• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1041-1043
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• 1993

Fuzzy logic based Control Theory has gained much interest in the industrial world, thanks to its ability to formalize and solve in a very natural way many problems that are very difficult to quantify at an analytical level. This paper shows a solution for treating membership function inside hardware circuits. The proposed hardware structure optimizes the memoried size by using particular form of the vectorial representation. The process of memorizing fuzzy sets, i.e. their membership function, has always been one of the more problematic issues for the hardware implementation, due to the quite large memory space that is needed. To simplify such an implementation, it is commonly [1,2,8,9,10,11] used to limit the membership functions either to those having triangular or trapezoidal shape, or pre-definite shape. These kinds of functions are able to cover a large spectrum of applications with a limited usage of memory, since they can be memorized by specifying very few parameters ( ight, base, critical points, etc.). This however results in a loss of computational power due to computation on the medium points. A solution to this problem is obtained by discretizing the universe of discourse U, i.e. by fixing a finite number of points and memorizing the value of the membership functions on such points [3,10,14,15]. Such a solution provides a satisfying computational speed, a very high precision of definitions and gives the users the opportunity to choose membership functions of any shape. However, a significant memory waste can as well be registered. It is indeed possible that for each of the given fuzzy sets many elements of the universe of discourse have a membership value equal to zero. It has also been noticed that almost in all cases common points among fuzzy sets, i.e. points with non null membership values are very few. More specifically, in many applications, for each element u of U, there exists at most three fuzzy sets for which the membership value is ot null [3,5,6,7,12,13]. Our proposal is based on such hypotheses. Moreover, we use a technique that even though it does not restrict the shapes of membership functions, it reduces strongly the computational time for the membership values and optimizes the function memorization. In figure 1 it is represented a term set whose characteristics are common for fuzzy controllers and to which we will refer in the following. The above term set has a universe of discourse with 128 elements (so to have a good resolution), 8 fuzzy sets that describe the term set, 32 levels of discretization for the membership values. Clearly, the number of bits necessary for the given specifications are 5 for 32 truth levels, 3 for 8 membership functions and 7 for 128 levels of resolution. The memory depth is given by the dimension of the universe of the discourse (128 in our case) and it will be represented by the memory rows. The length of a world of memory is defined by: Length = nem (dm(m)＋dm(fm) Where: fm is the maximum number of non null values in every element of the universe of the discourse, dm(m) is the dimension of the values of the membership function m, dm(fm) is the dimension of the word to represent the index of the highest membership function. In our case then Length=24. The memory dimension is therefore 128*24 bits. If we had chosen to memorize all values of the membership functions we would have needed to memorize on each memory row the membership value of each element. Fuzzy sets word dimension is 8*5 bits. Therefore, the dimension of the memory would have been 128*40 bits. Coherently with our hypothesis, in fig. 1 each element of universe of the discourse has a non null membership value on at most three fuzzy sets. Focusing on the elements 32,64,96 of the universe of discourse, they will be memorized as follows: The computation of the rule weights is done by comparing those bits that represent the index of the membership function, with the word of the program memor . The output bus of the Program Memory (μCOD), is given as input a comparator (Combinatory Net). If the index is equal to the bus value then one of the non null weight derives from the rule and it is produced as output, otherwise the output is zero (fig. 2). It is clear, that the memory dimension of the antecedent is in this way reduced since only non null values are memorized. Moreover, the time performance of the system is equivalent to the performance of a system using vectorial memorization of all weights. The dimensioning of the word is influenced by some parameters of the input variable. The most important parameter is the maximum number membership functions (nfm) having a non null value in each element of the universe of discourse. From our study in the field of fuzzy system, we see that typically nfm 3 and there are at most 16 membership function. At any rate, such a value can be increased up to the physical dimensional limit of the antecedent memory. A less important role n the optimization process of the word dimension is played by the number of membership functions defined for each linguistic term. The table below shows the request word dimension as a function of such parameters and compares our proposed method with the method of vectorial memorization[10]. Summing up, the characteristics of our method are: Users are not restricted to membership functions with specific shapes. The number of the fuzzy sets and the resolution of the vertical axis have a very small influence in increasing memory space. Weight computations are done by combinatorial network and therefore the time performance of the system is equivalent to the one of the vectorial method. The number of non null membership values on any element of the universe of discourse is limited. Such a constraint is usually non very restrictive since many controllers obtain a good precision with only three non null weights. The method here briefly described has been adopted by our group in the design of an optimized version of the coprocessor described in [10].

