• The Korean Journal of Nuclear Medicine Technology
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• v.16 no.1
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• pp.115-118
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• 2012

Purpose: The Levey-Jennings chart controlled measurement values that deviated from the tolerance value (mean ${\pm}2SD$ or ${\pm}3SD$). On the other hand, the upgraded Westgard Multi-Rules are actively recommended as a more efficient, specialized form of hospital certification in relation to Internal Quality Control. To apply Westgard Multi-Rules in quality control, credible quality control substance and target value are required. However, as physical examinations commonly use quality control substances provided within the test kit, there are many difficulties presented in the calculation of target value in relation to frequent changes in concentration value and insufficient credibility of quality control substance. This study attempts to improve the professionalism and credibility of quality control by applying Westgard Multi-Rules and calculating credible target value by using a commercialized quality control substance. Materials and Methods : This study used Immunoassay Plus Control Level 1, 2, 3 of Company B as the quality control substance of Total T3, which is the thyroid test implemented at the relevant hospital. Target value was established as the mean value of 295 cases collected for 1 month, excluding values that deviated from ${\pm}2SD$. The hospital quality control calculation program was used to enter target value. 12s, 22s, 13s, 2 of 32s, R4s, 41s, $10\bar{x}$, 7T of Westgard Multi-Rules were applied in the Total T3 experiment, which was conducted 194 times for 20 days in August. Based on the applied rules, this study classified data into random error and systemic error for analysis. Results: Quality control substances 1, 2, and 3 were each established as 84.2 ng/$dl$, 156.7 ng/$dl$, 242.4 ng/$dl$ for target values of Total T3, with the standard deviation established as 11.22 ng/$dl$, 14.52 ng/$dl$, 14.52 ng/$dl$ respectively. According to error type analysis achieved after applying Westgard Multi-Rules based on established target values, the following results were obtained for Random error, 12s was analyzed 48 times, 13s was analyzed 13 times, R4s was analyzed 6 times, for Systemic error, 22s was analyzed 10 times, 41s was analyzed 11 times, 2 of 32s was analyzed 17 times, $10\bar{x}$ was analyzed 10 times, and 7T was not applied. For uncontrollable Random error types, the entire experimental process was rechecked and greater emphasis was placed on re-testing. For controllable Systemic error types, this study searched the cause of error, recorded the relevant cause in the action form and reported the information to the Internal Quality Control committee if necessary. Conclusions : This study applied Westgard Multi-Rules by using commercialized substance as quality control substance and establishing target values. In result, precise analysis of Random error and Systemic error was achieved through the analysis of 12s, 22s, 13s, 2 of 32s, R4s, 41s, $10\bar{x}$, 7T rules. Furthermore, ideal quality control was achieved through analysis conducted on all data presented within the range of ${\pm}3SD$. In this regard, it can be said that the quality control method formed based on the systematic application of Westgard Multi-Rules is more effective than the Levey-Jennings chart and can maximize error detection.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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• v.18 no.1
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• pp.40-46
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• 2013

