Large classes

The Authors study the ideal I(U) formed by the polynomial relations satisfied by an endomorphism u of a module M that has a finite free resolution. When M is torsion free, the ideal I(U) is characterized in terms of the characteristic polynomial X(U, X) of u. This result gives a natural generalization of McCoy's theorem. The ideal I(U) is also related to the invariant factors of u. It is proved that in a large class of rings the ideal I(u) is principally generated by the last proper invariant factor of u. One obtains, for these cases, complete similarity with the classical case of fields.

Playing the martingale strategy is an anomaly, reverse to that observed in the St. Petersburg paradox. This paper rationalizes the demonstrated irrationality of playing, by characterizing necessary and sufficient conditions under which a utility maximizing decision maker would play the strategy. An individual willing to play the martingale may not be deterred by a finite cap on wagers. Individuals will continue with the strategy in the face of mounting consecutive losses which is, thus, sequentially rational. These results give insight into instances of escalating commitment to a losing cause, by analyzing one specific instance of such behavior.

Most algorithms of computational geometry are designed for the Real-RAM and non-degenerate inputs. We call such algorithms idealistic. Executing an idealistic algorithm with floating point arithmetic may fail. Controlled perturbation replaces an input x by a random nearby x in the δ-neighborhood of x and then runs the floating point version of the idealistic algorithm on x. The hope is that this will produce the correct result for x with constant probability provided that δ is small and the precision L of the floating point system is large enough. We turn this hope into a theorem for a large class of geometric algorithms and describe a general methodology for deriving a relation between δ and L. We exemplify the usefulness of the methodology by examples.

This paper addresses the deadlock avoidance problems in manufacturing systems with sequence and route flexibility. It is shown that for a large class of such systems, through one-step look ahead, an optimal deadlock avoidance policy can be obtained. For a general system the authors present a system reduction method by which the system is reduced and the reduced system has an optimal deadlock avoidance policy. Using this optimal control policy and restricting the allocation of resources with capacity one, a sub-optimal deadlock avoidance policy for the system is obtained. The proposed policies are with polynomial computation complexity.

This paper addresses the deadlock avoidance problems in manufacturing systems with sequence and route flexibility. It is shown that for a large class of such systems, through one-step look ahead, an optimal deadlock avoidance policy can be obtained. For a general system the authors present a system reduction method by which the system is reduced and the reduced system has an optimal deadlock avoidance policy. Using this optimal control policy and restricting the allocation of resources with capacity one, a sub-optimal deadlock avoidance policy for the system is obtained. The proposed policies are with polynomial computation complexity.

We provide some additional evidence in favour of the strong-weak coupling duality between the SO(32) heterotic and type I superstring theories by comparing terms quartic in the gauge field strength in their low-energy effective actions. We argue that these terms should not receive higher-loop string corrections so that duality should relate the leadingorder perturbative coefficients in the two theories. In particular, we demonstrate that the coefficient of the F 4-term in the one-loop (torus) part of the SO(32) heterotic string action is exactly the same as the coefficient of the F 4-term in the tree-level (disc) part of the type I action.

Let G be an abelian group and let λ be the smallest rank of any group whose direct sum with a free group is isomorphic to G. If λ is uncountable, then G has λ pairwise disjoint, non-free subgroups. There is an example where λ is countably infinite and G does not have even two disjoint, non-free subgroups.

This paper compares mathematics assessment between Australian and Chinese primary schools to investigate assessment factors accounting for the mathematics achievement. The paper shows that there are considerable differences in assessment practice, but also many similarities in assessment policy. It found a gap existed between the assessment policy and practice in both Australian and Chinese primary schools, partly because teachers are not given training in mathematics assessment. To bridge this gap between intended and implemented assessment, it argued that explicit professional training in mathematics assessment is essential for both pre-service and inservice teachers in both countries.

In the focus of our attention is the asymptotic properties of the sequence of convex hulls which arise as a result of a peeling procedure applied to the convex hull generated by a Poisson point process. Processes of the considered type are tightly connected with empirical point processes and stable random vectors. Results are given about the limit shape of the convex hulls in the case of a discrete spectral measure. We give some numerical experiments to illustrate the peeling procedure for a larger class of Poisson point processes.

