Earticle

This paper proposes mathematical models of the process of information interaction between a set of subjects (IoT devices) and a base station in the 5G-IoT ecosystem. The researched process, in this case, is represented by a queuing system with a flow of new incoming requests with needs for the desired volumes of system resources and a flow of service signals, the receipt of which initiates redefinition of allocated for received incoming requests volumes of system resources. A controlled parameter in the created queuing system is the acceptance or rejection of new incoming requests. The priority is to support active sessions of subject-system interaction initiated for the received incoming requests. We consider two functional scenarios, which differ asynchronously or synchronously when a service signal comes to the base station’s front-end interface. The receipt marks a partial or complete redefinition of system resources involved in supporting active sessions of subject-system interaction. Formalized in the basis of a single queuing system, mathematical models of development of these functional scenarios allow calculating the probability of rejection of a new incoming request and the percentage of occupied system resources, combined in the metrics of quality indicators, in the conditions of asynchronous or synchronous change of the spatial location relative to the base station of the end IoT devices, the received input requests from which are active in the 5G-IoT ecosystem.

Due to environmental disturbance and human aggregation, alien species invade new area rapidly; especially disease expansion is critical due to high possibility of contagion and contamination. Since numerous factors including pathogens, hosts, environmental factors and human involvements are closely associated with disease transmission in a complex manner, mathematical models are required to predict disease dispersal objectively and provide optimal management strategies for disease control. Mathematical models are reviewed regarding virus diseases that have a strong possibility of invading in Korea, including Lumpy skins virus, Nipah virus and West Nile virus. With data-driven models, statistical models were used to determine disease occurrences and spatio-temporal distributions. Technics in machine learning (e.g., Maxent, genetic algorithm) were utilized to present associative properties and causality relationships between pathogens, hosts and environmental factors and to be able to predict disease outbreaks. Regarding mechanistic models, mathematical structure models were developed to present the quantitative framework of dynamical disease transmission between variables, for instance, susceptible, infected and recovered populations. The possibility of using simulation models (e.g., individual based models, lattice structure models) based on transmission rules applied to complex environmental and dispersal conditions is additionally discussed to identify risk factors, prognose disease occurrences and select optimal strategies for control management according to various scenarios.

미생물(微生物)의 부착식(附着式) 성장(成長)을 이용(利用)한 폐수처리(廢水處理)의 이해(理解)를 돕기 위해 미생물막모형(微生物膜模型)을 정립(定立)하고 이의 simulation을 통하여 처리효율(處理効率)과 각종(各種) parameter 사이의 관계(關係)를 살펴보았다. 미생물막모형(微生物膜模型)은 기질(基質)의 침투정도(浸透程度)에 따라 두꺼운 막(膜)과 얇은 막(膜)으로 구분(區分)하고 각(各) 경우(境遇)에 대하여 미생물막내부(微生物膜內部)에서의 기질농도(基質濃度)와 flux를 산정(算定)할 수 있게 구성(構成)되어 있다. 모형(模型)의 정립과정(定立過程)에서 얻어진 무차원상수(無次元常數)인 ${\phi}_1$, ${\phi}_2$, 그리고 $\bar{S}_b$에 의해 기질농도(基質濃度)와 flux가 결정(決定)될 수 있음을 알았으며, ${\phi}_1$의 증가(增加)나 ${\phi}_2$의 감소(減少)에 의해 처리효율(處理効率)이 증가(增加)함을 알 수 있다. 또한 높은 처리효율(處理効率)을 유지(維持)하는 system은 모두 두꺼운 막(膜)에 속하는 것을 알 수 있다. 미생물막표면(微生物膜表面) 근처에서의 유속(流速)을 증가(增加)시킴으로써 두께가 일정(一定)한 막(膜)에 있어서 처리효율(處理効率)을 증가(增加)시킬 수 있다. 하지만 유속(流速)의 증가(增加)로 인해 sloughing이 많아져서 막(膜)의 두께가 감소(減少)하여 새로운 정상상태(定常狀態)로 바뀌게 된다. 현재(現在)까지 유속(流速)과 미생물막(微生物膜)두께사이의 관계(關係)가 정량적(定量的)으로 규명(糾明)되지 못하고 있으므로 새로운 정상상태(定常狀態)에서의 효율(効率)은 명백히 규정지을 수 없다.

