A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.     

Changes in red blood cell volume on fixation in glutaraldehyde solutions

Summary Light scattering (nephelometry) was used to determine directly the change in volume of red blood cells immersed in a variety of buffer and fixative solutions. Cells immersed in saline or phosphate buffer solutions showed a change in volume that reflected the osmolarity of the solution, shrinkage taking place in hypertonic solutions and swelling and haemolysis occurring in strongly hypotonic solutions. On the other hand, while there was considerable shrinkage in hypertonic glutaraldehyde solutions, swelling was more restricted and haemolysis was prevented in the weaker glutaraldehyde solutions. Thus, while glutaraldehyde exerts a definite osmotic effect on cells in fixative solutions, the magnitude of this effect seems to be limited by its direct action as a fixative.     

Rotating wave solutions of the FitzHugh–Nagumo equations

This paper will treat the bifurcation and numerical simulation of rotating wave (RW) solutions of the FitzHugh-Nagumo (FHN) equations. These equations are often used as a simple mathematical model of excitable media. The dependence of the solutions on a uniformly applied current, and also on the diffusion coefficients or domain size will be studied. Ranges of applied current and/or diffusion coefficients in which RW solutions are observed will be described using bifurcation theory and continuation methods. The bifurcation of time-periodic solutions of these FHN equations without diffusion is described first. Similar methods are then used to find RW solutions on a circular ring and numerical simulations are described. These results are then extended to investigate RW solutions on annular rings of finite cross-section. Scaling arguments are used to show how the existence of solutions depends on either the diffusion coefficient or on the size of the region.     

Faster gastric emptying for glucose-polymer and fructose solutions than for glucose in humans

This study examined the rates of gastric emptying for water and 13 different carbohydrate-containing solutions in seven subjects, using conventional gastric intubation techniques. The rates of gastric emptying for water and a 10% glucose-polymer solution were also measured during 90 min of treadmill running at 75% of each subject's maximum oxygen consumption (VO2max). At rest, 15% glucose-polymer (P) and fructose (F) solutions emptied more rapidly from the stomach and provided a faster rate of carbohydrate delivery than did a 15% glucose (G) solution (p less than 0.05). The G solutions showed a constant energy delivery rate of 3.3 kcal.min-1; energy delivery from P and F solutions rose with increasing solution concentrations. The osmolality of the gastric aspirate predicted the rate of gastric emptying for all solutions (p less than 0.05) but overestimated rates of emptying for 10% and 15% P solutions and underestimated emptying rates for 10% and 15% F solutions. Exercise at 75% VO2max decreased the rate of gastric emptying of water but not of 10% P solutions. Thus the different rates of gastric emptying for different carbohydrate-containing solutions were not entirely explained by differences in osmolality. Furthermore, exercise may have different effects on the gastric emptying rates of water and carbohydrate solutions.     

Improved stability of Drosophila larval neuromuscular preparations in haemolymph-like physiological solutions

Neuromuscular preparations from third instar larvae of Drosophila are not well-maintained in commonly used physiological solutions: vacuoles form in the muscle fibers, and membrane potential declines. These problems may result from the NaK ratio and total divalent cation content of these physiological solutions being quite different from those of haemolymph. Accordingly haemolymph-like solutions, based upon ion measurements of major cations, were developed and tested. Haemolymph-like solutions maintained the membrane potential at a relatively constant level, and prolonged the physiological life of the preparations. Synaptic transmission was well-maintained in haemolymph-like solutions, but the excitatory synaptic potentials had a slower time course and summated more effectively with repetitive stimulation, than in standard Drosophila solutions. Voltage-clamp experiments suggest that these effects are linked to more pronounced activation of muscle fiber membrane conductances in standard solutions, rather than to differences in passive muscle membrane properties or changes in postsynaptic receptor channel kinetics. Calcium dependence of transmitter release was steep in both standard and haemolymph-like solutions, but higher external calcium concentrations were required for a given level of release in haemolymph-like solutions. Thus, haemolymph-like solutions allow for prolonged, stable recording of synaptic transmission.Abbreviations HL haemolymph-like     

Spatial stability of traveling wave solutions of a nerve conduction equation.

