REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW

In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations{-△u=λ∑1Bδ（x0,j）（u-kj）p＋,in Ω,u=0,onΩ is a bounded simply-connected smooth domain, ki （i = 1,… , k） is prescribed positive constant. The result we prove is that for any given non-degenerate critical pointX0=（x0,1,…,x0,k of the Kirchhoff-Routh function defined on Ωk corresponding to （ k1,……kk ）there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as λ→＋∞ shrinks to {x05}, and the local vorticity strength near each x0,j approaches kj, j = 1,… , k. This result makes the study of the above problem with p _〉 0 complete since the cases p 〉 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.

The Effects of Shade Tree Types on Light Variation and Robusta Coffee Production in Vietnam

Vietnam is well-known as the second largest global coffee producer and the largest worldwide exporter of Robusta coffee. However, the Robusta coffee sector in Vietnam is facing many problems, including low quality, high external inputs and water shortages as a result of shade tree eradication. A six-month research project was conducted that focused on effects of shaded tree types on variation of light intensity and aspects of Robusta production. Three shade tree species at different planting densities and shade provision were investigated, including 46 trees of Durian ha–1 (14% shade), 35 trees of Sennaha–1 (17% shade), and 60 trees of Leucaena ha–1 (34% shade), and unshaded site (Open) was used as a control. The study found that light intensity declined 50% with Durian, 58% with Senna and 60% with Leucaena compared with the Open site (2096 μmol?m–2?s–1). Within the coffee canopy, a significant decline in light intensity was observed from the top of the canopy to the bottom. The percentage of light at the middle (90 cm above ground) and bottom (30cm) levels of the coffee canopy was declined by 81% and 88% respectively for the Open site, and 86% and 92% for the Leucaena site. There were no differences in the number of flowers branch–1 tree–1 and fruit set between shaded and unshaded coffee sites. However, a significant difference in first fruit drop was observed.

FOUNTAIN THEOREM OVER CONES AND APPLICATIONS

In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solutions, where 1 〈 p 〈 N, 1 〈 q 〈 P 〈 γ, Ω∩→ R^N is a smooth bounded domain and λ, μ∈ R.

The future of feed formulation for poultry:Toward more sustainable production of meat and eggs

Current methods for feed formulation are based on minimizing costs,not maximizing profits.Complex models of bird growth and reproduction as functions of genetic,feed and other environmental variables are being developed,but their adaptation has been slow.The development of profit maximizing models will evolve to center on the production functions of broilers and layers.The production functions are the relationship between the value of products(mainly meat and eggs)and the cost of feed.The production function is the tool used to maximize profits subject to all the various inputs,not just feed or nutrition.The production function is subject to the law of diminishing returns.The most profitable output levels are those where the marginal value(price)of the meat or eggs is just equal to the marginal cost of the inputs including feed,housing,processing and all other costs.Anything that affects the production function,bird genetics,feed quality,housing and environment,will be considered to maximize profits for the poultry firm.The profit maximizing models of poultry firms will improve as various technical improvements are made:metabolizable energy to describe ingredients will evolve to net energy systems that consider that the heat production(and therefore energetic efficiency)of broilers is different depending on the ingredients used to formulate the feed and the environmental temperatures under which they are reared.Amino acid needs will include a method to find the birds’needs for the nonessential amino acids.“Digestible”amino acid assays will differentiate between digestion and absorption to best balance various sources.The carbohydrate fractions of feed ingredients will be determined to optimize the use of exogenous enzymes.The value of meat and egg co-products will reduce overall costs(e.g.,organic fertilizer for crop enhancement).Future profit maximizing production models will be ever evolving processes where field conditions and results are continually being utilized to re-calibrate the technical models so that the management team can use them with cost and return projections to decide on the best choices of inputs and outputs.