A model of substrate utilization witbin bacterial films has been developed and simulated for a better understanding of fixed film treatment processes. The model consists of two parts, a deep biofilm and a thin biofilm, which are classified based on substrate penetration into the biofilm. Substrate concentration and flux within a biofilm can be computed from the model. Three dimensionless parameters, ${\phi}_1$, ${\phi}_2$ and $\bar{S}_b$ were obtained during model construction, and the substrate concentration and flux can be expressed in terms of these parameters. It has been found that an. increase of ${\phi}_1$ or a decrease of ${\phi}_2$ results in an increase of treatment efficiencies. It has also been found that systems maintaining high efficiencies belong to a deep biofilm. Among the constants involved, the mass transfer coefficient is the only controllable term and it depends Largely on fluid velocity near the biofilm surface. Substrate removal efficiency may be increased with an increase of fluid velocity for a biofilm of fixed depth. However, film depth is decreased due to sloughing with increasing velocity, and the system reaches a new steady state. Because changes in film depth are not well defined quantitatively yet, the efficiency can not be clearly described at a new steady state.

학교 교육을 통하여 창의적인 인간을 양성해야 한다는 요구가 계속되고 있다. 특히 2011 수학과 교육과정 개정에서는 수학적 창의성과 인성을 길러주는데 초점을 두고 있다. 이를 위해 교육 현장에서 학생들의 창의성 개발을 위한 구체적인 방안의 모색이 필요하다. 이에 본 연구에서는 수학적 창의성의 요소를 추출하고, 창의성 개발을 위한 수업 모델을 탐색해 보았다. 먼저, 수학적 창의성에서의 논점과 수학적 창의성의 요소를 인지적, 정의적, 태도적 측면으로 알아보았다. 이러한 요소들은 수학적 창의성 개발 수업에서 창의성 개발에 영향을 주는 요소이며, 창의성을 평가하는 요소가 될 것이다. 이러한 기저를 바탕으로 수학 학습에서 학생들의 수학적 창의성을 기를 수 있는 8가지 수학과 창의성 개발 수업 모델을 제시하였다. 8가지 수학적 창의성 개발을 위한 수업 모델은 수학의 특성과 최근에 강조되는 수학교육 이론 및 창의성 이론을 바탕으로 하였다.

Mathematical creativity is essential in school mathematics and mathematics curriculum and ensures the growth of mathematical ability. Therefore mathematics educators try to develop students' creativity via mathematics education for a long time. In special, 2011 revised mathematics curriculum emphasizes mathematical creativity. Yet, it may seem like a vague characterization of mathematical creativity. Furthermore, it is needed to develop the methods for developing the mathematical creativity. So, the goal of this paper is to search for teaching and learning models for developing the mathematical creativity. For this, I discuss about issues of mathematical creativity and extract the factors of mathematical creativity. The factors of mathematical creativity are divided into cognitive factors, affective factors and attitude factors that become the factors of development of mathematical creativity in the mathematical instruction. And I develop 8-teaching and learning models for development of mathematical creativity based on the characters of mathematics and the most recent theories of mathematics education. These models make it crucial for students to develop the mathematical creativity and create the new mathematics in the future.

Nowadays, sub developed countries are presenting a growing tendency of technological implementation based on renewable energy. For which is very common to make meteorological factors predictions, to guarantee a better performance in accord to the climate variability. With this work the validation of the global solar radiation predicting models involving geographic and / or meteorological factors for the city of Bogota DC is made. This validation is based on the comparison of the results from the models with the experimental data and NASA, IDEAM, SWERA, METEONORM, CAR data bases. The results obtained from this work identify the error of the used models, defining the most appropriate one to predict the global solar radiation including the location and weather of the northern area of Bogota.

