Solution of a class of surface water wave scattering problems involving non-reflecting vertical barriers

A large class of scattering problems of surface water waves by vertical barriers lead to mixed boundary value problems for Laplace equation. Specific attentions are paid, in the present article, to highlight an analytical method to handle this class of problems of surface water wave scattering, when the barriers in question are non-reflecting in nature. A new set of boundary conditions is proposed for such non-reflecting barriers and tile resulting boundary value problems are handled in the linearized theory of water waves. Three basic poblems of scattering by vertical barriers are solved. The present new theory of non-reflecting vertical barriers predict new transmission coefficients and tile solutions of tile mathematical problems turn out to be extremely simple and straight forward as compared to the solution for other types of barriers handled previously.

Resolution of Singularities for a Class of Hilbert Modules

Let M be the completion of the polynomial ring C(z) under bar] with respect to some inner product, and for any ideal I subset of C (z) under bar], let I] be the closure of I in M. For a homogeneous ideal I, the joint kernel of the submodule I] subset of M is shown, after imposing some mild conditions on M, to be the linear span of the set of vectors {p(i)(partial derivative/partial derivative(w) over bar (1),...,partial derivative/partial derivative(w) over bar (m)) K-I] (., w)vertical bar(w=0), 1 <= i <= t}, where K-I] is the reproducing kernel for the submodule 2] and p(1),..., p(t) is some minimal ``canonical set of generators'' for the ideal I. The proof includes an algorithm for constructing this canonical set of generators, which is determined uniquely modulo linear relations, for homogeneous ideals. A short proof of the ``Rigidity Theorem'' using the sheaf model for Hilbert modules over polynomial rings is given. We describe, via the monoidal transformation, the construction of a Hermitian holomorphic line bundle for a large class of Hilbert modules of the form I]. We show that the curvature, or even its restriction to the exceptional set, of this line bundle is an invariant for the unitary equivalence class of I]. Several examples are given to illustrate the explicit computation of these invariants.

Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling alpha(s) and other QCD parameters from the hadronic decays of the tau lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ``reference model,'' including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.

Sufficiency of Favard's condition for a class of band-dominated operators on the axis

The purpose of this paper is to show that, for a large class of band-dominated operators on $\ell^\infty(Z,U)$, with $U$ being a complex Banach space, the injectivity of all limit operators of $A$ already implies their invertibility and the uniform boundedness of their inverses. The latter property is known to be equivalent to the invertibility at infinity of $A$, which, on the other hand, is often equivalent to the Fredholmness of $A$. As a consequence, for operators $A$ in the Wiener algebra, we can characterize the essential spectrum of $A$ on $\ell^p(Z,U)$, regardless of $p\in[1,\infty]$, as the union of point spectra of its limit operators considered as acting on $\ell^p(Z,U)$.

Spectral gap for Glauber type dynamics for a special class of potentials

We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on Rd. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carré du champ'' and ``second carré du champ'' for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.

‘Did Ronald McDonald also tend to scare you as a child?’: working to emplace consumption, commodities, and citizen-students in a large classroom setting

So-called ‘radical’ and ‘critical’ pedagogy seems to be everywhere these days on the landscapes of geographical teaching praxis and theory. Part of the remit of radical/critical pedagogy involves a de-centring of the traditional ‘banking’ method of pedagogical praxis. Yet, how do we challenge this ‘banking’ model of knowledge transmission in both a large-class setting and around the topic of commodity geographies where the banking model of information transfer still holds sway? This paper presents a theoretically and pedagogically driven argument, as well as a series of practical teaching ‘techniques’ and tools—mind-mapping and group work—designed to promote ‘deep learning’ and a progressive political potential in a first-year large-scale geography course centred around lectures on the Geographies of Consumption and Material Culture. Here students are not only asked to place themselves within and without the academic materials and other media but are urged to make intimate connections between themselves and their own consumptive acts and the commodity networks in which they are enmeshed. Thus, perhaps pedagogy needs to be emplaced firmly within the realms of research practice rather than as simply the transference of research findings.

An operationally simple sonogashira reaction for an undergraduate organic chemistry laboratory class

An operationally simple, reliable, and cheap Sonogashira reaction suitable for an undergraduate laboratory class that can be completed within a day-long (8 h) laboratory session has been developed. Cross-coupling is carried out between 2-methyl-3-butyn-2-ol and various aryl iodides using catalytic amounts of bis-(triphenylphosphine)palladium(II) dichloride, with copper(I) iodide as a cocatalyst, in triethylamine at room temperature, so a range of products can be prepared within a single group and results compared. The coupling itself is usually complete within 1.5 h and is easily monitored by TLC, leaving up to 6 h for purification and characterization. Purification is by “mini flash column chromatography” through a plug of silica encased in the barrel of a plastic syringe, so the procedure is amenable to large class sizes.

Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a(0) + a(1)x(1) + ... + a(n)x(n) subject to certain constraints to solve the problem of minimizing a rational function of the form (a(0) + a(1)x(1) + ... + a(n)x(n))/(b(0) + b(1)x(1) + ... + b(n)x(n)) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo`s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo`s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an alpha-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an alpha-approximation (1 1/alpha-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.

Losing their marbles : syntax-free programming for assessing problem-solving skills

Novice programmers have difficulty developing an algorithmic solution while simultaneously obeying the syntactic constraints of the target programming language. To see how students fare in algorithmic problem solving when not burdened by syntax, we conducted an experiment in which a large class of beginning programmers were required to write a solution to a computational problem in structured English, as if instructing a child, without reference to program code at all. The students produced an unexpectedly wide range of correct, and attempted, solutions, some of which had not occurred to their teachers. We also found that many common programming errors were evident in the natural language algorithms, including failure to ensure loop termination, hardwiring of solutions, failure to properly initialise the computation, and use of unnecessary temporary variables, suggesting that these mistakes are caused by inexperience at thinking algorithmically, rather than difficulties in expressing solutions as program code.

On the consistency of multiclass classification methods

Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that not all generalizations preserve the nice property of Bayes consistency. We provide a necessary and sufficient condition for consistency which applies to a large class of multiclass classification methods. The approach is illustrated by applying it to some multiclass methods proposed in the literature.

Applying threshold learning theory to teach sustainable business practice in post-graduate engineering education

This paper presents the results of a qualitative action-research inquiry into how a highly diverse cohort of post-graduate students could develop significant capacity in sustainable development within a single unit (course), in this case a compulsory component of four built environment masters programs. The method comprised applying threshold learning theory within the technical discipline of sustainable development, to transform student understanding of sustainable business practice in the built environment. This involved identifying a number of key threshold concepts, which once learned would provide a pathway to having a transformational learning experience. Curriculum was then revised, to focus on stepping through these targeted concepts using a scaffolded, problem-based-learning approach. Challenges included a large class size of 120 students, a majority of international students, and a wide span of disciplinary backgrounds across the spectrum of built environment professionals. Five ‘key’ threshold learning concepts were identified and the renewed curriculum was piloted in Semester 2 of 2011. The paper presents details of the study and findings from a mixed-method evaluation approach through the semester. The outcomes of this study will be used to inform further review of the course in 2012, including further consideration of the threshold concepts. In future, it is anticipated that this case study will inform a framework for rapidly embedding sustainability within curriculum.