The use of relations, represented as tables, for documenting the requirements and behaviour of software is motivated and explained. A formal model of tabular expressions, defining the meaning of a large class of tabular forms, is presented. Finally, we discuss the transformation of tabular expressions from one form to another, and illustrate some useful transformations. February 13, 1996 1:25 pm 2/15 brink included in the specified relation, it is complete. No additional information should be included. Below we give two examples of such document definitions, one for a system requirements document, the other for a program specification. 1.1 The System Requirements Document The first step in documenting the requirements of a computer system is the identification of the environmental quantities to be measured or controlled and the association of those quantities with mathematical variables. The environmental quantities include: physical properties (such as temperatures and pressures), the readings on user-visible displays, etc. The association of these quantities with mathematical variables must be carefully defined, and coordinate systems, signs etc. must be unambiguously stated. It is useful to characterise each environmental quantity as monitored, controlled, or both. Monitored quantities are those that the user wants the system to measure. Controlled quantities are those whose values the system is intended to control. For real-time systems, time can be treated as a monitored quantity. We will use m 1 , m 2 , …, m p to denote the monitored quantities, and c 1 , c 2 , …, c q to denote the controlled ones.

Small subgraph counts can be used as summary statistics for large random graphs. We use the Stein-Chen method to derive Poisson approximations for the distribution of the number of subgraphs in the stochastic block model which are isomorphic to some fixed graph. We also obtain Poisson approximations for subgraph counts in a graphontype generalisation of the model in which the edge probabilities are (possibly dependent) random variables supported on a subset of [0, 1]. Our results apply when the fixed graph is a member of the class of strictly balanced graphs.

Delegating pricing decisions to the salesforce has been a salient issue for marketing academics and practitioners. We examine this issue in a competitive market using standard agency theory with symmetric and asymmetric information. Under symmetric information we find that the optimal contracts have a nice property that allows managers to reach the upper bound on firms’ profit by using either centralized or delegated pricing, and hence there are no incentive-based reasons to prefer centralized versus delegated contract types. Thus, managers can focus on the design of the optimal incentive scheme without worrying about the contract type. Under asymmetric information we find that there always exists an equilibrium where all firms use centralized pricing that is either unique or payoff equivalent to equilibria that have a combination of contract types. These results are robust to a large class of agent and market parameters. However, if restrictions are exogenously imposed on contract ...

We consider the Weil-Petersson gradient vector field of renormalized volume on the deformation space of convex cocompact hyperbolic structures on (relatively) acylindrical manifolds. In this paper we prove the conjecture that the flow has a global attracting fixed point at the structure M geod the unique structure with minimum convex core volume.

The present project uses cooperative learning strategies that requires students in large classes to collaborate in applying intellectually challenging articles on place, space, sacred spaces, tourist places, and commodification of place to the development of a video project linking music to place and landscape. As an extension of their group activity, students are teaching each other how to apply concepts from the assigned articles to their projects in creative ways while engaging in critical thinking and exercising their geographical imagination.

We report the femtosecond transient absorption spectra of the CHJ photoproduct of the methylene iodide (CH&) photodissociation. The results indicate a disappearance of this photofragment on a z 350 fs time scale in several different solvents. The implication is that in these simple liquids, methylene iodide is undergoing geminate recombination. Recombination yields, but not rates are shown to be solvent dependent. Comparison to the photodissociation dynamics of other small molecules suggests that the kinetics of geminate recombination are dominated by a single collision with the surrounding solvent cage in a large class of molecules and that the process may be universal.

We report the femtosecond transient absorption spectra of the CHJ photoproduct of the methylene iodide (CH&) photodissociation. The results indicate a disappearance of this photofragment on a z 350 fs time scale in several different solvents. The implication is that in these simple liquids, methylene iodide is undergoing geminate recombination. Recombination yields, but not rates are shown to be solvent dependent. Comparison to the photodissociation dynamics of other small molecules suggests that the kinetics of geminate recombination are dominated by a single collision with the surrounding solvent cage in a large class of molecules and that the process may be universal.

We study the monotonicity of the equilibrium bid with respect to the number of bidders n in aliated private value models of first-price sealed-bid auctions and prove the existence of a large class of such models in which the equilibrium bid function is not increasing in n. We moreover decompose the eect of a change in n on the bid level into a competition eect and an aliation eect . The latter suggests to the winner of the auction that competition is less intense than she had thought before the auction. Since the aliation eect can occur in both private and common value models, a negative relationship between the bid level and n does not allow one to distinguish between the two models and is also not necessarily (only) due to bidders taking account of the winner's curse.

