Alternative Analytical Expressions for the General van Genuchten-Mualem and van Genuchten-Burdine Hydraulic Conductivity Models

The van Genuchten expressions for the unsaturated soil hydraulic properties, first published in 1980, are used frequently in various vadose zone flow and transport applications assuming a specific relationship between the m and n soil hydraulic parameters. By comparison, probably because of the complexity of the hydraulic conductivity equations, the more general solutions with independent m and n values are rarely used. We expressed the general van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity equations in terms of hypergeometric functions, which can be approximated by infinite series that converge rapidly for relatively large values of the van Genuchten-Mualem parameter n but only very slowly when n is close to one. Alternative equations were derived that provide very close approximations of the analytical results. The newly proposed equations allow the use of independent values of the parameters m and n in the soil water retention model of van Genuchten for subsequent prediction of the van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity models, thus providing more flexibility in fitting experimental pressure-head-dependent water content, theta(h), and hydraulic conductivity, K(h), or K(theta) data.

Determination of Atropine Enantiomers in Ophthalmic Solutions by Liquid Chromatography Using a Chiral AGP (R) Column

Many therapeutic agents are commercialized under their racemic form. The enantiomers can show differences in the pharmacokinetic and pharmacodynamic profile. The use of a pure enantiomer in pharmaceutical formulations may result in a better therapeutic index and fewer adverse effects. Atropine, an alkaloid of Atropa belladonna, is a racemic mixture of l-hyoscyamine and d-hyoscyamine. It is widely used to dilate the pupil. To quantify these enantiomers in ophthalmic solutions, an HPLC method was developed and validated using a Chiral AGP (R) column at 20 degrees C. The mobile phase consisted of a buffered phosphate solution (containing 10 mM 1-octanesulfonic acid sodium salt and 7.5 mM triethylamine, adjusted to pH 7.0 with orthophosphoric acid) and acetonitrile (99 + 1, v/v). The flow rate was 0.6 mL/min, with UV detection at 205 nm. In the concentration range of 14.0-26.0 mu g/mL, the method was found to be linear (r > 0.9999), accurate (with recovery of 100.1-100.5%), and precise (RSD system: <= 0.6%; RSD intraday: <= 1.1%; RSD interday: <= 0.9%). The method was specific, and the standard and sample solutions were stable for up to 72 h. The factorial design assures robustness with a variation of +/-10% in the mobile phase components and 2 degrees C of column temperature. The complete validation, including stress testing and factorial design, was studied and is presented in this research.

Simultaneous Determination of Choline Citrate and Acetylmethionine in Injectable Solutions by High Performance Liquid Chromatography

Choline citrate (CC) and acetylmethionine (AM) are lipotropic drugs used in several pharmaceutical formulations. The objective of this research was to develop and validate a high performance liquid chromatographic (HPLC) method for simultaneous determination of CC and AM in injectable solutions, aiming its application in routine analysis for quality control of these pharmaceutical formulations. The method was validated using a Shim-Pack (R) C18 (250 x 4.6 mm, 5 mu m) column. The mobile phase was constituted of 25 mM potassium phosphate buffer solution, pH 5.7, adjusted with 10 % orthophosphoric acid, acetonitrile and methanol (88:10:2, v/v/v). The flow rate was 1.1 mL.min(-1) and the UV detection was made at 210 nm. The analyses were made at room temperature (25 +/- 1 degrees C). The method is precise, selective, accurate and robust, and was successfully applied for simultaneous quantitative determination of CC and AM in injectables.

Influence of Pluronic (R) F68 on Ceftazidime Biological Activity in Parenteral Solutions

beta-Lactam antimicrobials are known to have a low concentration/therapeutic response. However, extending the period in which beta-lactam are free in the plasma does directly influence therapeutic outcomes. The objective of this study was to evaluate the influence of Pluronic (R) F68 on the antimicrobial activity of ceftazidime when admixed with aminophylline in parenteral solutions by the evaluation of its minimal inhibitory concentration (MIC) within 24 h. Ceftazidime, aminophylline, and Pluronics (R) F68 were evaluated using the MIC method against Escherichia coli and Pseudomonas aeruginosa, with these compounds individually and associated in the same parenteral solutions. When Pluronics (R) F68 was admixtured with ceftazidime alone or with ceftazidime and aminophylline, it was possible to observe lower MIC values not only at 24 h but also at 0 h for both microorganisms. This indicates that Pluronics (R) F68 may be able to enhance ceftazidime antimicrobial activity in the presence or absence of aminophylline. This fact suggests that Pluronics (R) F68 can be applied to allow the administration of ceftazidime under continuous infusion in parenteral solutions, beneficiating hospital pharmacotherapy. It may also be possible to reduce ceftazidime doses in formulations achieving the same therapeutic results. (C) 2010 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 100:715-720, 2011

Gauge P-representations for quantum-dynamical problems: Removal of boundary terms

P-representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum-dynamical many-body calculations such as Bose-Einstein condensation. We introduce a representation called the gauge P representation, which greatly widens the range of tractable problems. Our treatment results in an infinite set of possible time evolution equations, depending on arbitrary gauge functions that can be optimized for a given quantum system. In some cases, previous methods can give erroneous results, due to the usual assumption of vanishing boundary conditions being invalid for those particular systems. Solutions are given to this boundary-term problem for all the cases where it is known to occur: two-photon absorption and the single-mode laser. We also provide some brief guidelines on how to apply the stochastic gauge method to other systems in general, quantify the freedom of choice in the resulting equations, and make a comparison to related recent developments.

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.

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.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

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.

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.