible solution sets and demonstrate the absence of solutions outside these conditions. The results are expected to deepen the theoretical understanding of exponential Diophantine equations involving prime powers and perfect squares under modular constraints, extend classical results, and provide a framework for investigating more complex cases in future research.

Methodology : The investigation begins by transforming the equation p^x + n^y = z² where p is an odd prime, and n, x, y, z are non-negative integers, into forms that are amenable to analysis using modular arithmetic and the properties of quadratic residues. A key insight involves the application of quadratic residues modulo 12, which impose stringent restrictions on the possible values of thereby significantly influencing the solvability of the equation. Specifically, the congruence condition n 7(mod 12) emerges naturally from residue computations and serves as a critical criterion for filtering candidate solutions. The research further explores the relationship between the given Diophantine equation and the generalized Pell equation of the form x² - Dy²= 1 , which is known to have infinitely many integer solutions under certain conditions. By establishing this connection, the study relates the growth behavior of the original equation’s solutions to those of Pell-type equations. Techniques derived from the theory of linear forms in logarithms, inspired by the foundational work of Tijdeman and Baker, are employed to establish explicit upper bounds on the exponents x and y in terms of p and n. Throughout the analysis, modular constraints and the greatest common divisor condition gcd(n, p) = 1 are examined systematically. The proof strategy integrates modular arithmetic with prime factorization methods and classical analytic number theory to derive necessary and sufficient conditions for the existence of non-negative integer solutions to the equation.

Main Results : The research shows that the Diophantine equation p^x + n^y = z² admits non-negative integer solutions only under highly restrictive circumstances. Specifically, the equation has solutions precisely when p = 3 and gcd(n, p) = 1, with the complete solution set given by (p, n, x, y, z) where is a non-negative integer parameter that generates an infinite family of solutions directly related to Pell-type equations. This characterization reveals an intricate structural link between the original exponential Diophantine equation and quadratic forms. Additionally, the modular condition n 7(mod 12) is proven to be both necessary and natural for solutions to exist. The analysis confirms that for any other values of p or n not satisfying these conditions, the equation has no non-negative integer solutions. This result not only aligns with but also extends existing theorems on the rarity of solutions to exponential Diophantine equations. It demonstrates how quadratic residue conditions can tightly constrain possible solutions, providing a deep understanding of the interplay between the arithmetic properties of p and the modular behavior of n Furthermore, the results establish a bridge to classical results on Pell equations by showing that the infinite familie of solutions correspond precisely to sequences generated by fundamental solutions to related Pell-type equations.

Conclusions : This study provides a complete characterization of non-negative integer solutions to the Diophantine equation p^x + n^y = z² for odd primes p, demonstrating that solutions exist only under the specific modular condition n 7(mod 12) and with p = 3 satisfying gcd(n, p) = 1.The explicit forms of the solutions reveal a unique structure rooted in connections to Pell-type equations and quadratic residue theory. These findings deepen our understanding of exponential Diophantine equations involving prime powers and perfect squares under modular constraints. The research contributes new insight to the field by elucidating the conditions under which such equations are solvable, laying a foundation for future work on more complex equations involving higher powers or additional variables. Potential applications of the methodological advances include algorithmic number theory, cryptography, and computational mathematics, where understanding the interaction between primes, exponents, and perfect powers is crucial. By combining classical and modern techniques, this research not only extends the known results but also provides a template for studying other exponential Diophantine equations with similar structural properties, opening avenues for further exploration in both pure and applied mathematics

Forecasting the Number of Tourists and Managing Interrupted Time Series Data for Sustainable Tourism Development in Thailand's Eastern Marine National Parks

