• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2065-2079
• /
• 2017

This paper is devoted to the minimal and maximal bounded solutions for general time interval quadratic backward stochastic differential equations with stochastic conditions. A general existence result is established by the method of convolution, the exponential transform, Girsanov's transform and a priori estimates, where the terminal time is allowed to be finite or infinite, and the generator g is allowed to have a stochastic semi-linear growth and a general growth in y, and a quadratic growth in z. This improves some existing results at some extent. Some new ideas and techniques are also applied to prove it.

• Asian-Australasian Journal of Animal Sciences
• /
• v.16 no.6
• /
• pp.894-902
• /
• 2003

Prebiotics (peptides, N-acetyglucoamine, fructo-oligosaccharides, isomalto-oligosaccharides and galactooligosaccharides) were added to skim milk in order to improve the growth rate of contained Lactobacillus acidophilus, Lactobacillus casei, Bifidobacterium longum and Bifidobacterium bifidum. The purpose of this research was to study the potential synergy between probiotics and prebiotics when present in milk, and to apply modern optimization techniques to obtain optimal design and performance for the growth rate of the probiotics using a response surface-modeling technique. To carry out response surface modeling, the regression method was performed on experimental results to build mathematical models. The models were then formulated as an objective function in an optimization problem that was consequently optimized using a genetic algorithm and sequential quadratic programming approach to obtain the maximum growth rate of the probiotics. The results showed that the quadratic models appeared to have the most accurate response surface fit. Both SQP and GA were able to identify the optimal combination of prebiotics to stimulate the growth of probiotics in milk. Comparing both methods, SQP appeared to be more efficient than GA at such a task.

• Asian-Australasian Journal of Animal Sciences
• /
• v.29 no.8
• /
• pp.1166-1172
• /
• 2016

This study was conducted to determine the effect of dietary supplementation of liquid DL-methionine hydroxy analog free acid (DL-MHA) on growth performance and gastrointestinal conditions of piglets. One hundred and eighty crossbred barrow piglets (Large White${\times}$Landrace, body weight: $12.48{\pm}0.33kg$) were divided into three groups with ten replications of six piglets each. Piglets received DL-MHA in diet at a concentration of 0 (control group), 0.15%, or 0.24%. The results indicated that increasing the standardized ileal digestible (SID) of sulfur amino acids (SAA) to lysine (SID SAA:Lys) ratio by supplementation of DL-MHA tended to increase (quadratic; p<0.10) weight gain and ADG, and showed slightly greater (linear; p<0.10) gain:feed ratio. The pH in the diet and cecum linearly decreased (p<0.01), whereas pH in colon had a quadratic response (p<0.01) with increasing supplementation of DL-MHA. By greater supplementation of DL-MHA, the population of Lactobacillus spp. in rectum was likely to increase (quadratic; p<0.10), but Escherichia coli population in the diet was reduced (quadratic; p<0.05). Acetic acid concentration and total short-chain fatty acids in cecum linearly increased (p<0.05), whereas valeric acid in cecum quadratically increased (p<0.05) with increasing DL-MHA levels. Moreover, the villous height of the jejunum quadratically increased (p<0.01) as the supplementation of DL-MHA was increased. It is concluded that the addition of DL-MHA in diet improved the growth performance and the morphology of gastrointestinal tract of piglets.

• Asian-Australasian Journal of Animal Sciences
• /
• v.27 no.3
• /
• pp.383-390
• /
• 2014

A 15-wk feeding trial was conducted to examine the supplemental effects of Barodon on growth performance, gastrointestinal histology, feed digestibility and innate immunity in olive founder. A basal commercial diet was used as a control and two other diets were prepared by spraying 0.1% or 0.2% of Barodon. Triplicate groups of fish (BW, 145 g) were fed one of the test diets to apparent satiation twice daily. At the end of the feeding trial, fish growth performance was not significantly affected by dietary treatments; however, feed utilization was significantly improved (linear and quadratic, p<0.05) by Barodon supplementation. Significantly higher (p<0.05) survival rates were obtained in fish fed Barodon containing diets. Hepatosomatic index increased significantly in Barodon treated groups. Also, the use of Barodon resulted in significant increase (linear and quadratic, p<0.05) of intestine length and number of goblet cells. Significantly higher (Quadratic, p<0.05) apparent digestibility coefficient of DM was obtained by supplementation of Barodon. Lysozyme and myeloperoxidase activities increased quadratically and linearly, respectively, in Barodon treated fish. Also, significantly higher (linear and quadratic, p<0.05) superoxide dismutase activity was found in Barodon fed fish. The findings in this study show that inclusion of Barodon in diets for olive flounder improves feed utilization and digestibility, and positively affects digestive tract histology and innate immunity.

