CERES in higher-order logic

We define a generalization of the first-order cut-elimination method CERES to higher-order logic. At the core of lies the computation of an (unsatisfiable) set of sequents (the characteristic sequent set) from a proof π of a sequent S. A refutation of in a higher-order resolution calculus can be used to transform cut-free parts of π (the proof projections) into a cut-free proof of S. An example illustrates the method and shows that can produce meaningful cut-free proofs in mathematics that traditional cut-elimination methods cannot reach.     

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j Symbols, and Character Localization

In this paper, we employ a technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index J) of generic Wigner matrix elements D^J_MM￠(g){D^{J}_{MM'}(g)} . We use this result to derive asymptotic formulae for the character χ ^J (g) of an SU(2) group element and for Wigner’s 3j symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for χ ^J (g) is in fact exact. The result hints at a “Duistermaat-Heckman like” localization property for discrete sums.     

Valuations and closure operators on finite lattices

Let L be a lattice. A function f:L→R (usually called evaluation) is submodular if f(x∧y)+f(x∨y)≤f(x)+f(y), supermodular if f(x∧y)+f(x∨y)≥f(x)+f(y), and modular if it is both submodular and supermodular. Modular functions on a finite lattice form a finite dimensional vector space. For finite distributive lattices, we compute this (modular) dimension. This turns out to be another characterization of distributivity (Theorem 3.9). We also present a correspondence between isotone submodular evaluations and closure operators on finite lattices (Theorem 5.5). This interplay between closure operators and evaluations should be understood as building a bridge between qualitative and quantitative data analysis.     

Continuous Blooming of Convex Polyhedra

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.     

Supporting offshoring and nearshoring decisions for mass customization manufacturing processes

Offshore countries attract companies for a possible relocation of production processes through extremely low worker wages. Particularly, mass production processes seem to be highly appropriate for a relocation. However, while the impact of wage reductions can be directly estimated, an appropriate determination of additional cost consequences proves to be a complex task. For instance, on account of lower education standards and higher fluctuation rates, the average worker skills in offshore countries are often significantly lower than in high-wage countries like the United States. In order to appropriately analyze and evaluate the resulting tradeoff between wages and worker skills for mass customization manufacturing systems, this paper introduces a new approach that comprises a detailed mixed-model assembly line balancing. This approach provides a direct comparison of the estimated variable manufacturing costs by generating a country-dependent line layout for all competing locations. In order to validate the efficiency of the balancing approach and, in particular, derive general implications for management, several test series with various country configurations were executed. First, by attaining improvement rates of up to 40%, the capability of a generated Tabu Search procedure for finding appropriate line layouts was proven. Second, as the main result, the complexity of the variant program was identified as a crucial factor for offshoring decisions since it substantially affects variable manufacturing costs. This was particularly proven for countries with low worker skills, which attract offshoring/nearshoring through exceptionally low labor costs. Hence, companies that consider outsourcing production systems to those countries are strongly hold to examine these decisive effects thoroughly. Regarding this, offshoring becomes very promising for manufacturing processes characterized by a moderate variant complexity level.     

A comparison of multiple criteria analysis techniques for water resource management

Multiple criteria analysis (MCA) is a framework for evaluating decision options against multiple criteria. Numerous techniques for solving an MCA problem are available. This paper applies MCA to six water management decision problems. The MCA methods tested include weighted summation, range of value, PROMTHEE II, Evamix and compromise programming. We show that different MCA methods were in strong agreement with high correlations amongst rankings. In the few cases where strong disagreement between MCA methods did occur it was due to presence of mixed ordinal-cardinal data in the evaluation matrix. The results suggest that whilst selection of the MCA technique is important more emphasis is needed on the initial structuring of the decision problem, which involves choosing criteria and decision options.     

Radial equivalence for the two basic nonlinear degenerate diffusion equations

In this paper we prove that there exists an explicit correspondence between the radially symmetric solutions of two well-known models of nonlinear diffusion, the porous medium equation and the p-Laplacian equation. We establish exact correspondence formulas between these solutions. We also study in detail the application of the results in the important case of self-similar solutions. In particular, we derive the existence of new self-similar solutions for the evolution p-Laplacian equation.     

Telescoping, rational-valued series, and zeta functions

We give an effective procedure for determining whether or not a series telescopes when is a rational function with complex coefficients. We give new examples of series , where is a rational function with integer coefficients, that add up to a rational number. Generalizations of the Euler phi function and the Riemann zeta function are involved. We give an effective procedure for determining which numbers of the form are rational. This procedure is conditional on 3 conjectures, which are shown to be equivalent to conjectures involving the linear independence over the rationals of certain sets of real numbers. For example, one of the conjectures is shown to be equivalent to the well-known conjecture that the set is linearly independent, where is the Riemann zeta function.

Some series of the form , where is a quotient of symmetric polynomials, are shown to be telescoping, as is . Quantum versions of these examples are also given.

     

Analyzing the sustainability of harvesting behavior and the relationship to personality traits in a simulated Lotka–Volterra biotope

For the analysis presented in this paper we use experiments to study human behavior in a simulation environment based on a simple Lotka–Volterra predator–prey ecology. The aim is to study the influence of different harvesting strategies and of certain personality traits derived from the Hamburg Personality Inventory (HPI) [Andresen, B., 2002. HPI – Hamburger Persönlichkeitsinventar. Hogrefe, Göttingen] on the outcome in terms of sustainability and economic performance.     

The impact of dynamic pricing on the economic order decision

This paper analyzes the impact of dynamic pricing on the single product economic order decision of a monopolist retailer. Items are procured from an external supplier according to the economic order quantity (EOQ) model and are sold to customers on a single market without competition following the simple monopolist pricing problem. Coordinated decision making of optimal pricing and ordering is influenced by operating costs – including ordering and inventory holding costs – and the demand rate obtained from a price response function. The retailer is allowed to vary the selling price, either in a fixed number of discrete points in time or continuously. While constant and continuous pricing have received much attention in the literature, problems with a limited number of price changes are rather rare. This paper illustrates the benefit of dynamically changing prices to achieve operational efficiency in the EOQ model, that is to trigger high demand rates when inventories are high. We provide structural properties of the optimal time instants when the price should be changed. Taking into account costs for changes in price, it provides numerical guidance on number, timing, and size of price changes during an order cycle. Numerical examples show that the benefits of dynamic pricing in an EOQ framework can be achieved with only a few price changes and that products being unprofitable under static pricing may become profitable under dynamic pricing.