The isotope ratios of $^{13}C/^{12}C$ and $^{18}O/^{16}O$ for a sample in a mass spectrometer are measured relative to those of a pure $CO_2$ reference gas (i.e., laboratory working standard). Thus, the calibration of a laboratory working standard gas to the international isotope scales (Pee Dee Belemnite (PDB) for ${\delta}^{13}C$ and Vienna Standard Mean Ocean Water (V-SMOW) for ${\delta}^{18}O$) is essential for comparisons between data sets obtained by other groups on other mass spectrometers. However, one often finds difficulties in getting well-calibrated standard gases, because of their production time and high price. Additional difficulty is that fractionation processes can occur inside the gas cylinder most likely due to pressure drop in long-term use. Therefore, studies on laboratory production of pure $CO_2$ isotope standard gas from stable solid calcium carbonate standard materials, have been performed. For this study, we propose a method to extract pure $CO_2$ gas without isotope fractionation from a solid calcium carbonate material. The method is similar to that suggested by Coplen et al., (1983), but is better optimized particularly to make a large amount of pure $CO_2$ gas from calcium carbonate material. The $CaCO_3$ releases $CO_2$ in reaction with 100% pure phosphoric acid at $25^{\circ}C$ in a custom designed, evacuated reaction vessel. Here we introduce optimal procedure, reaction conditions, and samples/reactants size for calcium carbonate-phosphoric acid reaction and also provide the details for extracting, purifying and collecting $CO_2$ gas out of the reaction vessel. The measurements for ${\delta}^{18}O$ and ${\delta}^{13}C$ of $CO_2$ were performed at Seoul National University using a stable isotope ratio mass spectrometer (VG Isotech, SIRA Series II) operated in dual-inlet mode. The entire analysis precisions for ${\delta}^{18}O$ and ${\delta}^{13}C$ were evaluated based on the standard deviations of multiple measurements on 15 separate samples of purified $CO_2$. The pure $CO_2$ samples were taken from 100-mg aliquots of a solid calcium carbonate (Solenhofen-ori $CaCO_3$) during 8-day experimental period. The multiple measurements yielded the $1{\sigma}$ precisions of ${\pm}0.01$‰ for ${\delta}^{13}C$ and ${\pm}0.05$‰ for ${\delta}^{18}O$, comparable to the internal instrumental precisions of SIRA. Therefore, we conclude the method proposed in this study can serve as a way to produce an accurate secondary and/or laboratory $CO_2$ standard gas. We hope this study helps resolve difficulties in placing a laboratory working standard onto the international isotope scales and does make accurate comparisons with other data sets from other groups.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.40 no.4
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• pp.268-281
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• 2004

A study was carried out in order to estimate the deformation of the pound net according to the current by the model test in the circulating water channel. The tension of the frame rope and the variation of net shape were measured to investigate the deforming of the model pound net in the flow. The results are obtained as follows; 1. The experimental equation between tensions (R) of the frame rope and velocity (ν)was found to be R=$19.58v^{1.98}$($r^2$=0.98) in case of the upperward flow with fish court net and R=$26.90v^{1.72}$($r^2$=0.95)at the upperward flow with bag net according to the velocity from 0.0m/s to 0.6m/s, respectively. 2. As the variation of flow speed inside of the model net was gradually decreased according as which is passed through netting panels, in case of the upperward flow with fish court net, the flow speed was about 70% of initial flow speed at 0.1m/s, 60% at 0.2m/s, 50% at 0.3m/s and 40% 0.4~0.6m/s at the measurement point(h) inside of the first bag net, respectively. In case of the upperward flow with bag net, as the flow speed was steeply decreased according as which if passed through the second bag net, it was 30~60% of the initial flow speed and was 20~30% inside of the first bag net and was about 10~20% inside of the inclined passage net. 3. In case of the upperward flow with fish court net, the variation of deformed angle of fish court net was from 0$^{\circ}$ to 70$^{\circ}$and that of inclined passage net was from 0$^{\circ}$ to 63$^{\circ}$and that of the second bag net was from 0$^{\circ}$ to 47$^{\circ}$ . 4. In case of the upperward flow with fish court net, the variation of deformed angle of the second bag net was changed from 0$^{\circ}$ to 70$^{\circ}$and that of the inclined passage net was from 0$^{\circ}$ to 55$^{\circ}$ and that of the fish court net was from 0$^{\circ}$ to 50$^{\circ}$. The depth ratio of the first bag net was changed from 0% to 35% and that of the second bag net was from 0% to 20% and that of the inclined passage net was from 0% to 35%. In the flow speed 0.5m/s, the inclined passage net was raised up to the entry of the bag net and then prevented it more over 90%. 5. To be increased the opening volume of pound net, it needs to attach the added weight outside of the fish court net, inclined passage net and bag net. At the same time, it needs to adjust the tension of the twine for maintenance of the shape.

• Journal of Distribution Research
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• v.17 no.1
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• pp.37-63
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• 2012