This paper is largely based on the experience of teaching law to students with non-legal background in business schools, with a focus on internationalisation and the large class lecture format. Business schools often consist of large classes which include a significant proportion of Culturally and Linguistically Diverse (CaLD) students. Teaching a difficult and demanding subject to a large cohort of students from increasingly diverse backgrounds can be an onerous task. The existence of these conditions present different teaching challenges and requires a re-examination of teachers’ approaches to student learning. In this article, the experience of teaching law in business schools is approached through an examination of the challenges and problems arising from (a) teaching law to non-law students (b) teaching CaLD students (c) teaching large classes. At each stage, the writers explore effective solutions and strategies to deal with these issues.

Abstract. Dictionary base methods have the advantage that they can be applied to texts written in different languages if there exist an electronically dictionary for that specific language. As a consequence, these kinds of methods can be used to identify the part of ...

Using primary literature is an effective tool for promoting active learning and critical thinking in science classes. However, it can be challenging to use primary literature in large classes and in classes for nonscience majors. We describe the development and implementation of an online tutorial for helping nonscience majors learn to read primary literature in biology. The tutorial includes content about the scientific process and the structure of scientific papers and provides opportunities for students to practice reading primary literature. We describe the use of the tutorial in Biology of Exercise, a course for nonscience majors. Students used the tutorial outside of class to learn the basic principles involved in reading scientific papers, enabling class sessions to focus on active-learning activities and substantive class discussions.

The application of geometrical schemes, similar to geodesic domes, to large spherical antenna reflectors was investigated. The shape and size of flat segmented latticed surfaces which approximate general shells of revolution, and in particular spherical and paraboloidal reflective surfaces, were determined. The extensive mathematical and computational geometric analyses of the reflector resulted in the development of a general purpose computer program capable of generating the complete design parameters of the dish. The program also includes a graphical self contained subroutine for graphic display of the required design.

We use the canonical quantization of spherically symmetric dust universes, and calculate the expectation values of the quantized metric, < Ψ|ĝ µν |Ψ >. Though the classical solutions are singular, and the wave functions have no zero support on singular geometries, the expectation value (for a general quantum state) is everywhere regular. For a quasi-classical (coherent) state, |α >, the expectation value, < α|ĝ|α > describes a universe (or star) that collapses to a minimum radius, the Planck radius, and re-expands again.

We use the canonical quantization of spherically symmetric dust universes, and calculate the expectation values of the quantized metric, < Ψ|ĝ µν |Ψ >. Though the classical solutions are singular, and the wave functions have no zero support on singular geometries, the expectation value (for a general quantum state) is everywhere regular. For a quasi-classical (coherent) state, |α >, the expectation value, < α|ĝ|α > describes a universe (or star) that collapses to a minimum radius, the Planck radius, and re-expands again.

We establish sufficient conditions for the hyperbolicity of the billiard dynamics on surfaces of constant curvature. This extends known results for planar billiards. Using these conditions, we construct large classes of billiard tables with positive Lyapunov exponents on the sphere and on the hyperbolic plane.

In this paper, we introduce Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine elements from Gabor and wavelet frames in their construction. As a consequence, they can be implemented with standard filters from wavelet theory in combination with standard Gabor windows. Unlike the usual shearlets, the new construction can achieve a redundancy as close to one as desired. Our construction follows the general strategy for shearlets. First we define group-based Gabor shearlets and then modify them to a cone-adapted version. In combination with Meyer filters, the cone-adapted Gabor shearlets constitute a tight frame and provide low-redundancy sparse approximations of the common model class of anisotropic features which are cartoon-like functions.

Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few construction strategies for discrete shearlet systems are known so far. In this paper, we take a geometric approach to this problem. Utilizing the close connection with group representations, we first introduce and analyze an upper and lower weighted shearlet density based on the shearlet group. We then apply this geometric measure to provide necessary conditions on the geometry of the sets of parameters for the associated shearlet systems to form a frame for L 2 (R 2), either when using all possible generators or a large class exhibiting some decay conditions. While introducing such a feasible class of shearlet generators, we analyze approximation properties of the associated shearlet systems, which themselves lead to interesting insights into homogeneous approximation abilities of shearlet frames. We also present examples, such a oversampled shearlet systems and coshearlet systems, to illustrate the usefulness of our geometric approach to the construction of shearlet frames.

We give a simple proof of the fact that for a large class of quasilinear elliptic equations and systems the solutions that minimize the corresponding energy in the set of all solutions are radially symmetric. We require just continuous nonlinearities and no cooperative conditions for systems. Thus, in particular, our results cannot be obtained by using the moving planes method. In the case of scalar equations, we also prove that any least energy solution has a constant sign and is monotone with respect to the radial variable. Our proofs rely on results in [14, 6] and answer questions from [3, 11].