• Proceedings of the Korean Information Science Society Conference
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• 2007.06a
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• pp.17-18
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• 2007

데이터베이스 튜닝은 일반적으로 데이터베이스 어플리케이션을 "좀 더 빠르게" 실행하게 하는 일련의 활동을 뜻한다[1]. 데이터베이스 관리자가 튜닝에 필요한 주먹구구식 룰(Rule of thumb)들을 모두 파악 하고 상황에 맞추어 적용하는 것은 비싼 비용과 오랜 시간을 요구한다. 그렇게 때문에 서로 다른 어플 리케이션들이 맞물려 있는 복잡한 서비스는 필수적으로 자동화된 데이터베이스 성능 관리와 튜닝을 필 요로 한다. 본 논문에서는 이를 해결하기 위하여 지식 도매인(Knowledge Domain)을 기초로 한 자동화 된 데이터베이스 튜닝 원칙(Tuning Principle)을 제시하는 시스템을 제안한다. 각각의 데이터베이스 튜닝 이론들은 지식 도매인의 지식으로 활용되며, 성능에 영향을 미치는 요소들을 개체(Object)와 콘셉트 (Concept)로 구성하고 추론 시스템을 통해 튜닝 원칙을 추론하여 쉽고 빠르게 현재 상황에 맞는 튜닝 방법론을 적용시킬 수 있다. 자동화된 데이터베이스 튜닝에 대해 여러 분야에 걸쳐 학문적인 연구가 이루어지고 있다. 그 예로써 Microsoft의 AutoAdmin Project[2], Oracle의 SQL 튜닝 아키텍처[3], COLT[4], DBA Companion[5], SQUASH[6] 등을 들 수 있다. 이러한 최적화 기법들을 각각의 기능적인 방법론에 따라 다시 분류하면 크게 Design Tuning, Logical Structure Tuning, Sentence Tuning, SQL Tuning, Server Tuning, System/Network Tuning으로 나누어 볼 수 있다. 이 중 SQL Tuning 등은 수치적으로 결정되어 이미 존재하는 정보를 이용하기 때문에 구조화된 모델로 표현하기 쉽고 사용자의 다양한 요구에 의해 변화하는 조건들을 수용하기 쉽기 때문에 이에 중점을 두고 성능 문제를 해결하는 데 초점을 맞추었다. 데이터베이스 시스템의 일련의 처리 과정에 따라 DBMS를 구성하는 개체들과 속성, 그리고 연관 관계들이 모델링된다. 데이터베이스 시스템은 Application / Query / DBMS Level의 3개 레벨에 따라 구조화되며, 본 논문에서는 개체, 속성, 연관 관계 및 데이터베이스 튜닝에 사용되는 Rule of thumb들을 분석하여 튜닝 원칙을 포함한 지식의 형태로 변환하였다. 튜닝 원칙은 데이터베이스 시스템에서 발생하는 문제를 해결할 수 있게 하는 일종의 황금률로써 지식 도매인의 바탕이 되는 사실(Fact)과 룰(Rule) 로써 표현된다. Fact는 모델링된 시스템을 지식 도매인의 하나의 지식 개체로 표현하는 방식이고, Rule 은 Fact에 기반을 두어 튜닝 원칙을 지식의 형태로 표현한 것이다. Rule은 다시 시스템 모델링을 통해 사전에 정의되는 Rule와 튜닝 원칙을 추론하기 위해 사용되는 Rule의 두 가지 타업으로 나뉘며, 대부분의 Rule은 입력되는 값에 따라 다른 솔루션을 취하게 하는 분기의 역할을 수행한다. 사용자는 제한적으로 자동 생성된 Fact와 Rule을 통해 튜닝 원칙을 추론하여 데이터베이스 시스템에 적용할 수 있으며, 요구나 필요에 따라 GUI를 통해 상황에 맞는 Fact와 Rule을 수동으로 추가할 수도 었다. 지식 도매인에서 튜닝 원칙을 추론하기 위해 JAVA 기반의 추론 엔진인 JESS가 사용된다. JESS는 스크립트 언어를 사용하는 전문가 시스템[7]으로 선언적 룰(Declarative Rule)을 이용하여 지식을 표현 하고 추론을 수행하는 추론 엔진의 한 종류이다. JESS의 지식 표현 방식은 튜닝 원칙을 쉽게 표현하고 수용할 수 있는 구조를 가지고 있으며 작은 크기와 빠른 추론 성능을 가지기 때문에 실시간으로 처리 되는 어플리케이션 튜닝에 적합하다. 지식 기반 모률의 가장 큰 역할은 주어진 데이터베이스 시스템의 모델을 통하여 필요한 새로운 지식을 생성하고 저장하는 것이다. 이를 위하여 Fact와 Rule은 지식 표현 의 기본 단위인 트리플(Triple)의 형태로 표현된다, 트리플은 Subject, Property, Object의 3가지 요소로 구성되며, 대부분의 Fact와 Rule들은 트리플의 기본 형태 또는 트리플의 조합으로 이루어진 C Condition과 Action의 두 부분의 결합으로 구성된다. 이와 같이 데이터베이스 시스템 모델의 개체들과 속성, 그리고 연관 관계들을 표현함으로써 지식들이 추론 엔진의 Fact와 Rule로 기능할 수 있다. 본 시스템에서는 이를 구현 및 실험하기 위하여 웹 기반 서버-클라이언트 시스템을 가정하였다. 서버는 Process Controller, Parser, Rule Database, JESS Reasoning Engine으로 구성 되 어 있으며, 클라이 언트는 Rule Manager Interface와 Result Viewer로 구성되어 었다. 실험을 통해 얻어지는 튜닝 원칙 적용 전후의 실행 시간 측정 등 데이터베이스 시스템 성능 척도를 비교함으로써 시스템의 효용을 판단하였으며, 실험 결과 적용 전에 비하여 튜닝 원칙을 적용한 경우 최대 1초 미만의 전처리에 따른 부하 시간 추가와 최소 약 1.5배에서 최대 약 3배까지의 처리 시간 개선을 확인하였다. 본 논문에서 제안하는 시스템은 튜닝 원칙을 자동으로 생성하고 지식 형태로 변형시킴으로써 새로운 튜닝 원칙을 파생하여 제공하고, 성능에 영향을 미치는 요소와 함께 직접 Fact과 Rule을 추가함으로써 커스터마이정된 튜닝을 수행할 수 있게 하는 장점을 가진다. 추후 쿼리 자체의 튜닝 및 인텍스 최적화 등의 프로세스 자동화와 Rule을 효율적으로 정의하고 추가하는 방법 그리고 시스템 모델링을 효과적으로 구성하는 방법에 대한 연구를 통해 본 연구를 더욱 개선시킬 수 있을 것이다.

