• 대한수학회지
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• 제54권4호
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• 조명전기설비학회논문지
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• 제13권4호
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• pp.75-81
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• 1999

본 연구에서는 직교 다항 회귀모델을 이용하여 수용설비의 소비전력을 추정하는 알고리즘을 제시한다. 제시하는 추정모델은 수학적인 방법인 외삽법과 상관법을 이용할 수 있고, 저차의 방정식을 고차의 방정식에 어떤 수정도 없이 그대로 저차의 계수를 사용할 수 있어 다중 회귀모델에 비해 계산시간 및 계산용량이 절약되며, 이것의 반대 상황도 성립하여 소비전력을 추정하는데 매우 유용한 방법이라 할 수 있다. 추정 모델을 2차, 3차 4차로 구성하고 추정한 결과 4차 모델이 양호한 결과를 나타내었으며, 상관법에 의해 수용설비의 소비전력을 추정한 결과 추정 오차율이 2[%] 이하로 양호하였다. 그리고 외삽법에 의해 1997년의 소비전력을 추정한 결과 4차 모델의 추정 오차율이 1[%]대를 나와 추정모델의 유효성과 타당성을 검증할 수 있었다.

• 한국축산식품학회지
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• 제40권6호
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• pp.938-945
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• 2020

A dynamic model was developed to predict the Escherichia coli cell counts in pig trotters at changing temperatures. Five-strain mixture of pathogenic E. coli at 4 Log CFU/g were inoculated to cooked pig trotter samples. The samples were stored at 10℃, 20℃, and 25℃. The cell count data was analyzed with the Baranyi model to compute the maximum specific growth rate (μ_max) (Log CFU/g/h) and lag phase duration (LPD) (h). The kinetic parameters were analyzed using a polynomial equation, and a dynamic model was developed using the kinetic models. The model performance was evaluated using the accuracy factor (A_f), bias factor (B_f), and root mean square error (RMSE). E. coli cell counts increased (p<0.05) in pig trotter samples at all storage temperatures (10℃-25℃). LPD decreased (p<0.05) and μ_max increased (p<0.05) as storage temperature increased. In addition, the value of h₀ was similar at 10℃ and 20℃, implying that the physiological state was similar between 10℃ and 20℃. The secondary models used were appropriate to evaluate the effect of storage temperature on LPD and μ_max. The developed kinetic models showed good performance with RMSE of 0.618, B_f of 1.02, and A_f of 1.08. Also, performance of the dynamic model was appropriate. Thus, the developed dynamic model in this study can be applied to describe the kinetic behavior of E. coli in cooked pig trotters during storage.

• 생물환경조절학회지
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• 제32권4호
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• pp.384-395
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• 2023

증산은 적정 관수 관리에 중요한 역할을 하므로 수분 스트레스에 취약한 토마토와 같은 작물의 관개 수요에 대한 지식이 필요하다. 관수량을 결정하는 한 가지 방법은 증산량을 측정하는 것인데, 이는 환경이나 생육 수준의 영향을 받는다. 본 연구는 분단위 데이터를 통해 수학적 모델과 딥러닝 모델을 활용하여 토마토의 증발량을 추정하고 적합한 모델을 찾는 것을 목표로 한다. 라이시미터 데이터는 1분 간격으로 배지무게 변화를 측정함으로써 증산량을 직접 측정했다. 피어슨 상관관계는 관찰된 환경 변수가 작물 증산과 유의미한 상관관계가 있음을 보여주었다. 온실온도와 태양복사는 증산량과 양의 상관관계를 보인 반면, 상대습도는 음의 상관관계를 보였다. 다중 선형 회귀(MLR), 다항 회귀 모델, 인공 신경망(ANN), Long short-term memory(LSTM), Gated Recurrent Unit(GRU) 모델을 구축하고 정확도를 비교했다. 모든 모델은 테스트 데이터 세트에서 0.770-0.948 범위의 R² 값과 0.495mm/min-1.038mm/min의 RMSE로 증산을 잠재적으로 추정하였다. 딥러닝 모델은 수학적 모델보다 성능이 뛰어났다. GRU는 0.948의 R² 및 0.495mm/min의 RMSE로 테스트 데이터에서 최고의 성능을 보여주었다. LSTM과 ANN은 R² 값이 각각 0.946과 0.944, RMSE가 각각 0.504m/min과 0.511로 그 뒤를 이었다. GRU 모델은 단기 예측에서 우수한 성능을 보였고 LSTM은 장기 예측에서 우수한 성능을 보였지만 대규모 데이터 셋을 사용한 추가 검증이 필요하다. FAO56 Penman-Monteith(PM) 방정식과 비교하여 PM은 MLR 및 다항식 모델 2차 및 3차보다 RMSE가 0.598mm/min으로 낮지만 분단위 증산의 변동성을 포착하는 데 있어 모든 모델 중에서 가장 성능이 낮다. 따라서 본 연구 결과는 온실 내 토마토 증산을 단기적으로 추정하기 위해 GRU 및 LSTM 모델을 권장한다.

• 한국임상약학회지
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• 제21권2호
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• pp.145-155
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• 2011

The objective of this study was to determine whether any pretreatment parameters were associated with pharmacological effect or toxicity parameters after vincristine administration and to describe a mathematical model, which explains the interpatient pharmacodynamic variability. The relationship between patient characteristics and vincristine dose and hematological toxicity were evaluated. 68 pediatric and adolescence patients and 107 adults with acute lymphoblastic leukemia were treated with vincristine $1.5mg/m^2/day$ IV and other anticancer drugs as scheduled. Complete blood counts and other blood test results were obtained. The input variables were age, gender, weight, lean body weight (LBW), height, body surface area, vincristine dose and total vincristine dose. The outcome measures were nadir values (white blood cells, absolute neutrophil counts, hemoglobin, and platelets); the absolute decrease, relative decrease, and survival fraction of blood cells. Polynomial regression analysis was carried out to determine the other significant covariates. The variability of $WBC_{nadir}$ was modeled with good precision and accuracy with a two-covariate model. This model should be validated and improved on with further clinical data. We believe that such pharmacodynamic modeling should be explored further to determine its performance and clinical relevance compared with modeling using pharmacokinetic parameter.

