scholarly journals Optimal and efficient production of rose coco beans through the twenty-four points second order rotatable design

2017 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
Isaac Tum ◽  
Joseph Koske ◽  
John Mutiso
Keyword(s):  
Response Surface ◽  
Maximum Yield ◽  
Response Surfaces ◽  
Second Order ◽  
Three Dimensions ◽  
Coefficient Of Determination ◽  
Efficient Production ◽  
Phosphorus And Potassium ◽  
Nitrogen Phosphorus ◽  
Rotatable Design

The yield results of the twenty four points response surface methodology (RSM) design permitted a response surface to be fitted easily and provided spherical information contours besides the realizations of an optimum combination of the fertilizers in rose coco beans, which resulted in economic use of scarce resources for optimal production of rose coco beans. In this study an existing A-optimum and D-efficient second order rotatable design in three dimensions was used to produce rose coco beans optimally and efficiently. The general objective of the study was to produce rose coco beans (Phaseolus vulgaris) optimally and efficiently using an existing A-optimum and D-efficient twenty four points second order rotatable design in three dimensions in a greenhouse setting using three inorganic fertilizers, namely, nitrogen, phosphorus and potassium. Thus the study was accomplished using the calculus optimum value of the free/letter parameter f=1.1072569. The specific objectives were to estimate the linear parameters, thereby making available for the yield response of rose coco beans at calculus optimum value design for the first time, fitted and tested the model adequacy via lack of fit test, and then found the setting of the experimental factors that produces optimal response using contour plots to assist visualizes the response surfaces. This study demonstrated the importance of statistical methods in the optimal and efficient production of rose coco beans. The results showed that the three factors: nitrogen, phosphorus, and potassium contributed significantly on the yield of rose coco beans (p<0.05). The regression coefficients were determined by employing least square's techniques to predict quadratic polynomial model for group 3 greenhouse (GP3G) for the three fertilizer combinations. In GP3G, the second-order model was adequate at 1% level of significance with a p-value of 0.0034. The analysis of variance (ANOVA) of response surface for rose coco yield showed that this design was adequate due to satisfactory level of a coefficient of determination, R2, 0.8066 (GP3G) and coefficient variation, CV was 10.30. The canonical analysis showed that there was the saddle point for GP3G, meaning there was no unique optimum; therefore, ridge analysis was used to overcome the saddle problem. The result from ridge analysis provided the maximum yield of 70.25grams for the three fertilizer combinations at radii of one. We, therefore, recommend the use of GP3G design since it gave the required coefficient of determination (R2=80.66) and the maximum yield (70. 25grams) was achieved.

scholarly journals Modeling of rose coco beans using twenty four points optimum second order rotatable design

2017 ◽  
Vol 5 (2) ◽  
pp. 96
Author(s):  
Isaac Tum ◽  
John Mutiso ◽  
Joseph Koske
Keyword(s):  
Response Surface ◽  
Maximum Yield ◽  
Second Order ◽  
Three Dimensions ◽  
Coefficient Of Determination ◽  
Yield Response ◽  
Efficient Production ◽  
Phosphorus And Potassium ◽  
Nitrogen Phosphorus ◽  
Rotatable Design

The response surface methodology (RSM) is a collection of mathematical and statistical techniques useful for the modeling and analysis of problems in which a response of interest is influenced by several variables, and the objective is to optimize the response. The objective of the study was to model the rose coco beans (Phaseolus vulgaris) through an existing A-optimum and D-efficient second order rotatable design of twenty four points in three dimensions in a greenhouse setting using three inorganic fertilizers, namely, nitrogen, phosphorus and potassium. Thus, the objective of the study was accomplished using the calculus optimum value of the free/letter parameter f=1.1072569. This was done by estimating the parameters via least square's techniques, by making available for the yield response of rose coco beans at calculus optimum value design for the first time. The results showed that, the three factors: nitrogen, phosphorus, and potassium contributed significantly on the yield of rose coco beans (p<0.05). In GP3G, the second-order model was adequate for 1% level of significance with p value of 0.0034. The analysis of variance (ANOVA) of response surface for rose coco yield showed that this design was adequate due to satisfactory level of a coefficient of determination, R2, 0.8066 and coefficient variation, CV was 10.30. This study demonstrated the importance of statistical methods in the optimal and efficient production of rose coco beans. We do recommend a randomize screening of all the fertilizer components with which it has influence on rose coco beans be done to ascertain the right initial amount of each fertilizer that could achieve maximum yield than this study realized.

scholarly journals Construction of twenty-six points specific optimum second order rotatable designs in three dimensions with a practical example

2020 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Tum Isaac Kipkosgei
Keyword(s):  
Response Surface ◽  
Second Order ◽  
Three Dimensions ◽  
Predictor Variables ◽  
Scarce Resources ◽  
Quadratic Response Surface ◽  
Quadratic Response ◽  
Free Parameters ◽  
Economic Use ◽  
Rotatable Design