• The Journal of Korean Academy of Prosthodontics
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• v.43 no.4
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• pp.528-543
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• 2005

Statement of problem: Repeated delivery and removal of abutment cause some changes such as wear, scratch or defect of hexagonal structure. It may increase the value of rotational freedom(RF) between hexagonal structures. Purpose: The purpose of this study was to evaluate surface changes and rotational freedom between the external hexagon of the implant fixture and internal hexagon of abutment after repeated delivery and removal under SEM and toolmaker's microscope. Materials and methods: Implant systems used for this study were 3i and Avana. Seven pail's of implant fixture, abutment and abutment screws for each system were selected and all fixtures were perpendicularly mounted in liquid unsaturated polyesther with dental surveyor. Each one was embedded beneath the platform of fixture. Surfaces of hexagonal structure before repeated closing and opening of abutment were observed using SEM and rotational freedom was measured by using toolmaker's microscope. Each abutment was secured to the implant future by each abutment screw with recommended torque value using a digital torque controller and was repeatedly delivered and removed by 20 times respectively. After experiment, evaluation for the change of hexagonal structures and measurement of rotational freedom were performed. Result : The results were as follows; 1. Wear of contact area between implant fixture and abutment was considerable in both 3i and Avana system. Scratches and defects were frequently observed at the line-angle of hexagonal structures of implant fixture and abutment. 2. In the SEM view of the external hexagon of implant fixture, the point-angle areas at the corner edge of hexagon were severely worn out in both systems. It was more notable in the case of 3i systems than in that of Avana systems. 3. In the SEM view of the internal hexagon of abutment, Gingi-Hue abutment of 3i systems showed severe wear in micro-stop contacts that were machined into the corners to prevent rotation and cemented abutment of Avana systems showed wear in both surface area adjacent to the corner mating with external hexagon of implant fixture. 4 The mean values of rotational freedom between the external hexagon of the implant fixture and internal hexagon of abutment were 0.48$\pm$0.04$^{\circ}$ in pre-tested 3i systems and 1.18$\pm$0.25$^{\circ}$ after test, and 1.80$\pm$0.04$^{\circ}$ in pre-tested Avana systems and 2.61$\pm$0.16$^{\circ}$ after test. 5. Changes of rotational freedom after test shouted statistical)y a significant increase in both 3i and Avana systems(P<0.05, paired t-test). 6. Statistically, there was no significant difference between amount of increase in the rotational freedom of 3i systems and amount of increase in that of Avana ones(P>0.05, unpaired t-test). Conclusion: Conclusively, it was considered that repeated delivery and remove of abutment by 20 times would not have influence on screw joint stability. However, it caused statistically the significant change of rotational freedom in tested systems. Therefore, it is suggested that repeated delivery and remove of abutment should be minimal as possible as it could be and be done carefully Additionally, it is suggested that the means or treatment to prevent the wear of mating components should be devised.