In franchise business, exclusive sales territory (sometimes EST in table) protection is a very important issue from an economic, social and political point of view. It affects the growth and survival of both franchisor and franchisee and often raises issues of social and political conflicts. When franchisee is not familiar with related laws and regulations, franchisor has high chance to utilize it. Exclusive sales territory protection by the manufacturer and distributors (wholesalers or retailers) means sales area restriction by which only certain distributors have right to sell products or services. The distributor, who has been granted exclusive sales territories, can protect its own territory, whereas he may be prohibited from entering in other regions. Even though exclusive sales territory is a quite critical problem in franchise business, there is not much rigorous research about the reason, results, evaluation, and future direction based on empirical data. This paper tries to address this problem not only from logical and nomological validity, but from empirical validation. While we purse an empirical analysis, we take into account the difficulties of real data collection and statistical analysis techniques. We use a set of disclosure document data collected by Korea Fair Trade Commission, instead of conventional survey method which is usually criticized for its measurement error. Existing theories about exclusive sales territory can be summarized into two groups as shown in the table below. The first one is about the effectiveness of exclusive sales territory from both franchisor and franchisee point of view. In fact, output of exclusive sales territory can be positive for franchisors but negative for franchisees. Also, it can be positive in terms of sales but negative in terms of profit. Therefore, variables and viewpoints should be set properly. The other one is about the motive or reason why exclusive sales territory is protected. The reasons can be classified into four groups - industry characteristics, franchise systems characteristics, capability to maintain exclusive sales territory, and strategic decision. Within four groups of reasons, there are more specific variables and theories as below. Based on these theories, we develop nine hypotheses which are briefly shown in the last table below with the results. In order to validate the hypothesis, data is collected from government (FTC) homepage which is open source. The sample consists of 1,896 franchisors and it contains about three year operation data, from 2006 to 2008. Within the samples, 627 have exclusive sales territory protection policy and the one with exclusive sales territory policy is not evenly distributed over 19 representative industries. Additional data are also collected from another government agency homepage, like Statistics Korea. Also, we combine data from various secondary sources to create meaningful variables as shown in the table below. All variables are dichotomized by mean or median split if they are not inherently dichotomized by its definition, since each hypothesis is composed by multiple variables and there is no solid statistical technique to incorporate all these conditions to test the hypotheses. This paper uses a simple chi-square test because hypotheses and theories are built upon quite specific conditions such as industry type, economic condition, company history and various strategic purposes. It is almost impossible to find all those samples to satisfy them and it can't be manipulated in experimental settings. However, more advanced statistical techniques are very good on clean data without exogenous variables, but not good with real complex data. The chi-square test is applied in a way that samples are grouped into four with two criteria, whether they use exclusive sales territory protection or not, and whether they satisfy conditions of each hypothesis. So the proportion of sample franchisors which satisfy conditions and protect exclusive sales territory, does significantly exceed the proportion of samples that satisfy condition and do not protect. In fact, chi-square test is equivalent with the Poisson regression which allows more flexible application. As results, only three hypotheses are accepted. When attitude toward the risk is high so loyalty fee is determined according to sales performance, EST protection makes poor results as expected. And when franchisor protects EST in order to recruit franchisee easily, EST protection makes better results. Also, when EST protection is to improve the efficiency of franchise system as a whole, it shows better performances. High efficiency is achieved as EST prohibits the free riding of franchisee who exploits other's marketing efforts, and it encourages proper investments and distributes franchisee into multiple regions evenly. Other hypotheses are not supported in the results of significance testing. Exclusive sales territory should be protected from proper motives and administered for mutual benefits. Legal restrictions driven by the government agency like FTC could be misused and cause mis-understandings. So there need more careful monitoring on real practices and more rigorous studies by both academicians and practitioners.

• Journal of Korean Medicine Rehabilitation
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• v.18 no.4
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• pp.39-61
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• 2008

