Least energy solutions of a critical Neumann problem with a weight

We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.

A fast cross-entropy method for estimating buffer overflows in queuing networks

In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level. Finally, the tilting parameter just found is used to estimate the overflow probability of interest. We study various properties of the method in more detail for the M/M/1 queue and conjecture that similar properties also hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.

Useful representations of series solutions for transport problems

Simple techniques are presented for rearrangement of an infinite series in a systematic way such that the convergence of the resulting expression is accelerated. These procedures also allow calculation of required boundary derivatives. Several examples of conduction and diffusion-reaction problems illustrate the methods.

The transient response of a CSTR containing porous catalyst pellets. Asymptotic solutions

Transient response of a CSTR containing porous catalyst pellets is analyzed theoretically using a matched asymptotic expansion technique. This singular perturbation technique leads directly to the conditions under which the minima of reservoir concentration occur. The existence of the minima may be used to estimate some inherent parameters of the catalyst pellet.

Approximate analytical solutions for porous catalysts with nonuniform activity

Using a novel finite integral transform technique, the problem of diffusion and chemical reaction in a porous catalyst with general activity profile is investigated theoretically. Analytical expressions for the effectiveness factor are obtained for pth order and Michaelis-Menten kinetics. Perturbation methods are employed to provide useful asymptotic solutions for large or small values of Thiele modulus and Biot number.

Evaluating Flexible Transport Solutions

Flexible transport services (FTS) have been of increasing interest in developed countries as a bridge between the use of personal car travel and fixed route transit services. This paper reports on findings from a recent study in Queensland Australia, which identified lessons from an international review and implications for Australia. Potential strategic directions, including a vision, mission, key result areas, strategies, and identified means of measuring performance are described. Evaluation criteria for assessing flexible transport proposals were developed, and approaches to identifying and assessing needs and demands outlined. The use of emerging technologies is also a key element of successful flexible transport services.

Control of nutrient solutions for studies at high pH

Little is known about factors effecting plant growth at high pH, with research often limited by the inability to separate nutritional deficiencies and HCO3- toxicity from the direct limitations imposed under high pH conditions. Various methods of controlling dilute nutrient solutions for studies at high pH were investigated. For short-term studies, it was found that a solution without Cu, Fe, Mn and Zn and aerated with CO2 depleted air, greatly reduced nutrient precipitation at high pH, thus eliminating nutritional differences between treatments. Manual pH adjustment and the use of ion exchange resins as pH buffers were unsuitable methods of pH control. However, pH control by automated titration had little effect on solution composition while maintaining constant pH. The system described is suitable for studies in which the pH of the bulk nutrient solution must be maintained. The system was used to examine OH- toxicity in mungbeans (Vigna radiata (L.) Wilczek cv. Emerald), with root length reduced at a bulk solution pH of 8.5 and greater.

Effect of Cu Toxicity on Growth of Cowpea (Vigna unguiculata)

Accurate determination of the rhizotoxicity of Cu in dilute nutrient solutions is hindered by the difficulty of maintaining constant, pre-determined concentrations of Cu (micromolar) in solution. The critical Cu2+ activity associated with a reduction in the growth of solution-grown cowpea (Vigna unguiculata (L.) Walp. cv Caloona) was determined in a system in which Cu was maintained constant through the use of a cation exchange resin. The growth of roots and shoots was found to be reduced at solution Cu2+ activities ≥ 1.7 µM (corresponding to 90 % maximum growth). Although root growth was most likely reduced due to a direct Cu2+ toxicity, it is considered that the shoot growth reduction is attributable to a decrease in tissue concentrations of K, Ca, Mg, and Fe and the formation of interveinal chlorosis. At high Cu2+ activities, roots were brown in color, short and thick, had bent root tips with cracking of the epidermis and outer cortex, and had local swellings behind the roots tips due to a reduction in cell elongation. Root hair growth was reduced at concentrations lower than that which caused a significant reduction in overall root fresh weight.

The anodic dissolution of magnesium in chloride and sulphate solutions

The electrochemical behaviour of magnesium was studied in representative chloride and sulphate solutions including NaCl, Na2SO4, NaOH and their mixed solutions, HCl, and H2SO4: (1) by measuring electrochemical polarisation curves, (2) by using electrochemical impedance spectroscopy (EIS), and (3) by simultaneous measurement of hydrogen gas evolution and measurement of magnesium dissolution rates using inductively coupled plasma atomic emission spectrophotometry (ICPEAS). These experiments showed that a partially protective surface film played an important role in the dissolution of magnesium in chloride and sulphate solutions. Furthermore, the experimental data were consistent with the involvement of the intermediate species Mg+ in magnesium dissolution at film imperfections or on a film-free surface. At such sites, magnesium first oxidised electrochemically to the intermediate species Mg+, and then the intermediate species chemically reacted with water to produce hydrogen and Mg2+. The presence of Cl- ions increased the film free area, and accelerated the electrochemical reaction rate from magnesium metal to Mg+. (C) 1997 Elsevier Science Ltd.

Media influence to suicide: The search for solutions

This review explores the influence to suicide in print and electronic media, and considers both real and fictional deaths. The conclusion appears inescapable that reports about celebrities which are multi-modal, repeated, explicit, front page, glorify the suicide, and describe the method lead to an increase in deaths from suicide, particularly in the region in which reports are published. The paper argues that even if there was multi-national agreement to international guidelines, media will continue to report suicide when it is considered to be a matter of public interest. What appears crucial is a collaborative approach between professionals and the media to promote a negative attitude toward suicide without increasing stigma toward those with mental health problems.

Asymptotic solutions to the Gross-Pitaevskii gain equation: Growth of a Bose-Einstein condensate

We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced center-of-mass temperature.