Janjira Piladaeng — 2025-11-07

Background and Objectives : Thailand is internationally recognized as one of the world's major tourist destinations. Tourism also plays an important role in driving the country's economic growth. The tourism industry is not only a primary source of national revenue, but also a key mechanism for promoting employment and overall economic development. However, the outbreak of COVID-19 in late 2019 significantly affected the domestic tourism industry due to the implementation of strict public health measures, such as lockdowns and travel restrictions. As a result, no international tourists have entered Thailand since April 2020. Additionally, important popular marine tourist attractions in the eastern region, including Mu Ko Chang National Park and Khao Laem Ya – Mu Ko Samet National Park, were affected by the closure of tourism in national parks and forest parks. After the country reopened in late 2021, the tourism industry began to recover, resulting in a noticeable increase in visitors to these two eastern marine national parks. Thus, accurate forecasting of tourist numbers is important for helping related agencies manage tourism sustainably. Moreover, forecasting can provide accurate results when the data used for analysis is continuous and consistent. However, the COVID-19 outbreak resulted in no tourists visiting the national parks during that period, resulting in some data being zero and discontinuous. This may affect the performance of the forecasting model. Therefore, this research aims at forecasting the number of tourists in Mu Ko Chang National Park and Khao Laem Ya – Mu Ko Samet National Park during the period affected by the COVID-19 pandemic. To improve the continuity and quality of the data, a missing value imputation technique was applied. An appropriate forecasting model was then developed using the widely well-known and commonly applied Box-Jenkins statistical method.

Methodology : This study used data on the number of tourists visiting Mu Ko Chang National Park and Khao Laem Ya – Mu Ko Samet National Park from October 2015 to March 2025, covering a total of 114 months. The data were obtained from the Department of National Parks, Wildlife and Plant Conservation. Three data scenarios were defined for building the forecasting model: 1. Using actual data with zero values, 2. Treating zero values as missing data, and 3. Treating data during the COVID-19 outbreak from January 2020 to December 2021 as missing data. A seasonal decomposition technique combined with mean imputation was used to fill in the missing values. Subsequently, the forecasting models were constructed using data from October 2015 to September 2023 using the Box-Jenkins method. The Akaike Information Criterion (AIC) was employed to select the appropriate model among several SARIMA models using the same dataset. The root mean square error (RMSE) was used as a criterion to determine the suitable model for forecasting tourist arrivals in Mu Ko Chang National Park and Khao Laem Ya – Mu Ko Samet National Park. The accuracy of the forecasts was then validated using data from October 2023 to March 2025, with the mean absolute percentage error (MAPE) used to assess forecasting performance.

Main Results : The estimation of time series data with interrupted tourist numbers in Mu Ko Chang National Park and Khao Laem Ya – Mu Ko Samet National Park was conducted using a seasonal decomposition approach combined with the mean algorithm under three patterns of missing data conditions. The imputed results yielded positive values, which are reasonable within the context of tourist numbers and can be further utilized in forecasting models. The suitable models for forecasting the number of tourists visiting Ko Chang National Park and Khao Laem Ya – Mu Ko Samet National Park are SARIMA(2,1,0)(0,1,1)₁₂ and SARIMA(0,1,0)(0,1,1)₁₂, respectively. Both models were developed using data in which the period of the COVID-19 outbreak from January 2020 to December 2021 was treated as missing and replaced using imputation techniques. Although these models may not be the most suitable, they can still be used for forecasting. The SARIMA(2,1,0)(0,1,1)₁₂ model provides acceptable accuracy for forecasting tourist numbers at Mu Ko Chang National Park with a mean absolute percentage error of 23.79%, while the SARIMA(0,1,0)(0,1,1)₁₂ model shows good accuracy for forecasting visitors at Khao Laem Ya – Mu Ko Samet National Park with a mean absolute percentage error of 12.94%. Additionally, the forecast of tourist numbers from April to December 2025 indicates that the number of tourist arrivals to Mu Ko Chang National Park and Khao Laem Ya–Mu Ko Samet National Park remains relatively stable, following seasonal patterns.

Conclusions : Although there were periods with no tourist visits to Mu Ko Chang National Park and Khao Laem Ya – Mu Ko Samet National Park, resulting in data discontinuity, the missing data imputation technique enabled the use of available data to construct an appropriate preliminary forecasting model. This approach helps relevant agencies improve the planning and management of tourism more effectively. However, the impact of the COVID-19 pandemic still remains until sufficient additional data becomes available to develop more accurate forecasting models in the future.