• Animal Bioscience
• /
• v.36 no.5
• /
• pp.776-784
• /
• 2023

Objective: This experiment was conducted to evaluate the inclusion of dietary nontoxic sulfur (NTS) on growth performance, immune response, sulfur amino acid composition and meat characteristics in growing-finishing pigs. Methods: A total of 140 crossbred pigs ([Yorkshire×Landrace]×Duroc) with an average body weight of 34.73±0.66 kg were used for the 12-week feeding trial. Experimental pigs were allotted to one of 5 treatments in 4 replicates of 7 pigs per pen in a randomized complete block (RCB) design. The experimental treatments were as follows (0%, 0.1%, 0.2%, and 0.4% NTS levels): i) Control, corn soybean meal (SBM)-based diet; ii) NTS 0.1, basal diet + NTS 0.1%; iii) NTS 0.2, basal diet + NTS 0.2%; iv) NTS 0.4, basal diet + NTS 0.4%. Results: Body weight increased linearly as dietary NTS levels increased up to 0.2% (linear; p = 0.04) in the early finishing phase (9 weeks). During the whole experimental period, body weight and average daily gain linearly increased as the dietary NTS level increased in the diet (linear; both p = 0.01), but quadratic responses in body weight and average daily gain were observed with the addition of NTS 0.4% (quadratic, both p = 0.01). In the late finishing period, the IgG concentration increased linearly (linear; p = 0.01) as the dietary NTS level increased up to 4%. In the finishing period, a linear response was observed as a dietary NTS level was added (linear; p = 0.03), and supplementation with 0.2% NTS resulted in a higher methionine content than the other treatments (quadratic; p = 0.01). NST 0.2% had a lower value of thiobarbituric acid reactive substances (quadratic; p = 0.01). Conclusion: Consequently, supplementation with dietary NTS up to 0.2% could improve growth performance, amino acid composition in hair and meat antioxidation capacity.

• Journal of the Korean Data and Information Science Society
• /
• v.25 no.2
• /
• pp.411-422
• /
• 2014

This study analyzed how average GPA (grade point average) changes as the number of completed semesters increases based on the estimates of intercept, slope, and quadratic term. The students included in this study are those who was admitted in 2011 and took 6 consecutive semesters. More precisely, it was analyzed if intercept, slope and quadratic term of average GPA were different between gender and selection method. The results showed that the intercept was different between selection method, the slope was different between gender, but the quadratic term was different between neither selection method nor gender.

• Asian-Australasian Journal of Animal Sciences
• /
• v.19 no.8
• /
• pp.1197-1205
• /
• 2006

This experiment was conducted to compare the effects of feeding DL-2-hydroxy-4-(methylthio)butanoic acid (HMTBA) and DL-methionine (DLM) supplemented corn-soybean-cottonseed meal diets on growth performance, carcass composition, and muscle color of broilers. The trial was designed as a $2{\times}3{\times}2$ factorial experiment, including two methionine (Met) sources (HMTBA and DLM), three equimolar graded levels of Met supplementation (i.e., 0.08, 0.16, and 0.24% in the starter diet and 0.07, 0.14, and 0.21% in the grower and finisher diets, respectively), and two sexes (male and female). Additionally, one basal diet for each sex was formulated to be limiting in Met to test the dosage response of increasing supplemental Met levels. Four hundred and twenty 10-d-old broilers were randomly allotted to 14 treatments (seven each for males and females), with five replicate pens per treatment and six chicks per pen. There was no difference (p>0.05) between the two Met sources in growth performance and muscle deposition of broilers throughout the whole experimental period (d 10 to 49). With the increasing Met supplementation levels, average daily gain was increased (quadratic; p<0.01) during the starter, grower, and overall phases, average daily feed intake was increased (quadratic; p<0.01) during the starter phase, and feed:gain ratio was decreased (quadratic; p<0.05) during the grower and overall phases. At the end of finisher phase, Met supplementation increased breast muscle content (quadratic; p<0.01) and thigh muscle content (linear; p<0.05), and decreased abdominal fat content (quadratic; p<0.02). Compared to the broiler fed DLM, broilers fed HMTBA had superior breast and thigh muscle coloration (p<0.01). Male broilers had higher weight gain and feed intake and better feed conversion than female broilers (p<0.01). The fat content of thigh muscle in female broilers was higher than that of male broilers (p<0.03). The best fit comparison of HMTBA vs. DLM was determined by Schwarz Bayesian Criteria index, which indicated that the average relative bioefficacy of HMTBA vs. DLM was 120% with 95% confidence limit 67 to 172%. These results indicated that Met supplementation improved growth performance and carcass quality of broilers fed corn-soybean-cottonseed meal diets irrespective of Met sources. Compared to DLM, HMTBA has the same molar bioefficacy on improving the growth performance and carcass quality of broilers; however, HMTBA fed birds had superior meat color to DLM fed birds.

