The deterministic EOQ with partial backordering: A new approach

Previous authors have shown that if demand that cannot be filled from stock is partially backordered, then using the full-backordering model or assuming that all stockouts will result in lost sales can lead to substantial increases in cost relative to using a model that specifically recognizes the percentage of the stockouts that will be backordered. The models that these authors developed resulted in procedures or equations that are relatively difficult to use. In this paper we take a different approach to modeling the deterministic EOQ with partial backordering that results in equations that are more like the comparable equations for the basic EOQ and its full-backordering extension.     

Possibly v. actually the case: Davidson’s omniscient interpreter at twenty

The publication of Davidson 2001, anthologizing articles from the 1980s and 1990s, encourages reconsidering arguments contained in them. One such argument is Davidson’s omniscient-interpreter argument (‘OIA’) in Davidson 1983. The OIA allegedly establishes that it is necessary that most beliefs are true. Thus the omniscient interpreter, revived in 2001 and now 20 years old, was born to answer the skeptic. In Part I of this paper, I consider charges that the OIA establishes only that it is possible that most beliefs are true; if correct, then it is also possibly the case that most beliefs are false—the skeptic’s very position. Next, I consider two responses on Davidson’s behalf, showing that each fails. In Part II, I show that the OIA establishes neither that it is necessarily merely possibly but actually the case that most beliefs are true. I then conclude that this is enough to answer the skeptic.     

Ten Myths of Science: Reexamining What We Think We Know About the Nature of Science

This article addresses and attempts to refute several of the most widespread and enduring misconceptions held by students regarding the enterprise of science. The ten myths discussed include the common notions that theories become laws, that hypotheses are best characterized as educated guesses, and that there is a commonly-applied scientific method. In addition, the article includes discussion of other incorrect ideas such as the view that evidence leads to sure knowledge, that science and its methods provide absolute proof, and that science is not a creative endeavor. Finally, the myths that scientists are objective, that experiments are the sole route to scientific knowledge and that scientific conclusions are continually reviewed conclude this presentation. The paper ends with a plea that instruction in and opportunities to experience the nature of science are vital in preservice and inservice teacher education programs to help unseat the myths of science.     

Homological properties of generic matrix rings

It is shown that the ring of two 2×2 generic matrices over a field has infinite global dimension. It is also proved that there is a non-free projective module over that ring. Finally, the authors show that the trace ring of that generic matrix ring is an iterated Ore extension from which it follows that the trace ring has global dimension five and that the finitely-generated projective modules are stably free.     

Optimal cutting directions and rectangle orientation algorithm

The first stage in hierarchical approaches to Floorplan Design defines topological relations between components that intend to optimize a given objective in a circuit board. These relations determine a placement that is subsequently optimized in order to minimize a cost measurement (that will probably be one between chip area or perimeter). The board optimization gives rise to multiple subproblems that need to be answered in order to obtain a good solution. Among the most relevant ones we find the problem of defining the optimal orientation of cells and the definition of the optimal cutting sequence that minimize the placement board area. We will present a generalization of an algorithm due to Stockmeyer so that it obtains a solution that not only defines the optimal cell orientation but also the slicing cuts sequence that will lead to this optimal orientation and overall area minimization.     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

THE POSSIBILITY OF CONTINUOUS GROWTH WITH EXHAUSTIBLE RESOURCES: UNKNOWINGLY AN AGREEMENT HAS BEEN REACHED,BUT IT MAY NOT BE CORRECT

ABSTRACT. It is the size of the elasticity of substitution that has been the central issue in the long debate over the possibility of continuous growth in the presence of exhaustible resources. This paper reviews the debate and comes to the surprising conclusion that, unnoticed by pessimists, the optimist position has gradually evolved so that it now approximates that of the pessimists. The paper also summarizes some preliminary work by the author that indicates that this common position may not be correct.     

Relational properties, causal powers and psychological laws

This paper argues that Twin Earth twins belong to the same psychological natural kind, but that the reason for this is not that the causal powers of mental states supervene on local neural structure. Fodor’s argument for this latter thesis is criticized and found to rest on a confusion between it and the claim that Putnamian and Burgean type relational psychological properties do not affect the causal powers of the mental states that have them. While it is true that Putnamian and Burgean type relational psychological properties do not affect causal powers, it is false that no relational psychological properties do. Examples of relational psychological properties that do affect causal powers are given and psychological laws are sketched that subsume twins in virtue of them instantiating these relational properties rather than them sharing the narrow contents of their thoughts.     