A simplified FitzHugh-Nagumo nerve conduction equation with known traveling wave solutions is considered. The spatial stability of these solutions is analyzed to determine which solutions should occur in signal transmission along such a nerve model. It is found that the slower of the two pulse solutions is unstable while the faster one is stable, so the faster one should occur. This agrees with conjectures which have been made about the solutions of other nerve conduction equations. Furthermore for certain parameter values the equation has two periodic wave solutions, each representing a train of impulses, at each frequency less than a maximum frequency wmax. The slower one is found to be unstable and the faster one to be stable, while that at wmax is found to be neutrally stable. These spatial stability results complement the previous results of Rinzel and Keller (1973. Biophys. J. 13: 1313) on temporal stability, which are applicable to the solutions of initial value problems.     

Solutions to axon equations

The solutions to a general class of axon partial differential equations proposed by FitzHugh which includes the Hodgkin-Huxley equations are studied. It is shown that solutions to the partial differential equations are exactly the solutions to a related set of integral equations. An iterative procedure for constructing the solutions based on standard methods for ordinary differential equations is given and each set of initial values is shown to lead to a unique solution. Continuous dependence of the solutions on the initial values is established and solutions with initial values in a restricted (physiological) range are shown to remain in that range for all time. The iterative procedure is not suggested as the basis for numerical integration.     

On the stability of separable solutions of a sexual age-structured population dynamics model

The Sharpe-Lotka-McKendrick-von Foerster equations for non-dispersing age-sex-structured populations with a harmonic mean type mating law are considered and their separable solutions are analysed. For certain forms of the demographic rates the underlying evolution equations are reduced to systems of ODEs, the long time behavior of their solutions is studied, and the stability of separable solutions is discussed. It is found that for the constant death rates and constant sex ratio of newborns with stationary birth rates this model admits one one-parameter class of separable solutions, two such classes (repeated or different) or no such ones. In the case of special forms of age-dependent birth rates, solutions of one of these two different classes corresponding to the greater root of the characteristic equation are locally stable, solutions of the other one corresponding to the smaller root are unstable, and the population dies out if the model does not admit separable solutions or if initial densities of newborns are small enough in the case of the existence of separable solutions. In the case of constant vital rates, the model has no separable solutions or admits only one class of such ones that are globally stable.     

Non-steady-state O(2) diffusion in metmyoglobin solutions studied in a diffusion chamber

In this study, we studied the "passive" diffusion through myoglobin solutions by determining the oxygen diffusion coefficient (DO(2)) and the oxygen permeability (permeability O(2)) of metmyoglobin (metMb) solutions (3-33 g. 100 mL(-1)) at 25 degrees C. These oxygen diffusion parameters were determined in a diffusion chamber using a non-steady-state method and were also determined of albumin solutions (4-32 g. 100 mL(-1)) and distilled water for comparison. From these parameters, the oxygen solubility (alphaO(2)) could be calculated, because alphaO(2) = permeabilityO(2)/DO(2). Both DO(2) and permeabilityO(2) decreased with increasing metMb and albumin concentration. The values of DO(2), permeabilityO(2) and alphaO(2) of both metMb solutions and albumin solutions were comparable with literature values of methemoglobin (metHb) and serum protein solutions. The values of the metMb solutions can be used in following studies of facilitated oxygen diffusion through myoglobin solutions.     

Evolution,games theory and polyhedra

The problem of finding an Evolutionary Stable Strategy (ESS) for an animal species is defined. It is shown how such strategies are a subset of the equilibrium solutions for a particular non-zero sum game. These equilibrium solutions are then shown to arise from the vertices of a particular convex polyhedron. A method of finding these equilibrium solutions through the vertices and then the ESS solutions is given. This is illustrated by a number of numerical examples taken from the literature. Finally an alternative approach based on solving a Linear Complementarity Problem is discussed.     