Objectives : The present study was performed to investigate whether acupuncture stimulation in the rats affected regeneration properties of the injured sciatic nerve. A differential effect of acupuncture stimulation on the one point near the spinal nerve root controlling sciatic nerve activity and the other point in the peripheral area subordinated by injured nerve was compared. Materials and Methods: Rat sciatic nerves were injured by crush, and the effects on axonal regeneration on injured sciatic nerves were evaluated by acupuncture stimulation at two different regions. In proximal acupuncture stimulation group, acupuncture stimulation was performed on Huatuo Jiaji(EX B2) points located from L5 to S1 vertebral levels to stimulate the nearest spinal nerve root that innervates sciatic nerves. In distal acupuncture stimulation group, acupuncture stimulation was performed on Zusanli(ST 36) and Weizhong(BL 40) points to stimulate at peripheral area dominated by injured sciatic nerves. Acupuncture stimulation was given every other days for 1 or 2 weeks. Sciatic nerve tissues collected from acupuncture stimulation experimental groups, injury control group, and intact animal group were used for protein analysis by Western blotting or Hoechst nuclear staining. To determine axonal regeneration, Dil fluorescence dye was injected into the sciatic nerve 0.5 cm distal to the injury site in individual animal groups and Dil-labeled cells by retrograde tracing were measured in the DRG at lumbar 5 or in the spinal cord. DRG sensory neurons prepared from individual animal groups were used to measure the extent of neurite outgrowth and for immunofluorescence staining with anti-GAP-43 antibody. Results : Animal groups given proximal or distal acupuncture stimulation showed upregulation of GAP-43 and Cdc2 protein levels in the sciatic nerve at 7 days after injury. Cdk2 protein levels were strongly induced by nerve injury, but did not show changes by acupuncture stimulation. Phospho-Erk1/2 protein levels were elevated by acupuncture stimulation above those present in the injury control animals. These increase in regeneration-associated protein levels appeared to be related with increase cell proliferation in the injured sciatic nerves. Hoechst 33258 staining of sciatic nerve tissue to visualize nuclei of individual cells showed increased Schwann cell number in the distal portion of the injured nerve 7 and 14 days after injury and further increases by acupuncture stimulation particularly at the proximal position. Measurement of axonal regeneration by retrograde tracing showed significantly increased Dil-labeled cells in proximal acupuncture stimulation group compared to distal acupuncture stimulation group and injury control group. Finally, an evaluation of axonal regeneration by retrograde tracing showed increased number of Dil labeled cells in the DRG at lumbar 5 or in the ventral horn of the spinal cord at lower thoracic level at 7 days after nerve injury. Conclusions : The present data show that the proximal acupuncture stimulation at Huatuo Jiaji(EX B2) points governing injured sciatic nerves was more effective for axonal regeneration than the distal acupuncture stimulation. Further studies on functional recovery or associated molecular mechanisms should be critical for developing animal models and clinical applications.

• Journal of Global Scholars of Marketing Science
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• v.18 no.3
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• pp.59-88
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• 2008

