I. Singular perturbation problems involving singular points and turning points. II. On the averaged Lagrangian technique for nonlinear dispersive waves

In Part I a class of linear boundary value problems is considered which is a simple model of boundary layer theory. The effect of zeros and singularities of the coefficients of the equations at the point where the boundary layer occurs is considered. The usual boundary layer techniques are still applicable in some cases and are used to derive uniform asymptotic expansions. In other cases it is shown that the inner and outer expansions do not overlap due to the presence of a turning point outside the boundary layer. The region near the turning point is described by a two-variable expansion. In these cases a related initial value problem is solved and then used to show formally that for the boundary value problem either a solution exists, except for a discrete set of eigenvalues, whose asymptotic behaviour is found, or the solution is non-unique. A proof is given of the validity of the two-variable expansion; in a special case this proof also demonstrates the validity of the inner and outer expansions.

Nonlinear dispersive wave equations which are governed by variational principles are considered in Part II. It is shown that the averaged Lagrangian variational principle is in fact exact. This result is used to construct perturbation schemes to enable higher order terms in the equations for the slowly varying quantities to be calculated. A simple scheme applicable to linear or near-linear equations is first derived. The specific form of the first order correction terms is derived for several examples. The stability of constant solutions to these equations is considered and it is shown that the correction terms lead to the instability cut-off found by Benjamin. A general stability criterion is given which explicitly demonstrates the conditions under which this cut-off occurs. The corrected set of equations are nonlinear dispersive equations and their stationary solutions are investigated. A more sophisticated scheme is developed for fully nonlinear equations by using an extension of the Hamiltonian formalism recently introduced by Whitham. Finally the averaged Lagrangian technique is extended to treat slowly varying multiply-periodic solutions. The adiabatic invariants for a separable mechanical system are derived by this method.

Problems with Unofficial and Inaccurate Geographical Names in the Fisheries Literature

Over a century of fi shery and oceanographic research conducted along the Atlantic coast of the United States has resulted in many publications using unofficial, and therefore unclear, geographic names for certain study areas. Such improper usage, besides being unscholarly, has and can lead to identification problems for readers unfamiliar with the area. Even worse, the use of electronic data bases and search engines can provide incomplete or confusing references when improper wording is used. The two terms used improperly most often are “Middle Atlantic Bight” and “South Atlantic Bight.” In general, the term “Middle Atlantic Bight” usually refers to an imprecise coastal area off the middle Atlantic states of New York, New Jersey, Delaware, Maryland, and Virginia, and the term “South Atlantic Bight” refers to the area off the southeastern states of North Carolina, South Carolina, Georgia, and Florida’s east coast.

An efficient frequency-domain algorithm for wave scattering problems with application to jet noise

This paper presents a pseudo-time-step method to calculate a (vector) Green function for the adjoint linearised Euler equations as a scattering problem in the frequency domain, for use as a jet-noise propagation prediction tool. A method of selecting the acoustics-related solution in a truncated spatial domain while suppressing any possible shear-layer-type instability is presented. Numerical tests for 3-D axisymmetrical parallel mean flows against semi-analytical reference solutions indicate that the new iterative algorithm is capable of producing accurate solutions with modest computational requirements.

Performance of genetically improved farmed tilapia (GIFT) under mono and mixed cui ture with silver barb (Barbodes gonionotus) in south-west Bangladesh

A participatory on-farm trial was carried out to evaluate the production performance of GIFT (genetically improved farmed tilapia) strain of Oreochmis sp., either alone or with silver barb (Barbodes gonionotus), in six rain-fed freshwater ponds of coastal area. There vvere two treatments; (i) GIFT alone at a stocking density of 24,700/ha (T1) and (ii) 1:1 combination of GIFT and silver barb (T1). Each of the treatments had three replications. A significantly (p

Methods of sensory evaluation of quality and application of statistical methods in sensory evaluation problems with special reference to fishery products

The quality of raw and processed fishery products depend on several factors like physiological conditions at the time of capture, morphological differences, rigor mortis, species, rate of icing and subsequent storage conditions. Sensory evaluation is still the most reliable method for evaluation of the freshness of raw processed fishery products. Sophisticated methods like Intelectron fish tester, cell fragility technique and chemical and bacteriological methods like estimation of trimethylamine, hypoxanthine, carbonyl compounds, volatile acid and total bacterial count have no doubt been developed for accessing the spoilage in fish products.

Dynamic programming solutions for decentralized state-feedback LQG problems with communication delays

This paper presents explicit solutions for a class of decentralized LQG problems in which players communicate their states with delays. A method for decomposing the Bellman equation into a hierarchy of independent subproblems is introduced. Using this decomposition, all of the gains for the optimal controller are computed from the solution of a single algebraic Riccati equation. © 2012 AACC American Automatic Control Council).