• International Journal of Ocean System Engineering
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• v.2 no.3
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• pp.185-194
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• 2012

A Macroscopic combination of two or more distinct materials is commonly referred to as a "Composite Material", having been designed mechanically and chemically superior in function and characteristic than its individual constituent materials. Composite materials are used not only for aerospace and military, but also heavily used in boat/ship building and general composite industries which we are seeing increasingly more. Regardless of the various applications for composite materials, the industry is still limited and requires better fabrication technology and methodology in order to expand and grow. An example of this is that the majority of fabrication facilities nearby still use an antiquated wet lay-up process where fabrication still requires manual hand labor in a 3D environment impeding productivity of composite product design advancement. As an expert in the advanced composites field, I have developed fabrication skills with the use of machinery based on my past composite experience. In autumn 2011, the Korea government confirmed to fund my project. It is the development of a composite sanding machine. I began development of this semi-robotic prototype beginning in 2009. It has possibilities of replacing or augmenting the exhaustive and difficult jobs performed by human hands, such as sanding, grinding, blasting, and polishing in most often, very awkward conditions, and is also will boost productivity, improve surface quality, cut abrasive costs, eliminate vibration injuries, and protect workers from exposure to dust and airborne contamination. Ease of control and operation of the equipment in or outside of the sanding room is a key benefit to end-users. It will prove to be much more economical than normal robotics and minimize errors that commonly occur in factories. The key components and their technologies are a 360 degree rotational shoulder and a wrist that is controlled under PLC controller and joystick manual mode. Development on both of the key modules is complete and are now operational. The Korean government fund boosted my development and I expect to complete full scale development no later than 3rd quarter 2012. Even with the advantages of composite materials, there is still the need to repair or to maintain composite products with a higher level of technology. I have learned many composite repair skills on composite airframe since many composite fabrication skills including repair, requires training for non aerospace applications. The wind energy market is now requiring much larger blades in order to generate more electrical energy for wind farms. One single blade is commonly 50 meters or longer now. When a wind blade becomes damaged from external forces, on-site repair is required on the columns even under strong wind and freezing temperature conditions. In order to correctly obtain polymerization, the repair must be performed on the damaged area within a very limited time. The use of pre-impregnated glass fabric and heating silicone pad and a hot bonder acting precise heating control are surely required.

• Journal of Bio-Environment Control
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• v.23 no.4
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• pp.293-302
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• 2014