This quadratic response surface methodology focuses on finding the levels of some (coded) predictor variables x = (x1u, x2u, x3u)' that optimize the expected value of a response variable yu from natural levels. The experiment starts from some best guess or “control” combination of the predictor variables (usually coded to x = 0 for this case x1u=30, x2u=25 and x3u =40) and experiment is performed varying them in a region around this center point.We go further to construct a specific optimum second order rotatable design of three factors in twenty-six points. The achievement of this is done with estimation of the free parameters using calculus in an existing second order rotatable design of twenty-six points. Such a design permits a response surface to be fitted easily and provides spherical information contours besides the realizations of optimum combination of ingredients in Agriculture, horticulture and allied sciences which results in economic use of scarce resources in relevant production processes. The expected second order rotatable design model in three dimensions is available where the responses would then facilitate the estimation of the linear and quadratic coefficients. An example involving Phosphate (x1u), Nitrogen (x2u) and Potassium (x3u) is used to represent the three factors in the coded level and converted into natural levels.  

Foliar Analysis as a Guide to NPK Nutrition of Pineapples in the Forest Zone of Ghana

1970 ◽  
Vol 6 (4) ◽  
pp. 327-333 ◽  
Author(s):  
W. Godfrey-Sam-Aggrey
Keyword(s):  
Maximum Yield ◽  
Second Order ◽  
Fruit Yield ◽  
Foliar Analysis ◽  
Forest Zone ◽  
Fruit Length ◽  
Nutrient Levels ◽  
Central Composite ◽  
Plot Experiment ◽  
Rotatable Design

SUMMARYIn a 20 plot experiment with central composite second-order rotatable design, basal non-chlorophyllous sections of “D” leaves of Sugarloaf pineapples were sampled at harvest and analysed for N, P, K. Maximum yield of 17·8 tons per acre of good quality Sugarloaf pineapples and maximum fruit length of 27·4 cm. were associated with the nutrient combination of 36–42–32 lb/acre N P K applied at 4, 6, 11 and 12 months. The nutrient levels in the basal sections of “D” leaves corresponding to maximum fruit yield were 0·35–0·40% N; 0·04% P; 0·44% K; K/P 11·2–11·5: 1. K/P ratio for maximum fruit length was 10·4–11·5: 1. N/K ratio was associated with lodging.

Extraction of Flavonoids from Clovers

2012 ◽  
Vol 195-196 ◽  
pp. 360-363
Author(s):  
Chun Gang Chen ◽  
Fen Xia Han ◽  
Yuan Zhang ◽  
Yu Zhong Shi
Keyword(s):  
Response Surface Methodology ◽  
Optimum Condition ◽  
Central Composite Design ◽  
Response Surface ◽  
Ethanol Concentration ◽  
Response Surfaces ◽  
Second Order ◽  
Order Model ◽  
Solid Ratio ◽  
Central Composite

The extraction of flavonoids from clovers was optimized to maximize flavonoid yield Y in this study. A central composite design of response surface methodology involving extracting time, liquid-solid ratio, extracting temperature and ethanol concentration was used, and second-order model for Y was employed to generate the response surfaces. The optimum condition for Y was determined as follows: extracting time 24min, liquid-solid ratio 20, extracting temperature 80°C, and ethanol concentration 72%. Under the optimum condition, the flavonoid yield was 2.49%.

scholarly journals Digital methodology for analyzing the yield of sugar beet on leached chernozem of the Krasnodar Territory

2021 ◽  
Vol 36 ◽  
pp. 08003
Author(s):  
Victoria Drozdova ◽  
Irina Buldykova ◽  
Anastasia Kazakevich ◽  
Vladimir Griguletsky
Keyword(s):  
Mathematical Model ◽  
Sugar Beet ◽  
Maximum Yield ◽  
Mathematical Expression ◽  
Root Crops ◽  
Leached Chernozem ◽  
Optimal Values ◽  
Phosphorus And Potassium ◽  
Complete Fertilizer ◽  
Nitrogen Phosphorus

In the article, a mathematical expression is obtained that characterizes the effect of the doses of introduced fertilizers, the content of nutrients in the soil and their absorption by sugar beet plants on the yield of this crop. With the help of the developed mathematical model, the optimal values of the content of macronutrients in soil and plants are determined: nitrogen ~ 21.81 mg/kg and 1.02 %; phosphorus ~ 58.88 mg/kg and 0.33 %; potassium ~ 120.21 mg/kg and 1.33%, respectively, which accumulate when introducing a complete fertilizer at a dose of N80P80K80. This leads to the achievement of the maximum yield of root crops, which corresponds to the calculated value of this indicator ≈of 56.94 and 64.6 t/ha and coincides with the experimental one = 57.9 and 62.0 t/ha, respectively, obtained in this variant. The introduced fertilizers containing boron contributed to a more intensive absorption of nitrogen, phosphorus and potassium by root crops. The use of trace elements causes a tendency to increase the yield of this crop.