• Journal of Microbiology and Biotechnology
• /
• v.19 no.7
• /
• pp.718-726
• /
• 2009

The objective of this study was to develop and validate secondary models that can predict growth parameters of L. monocytogenes Scott A as a function of concentrations (0-3%) of a commercial potassium lactate (PL) and sodium diacetate (SDA) mixture, pH (5.5-7.0), and temperature (4-37DC). A total of 120 growth curves were fitted to the Baranyi primary model that directly estimates lag time (LT) and specific growth rate (SGR). The effects of the variables on L. monocytogenes Scott A growth kinetics were modeled by response surface analysis using quadratic and cubic polynomial models of the natural logarithm transformation of both LT and SGR. Model performance was evaluated with dependent data and independent data using the prediction bias ($B_f$) and accuracy factors ($A_f$) as well as the acceptable prediction zone method [percentage of relative errors (%RE)]. Comparison of predicted versus observed values of SGR indicated that the cubic model fits better than the quadratic model, particularly at 4 and $10^{\circ}C$. The $B_f$and $A_f$for independent SGR were 1.00 and 1.08 for the cubic model and 1.08 and 1.16 for the quadratic model, respectively. For cubic and quadratic models, the %REs for the independent SGR data were 92.6 and 85.7, respectively. Both quadratic and cubic polynomial models for SGR and LT provided acceptable predictions of L. monocytogenes Scott A growth in the matrix of conditions described in the present study. Model performance can be more accurately evaluated with $B_f$and $A_f$and % RE together.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.6
• /
• pp.1673-1685
• /
• 2023

Inspired by Hongjie Dong and Qi S. Zhang's article [3], we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain L^p spaces with p ∈ [2, +∞) and prove its analyticity with respect to time.

• Journal of Animal Science and Technology
• /
• v.49 no.4
• /
• pp.501-508
• /
• 2007

This study was conducted to evaluate effect of probiotic complex(Lactobacillus acidophilus, Bacillus subtilis and Aspergillus oryzae) on growth performance, blood immunological parameters and fecal malodor gas emissions in growing pigs. Forty-eight pigs[(Landrace × Yorkshire) × Duroc, 25.31±1.29kg average initial body weight] were used in 35d growth trial. Dietary treatments included CON(basal diet), PC1(basal diet + 0.1% probiotic complex) and PC2(basal diet + 0.2% probiotic complex). From d 0 to 20, ADFI was significantly increased in PC1 and PC2 compared to CON(Linear effect, P=0.013). From d 21 to 35, ADFI was increased in PC1 compared to CON(Quadratic effect, P=0.024). For the whole period, ADFI was increased PC2 and PC1 compared to CON(Linear effect, P=0.009, Quadratic effect, P=0.004). For the whole period, ADG was increased in PC1 compared to CON(Quadratic effect, P=0.017). G/F was not affected by treatments. Dry matter digestibility in PC2 was higher than PC1 and CON(Linear effect, P=0.001). Nitrogen digestibility was significantly higher in PC2 and PC1 than CON(Linear effect, P=0.005). In blood immunological parameters, Total protein, IgG, red blood cell(RBC) and white blood cell(WBC) were increased in PC2 compared to PC1 and CON(Linear effect, P<0.001, Quadratic effect, P<0.001). In fecal malodor gas emission, ammonia and acetic acid were significantly reduced in PC2 compared to CON(Linear effect, P<0.02). Hydrogen sulfide was significantly reduced in PC2 compared to CON(Linear effect, P=0.0002, Quadratic effect, P=0.018). However, total mercaptans was not affected by treatments. Water content of feces was not significantly different among the treatments. In conclusion, 0.2 % probiotic complex improved ADFI, apparent dry matter and nitrogen digestibility, Total protein, IgG, RBC and WBC. Also, it decreased ammonia, acetic acid and hydrogen sulfide emissions in growing pigs.