This study was carried out to develop rain shelter which can make an appropriate size and environment for Chinese cabbage rainproof cultivation. Fifty three farms with chinese cabbage rainproof cultivation system have been investigated to set up width and height of rain shelter. Mostly the width of 6m was desired for rain shelter and the height of 1.6m for their eaves, so these values were chosen as the dimensions for rain shelter. After an analysis of their structural safety and installation costs by the specifications of the rafter pipe, Ø$25.4{\times}1.5t$ and 90cm have been set as the size of rafter that such size costs the least. This size is stable with $27m{\cdot}s^{-1}$ of wind velocity and 17cm of snow depth. Therefore it is difficult to apply this dimension to area with higher climate load. In order to sort out such problem, the rain shelter has been designed to avoid damage on frame by opening plastic film to the ridge. Once greenhouse band is loosen by turning the manual switch at the both sides of rain shelter and open button of controller is pushed then switch motor rises up along the guide pipe and plastic film is opened to the ridge. Chinese cabbage can be damaged by insects if rain shelter is opened completely as revealed a field. To prevent this, farmers can install an insect-proof net. Further, the greenhouse can be damaged by typhoon while growing Chinese cabbage therefore the effect of an insect-proof net on structural safety has been analyzed. And then structural safety has been analyzed through using flow-structure interaction method at the wind condition of $40m{\cdot}s^{-1}$. And it assumed that wind applied perpendicular to side of the rain shelter which was covered by insect-proof net. The results indicated that plastic film was directly affected by wind therefore high pressure occurred on the surface. But wind load on insect-proof net was smaller than on plastic film and pressure distribution was also uniform. The results of structural analysis by applying pressure data extracted from flow analysis indicated that the maximum stress occurred at the end of pipe which is the ground part and the value has been 54.6MPa. The allowable stress of pipe in the standard of structural safety must be 215 MPa or more therefore structural safety of this rain shelter is satisfied.

• Korean Journal of Ecology and Environment
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• v.41 no.3
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• pp.402-411
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• 2008

Grazing effects of two freshwater shellfish, Unio douglasiae (UNIO) and Cipangoplaudina chinese malleata (CCM), on the hibernal diatom communities in eutrophic water was examined in a laboratory. Two animals having different feeding types used in the study were collected from Keum River (Boryeong, Korea), acclimatized in the artificial management system in a laboratory over at least one month, and starved in a laboratory for 2 days before the experiment. Experimental waters, which dominated by Synedra ulna-Scenedesmus sp. (ca. 80%), was collected from eutrophic lake, Lake Ilgam (Seoul) in Feb., 19, 2008 at AM 10:00, and used in the study after the filtration with 1 mm Nylon mesh. Feeding experiments were largely divided into three kinds of animal treatments; five densities of UNIO (U0, U1, U2, U3, U4) and CCM (C0, C1, C2, C3, C4), and four combined densities of two shellfish (M0, M1, M2, M3). U0 and C0 were control (no addition of UNIO or CCM), U1 or C1 (each animal density at 0.5 ind. $L^{-1}$), U2 or C2 (1.0 ind. $L^{-1}$), U3 or C3 (1.5 ind. $L^{-1}$), and U4 or C4 (2.0 ind. $L^{-1}$), respectively. Four combined treatments were consisted of M0 (no animals), M1 (U1+C3), M2 (U2+C2), and M3 (U4+C1), respectively. Under the presence of animal, the concentration of Chl-a and algal abundance were clearly decreased with the increase of UNIO density and the treated time, while in combined group a strong decrease of algal density showed with the increase of UNIO density. Total phytoplankton density shifted as the similar patterns to that of Chl-a concentration (r=0.6527, p<0.0001), however, there showed the differences following a species. There were strong decreases of dominant species Synedra ulna, Scenedesmus sp., Ankistrodesmus falcatus in UNIO treatment group, Diatoma vulgare in combined group, while Cryptomonas ovata in high density of CCM increased about 20% in algal density. Grazing rates (GRs) based on the concentration of Chl-a was depend on the kind of shellfish and treatment time; a strong feeding of CCM showed in the initial stage, and four hours later, UNIO and combined group with high UNIO density showed the high GRs. Interestingly, faeces production of shellfish was highest in combined group with high density of CCM, while their size over 60 ${\mu}m$ was much higher in production magnitude than that less 60 ${\mu}m$. Collectively, these results suggest that two domestic shellfish and its combined treatment have a strong potential as an effective biological controller of diatom bloom in cold eutrophic waters.