• 대한공간정보학회지
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• 제10권3호
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• pp.115-122
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• 2002

위성으로 취득되는 영상이 원천적으로 가지게 되는 기하적, 물리적인 왜곡을 제거하기 위해서는 보정 과정이 필요하다. 기하 보정 방법에는 시스템 기하보정과 지상기준점을 이용한 기하보정 방법이 있는데, 본 논문에서는 지상기준점을 이용한 보정 방법에 대해 기술하고 TIN 단위로 기하보정하는 방법을 제안한다. 영상과 지상기준점과의 수학적인 상관 관계를 이용하여 왜곡을 보정하는 방법으로서 평면 전체를 변환시키는 평면기하보정이 주로 사용되어 왔으나, 이것은 지형 변화가 큰 지역의 왜곡을 제대로 보정하지 못하는 단점이 있다. 본 논문에서는 이를 보완하기 위해 TIN단위의 기하보정 방법을 제안하고 평면기하보정 방법과 결과를 비교하며, 지상기준점과의 상관성을 분석한다.

• 한국농업기계학회:학술대회논문집
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• 한국농업기계학회 1993년도 Proceedings of International Conference for Agricultural Machinery and Process Engineering
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• pp.1110-1116
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• 1993

A study on optimum operation performances of power efficiency, economy and exhaust emissions for a tractor was conducted. A mathematical model of multiple degree polynomial equation was applied to established the function of solid multiple parameter curves for specific fuel consumption (ge), cabon monoxide (CO) ,hydrcarbons (HC) and cabonaceous smoke (Rb). The optimum operation theorems for economy operation indicated by ge and for exhaust emissions described by Co , HC and Rb were obtained from analytical method and performance test data. The optimum operation theorems could exhibit optimum operation working points, curves, and regions. The optimum matching relations of engine speed and transmission parameters were analyzed by using computer simulation methods in accordance with the tractor specifications , actual farm working conditions in a typical drawbar pull work such as plowing , the optimum operation objective function, the ideal transmission ratio, practical gear shif ing positions and practical travel speed of the tractor TN55 medel. The results of the anlayzes indicated clearly that the optimum power efficient operation, energy saving and pollution reducing would be realized if the tractor would be operated according to theoptimum operation methods.

• 산업경영시스템학회지
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• 제27권2호
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• pp.37-43
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• 2004

High speed machining is a machining process which cuts materials with the fast movement and rotation of a spindle in a machine tool. It reduces machining time because of the high feed and the high speed of a spindle. In addition it gets rid of post processes for high precision machining. When the high speed machining is applied to especially hardened steel, operators should select the proper parameters of machining. This can produce machining surfaces which is qualified with good surface roughness. This paper presents a method for selecting machining parameters to minimize surface roughness with high speed machining in cutting the hardened steels. Experimental data for surface roughness are collected in a machining shop based on the cutting feed and the spindle rotation. The data fits in hi-cubic polynomial surface of mathematical form. From the model this research minimize the surface roughness to find the optimal values of the feed and the spindle speed. This paper presents a program which automatically generates optimal solutions from the raw data of experiments.

• Journal of Mechanical Science and Technology
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• 제20권3호
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• pp.366-375
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• 2006

In this paper, it is intended to introduce a method to solve multi-objective optimization problems and to evaluate its performance. In order to verify the performance of this method it is applied for a vertical roller mill for Portland cement. A design process is defined with the compromise decision support problem concept and a design process consists of two steps: the design of experiments and mathematical programming. In this process, a designer decides an object that the objective function is going to pursuit and a non-linear optimization is performed composing objective constraints with practical constraints. In this method, response surfaces are used to model objectives (stress, deflection and weight) and the optimization is performed for each of the objectives while handling the remaining ones as constraints. The response surfaces are constructed using orthogonal polynomials, and orthogonal array as design of experiment, with analysis of variance for variable selection. In addition, it establishes the relative influence of the design variables in the objectives variability. The constrained optimization problems are solved using sequential quadratic programming. From the results, it is found that the method in this paper is a very effective and powerful for the multi-objective optimization of various practical design problems. It provides, moreover, a reference of design to judge the amount of excess or shortage from the final object.

• 제어로봇시스템학회논문지
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• 제17권10호
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• pp.967-982
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• 2011

This paper presents a FTNCS (Fault-Tolerant Networked Control System) that can tolerate control surface failure and packet delay/loss in an UAV (Unmanned Aerial Vehicle). The proposed method utilizes the benefits of self-diagnosis by smart actuators along with the control allocation technique. A smart actuator is an intelligent actuation system combined with microprocessors to perform self-diagnosis and bi-directional communications. In the event of failure, the smart actuator provides the system supervisor with a set of actuator condition data. The system supervisor then compensate for the effect of faulty actuators by re-allocating redundant control surfaces based on the provided actuator condition data. In addition to the compensation of faulty actuators, the proposed FTNCS also includes an efficient algorithm to deal with network induced delay/packet loss. The proposed algorithm is based on a Lagrange polynomial interpolation method without any mathematical model of the system. Computer simulations with an UAV show that the proposed FTNCS can achieve a fast and accurate tracking performance even in the presence of actuator faults and network induced delays.