• Journal of Animal Science and Technology
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• v.63 no.4
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• pp.827-840
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• 2021

Several studies have focused on Ca and P requirements for pigs. These requirements are estimated from their retention and bone formation. However, modern pig breeds have different responses to dietary Ca and P than traditional breeds, and their requirements are expected to change on an annual basis. Besides individual Ca and P needs, the Ca to P ratio (Ca/P) is an important factor in determining requirements. This study aimed to implement a linear and quadratic regression analysis to estimate Ca and P requirements based on average daily gain (ADG), apparent total tract digestibility (ATTD) of Ca (ATTD-Ca), ATTD of P (ATTD-P), and crude protein (CP) digestibility. Results show that Ca/P had linear and quadratic effects on ADG in the phytase-supplemented (PS) group in both the 6-11 kg and 11-25 kg categories. In the latter category, the CP digestibility was linearly increased in response to increasing Ca/P in the without-phytase (WP) group. In the 25-50 kg category, there was a linear response of ADG and linear and quadratic responses of CP digestibility to Ca/P in the PS group, while a linear and quadratic increase in CP digestibility and a quadratic effect on ATTD-Ca were observed in the WP group. In the 50-75 kg category, Ca/P had significant quadratic effects on ADG in the PS and WP groups, along with significant linear and quadratic effects on ATTD-Ca. In addition, Ca/P had significant quadratic effects on ATTD-P and led to a significant linear and quadratic increase in the CP digestibility in the WP group. In the 75-100 kg category, analysis showed a significant decrease in ATTD-Ca and ATTD-P in the PS and WP groups; in the latter, ATTD-P and ATTD-Ca were linearly decreased by increasing Ca/P. In conclusion, our equations predicted a higher Ca/P in the 6-25 kg bodyweight categories and a lower Ca/P in the 50-100 kg category than that recommended in the literature.

• Journal of Environmental Science International
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• v.27 no.5
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• pp.333-340
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• 2018

This study aimed to estimate the effect of inoculant application level on chemical composition and bacterial count of fermented chestnut meal (FCM), and its rumen fermentation characteristics. The inoculant contained Lactobacillus acidophilus ($1.2{\times}10^{10}cfu/g$), Bacillus subtilis ($2.1{\times}10^{10}cfu/g$), and Saccharomyces cerevisiae ($2.3{\times}10^{10}cfu/g$). The chestnut meal mixed with molasses, double distilled water, and inoculant at 1 kg, 3 g, 480 mL, and 20 mL ratio for the basal chestnut meal diet. The double distilled water from basal chestnut meal diet was substituted with bacterial inoculant at a level of 0 (Control), 20 (Medium), and 40 mL (High) in the experimental diets. The mixed experimental diets were incubated at $39^{\circ}C$ for 7, 14, and 21 days, respectively. On 7 days of FCM incubation, the contents of crude protein (CP) (quadratic, P=0.043) and neutral detergent fiber (quadratic, P=0.071) decreased by increases of inoculant application levels, whereas bacterial count (quadratic, P=0.065) and rumen $NH_3-N$ (linear, P=0.063) increased. By increases of inoculant application levels on 14 days of FCM incubation, the increases were found on dry matter (DM) (quadratic, P=0.085), CP (quadratic, P=0.059), acid detergent fiber (quadratic, P=0.056), in vitro DM digestibility (linear, P=0.002), rumen total volatile fatty acid (VFA) (linear, P=0.057), and rumen iso-butyrate (linear, P=0.054). However, the decreases were found on bacterial count (linear, P=0.002), propionate (linear, P=0.099), and butyrate (quadratic, P=0.082). On 21 days of FCM incubation, in vitro DM digestibility (linear, P=0.002) and total VFA (linear, P=0.001) increased by increases of inoculant application levels, whereas the contents of CP (quadratic, P=0.034) and neutral detergent fiber (quadratic, P=0.047) decreased. These results indicate that the FCM with a medium level of inoculant application and 14 of fermentation had beneficial effects by increasing DM digestibility and rumen total VFA content, without altering bacterial count.

• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.765-773
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• 2017

The quadratic B-spline finite element method yields mass and stiffness matrices which are half the size of matrices obtained by the conventional finite element method. We solve the free vibration problem of a rotating Rayleigh beam using the quadratic B-spline finite element method. Rayleigh beam theory includes the rotary inertia effects in addition to the Euler-Bernoulli theory assumptions and presents a good mathematical model for rotating beams. Galerkin's approach is used to obtain the weak form which yields a system of symmetric matrices. Results obtained for the natural frequencies at different rotating speeds show an accurate match with the published results. A comparison with Euler-Bernoulli beam is done to decipher the variations in higher modes of the Rayleigh beam due to the slenderness ratio. The results are obtained for different values of non-uniform parameter ($\bar{n}$).