Digital Convergence means integration between industry, technology, and contents, and in marketing, it usually comes with creation of new types of product and service under the base of digital technology as digitalization progress in electro-communication industries including telecommunication, home appliance, and computer industries. One can see digital convergence not only in instruments such as PC, AV appliances, cellular phone, but also in contents, network, service that are required in production, modification, distribution, re-production of information. Convergence in contents started around 1990. Convergence in network and service begins as broadcasting and telecommunication integrates and DMB(digital multimedia broadcasting), born in May, 2005 is the symbolic icon in this trend. There are some positive and negative expectations about DMB. The reason why two opposite expectations exist is that DMB does not come out from customer's need but from technology development. Therefore, customers might have hard time to interpret the real meaning of DMB. Time is quite critical to a high tech product, like DMB because another product with same function from different technology can replace the existing product within short period of time. If DMB does not positioning well to customer's mind quickly, another products like Wibro, IPTV, or HSPDA could replace it before it even spreads out. Therefore, positioning strategy is critical for success of DMB product. To make correct positioning strategy, one needs to understand how consumer interprets DMB and how consumer's interpretation can be changed via communication strategy. In this study, we try to investigate how consumer perceives a new product, like DMB and how AD strategy change consumer's perception. More specifically, the paper segment consumers into sub-groups based on their DMB perceptions and compare their characteristics in order to understand how they perceive DMB. And, expose them different printed ADs that have messages guiding consumer think DMB in specific ways, either cellular phone or personal TV. Research Question 1: Segment consumers according to perceptions about DMB and compare characteristics of segmentations. Research Question 2: Compare perceptions about DMB after AD that induces categorization of DMB in direction for each segment. If one understand and predict a direction in which consumer perceive a new product, firm can select target customers easily. We segment consumers according to their perception and analyze characteristics in order to find some variables that can influence perceptions, like prior experience, usage, or habit. And then, marketing people can use this variables to identify target customers and predict their perceptions. If one knows how customer's perception is changed via AD message, communication strategy could be constructed properly. Specially, information from segmented customers helps to develop efficient AD strategy for segment who has prior perception. Research framework consists of two measurements and one treatment, O1 X O2. First observation is for collecting information about consumer's perception and their characteristics. Based on first observation, the paper segment consumers into two groups, one group perceives DMB similar to Cellular phone and the other group perceives DMB similar to TV. And compare characteristics of two segments in order to find reason why they perceive DMB differently. Next, we expose two kinds of AD to subjects. One AD describes DMB as Cellular phone and the other Ad describes DMB as personal TV. When two ADs are exposed to subjects, consumers don't know their prior perception of DMB, in other words, which subject belongs 'similar-to-Cellular phone' segment or 'similar-to-TV' segment? However, we analyze the AD's effect differently for each segment. In research design, final observation is for investigating AD effect. Perception before AD is compared with perception after AD. Comparisons are made for each segment and for each AD. For the segment who perceives DMB similar to TV, AD that describes DMB as cellular phone could change the prior perception. And AD that describes DMB as personal TV, could enforce the prior perception. For data collection, subjects are selected from undergraduate students because they have basic knowledge about most digital equipments and have open attitude about a new product and media. Total number of subjects is 240. In order to measure perception about DMB, we use indirect measurement, comparison with other similar digital products. To select similar digital products, we pre-survey students and then finally select PDA, Car-TV, Cellular Phone, MP3 player, TV, and PSP. Quasi experiment is done at several classes under instructor's allowance. After brief introduction, prior knowledge, awareness, and usage about DMB as well as other digital instruments is asked and their similarities and perceived characteristics are measured. And then, two kinds of manipulated color-printed AD are distributed and similarities and perceived characteristics for DMB are re-measured. Finally purchase intension, AD attitude, manipulation check, and demographic variables are asked. Subjects are given small gift for participation. Stimuli are color-printed advertising. Their actual size is A4 and made after several pre-test from AD professionals and students. As results, consumers are segmented into two subgroups based on their perceptions of DMB. Similarity measure between DMB and cellular phone and similarity measure between DMB and TV are used to classify consumers. If subject whose first measure is less than the second measure, she is classified into segment A and segment A is characterized as they perceive DMB like TV. Otherwise, they are classified as segment B, who perceives DMB like cellular phone. Discriminant analysis on these groups with their characteristics of usage and attitude shows that Segment A knows much about DMB and uses a lot of digital instrument. Segment B, who thinks DMB as cellular phone doesn't know well about DMB and not familiar with other digital instruments. So, consumers with higher knowledge perceive DMB similar to TV because launching DMB advertising lead consumer think DMB as TV. Consumers with less interest on digital products don't know well about DMB AD and then think DMB as cellular phone. In order to investigate perceptions of DMB as well as other digital instruments, we apply Proxscal analysis, Multidimensional Scaling technique at SPSS statistical package. At first step, subjects are presented 21 pairs of 7 digital instruments and evaluate similarity judgments on 7 point scale. And for each segment, their similarity judgments are averaged and similarity matrix is made. Secondly, Proxscal analysis of segment A and B are done. At third stage, get similarity judgment between DMB and other digital instruments after AD exposure. Lastly, similarity judgments of group A-1, A-2, B-1, and B-2 are named as 'after DMB' and put them into matrix made at the first stage. Then apply Proxscal analysis on these matrixes and check the positional difference of DMB and after DMB. The results show that map of segment A, who perceives DMB similar as TV, shows that DMB position closer to TV than to Cellular phone as expected. Map of segment B, who perceive DMB similar as cellular phone shows that DMB position closer to Cellular phone than to TV as expected. Stress value and R-square is acceptable. And, change results after stimuli, manipulated Advertising show that AD makes DMB perception bent toward Cellular phone when Cellular phone-like AD is exposed, and that DMB positioning move towards Car-TV which is more personalized one when TV-like AD is exposed. It is true for both segment, A and B, consistently. Furthermore, the paper apply correspondence analysis to the same data and find almost the same results. The paper answers two main research questions. The first one is that perception about a new product is made mainly from prior experience. And the second one is that AD is effective in changing and enforcing perception. In addition to above, we extend perception change to purchase intention. Purchase intention is high when AD enforces original perception. AD that shows DMB like TV makes worst intention. This paper has limitations and issues to be pursed in near future. Methodologically, current methodology can't provide statistical test on the perceptual change, since classical MDS models, like Proxscal and correspondence analysis are not probability models. So, a new probability MDS model for testing hypothesis about configuration needs to be developed. Next, advertising message needs to be developed more rigorously from theoretical and managerial perspective. Also experimental procedure could be improved for more realistic data collection. For example, web-based experiment and real product stimuli and multimedia presentation could be employed. Or, one can display products together in simulated shop. In addition, demand and social desirability threats of internal validity could influence on the results. In order to handle the threats, results of the model-intended advertising and other "pseudo" advertising could be compared. Furthermore, one can try various level of innovativeness in order to check whether it make any different results (cf. Moon 2006). In addition, if one can create hypothetical product that is really innovative and new for research, it helps to make a vacant impression status and then to study how to form impression in more rigorous way.