The risk of software projects is measured in terms of cost that is needed to abate the risk. Traditional practice to measure the risk of software projects uses risk exposure; however, risk measure cannot quantify the risk beyond the expected value of cost. Software project managers are keen to quantify the risk based on a certain probability which is beyond the expected value of the cost. This research work presents a model to measure the risk based on certain probability beyond the expectation. A case-study validates that proposed model shows an improvement in the measurement of risk of real software projects compared to the actual risk of software projects.

Wind tunnels have been used to test race cars, fighter planes etc. The hypersonic wind tunnel can hit the hypersonic speeds necessary to test the latest ultra fast aircraft and space planes. The wind tunnel is a major money saver. It allows us to make a reusable prototype and test it in the tunnel for a few hundred thousand dollars. Maintaining constant pressure in the settling chamber of the hypersonic intermittent blow down type wind tunnel is an important task for its effective performance. Here, a fuzzy assisted PI control system for the hypersonic intermittent blow down type wind tunnel is developed and analyzed.

Landslide is a type of mass movement that causes damage in many areas. The evolving remote sensing technology in producing high resolution images may help in landslide studies. However, the problem in detecting small size landslides is still challenging when suitable image resolution of the area being analyzed is not available. In this paper, a novel method based on elastic image registration, appropriate for the detection of small landslides will be presented. This method can be used to detect and quantify landslide movement with sub-pixel accuracy. It is based on the invocation of deformation operators which imitate the deformations expected to be observed when a landslide occurs. The similarity between two images is measured by a similarity function which takes into consideration grey level value correlation and geometric deformation. The geometric deformation term ensures that the minimum necessary deformation compatible with the two images is employed. An extra term, ensuring maximum overlap between the two images is also incorporated. There are two versions of this method. One using the correlation coefficient as a measure of similarity for the grey level value, and another one using mutual information. These methods are tested using known small scale landslides images of southern Italy taken from the Landsat 5 TM. The mutual information-based method gives more reliable results.

본 연구는 한국어 수학 데이터셋을 활용한 파인튜닝(Fine-tuning)이 거대언어모델(Large Language Model, LLM)의 수학적 성능을 개선할 수 있는지를 그 메커니즘과 함께 탐구하였다. 그 결과 한국어 수학 데이터셋을 활용한 파인튜닝은 LLM의 수학적 성능을 강화할 수 있음을 확인하였다. 구체적으로, 파인튜닝 후 LLM의 수학 문제 정답률이 65.79%에서 81.25%로 15.46% 상승하였다. 문제 풀이 과정에서는 수식화 성 능, 계산 성능, 풀이 설명력이 크게 강화되었고, 불필요한 비수학적 내용을 생성하는 현상과 언어 혼란(language confusion)이 사라졌다. 특히, 풀이 과정의 변화를 통해 LLM이 파인튜닝을 거치며 수학 데이터셋에 존재하는 풀이 패턴, 내용 전개 패턴, 내용 구조와 형식을 학습할 수 있으며, 이에 따른 풀이 과정의 개선이 정답률 향상에 기여하는 핵심 메커니즘임을 알 수 있었다. 한편, 파인튜닝 후 발생한 문제점으로는 텍스트 무한 생성 현상과 파괴적 망각(catastrophic forgetting)이 관찰되었다. 이러한 결과를 바탕으로 수학 도메인 특화 LLM 개발, 수학 데이터셋 구축, 파인튜닝 의 전략 및 문제점 대응 방안 측면에서 시사점을 논의하였다. 또한, 후속 연구를 위하여 여섯 가지 연구 방향을 제언하였으며, 본 연구에서 구축한 파인튜닝 파이썬 코드를 연구의 재현과 확장을 위해 연구자의 깃허브(Github) 저장소에 공개하였다.