Two problems with variational expectation maximisation for time-series models

Variational methods are a key component of the approximate inference and learning toolbox. These methods fill an important middle ground, retaining distributional information about uncertainty in latent variables, unlike maximum a posteriori methods (MAP), and yet generally requiring less computational time than Monte Carlo Markov Chain methods. In particular the variational Expectation Maximisation (vEM) and variational Bayes algorithms, both involving variational optimisation of a free-energy, are widely used in time-series modelling. Here, we investigate the success of vEM in simple probabilistic time-series models. First we consider the inference step of vEM, and show that a consequence of the well-known compactness property of variational inference is a failure to propagate uncertainty in time, thus limiting the usefulness of the retained distributional information. In particular, the uncertainty may appear to be smallest precisely when the approximation is poorest. Second, we consider parameter learning and analytically reveal systematic biases in the parameters found by vEM. Surprisingly, simpler variational approximations (such a mean-field) can lead to less bias than more complicated structured approximations.

New finite-difference scheme for simulations of step-index waveguides with tilt interfaces

A new finite-difference scheme is presented for the second derivative of a semivectorial field in a step-index optical waveguide with tilt interfaces. The present scheme provides an accurate description of the tilt interface of the nonrectangular structure. Comparison with previously presented formulas shows the effectiveness of the present scheme.

Studies on the elimination of NO over the La-Ba-Cu mixed oxide catalysts with perovskite structure

The mixed oxides, including YBa2Cu3O7, LaBa2Cu3O7, LaBaCu2O5, La2BaCu3O7, La4BaCu5O12 with perovskite structure, were prepared. The catalysts were characterized by means of chemical analysis, XRD, TPD and TPR method. It was found that they were the active catalysts for the NO decomposition and NO reduction by CO. The existance of Cu3+ is an important factor to give the catalysts a high activity for the NO reduction by CO.

Studies on the adsorption property of NO on the Ni-based mixed oxide catalysts with Perovskite-like (ABO(3) and A(2)BO(4)) structure

The mixed oxides LaNiO3, La0.1Sr0.9NiO3, La2NiO4 and LaSrNiO4 with perovskite (ABO(3)) and related(A(2)BO(4)) structures were prepared and the adsorption property for NO and the catalytic activity for NO decomposition over these oxidse were also tested. The catalysts were characterized by means of BET surface measurement, chemical analysis, NO-TPD etc.. It was shown that the adsorption amount of NO is correlated with the concentration of oxygen vacancy formed and the adsorption type and strength of NO are related to the valence of metallic ion. Generally there are three kinds of adsorption species, NO-, NO+ and NO on the mixed oxides, among them the negative adsorpion species (NO-) are active for NO decomposition. The weaker the adsorption of oxygen on the catalyst is, the faster the mobility of oxygen is and the easier the redox process takes place in reproducing the active sites in which the oxygen species (O-, O2-) would participate.

Sol-gel derived oxides and mixed oxides catalysts with narrow mesoporous distribution

A novel sol-gel process for preparing oxides and mixed oxides sols from precipitation and peptization process is reported in this article. Inorganic salts are used as raw materials in this study. It is found that the amount of acid has great influence on the stability and particle diameter distribution of the precursor sols. Ultrasonic treatment is used to prepare alumina sol at room temperature. The result of Al-27 NMR shows that there exist Al-13(7+) species in the sol. By controlling the sol particles with narrow particle diameter distribution, alumina, titania and silica-alumina (SA) materials with narrow mesoporous distribution are formed by regular packing of sol particles during gelation without using any templates. The results also show that the structure and particle diameter distribution of precursor sol determine the final materials' texture.

Problems with drawing lines: Theo-geographies of the Catholic parish in Ireland

While people in Catholic parishes in Ireland appear keenly aware of parish boundaries, these understandings are more often oral than cartographic. There is no digital map of all of the Catholic parishes in Ireland. However, the institutional Catholic Church insists that no square kilometre can exist outside of a parish boundary. In this paper, I explain a process whereby the Catholic parishes of Ireland were produced digitally. I will outline some of the technical challenges of digitizing such boundaries. In making these maps, it is not only a question of drawing lines but mapping people’s understanding of their locality. Through an example of one part of the digitisation project, I want to talk about how verifying maps with local people often complicates something which may have at first sight seemed simple. The paper ends on a comparison with how other communities of interest are territorialised in Ireland and elsewhere to draw out some broader theoretical and theological issues of concern.