• Korean Journal of Agricultural Science
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• v.16 no.1
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• pp.84-101
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• 1989

An accurate measurement of size, surface area and volume of agricultural products is essential in many engineering operations such as handling and sorting, and in heat transfer studies on heating and cooling processes. Little information is available on these properties due to their irregular shape, and moreover very little information on the rough rice, soybean, barley, and wheat has been published. Physical dimensions of grain, such as length, width, thickness, surface area, and volume vary according to the variety, environmental conditions, temperature, and moisture content. Especially, recent research has emphasized on the variation of these properties with the important factors such as moisture content. The objectives of this study were to determine physical dimensions such as length, width and thickness, surface area and volume of the rough rice, soybean, barley, and wheat as a function of moisture content, to investigate the effect of moisture content on the properties, and to develop exponential equations to predict the surface area and the volume of the grains as a function of physical dimensions. The varieties of the rough rice used in this study were Akibare, Milyang 15, Seomjin, Samkang, Chilseong, and Yongmun, as a soybean sample Jangyeobkong and Hwangkeumkong, as a barley sample Olbori and Salbori, and as a wheat sample Eunpa and Guru were selected, respectively. The physical properties of the grain samples were determined at four levels of moisture content and ten or fifteen replications were run at each moisture content level and each variety. The results of this study are summarized as follows; 1. In comparison of the surface area and the volume of the 0.0375m diameter-sphere measured in this study with the calculated values by the formula the percent error between them showed least values of 0.65% and 0.77% at the rotational degree interval of 15 degree respectively. 2. The statistical test(t-test) results of the physical properties between the types of rough rice, and between the varieties of soybean and wheat indicated that there were significant difference at the 5% level between them. 3. The physical dimensions varied linearly with the moisture content, and the ratios of length to thickness (L/T) and of width to thickness (W/T) in rough rice decreased with increase of moisture content, while increased in soybean, but uniform tendency of the ratios in barley and wheat was not shown. In all of the sample grains except Olbori, sphericity decreased with increase of moisture content. 4. Over the experimental moisture levels, the surface area and the volume were in the ranges of about $45{\sim}51{\times}10^{-6}m^2$, $25{\sim}30{\times}10^{-9}m^3$ for Japonica-type rough rice, about $42{\sim}47{\times}10^{-6}m^2$, $21{\sim}26{\times}10^{-9}m^3$ for Indica${\times}$Japonica type rough rice, about $188{\sim}200{\times}10^{-6}m^2$, $277{\sim}300{\times}10^{-9}m^3$ for Jangyeobkong, about $180{\sim}201{\times}10^{-6}m^2$, $190{\sim}253{\times}10^{-9}m^3$ for Hwangkeumkong, about $60{\sim}69{\times}10^{-6}m^2$, $36{\sim}45{\times}10^{-9}m^3$ for Covered barley, about $47{\sim}60{\times}10^{-6}m^2$, $22{\sim}28{\times}10^{-9}m^3$ for Naked barley, about $51{\sim}20{\times}10^{-6}m^2$, $23{\sim}31{\times}10^{-9}m^3$ for Eunpamill, and about $57{\sim}69{\times}10^{-6}m^2$, $27{\sim}34{\times}10^{-9}m^3$ for Gurumill, respectively. 5. The increasing rate of surface area and volume with increase of moisture content was higher in soybean than other sample grains, and that of Japonica-type was slightly higher than Indica${\times}$Japonica type in rough rice. 6. The regression equations of physical dimensions, surface area and volume were developed as a function of moisture content, the exponential equations of surface area and volume were also developed as a function of physical dimensions, and the regression equations of surface area were also developed as a function of volume in all grain samples.