Industrial chain is an integrated functional chain structure that formed among inter-related industries under specific economic relationship. As a functional chain structure, industrial chain emphasizes the inter-relationship among joints. Through an analysis on the definition of industrial chain, this essay shows the industrial chain cobweb model and the interrelationship among joints within the chain that serves as a basis for improving profitability and efficiency.

This paper develops algorithms for solving an undetermined coefficient problem for a wave equation. The algorithms are based on an integral representation for the solution to the wave equation obtained by using transmutation. The convergence of the algorithm is studied and numerical experiments are performed.

In this article, we obtain some results on the linearized oscillation of the odd-order neutral difference equation where Δ is the forward difference operator, m is odd, {pn },{qn } are sequences of nonnegative real numbers, k, l are nonnegative integers, g(x),h(x)∈ C(R,R) with xg(x) > 0 for x ≠0.

of the Clean Water Act directs the U.S. Army Corps of Engineers to administer a regulatory program for permitting the discharge of dredged or fill material in the "waters

Normal-mode expansions for Green's functions are derived for ocean–bottom systems. The bottom is modeled by Kirchhoff and Reissner–Mindlin plate theories for elastic and poroelastic materials. The resulting eigenvalue problems for the modal parameters are investigated. Normal modes are calculated by Hankel transformation of the underlying equations. Finally, the relation to the inverse problem is outlined.

In this paper the boundary integral equation method is used to solve a scattering problem in a shallow ocean with an elastic seabed. The Hankel transformation and Mittag–Leffler decomposition were used to construct the propagating solution for both far-field and near-field. In particular, necessary and sufficient conditions are found for the existence of the propagating solution. Using the propagating solution, the scattering problem is recast as a boundary integral equation. A numerical algorithm is developed for solving this boundary integral equation and its implementation on a T3D parallel computer is used to compute an illustrative example.

As a sequel to Refs. 1 and 2, this paper gives a numerical treatment of the inverse problem associated with the determination of the index of refraction. We show that the problem can be solved in two steps. First we must recover a function from its moments, problem (IM), which we may reformulate as a Fredholm integral equation of the first kind, problem (IE). Second we solve an inverse Goursat problem, (IG). Numerical schemes for both steps are given along with the results of some numerical experiments.

This paper which is Part I of a sequence deals with the problem of determining a radially dependent coefficient n (r) in the equation ∆ u − n2 (r) u = 0, in the unit disk Ω from the Dirichlet–Neumann data pair [Formula: see text]. We prove that the sufficiency condition for uniqueness established in Ref. 2 is, in some instances, also a necessity for uniqueness. We also discuss the solvability of this inverse problem. In Part II numerical experiments will be presented which illustrate the theory developed here.

In this paper we discuss the question of identifying the radially dependent coefficient a(r) in the elliptic equation div(a(r) ▽u)=0 in the unit disk by Dirichlet and Neumann data.We establish a condition to guarantee the uniqueness of this determination. One of the applications of this study is the determination of the radially dependent conductivity coefficient of layered medium. Keywords: Inverse problemellipticcoefficient

The objectives of this study were to determine and compare the Al tolerance of selected citrus rootstocks. Six-month-old seedlings of five citrus rootstocks were grown for 60 days in nutrient solutions. The solutions contained 7 levels of Al ranging from 4 to 1655-mu-M and similar P concentration of 28-mu-M. The nutrient solution pH was maintained at 4.0 +/- 0.1 and the temperature at 25 +/- 1-degrees-C. At high Al treatment levels, plants had thickened root tips and root caps covered with black gelatinous material. At high levels of Al treatments, seedlings of some rootstocks had yellow, mottled, and withered new leaves near end of experiment. New-growth root lengths and shoot height responded differently to Al concentrations in the nutrient solution. New-growth fresh weight of whole plants appeared to be the most sensitive indicator of Al tolerance. Based on response of fresh weight of whole plants to Al concentrations, relative Al tolerances of the rootstocks were Cleopatra mandarin > rough lemon > sour orange > Swingle citramelo > Carrizo citrange. The neutral or dividing Al concentrations in solution between beneficial and toxic effects were 371, 193, 189, 178, and < 100-mu-M Al, respectively, for the above rootstocks. Concentrations below or above the neutral Al levels caused either beneficial or toxic effects, respectively. The apparent optimum Al concentrations for the growth of whole plants were 163, 93, 89, 85, and < 50-mu-M, respectively.

Precipitation of Al(OH)3 and aluminum phosphate may occur in nutrient solution if a large amount of Al and P have been added to a relatively high pH. The objective of this study was to develop and test a supernatant-solution method for Al phytotoxicity studies with large and/or old plant seedlings. Effects of pH and additions of Al and P on ionic strength and concentrations of Al and P in supernatant nutrient solutions were investigated. Two sets of supernatant nutrient solutions at two pH levels were prepared. The pH 4.0 set and 4.5 set contained seven levels of Al (maximum Al concentration of 6355 and 378-mu-M) and similar P concentration about 32 and 6-mu-M P, respectively. The Al concentrations in supernatant solutions were dependent on preparation procedure. The pH 4.0 set was tested in the greenhouse study with 6-month-old citrus seedlings and found to be successful as culture solutions for Al phytotoxicity studies. These two sets are suitable for growth of large (about 0.3 m) and/or old (about 6 mon.) seedlings. This supernatant-solution method makes it possible to study Al phytotoxicity of large and/or old seedlings, to avoid the confounding effects of P on Al with respect to plant growth, and to report the actual concentrations of Al and P in growth solutions.

AbstractMost research on the effects of Al on citrus rootstocks has been limited to nutrient‐solution studies. This study employed an implanted soil‐mass technique to determine the effects of Al level in soils on growth and mineral content of fibrous citrus roots under field conditions. The implanted soil, E horizon material from an Immokalee fine sand (sandy, siliceous, hyperthermic Arenic Haplaquod), had a pH of 4.2 and a very low exchangeable‐Al content. It was either limed, unamended, or amended with three levels of Al using AlCl3. Each of the five treatments was replicated 15 times. Mesh bags containing the treated soil were placed in holes at the drip line of mature trees (Citrus aurantium L. sour orange rootstock) in a producing citrus grove. The bags were removed after 46 d. Results showed that, at a concentration of 9.14 mg Al L−1 of soil saturation extract, root density was twice that of the unamended treatment (0.13 mg Al L−1) and equaled that of the lime treatment (0.03 mg Al L−1). More roots grew into the bag, and they produced more lateral roots. Aluminum concentrations in roots were lower than those in the unamended treatment, however. Root‐length density decreased to about 60% of the value for the unamended treatment when Al concentration increased to 34.60 mg L−1. The optimum Al concentration for root growth appears to be 10 mg L−1 calculated by a curvilinear regression equation. In general, the concentrations of Zn, Fe, and Mn in roots decreased with increased Al application to the soil, while concentrations of Ca, Mg, K, P, and B were unchanged.