Rheological properties of water-soluble spruce O-acetyl galactoglucomannans

The thermal and rheological properties of spray-dried, ethanol-precipitated, purified, and deacetylated spruce galactoglucomannans (GGM) were investigated by rheological measurements and differential scanning calorimetry. The shear rate dependence of viscosity and the effects of the drying method, temperature, ionic strength, and deacetylation on rheological properties were studied. GGM solutions exhibited a shear thinning behaviour. GGM solutions did not obey the Cox–Merz rule. The storage modulus of GGM solutions increased with an increase in concentration; gradually until a concentration of 5%, but rapidly at higher concentrations. Ethanol-precipitated GGM solutions showed a more elastic behaviour than spray-dried GGM solutions. Deacetylation caused an increase in apparent viscosity and more significantly in storage modulus. The storage modulus increased slightly with a decrease in temperature. A small amount addition of NaCl slightly changed the oscillatory behaviour. The effects of above factors were discussed in terms of molecular interactions. The rheological measurements of GGM solutions provide the basis of functionalities of GGM solutions.     

The Effect of Sugars and Polyols on the Heat Resistance and Morphology of Osmophilic Yeasts

Heat resistance at 65· of Saccharomyces rouxii and Schizosaccharomyces pombe was enhanced in solutions of sugars and polyols, containing 0·1 M-phosphate buffer, pH 6·5, at a water activity of 0·95. Resistance was maximum in solutions of sucrose, less in sorbitol and least in solutions of glucose, fructose and glycerol. Examination of the yeast cells by phase contrast microscopy showed shrinkage of cells in all solutions. Electron microscopy of freeze-etched preparations of Sacch. rouxii indicated plasmolysis of cells in sucrose and sorbitol solutions only.     

Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis

The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.     

Effects of anion substitution on hydration behavior and water uptake of the red-spotted toad, Bufo punctatus: is there an anion paradox in amphibian skin?

Amphibians absorb water osmotically across their skins and rely on chemosensory information from the skin to assess the suitability of hydration sources. The time spent with skin in contact with a moist surface provides a quantitative measure of their ability to perceive the ionic and osmotic properties of aqueous solutions. Dehydrated toads given hyperosmotic (250 mM) solutions of NaCl or Na-gluconate showed significantly longer periods of hydration behavior on the gluconate solution, but they lost water osmotically when immersed in either solution. Similarly, dehydrated toads given 250 mM solutions of NaCl, Na-acetate, Na-phosphate or Na-gluconate showed a progressively greater length of hydration time on solutions with the larger mol. wt anions. These results are consistent with the chemosensory phenomenon previously described in mammalian tongue as 'anion paradox'. On dilute (50 mM) solutions of NaCl or Na-gluconate, the hydration time was not different between anions, despite toads gaining water more rapidly when immersed in dilute NaCl than in Na-gluconate solutions. The differing behavioral results with hyperosmotic and hypoosmotic salt solutions suggest that chemosensory transduction through toad skin involves both transcellular and paracellular pathways.     

Effects of ammonium ions on endplate channels

Miniature endplate currents, recorded from voltage-clamped toad sartorius muscle fibers in solutions containing ammonium ions substituted for sodium ions, were increased in amplitude and decayed exponentially with a slower time constant than in control (Na) solution. The peak conductance of miniature endplate currents was also greater in ammonium solutions. The acetylcholine null potential was - 2.8 +/- 0.8 mV in control solution, and shifted to 0.9 +/- 1.6 mV in solutions in which NH4Cl replaced half the NaCl. In solutions containing NH4Cl substituted for all the NaCl, the null potential was 6.5 +/- 1.3 mV. Single channel conductance and average channel lifetime were both increased in solutions containing ammonium ions. The exponential relationship between the time constant of decay of miniature endplate currents or channel lifetime and membrane potential was unchanged in ammonium solutions. A slight but consistent increase in peak conductance during miniature endplate currents and single channel conductance was seen as membrane potential became more positive (depolarized) in both control and ammonium solutions. Net charge transfer was greater in ammonium solutions than in control solution, whether measured during a miniature endplate current or through a single channel. The results presented here are consistent with an endplate channel model containing high field strength, neutral sites.     