• The Journal of Korean Academy of Prosthodontics
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• v.50 no.2
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• pp.92-98
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• 2012

Purpose: The aim of this study was to evaluate the effects of different abutment materials on abutment screw loosening and settling-down effect in conical connection type implant system. Materials and methods: Three types of abutment, cementation, gold UCLA, and metal UCLA abutment were used. Two UCLA groups were fabricated in a similar pattern to cementation abutment. Type III gold alloy and Nickel-Chromium alloy was used for casting gold UCLA abutment and metal UCLA abutment, respectively. Fixture and abutment were tightened to 30 Ncm by using digital torque controller and re-tightening was conducted with same force after 10 minutes. Digital torque gauge was used to measure loosening torque and fixture/abutment length was measured by digital micrometer. Dynamic loads between 25 N and 250 N were applied with $0^{\circ}$ angle to the abutment axis. After loading, fixture/abutment length was re-measured and amount of settlement was calculated. Loosening torque value was also measured for comparison Results: All three groups showed significant differences of length when comparing before and after loading, but there was no significant difference of settling amount in all groups. Loosening torque values were significantly decreased when comparing before and after loading in all groups($P$<.05). However, there was no significant difference in loss of loosening torque values when compared to groups. Conclusion: In internal conical connection type implants, dynamic load affected on settlement and loosening torque of implant, but there was no differences between abutments materials. Likewise gold UCLA abutment, metal UCLA abutment might be able to withstand functional load.

• Korean Journal of Soil Science and Fertilizer
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• v.10 no.3
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• pp.103-134
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• 1977

The physiological and biochemical role of potassium for upland crops according to recent research reports and the nutritional status of potassium in Korea were reviewed. Since physical and chemical characteristics of potassium ion are different from those of sodium, potassium can not completely be replaced by sodium and replacement must be limited to minimum possible functional area. Specific roles of potassium seem to keep fine structure of biological membranes such as thylacoid membrane of chloroplast in the most efficient form and to be allosteric effector and conformation controller of various enzymes principally in carbohydrate and protein metabolism. Potassium is essential to improve the efficiency of phoro- and oxidative- phosphorylation and involve deeply in all energy required metabolisms especially synthesis of organic matter and their translocation. Potassium has many important, physiological functions such as maintenance of osmotic pressure and optimum hydration of cell colloids, consequently uptake and translocation of water resulting in higher water use efficiency and of better subcellular environment for various physiological and biochemical activities. Potassium affects uptake and translocation of mineral nutrients and quality of products. potassium itself in products may become a quality criteria due to potassium essentiality for human beings. Potassium uptake is greatly decreased by low temperature and controlled by unknown feed back mechanism of potassium in plants. Thus the luxury absorption should be reconsidered. Total potassium content of upland soil in Korea is about 3% but the exchangeable one is about 0.3 me/100g soil. All upland crops require much potassium probably due to freezing and cold weather and also due to wet damage and drought caused by uneven rainfall pattern. In barley, potassium should be high at just before freezing and just after thawing and move into grain from heading for higher yield. Use efficiency of potassium was 27% for barley and 58% in old uplands, 46% in newly opened hilly lands for soybean. Soybean plant showed potassium deficiency symptom in various fields especially in newly opened hilly lands. Potassium criteria for normal growth appear 2% $K_2O$ and 1.0 K/(Ca+Mg) (content ratio) at flower bud initiation stage for soybean. Potassium requirement in plant was high in carrot, egg plant, chinese cabbage, red pepper, raddish and tomato. Potassium content in leaves was significantly correlated with yield in chinese cabbage. Sweet potato. greatly absorbed potassium subsequently affected potassium nutrition of the following crop. In the case of potassium deficiency, root showed the greatest difference in potassium content from that of normal indicating that deficiency damages root first. Potatoes and corn showed much higher potassium content in comparison with calcium and magnesium. Forage crops from ranges showed relatively high potassium content which was significantly and positively correlated with nitrogen, phosphorus and calcium content. Percentage of orchards (apple, pear, peach, grape, and orange) insufficient in potassium ranged from 16 to 25. The leaves and soils from the good apple and pear orchards showed higher potassium content than those from the poor ones. Critical ratio of $K_2O/(CaO+MgO)$ in mulberry leaves to escape from winter death of branch tip was 0.95. In the multiple croping system, exchangeable potassium in soils after one crop was affected by the previous crops and potassium uptake seemed to be related with soil organic matter providing soil moisture and aeration. Thus, the long term and quantitative investigation of various forms of potassium including total one are needed in relation to soil, weather and croping system. Potassium uptake and efficiency may be increased by topdressing, deep placement, slow-releasing or granular fertilizer application with the consideration of rainfall pattern. In all researches for nutritional explanation including potassium of crop yield reasonable and practicable nutritional indices will most easily be obtained through multifactor analysis.