Use of Wastewater for Woodworking Enterprises for Obtain a Prolonged-Action Complex Fertilizer

2018 ◽  
Vol 22 (5) ◽  
pp. 46-49
Author(s):  
S.V. Lukashov ◽  
V.P. Gamazin
Keyword(s):  
Urea Formaldehyde ◽  
Maximum Yield ◽  
Molar Ratio ◽  
Formaldehyde Resin ◽  
Prolonged Action ◽  
Potassium Nutrition ◽  
Cesium 137 ◽  
Insoluble Polymer ◽  
Phosphorus And Potassium ◽  
Nitrogen Phosphorus

The results of research on the optimal conditions for obtaining a prolonged-action complex fertilizer from wastewater from woodworking enterprises are presented. The main active substance of the fertilizer is a nitrogen-containing insoluble polymer, obtained by polycondensation of urea-formaldehyde resin with urea. To produce the finished product, the resulting polymer is mixed with ash. It was found that the maximum yield of a prolonged-action complex fertilizer based on the urea-formaldehyde polymer is achieved under the following conditions: pH = 2,0, molar ratio of formaldehyde: urea 1,0: 1,5, reaction time 3,5–4,0 h. It is shown that the fertilizer obtained can be used in agriculture to improve the nitrogen, phosphorus and potassium nutrition of plants, as well as to reduce the intake of cesium 137 radionuclides into agricultural products.

Some problems in the estimation of simultaneous fertilizer requirements of crops from response surfaces

1970 ◽  
Vol 10 (43) ◽  
pp. 183 ◽  
Author(s):  
JD Colwell ◽  
KM Stackhouse
Keyword(s):  
Response Surface ◽  
Interaction Effects ◽  
Surface Interaction ◽  
Response Surfaces ◽  
Fertilizer Treatment ◽  
Response Form ◽  
Interaction Terms ◽  
Experimental Errors ◽  
Time Required ◽  
Nitrogen Phosphorus

The estimation of the optimal fertilizer requirements of a crop from the data of fertilizer experiments depends on the response exhibiting the form of the law of diminishing returns with respect to all fertilizers. Deviations from the diminishing form are frequently encountered, particularly with experiments involving several fertilizers, because of experimental errors, extrapolation errors, and inappropriate choices of fertilizer treatment levels. Since the time required to repeat inadequate experiments is usually considerable the experimenter has to make the best use of admittedly inadequate data to obtain interim estimates of fertilizer requirements. A procedure is described for obtaining estimates of fertilizer requirements with such data despite the deviations from the expected diminishing response form. The procedure is based on the use of a polynomial model to represent the multidimensional response surface. Interaction terms which would normally be expected to make only small and negligible contributions to the model, are eliminated to avoid the influence of non-significant responses to particular fertilizers on the calculation of other fertilizer requirements. Where a fertilizer has given a significant but non-diminishing response, approximate estimates of the requirements of that fertilizer are substituted to allow approximately for interaction effects in the estimation of the remaining fertilizer requirements. The problems and the application of the procedure is illustrated with data from three fertilizer experiments involving nitrogen, phosphorus, potassium, and sulphur fertilizers.

scholarly journals A note on Variance-Sum Third Order Slope Rotatable Designs

2021 ◽  
Vol 9 (10) ◽  
pp. 760-766
Author(s):  
R. Md. Mastan Shareef
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Interesting Property ◽  
Response Surfaces ◽  
Statistical Techniques ◽  
Third Order ◽  
Controllable Factors ◽  
Four Levels ◽  
Rotatable Design

Abstract: Response Surface Methodology (RSM) is a collection of mathematical and statistical techniques useful for analyzing experiments where the yield is believed to be influenced by one or more controllable factors. Box and Hunter (1957) introduced rotatable designs in order to explore the response surfaces. The analogue of Box-Hunter rotatability criterion is a requirement that the variance of i yˆ(x)/ x be constant on circles (v=2), spheres (v=3) or hyperspheres (v 4) at the design origin. These estimates of the derivatives would then be equally reliable for all points (x , x ,...,x ) 1 2 v equidistant from the design origin. This property is called as slope rotatability (Hader and Park (1978)).Anjaneyulu et al (1995 &2000) introduced Third Order Slope Rotatable Designs. Anjaneyulu et al(2004) introduced and established that TOSRD(OAD) has the additional interesting property that the sum of the variance of estimates of slopes in all axial directions at any point is a function of the distance of the point from the design origin. In this paper we made an attempt to construct Variance-Sum Third Order Slope Rotatable in four levels. Keywords: Response Surface Methodology. Third Order Slope Rotatable Design; TOSRD (OAD), Variance-Sum Third Order Slope Rotatable Design.

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