This study investigates whether fine-tuning a Large Language Model (LLM) using a mathematical data set in Korean can enhance its mathematical performance and explores the underlying mechanisms. The findings confirm that fine-tuning with a mathematical data set in Korean improves the mathematical capabilities of LLMs. Specifically, after fine-tuning, the accuracy of solving mathematical problems increased from 65.79% to 81.25%, reflecting a 15.46% improvement. The problem-solving process also showed notable improvements in formalization, computational accuracy, and explanatory capability. Additionally, the generation of irrelevant non-mathematical content and language confusion issues were eliminated. Notably, the changes in the problem-solving process suggest that, through fine-tuning, the LLM learns the solution patterns, development structures, content organization, and formatting embedded in the mathematical dataset in Korean. This improvement in the problem-solving process serves as a key mechanism contributing to the increase in accuracy. However, fine-tuning also introduced challenges, such as continuous text generation and catastrophic forgetting. Based on these findings, this study provides insights into developing domain-specific mathematical LLMs, constructing mathematical data sets, fine-tuning strategies and its associated challenges. Furthermore, six key directions for future research are suggested. To promote reproducibility and further research, the Python code in this study have been made publicly available on the researcher’s GitHub repositories.

This paper presents the coordinate systems used for trawl doors modeling, and provides matrix equations of connection between these systems. The projections of the forces acting on the door into axes of various coordinate systems were obtained, which were used in the door equilibrium equations. Six equilibrium conditions for the door as a solid were obtained: formulas that allow for the door area in plan to be determined; its weight in water; its mass; three moment equations for determining the position of the warp and backstrops fastening points to the door with triangular and quadrangular backstrop arrangements. It was found that the moment equilibrium equations of trawl doors are generally incompatible, which was not found by any of the authors who have previously conducted research into trawl doors. Using the Kronecker-Capelli theorem, the compatibility equation is obtained. This equation includes the coordinates of the backstrop fastening points to the door, which means that these points cannot be randomly selected. The technique of determining the warp and backstrops' fastening points position to the door is described. Conditions of directional (by angle of attack) and roll (in angle of roll) stability of the doors' equilibrium are presented. The equations presented in this paper comprise a mathematical model that allows, when designing the doors, to select optimal parameters, as well as to carry out adjustments for trawling purposes to ensure the stable movement of the doors and the entire trawl system.

The present study obtained universal mathematical models of all elements and characteristics regarding hook and line fishing systems. To describe the hook and line fishing systems on site we used three kinds of coordinate systems: the earth based coordinate system, natural coordinate system, and flow (velocity) coordinate system. Mathematical models presented in this article allow us to define the shape of the fishing gear, the tension of the rope at different points, hydrodynamic resistance, diameter of the hook's wire, immersion depth of the fishing hooks, distance from hooks to the ground and the required lifting force of the floats. These models allow for the performance of computer simulations regarding any kinds of hook and line gears in still water or water where flow occurs.

The effect of particle size on the extraction rate of anthocyanin from Solanum tuberosum L. (purple-fleshed potato) peels (PFPPs) using the stagnant single-stage batch extraction system was investigated. Core pretreatment processes such as drying and grinding were quantitatively evaluated using mathematical models. The drying behavior of PFPP was successfully described using thin layer models (Page model and Midilli-Kucuk model). The effective diffusion coefficient of drying temperature at $40^{\circ}C$ was determined to be $1.67{\times}10^{-12}m^2/s$. The grinding time to obtain particles of a specific size was accurately estimated using the grinding kinetic model ($R^2=0.97$). The extraction rate of anthocyanin increased as the particle size decreased; however, when the particle size was 0.15 mm, the anthocyanin content decreased. Our study demonstrated that the grinding kinetic model is useful to estimate the grinding time to produce an optimum particle size for anthocyanin extraction from PFPP.

Competition among anion species in solution for same sorption sites and soil surface can be of major significance in determining the effective mobility of any potentially adsorbing species. Major soil anion species include $OH^-$, $F^-$, $Cl^-$, $HCO_3{^-}$, $CO_3{^-}$, $NO_3{^-}$, $SO_4{^{2-}}$, and $PO_4{^{3-}}$. And some micro nutrients such as boron and molybdenum exist as $H_2BO_3{^-}$ and $MoO_4{^{2-}}$, as do some heavy metals such as chrome and arsenic as $CrO_4{^{2-}}$ and $HAsO_4{^{2-}}$. Pesticides such as 2,4,5-T and 2,4-D also exist as anions. Many anion species are retained by more complex mechanisms than the simple electrostatic attractions involved in most cation adsorption reactions. In binary system composed of two anions, the adsorption of one anion is influenced by the other anion due to the competition for the available and limited binding sites in soil constituents. The specifically adsorbed anions may compete more effectively for sorption sites than that of nonspecifically adsorbed anion. In this study, we aim to evaluate the mathematical models to determine the magnitude of concentration variations in adsorption due to competitive interactions between anions introduced to a system in binary mixtures.

