Finite quotients of the automorphism group of a free group

The automorphism group AutF_n of a free group F_n of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group. This gives rise to an antihomomorphism from AutF_nto a permutation group. We determine this antihomomorphic image of AutF_n when G is the semidirect product Z_p x Z_q     

Vibration of thin pre-twisted helical beams

A helical beam has non-zero curvature and tortuosity. When there is a pre-twist, the Frenet triad is not necessary coincident with the principal triad. When an initially straight rod undergoing a large deformation, it will be curved and twisted during each deformation sequence. The purpose of the paper is to establish the governing equations and the associated natural boundary conditions for a pre-twisted helical beam by variational principles and differential geometry. Although circular helix is taken as example, the formulation is valid for inhomogeneous and non-uniform parameters along the centerline that variable curvature and tortuosity can be treated without difficulties. The method can be used to treat helical anisotropy. If the pre-twist rate of a ring is 0.5, we show a thick Möbius ring for the first time. The solution of the natural vibration problem is through Chebyshev discretization and Clenshaw–Curtis integration by means of the Galerkin formulation.     

Group and individual heterogeneity in a stochastic frontier model: Container terminal operators

Container ports are a major component of international trade and the global supply chain. Hence, the improvement of port efficiency can have a significant impact on the wider maritime economy. This paper deconstructs a representation in the existing literature that neglects the heterogeneity of individual and group-specific terminal operators. In its place, we present a hierarchical model to make a connection between efficiency and terminal operator group characteristics. The paper develops a stochastic frontier model that controls not only individual heterogeneity but also group-specific variations. The model decomposes the total stochastic derivation from the frontier into inefficiency, individual heterogeneity, group-specific variations, and noise components, with the estimation being performed using Markov chain Monte Carlo simulations. The validity of the model is tested with a panel of container terminal operator data from 1997-2004. Our findings show that terminal operator groups are important in promoting terminal efficiency at the global level, and that the operators with stevedore backgrounds show a higher efficiency than carriers.     

Counterexamples to Additivity of Minimum Output p-Rényi Entropy for p Close to 0

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Rényi entropies of channels are not generally additive for p > 1, we demonstrate here by a careful random selection argument that also at p = 0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Rényi entropy is non-additive for all p ≲ 0.11. We conjecture however that violations of additivity exist for all p < 1.     

A generalization of sensitivity of the inventory model with partial backorders

In this paper, we use the elementary techniques of differential calculus to investigate the sensitivity analysis of Montgomery et al.’s [Montgomery, D.C., Bazaraa, M.S., Keswani, A.K., 1973. Inventory models with a mixture of backorders and lost sales. Naval Research Logistics Quarterly 20, 225–263] inventory model with a mixture of backorders and lost sales and generalize Chu and Chung’s [Chu, P., Chung, K.J., 2004. The sensitivity of the inventory model with partial backorders. European Journal of Operational Research 152, 289–295] sensitivity analysis. We provide three numerical examples to demonstrate our findings, and remark the interpretation of the global minimum of the average annual cost at which the complete backordering occurs.     

A Construction of Partial Difference Sets in {\mathbb{Z}}_{p^{2 \times } } {\mathbb{Z}}_{p^{2 \times \cdot \cdot \cdot \times } } {\mathbb{Z}}_{p^2 }

In this paper, we give a construction of partial difference sets in _p ² x _p ² x ... x _p ²using some finite local rings.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe work of this paper was done when the authors visited the University of Hong Kong.     

Game Options Analysis of the Information Role of Call Policies in Convertible Bonds

Abstract

In debt financing, existence of information asymmetry on the firm quality between the firm management and bond investors may lead to significant adverse selection costs. We develop the two-stage sequential dynamic two-person game option models to analyse the market signalling role of the callable feature in convertible bonds. We show that firms with positive private information on earning potential may signal their type to investors via the callable feature in a convertible bond. We present the variational inequalities formulation with respect to various equilibrium strategies in the two-person game option models via characterization of the optimal stopping rules adopted by the bond issuer and bondholders. The bondholders’ belief system on the firm quality may be revealed with the passage of time when the issuer follows his optimal strategy of declaring call or bankruptcy. Under separating equilibrium, the quality status of the firm is revealed so the information asymmetry game becomes a new game under complete information. To analyse pooling equilibrium, the corresponding incentive compatibility constraint is derived. We manage to deduce the sufficient conditions for the existence of signalling equilibrium of our game option model under information asymmetry. We analyse how the callable feature may lower the adverse selection costs in convertible bond financing. We show how a low-quality firm may benefit from information asymmetry and vice versa, underpricing of the value of debt issued by a high-quality firm.     

Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.     

A stochastic programming approach for multi-site aggregate production planning

Production planning problems play a vital role in the supply chain management area, by which decision makers can determine the production loading plan—consisting of the quantity of production and the workforce level at each production plant—to fulfil market demand. This paper addresses the production planning problem with additional constraints, such as production plant preference selection. To deal with the uncertain demand data, a stochastic programming approach is proposed to determine optimal medium-term production loading plans under an uncertain environment. A set of data from a multinational lingerie company in Hong Kong is used to demonstrate the robustness and effectiveness of the proposed model. An analysis of the probability distribution of economic demand assumptions is performed. The impact of unit shortage costs on the total cost is also analysed.