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.

Immunology of multiple sclerosis

Multiple sclerosis (MS) is an autoimmune disease of the central nervous system (CNS) leading to demyelination, axonal damage, and progressive neurologic disability. The development of MS is influenced by environmental factors, particularly the Epstein-Barr virus (EBV), and genetic factors, which include specific HLA types, particularly DRB1*1501-DQA1*0102-DQB1*0602, and a predisposition to autoimmunity in general. MS patients have increased circulating T-cell and antibody reactivity to myelin proteins and gangliosides. It is proposed that the role of EBV is to infect autoreactive B cells that then seed the CNS and promote the survival of autoreactive T cells there. It is also proposed that the clinical attacks of relapsing-remitting MS are orchestrated by myelin-reactive T cells entering the white matter of the CNS from the blood, and that the progressive disability in primary and secondary progressive MS is caused by the action of autoantibodies produced in the CNS by ­meningeal lymphoid follicles with germinal centers.

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.

Substrate-inhibited kinetics with catalyst deactivation in an isothermal CSTR. II. Multiple pseudosteady states and reactor failure

Analytical expressions are derived for the time and magnitude of failure of an isothermal CSTR with substrate-inhibited kinetics, caused by slow catalyst deactivation under three types of parallel and series mechanisms. Reactors operating at high space velocity are found to be most susceptible to early failure and poisoning by product is more dangerous than by reactant. The magnitude of the jump across steady states depends solely on the Langmuir-Hinshelwood kinetic parameters and a detailed analysis of reactor behavior during the jump itself is given.

Analysis of multiple gas solid reactions

Multiple gas solid reactions involving one solid and N gaseous reactants are investigated in this study by using a matched asymptotic expansion technique. Two cases are particularly studied. In the first case all N chemical reaction rates are faster than the diffusion rate. While in the second case only M (M < N) chemical reaction rates are faster than the diffusion rate and the rates of the remaining (N-M) chemical reactions are comparable to that of diffusion. For these two cases the solid concentration profile behaves like a travelling wave. In the first case the wave front velocity is contributed linearly by all gaseous reactants (additive law) while in the second case this law does not hold.

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.

New calibration technique for multiple-component stress wave force balances

Force measurement in hypervelocity expansion tubes is not possible using conventional techniques. The stress wave force balance technique can be applied in expansion tubes to measure forces despite the short test times involved. This paper presents a new calibration technique for multiple-component stress wave force balances where an impulse response created using a load distribution is required and no orthogonal surfaces on the model exist.. This new technique relies on the tensorial superposition of single-component impulse responses analogous to the vectorial superposition of the calibration loads. The example presented here is that of a scale model of the Mars Pathfinder, but the technique is applicable to any geometry and may be useful for cases where orthogonal loads cannot be applied.

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.

Regulation of photosynthetic pigments in micro-algae by multiple environmental factors: a dynamic balance hypothesis

Environmental effects on the concentration of photosynthetic pigments in micro-algae can be explained by dynamics of photosystem synthesis and deactivation. A model that couples photosystem losses to the relative cellular rates of energy harvesting (light absorption) and assimilation predicts optimal concentrations of light-harvesting pigments and balanced energy flow under environmental conditions that affect light availability and metabolic rates. Effects of light intensity, nutrient supply and temperature on growth rate and pigment levels were similar to general patterns observed across diverse micro-algal taxa. Results imply that dynamic behaviour associated with photophysical stress, and independent of gene regulation, might constitute one mechanism for photo-acclimation of photosynthesis.

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.

The relationship between multiple birth children's early phonological skills and later literacy

Previous studies have shown that multiple ; birth children (MBC) are prone to early phonological ;difficulties and later literacy problems. However, to date, ;there has been no systematic long-term follow-up of MBC with phonological difficulties in the preschool years to determine whether these difficulties predict later literacy problems. In this study, 20 MBC whose early speech and language skills had been previously documented were compared to normative data and 20 singleton controls on tasks assessing phonological ; processing and literacy. The major findings indicated that MBC performed significantly more poorly on some tasks :df phonological processing than singleton controls did. Further, the early phonological skills of MBC (i.e., the number of inappropriate phonological processes used) correlated with poor performance on visual rhyme recognition, word repetition, and phoneme detection tasks 5 years later. There was no significant relationship between early biological factors (birth weight and gestation period) and performance on the phonological processing and literacy-related subtests. These results cl-support the hypothesis that MBC's early speech and language difficulties are not merely a transient phase;of; development, but a real disorder, with consequences for later academic achievement.