• KOREAN JOURNAL OF CROP SCIENCE
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• v.37 no.4
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• pp.320-328
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• 1992

The soybean yield forcasting models based on climatic elements in six locations were estimated by the STEPWISE/MAXR, Cp statistics and GLM procedure of SAS. The climatic elements were aerial temperature, sunshine hours and precipitation from May to October in 20 years. The investigated six locations were Chunchon, Suwon, Cheongju, Kwangju, Iri and Jinju. The important climatic elements for main effects in Chunchon model were August sunshine hours-linear term, August precipitation-quadratic. June temperature to August precipitation and May temperature to August precipitation were interaction terms. The quadratic August precipitation was assumed to be related to yield in Chunchon. The main effects of Suwon were linear-June temperature, quadratic June sunshine hours and June precipitation. These terms affected yields negatively. The main effects of Cheongju were linear June temperature and quadratic August precipitation. May temperature to June precipitation, July to August precipitations were interactions. The main effects of Kwangju were linear July precipitation, quadratic June temperature and July precipitation. June to July sunshine hours of interaction terms influenced yield negatively. The main effects of Iri were linear May sunshine hours, quadratic May and July sunshine hours. May temperature to May precipitation and June to July precipitations affected yields negatively. The main effects of Jinju were linear June and August precipitations. August temperature to August sunshine hours, June sunshine hours to July precipitation and June to August precipitation were interactions. In linear terms, June and August precipitations and, in interactions, August to August sunshine hours were negative efficacies respectively. The included year variables in Chunchon, Suwon, Kwangju, and Jinju model building were recognized as a linear trend based on an assumption that the technological factors have improved through times.

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.141-151
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• 2005

Under the assumption that the three-level factors are quantitative, the linear effects are taken more attention than the quadratic effects of the interaction terms. Webb (1971) presented some small incomplete factorial designs that are mixed two- and three-level designs with 20 or fewer runs. The designs provided the estimating linear-by-linear components of interactions between the three-level factors; moreover, they could also offer estimation of interactions that interest the experiments. Webb used ad hoc methods to find these plans; hence, there was still no unified structure to those experiments. In this paper, we develop the methods to construct the $2^{n}3^3$ and $2^{1}3^3$ designs. The designs constructed by these methods not only supply orthogonal estimates of all the main effects but also permit estimation of all the two-factor interactions not involving the quadratic effects. Furthermore, the designs we find are nearly orthogonal.

• Communications for Statistical Applications and Methods
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• v.25 no.3
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• pp.275-282
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• 2018

This paper discusses the use of projections for the sums of squares in the analyses of variance for two-way nested design data. The model for this data is assumed to only have random effects. Two different sizes of experimental units are required for a given experimental situation, since nesting is assumed to occur both in the treatment structure and in the design structure. So, variance components are coming from the sources of random effects of treatment factors and error terms in different sizes of experimental units. The model for this type of experimental situation is a random effects model with more than one error terms and therefore estimation of variance components are concerned. A projection method is used for the calculation of sums of squares due to random components. Squared distances of projections instead of using the usual reductions in sums of squares that show how to use projections to estimate the variance components associated with the random components in the assumed model. Expectations of quadratic forms are obtained by the Hartley's synthesis as a means of calculation.

• School Mathematics
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• v.16 no.4
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• pp.827-845
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• 2014

This study aims to investigate how the university educational programs about quadratic curves are operated in relation to the high school curriculum and what their effects may be, and the degree of understanding for the prospective and current teachers of the mathematical content knowledge about quadratic curves. To solve this research questions, we randomly selected three universities and one high school. Then we investigated the curricula of each department of mathematics education, compared them with the high school curricula, and conducted surveys of the professors' and students' conception on how much mathematical content knowledge they need to know about quadratic curves. The study resulted in the following conclusions. First, the curriculum on the subject of quadratic curves in the college of education is closely connected to the high school programs. This study's results showed that the college of education's curriculum includes a series of lectures regarding quadratic curves, and that within them, the mathematical content about quadratic curves associated with high school mathematics was thoroughly covered. Also, a large number of students who attended the lecture reported a significant increase in their understanding in regards to the quadratic curves. Second, it is strongly recommended to strengthen the connection between the college of education's curriculum and the actual high school education field. The prospective teachers think that there is a substantial need to learn about the quadratic curves because it is closely connected with the high school curriculum. But they find it challenging to put what they were taught into practical use in the high school education field, and feel that an improvement in this area is much needed. Third, it is necessary to promote, encourage and support the voluntary efforts to expand the range of the content knowledge in quadratic curves to cover the academic content associated with the high school mathematics.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• Structural Engineering and Mechanics
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• v.2 no.4
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• pp.345-357
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• 1994

The differential equations governing free, in-plane vibrations of linearly elastic circular arches with variable cross-sections are derived and solve numerically for quadratic arches with three types of rectangular cross sections. Frequencies, mode shapes, cross-sectional load distributions, and the effects of rotatory inertia on frequencies are reported. Experimental measurements of frequencies and their corresponding mode shapes agree closely with those predicted by theory. The numerical methods presented here for computing frequencies and mode shapes are efficient and reliable.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.8
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• pp.867-873
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• 1988

The degradation due to channel distortion in a quadrature modulation system from the ideal constant values over the bandwidth of a direct sequence spread spectrum signal are considered. Through using series expansion for the channel gain and phase response, the degradation in the correlator output at the receiver is found as a function of the parameters involved , including phase error, delay error, linear gin variation, quadratic gain variation, and quadratic phase variation.