본 연구는 가공치즈에서 Staphylococcus aureus의 생장을 예측하기 위한 수학적 모델을 개발하였다. 모짜렐라 슬라이스 치즈와 체다 슬라이스 치즈에 S. aureus 혼합균액(ATCC13565, ATCC14458, ATCC23235, ATCC27664, NCCP10826) 0.1 ml (log CFU/g)을 접종한 후 $4^{\circ}C$ (1440 h), $15^{\circ}C$ (288 h), $25^{\circ}C$ (72 h), and $30^{\circ}C$ (48 h)에 저장하면서 총 세균수와 S. aureus 세균수를 tryptic soy agar와 mannitol salt agar를 이용해 각각 확인하였다. S. aureus의 세균 수를 Baranyi model로 분석하여 생장률(${\mu}_{max}$; ${\log}CFU{\cdot}g^{-1}{\cdot}h^{-1}$), 유도기(LPD; h), 초기 세균 수(log CFU/g), 최대 생장 세균수(log CFU/g)를 계산함으로써 1차 모델을 개발하였다. 또한 저장온도와 S. aureus의 ${\mu}_{max}$, LPD의 관계를 분석하기 위해 square root model과 exponential decay model을 이용하였고 이를 통해 2차모델을 개발하였으며 개발된 모델의 평균제곱근 편차(RMSE)를 계산하여 적합성을 검증하였다. $4^{\circ}C$에서는 모든 가공치즈에서 황색포도상구균의 생장이 관찰되지 않았으나 $15^{\circ}C$, $25^{\circ}C$, $30^{\circ}C$에서는 모짜렐라 슬라이스와 체다 슬라이스 치즈에서 황색포도상구균이 생장하였으며($R^2=0.785-0.996$) 저장온도가 높아짐에 따라 생장률은 증가한 반면 유도기는 감소하였다($R^2=0.879-0.999$). 또한 개발된 모델의 RMSE 값은 0.3500-0.5344로 적합하였다. 따라서 본 연구결과는 가공치즈에서 황색포도상구균의 생장 예측에 유용하게 사용될 것이다.

This study developed predictive models for the kinetic behavior of Staphylococcus aureus on processed cheeses. Mozzarella slice cheese and cheddar slice cheese were inoculated with 0.1 ml of a S. aureus strain mixture (ATCC13565, ATCC14458, ATCC23235, ATCC27664, and NCCP10826). The inoculated samples were then stored at $4^{\circ}C$ (1440 h), $15^{\circ}C$ (288 h), $25^{\circ}C$ (72 h), and $30^{\circ}C$ (48 h), and the growth of all bacteria and of S. aureus were enumerated on tryptic soy agar and mannitol salt agar, respectively. The Baranyi model was fitted to the growth data of S. aureus to calculate growth rate (${\mu}_{max}$; ${\log}CFU{\cdot}g^{-1}{\cdot}h^{-1}$), lag phase duration (LPD; h), lower asymptote (log CFU/g), and upper asymptote (log CFU/g). The growth parameters were further analyzed using the square root model as a function of temperature. The model performance was validated with observed data, and the root mean square error (RMSE) was calculated. At $4^{\circ}C$, S. aureus cell growth was not observed on either processed cheese, but S. aureus growth on the mozzarella and cheddar cheeses was observed at $15^{\circ}C$, $25^{\circ}C$, and $30^{\circ}C$. The ${\mu}_{max}$ values increased, but LPD values decreased as storage temperature increased. In addition, the developed models showed acceptable performance (RMSE = 0.3500-0.5344). This result indicates that the developed kinetic model should be useful in describing the growth pattern of S. aureus in processed cheeses.