Logical Gaps in the Approximate Solutions of the Social Learning Game and an Exact Solution

After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introduce a minor extension to the original game so that not only logical differences but also differences in action outcomes among those solutions become visible.     

A Consideration of French's Test of Basic Fuchsin for Endo's Medium

In describing a method of testing for the return of color in decolorized fuchsin for use in Endo Medium, French states that variations in hydrogen ion concentration fail to influence the appearance of color in this medium.

Duplications of this test were made using alcoholic and aqueous solutions of fuchsin and both sodium sulfite and sodium bisulfite as decolorizing agents.

In the decolorized alcoholic solutions of fuchsin the color failed to reappear when formalin was added, but a small amount of a weak solution of lactic acid caused the color to return.

Alcoholic solutions of fuchsin failed to decolorize in sodium bisulfite solutions until a few drops of NaOH were added. The color, then, reappeared immediately.

Solutions of peptones to which fuchsin had been added were substituted for the original fuchsin solution. Alcoholic and aqueous solutions of fuchsin were added to equal amounts of a 1% peptone solution. The peptone solutions varied in their hydrogen ion concentration and the results showed that those which were neutral decolorized readily while the more acid solutions were but partially decolorized.

Fuchsin decolorized according to results found in this test, was not satisfactory in the Endo medium, especially in the case of the aqueous solutions of fuchsin.

Experiments which were carried on by other workers and checked with this method all indicated that some acid is necessary to secure the restoration of color.     

Multiplication of Nosocomial Pathogens in Intravenous Feeding Solutions

A major problem in total parenteral nutrition is sepsis, particularly that caused by Candida. Studies of four solutions, a casein hydrolysate, a fibrin hydrolysate, and two crystalline amino acid solutions, show that the protein hydrolysate solutions appear to be highly selective for Candida over bacteria, whereas the crystalline amino acid solutions are not. These findings suggest that the crystalline amino acid preparations may offer a partial solution to the infection problem by minimizing the contribution of the solution as a reservoir for organism multiplication, because they retard the growth of both bacteria and Candida.     

Iron-dependent vs. iron-independent cold-induced injury to cultured rat hepatocytes: a comparative study in physiological media and organ preservation solutions

We previously described the entity of cold-induced apoptosis to rat hepatocytes and characterized its major, iron-dependent pathway. However, after cold incubation in some solutions, e.g. cell culture medium, hepatocytes show an additional, yet uncharacterized component of cold-induced injury. We here assessed the effects of organ preservation solutions on both components of cold-induced injury and tried to further characterize the iron-independent component. None of the preservation solutions (University of Wisconsin, histidine-tryptophan-ketoglutarate, Euro-Collins, histidine-lactobionate, sodium-lactobionate-sucrose and Celsior solutions) provided significant protection against cold-induced cell injury (LDH release after 24-h cold incubation/3h rewarming >65% for all solutions); three solutions even enhanced cold-induced injury. However, when the predominant iron-dependent mechanism was eliminated by the addition of iron chelators, all preservation solutions yielded hepatocyte protection that was clearly superior to the one obtainable in cell culture medium or Krebs-Henseleit buffer with iron chelators (LDH release after 24-h cold incubation/3h rewarming 相似文献   

Mineral nutrition and the reaction of Lolium perenne to defoliation

Summary Plants were grown in nutrient solutions, defoliated to remove all expanded leaf blades and the amount of regrowth measured a week later. Prior to defolation, plants in concentrated nutrient solutions grew more rapidly than those in dilute solutions. After defoliation, the plants in concentrated solutions did not produce, however, a greater quantity of regrowth relative to their size than those in dilute solutions. Other things being equal, in environments which produced plants with a low root: shoot ratio, the greatest amount of regrowth was produced by genotypes with a higher than average root: shoot ratio, and vice versa.These results are discussed in relation to repeated defoliation, size and age of the plants, and the role of roots and reserve substances in recovery from defoliation