Total amino acid level affects the results of standardized ileal digestibility assays for feed ingredients for swine

It has been demonstrated that the fiber content of oilseed meals and total amino acids(AA)in distillers'grains products affects standardized ileal digestibility(SID)values from swine assays and that total protein concentration affects the AA digestibility in assays using chickens.This analysis was conducted to test the hypothesis that the total AA content of test samples affects the SID assay results.Databases containing total AA profiles and SID values of 20 feedstuffs commonly fed to pigs from 2 sources,AMINODat 5.0(Evonik Industries,2015)and the Nutrient Requirements of Swine,12th edition(NRC,2012)were used to compare AA concentration effects on standardized ileal digestibility coefficients.Databases were compared with AA and SID available in both data sets.The total AA values were similar for the 2 databases with an R2 of 0.979(P<0.001).The linear relationship between digestibility co-efficients from the 2 databases was highly significant,an R2 of 0.810(P<0.001).Both databases had increased SID values with increasing AA contents within and across feed ingredients.The SID=f(AA concentration)relationship was confirmed with an individual paper.Since SID,as typically measured,is a function of both digestion and absorption,both processes following MichaeliseMenten kinetics,SID=f(AA concentration)may simply be a natural phenomenon.Other reasons for the relationship were explored.Methods of estimating endogenous AA losses and misapplication statistical procedures may contribute to variation in results and at least partially explain why SID=f(AA concentration).

INFINITELY MANY SOLUTIONS FOR AN ELLIPTIC PROBLEM INVOLVING CRITICAL NONLINEARITY

We study the following elliptic problem：{-div（a（x）Du）=Q（x）｜u｜2-2u＋λu x∈Ω,u=0 onδΩ Under certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.

Abductive statistical methods improve the results of calibration curve bioassays:An example of determining zinc bioavailability in broiler chickens

In this paper,we discuss the theory behind calibration curve experiments and their application to a zinc(Zn)bioavailability study with broiler chickens.Seven replicates of 16 male commercial broiler chicks were fed starter diets for 14 days.Six diets had different levels of a potential Zn source and one was a positive control with standard industry levels of Zn for comparison.Four commonly used methods of calculating bioavailability means and confidence intervals(CI)from a calibration curve(standard curve)experiment to estimate the bioavailability of a new zinc source in broiler chickens were compared.The methods compared were the following:1)the Counter-Intuitive Method uses a multiple-range test to compare unknown test and standard samples;2)the Intuitive Method uses standard linear regression and inverts the equation to predict Zn bioavailability for each replicate of test samples;3)the Abductive Method uses Graybill's Equation,based on theory and observation,to estimate CI's;and 4)the Sophistic Method uses reverse regression,and calculates Zn bioavailability values directly from the equation.The Counter-Intuitive Method only gives information about which standards the test samples are,or are not,significantly different from respectively(average available Zn not predicted).The Intuitive Method ignores error about the standard curve and theoretically cannot estimate the CI directly(X±SEM=107.5±15.8 mg Zn/kg).The Sophistic Method underestimates and overestimates the test sample mean values above and below the mean of the standards,respectively(X=96.6 mg Zn/kg).The Abductive Method has an advantage over the other methods:The mean prediction estimation is consistent with theory(107.5±6.1 mg Zn/kg;X±SEM).When test or“unknown”samples are near the mean of the standard samples,the CI is smaller than when near the extremes of the calibration curve.When calibration curve error is small(R^(2)>approximately 0.95),there is little advantage to using the Abductive Method,but when calibration curve error is larger,as in many bioassays with growing animals,the Abductive Method improves the accuracy of the CI calculations.The Abductive Method was used to demonstrate the influence of the number of replicate samples on experimental power and cost.

Optimizing hairy root production from explants of Phyllanthus hainanensis,a shrub used for traditional herbal medicine

Phyllanthus hainanensis is a shrub that has been used in traditional herbal medicine.It has great pharmaceutical potential for treating diseases such as cancer and diabetes.As a prerequisite for propagation of this species on a large scale,hairy roots in P.hainanensis were induced using Rhizobium rhizogenes and various factors affecting hairy root induction and growth evaluated.Seven factors were tested:(1)type of explant,(2)type of culture medium,(3)duration of pre-culture,(4)R.rhizogenes inoculum cell density,(5)duration of infection,(6)acetosyringone concentration in the culture medium,and(7)duration of incubation.The optimal protocol for hairy root induction and growth was:young shoots,pre-cultured in Y1 for 2 d,inoculated with R.rhizogenes broth with an OD600 of 0.6 for 20 min,and incubated for 3 d.Putative transgenic hairy roots were initially identified by morphology and then confirmed by polymerase chain reaction.Successful and optimal production of hairy roots is a critical prerequisite for industrial scale clonal propagation of P.hainanensis.Being able to cultivate the plant on a large scale will provide rapid and ready supply of the plant materials that can be used in herbal medicine and in scientific and industrial exploitation.