A major concern in Gas Metal Arc (GMA) welding process is the determination of welding process variables such as wire diameter, gas flow rate, welding speed, arc current and welding voltage and their effects on the desired weld bead dimensions and shape. To successfully accomplish this objective, 81 welded samples from mild steel AS 1204 flats adopting the bead-on-plate technique were employed in the experiment. The experimental results were used to develop a mathematical model to predict the magnitude of bead geometry as follows; weld bead width, weld bead height, weld bead penetration depth, weld penetration shape factor, weld reinforcement shape factor, weld bead total area, weld bead penetration area, weld bead reinforcement area, weld bead dilution, length of weld bead penetration boundary and length of weld bead reinforcement boundary, and to establish the relationships between weld process parameters and bead geomery. Multiple regression analysis was employed for investigating and modeling the GMA process and significance test techniques were applied for the interpretation of the experimental data.

Mathematical models for hit probabilities of small arms are developed in order to estimate the expected hits on an aircraft for certain altitudes and air speeds. A model for the firing lead angle is developed for cases when the distribution of hits is normal and the firing angle is from 20 degrees to 160 degrees. probabilities of hit for single and multiple shots at various altitudes are calculated. Tables are given showing the probability of hits and kill for targets flying at high speed above 500 feet from ground level.

Multiple mathematical modeling for prediction of slump, compressive strength and depth of water penetration at 28 days were performed using statistical analysis for the concrete containing waste limestone powder as partial replacement of sand obtained from experimental program reported in this research. To extract experimental data, 180 concrete cubic samples with 20 different mix designs were investigated. The twenty non-linear regression models were used to predict each of the concrete properties including slump, compressive strength and water depth penetration of concrete with waste limestone powder. Evaluation of the models using numerical methods showed that the majority of models give acceptable prediction with a high accuracy and trivial error rates. The 15-term regression models for predicting the slump, compressive strength and water depth were found to have the best agreement with the tested concrete specimens.

The objective of this study was to compare the goodness of fit of four lactation curve models: Wood's Gamma model (WD), Wilmink (WL), and Pollott's multiplicative two (POL2) and three parameters (POL3) and to determine the environmental factors affecting the complete lactation curve of F1 dairy sheep under organic management. A total of 5,382 weekly milk yields records from 150 ewes, under organic management were used. Residual mean square (RMS), determination coefficients ($R^2$), and correlation (r) analysis were used as an indicator of goodness of fit for each model. WL model best fitted the lactation curves as indicated by the lower RMS values (0.019), followed by WD (0.023), POL2 (0.025) and POL3 (0.029). The four models provided total milk yield (TMY) estimations that were highly correlated (0.93 to 0.97) with observed TMY (89.9 kg). The four models under estimated peak yield (PY), whereas POL2 and POL3 gave nearer peak time lactation estimations. Ewes lambing in autumn had higher TMY and showed a typical curve shape. Higher TMY were recorded in second and third lambing. Season of lambing, number of lambing and type of lambing had a great influenced over TMY shaping the complete lactation curve of F1 dairy sheep. In general terms WL model showed the best fit to the F1 dairy sheep lactation curve under organic management.

The mathematical modelling of screw compressor processes and its implementation in their design began about 30 years ago with the publication of several pioneering papers on this topic, mainly at Purdue Compressor Conferences. This led to the gradual introduction of computer aided design, which, in turn, resulted in huge improvements in these machines, especially in oil-flooded air compressors, where the market is very competitive. A review of progress in such methods is presented in this paper together with their application in successful compressor designs. As a result of their introduction, even small details are now considered significant in efforts to improve performance and reduce costs. Despite this, there are still possibilities to introduce new methods and procedures for improved rotor profiles, design optimisation for each specified duty and specialized compressor design, all of which can lead to a better product and new areas of application. A review of methods and procedures which lead to modern screw compressor practice is presented in this paper. This paper is intended to give a cross section through activities being done in mathematical modelling of screw compressor process through last five decades. It is expected to serve as a basis for further contributions in the area and as a challenge to the forthcoming generations of scientists and engineers to concentrate their efforts in finding future and more extended approaches and submit their contributions.