Generalized Lorenz models and their routes to chaos. II. Energy-conserving horizontal mode truncations

All attempts to generalize the three-dimensional Lorenz model by selecting higher-order Fourier modes can be divided into three categories, namely: vertical, horizontal and vertical–horizontal mode truncations. The previous study showed that the first method allowed only construction of a nine-dimensional system when the selected modes were energy-conserving. The results presented in this paper demonstrate that a five-dimensional model is the lowest-order generalized Lorenz model that can be constructed by the second method and that its route to chaos is the same as that observed in the original Lorenz model. It is shown that the onset of chaos in both systems is determined by a number of modes that describe the vertical temperature difference in a convection roll. In addition, a simple rule that allows selecting modes that conserve energy for each method is derived.     

Implications of the constant rank constraint qualification

This paper investigates properties of a parametric set defined by finitely many equality and inequality constraints under the constant rank constraint qualification (CRCQ). We show, under the CRCQ, that the indicator function of this set is prox-regular with compatible parametrization, that the set-valued map that assigns each parameter to the set defined by that parameter satisfies a continuity property similar to the Aubin property, and that the Euclidean projector onto this set is a piecewise smooth function. We also show in the absence of parameters that the CRCQ implies the Mangasarian-Fromovitz constraint qualification to hold in some alternative expression of the set.     

Behaviorism and belief

The examination of now-abandoned behaviorist analysis of the concept of belief can bring to light defects in perspectives such as functionalism and physicalism that are still considered viable. Most theories have in common that they identify the holding of the belief that p by a subject S with some matter of fact in or about S that is distinct from and independent of p. In the case of behaviorism it is easy to show that this feature of the theory generates incoherence in the first-person point of view since it gives footing to the possibility that S could correctly assert “I believe that p,” (that is, “I have the complex disposition the behaviorist theory identifies with holding the belief that p”) and at the same time deny that p is the case. Parallel incoherence can be developed in the context of other philosophically popular accounts of the nature of belief.     

On the central charge of a factorizable Hopf algebra

For a semisimple factorizable Hopf algebra over a field of characteristic zero, we show that the value that an integral takes on the inverse Drinfel’d element differs from the value that it takes on the Drinfel’d element itself by at most a fourth root of unity. This can be reformulated by saying that the central charge of the Hopf algebra is an integer. If the dimension of the Hopf algebra is odd, we show that these two values differ by at most a sign, which can be reformulated by saying that the central charge is even. We give a precise condition on the dimension that determines whether the plus sign or the minus sign occurs. To formulate our results, we use the language of modular data.     

The Gergonne and Nagel centers of an n-dimensional simplex

In contrast with the analogous situation for a triangle, the cevians that join the vertices of a tetrahedron to the points where the faces touch the insphere (or the exspheres) are not concurrent in general. This observation led the present author and P. Walker in [4] to devise alternative definitions of the Gergonne and Nagel centers of a tetrahedron that do not assume the concurrence of such cevians and that coincide with the ordinary definitions in the case of a triangle. They then proved that the Gergonne center exists and is unique for all tetrahedra and that the Nagel center, though unique, exists only for tetrahedra that satisfy certain conditions. In this article, we extend these definitions to simplices of any dimension. By keeping the requirement that the Gergonne center be interior and relaxing such a condition for the Nagel center, we prove that both centers exist and are unique for all simplices, thus polishing the definitions and generalizing the results of the above-mentioned article.     

On evaluating the performance of GSS: Furthering the debate

Following criticism from proponents of workstation group support systems about the lack of validity of ‘wide-band’ group support systems (GSS), a recent article argued that it was inappropriate to attempt to establish the level of experimental validity for such GSS that is demanded by researchers working with 'narrow-band' GSS. It was argued that ‘wide-band’ and workstation GSS are very different and this means that it is unlikely that the same measures of success would be appropriate. This paper agrees with this view but not with its extension, that the overall validation requirement is different; theoretical validity is a necessary feature of a full evaluation but it is not sufficient by itself - experimental validity must also be sought. This paper argues against the view that since experimental validity cannot be obtained, theoretical validity will suffice. A twin-track research approach involving theoretical and experimental validity is proposed that can unite researchers investigating (almost) all forms of GSS, modelled on the PIMS programme and supported by one of the research frameworks that already exist.     

Ring graphs and complete intersection toric ideals

We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideals are minimally generated by Gröbner bases. We prove that any graph can be oriented such that its toric ideal is a complete intersection with a universal Gröbner basis determined by the cycles. It turns out that bipartite ring graphs are exactly the bipartite graphs that have complete intersection toric ideals for any orientation.     

The role of framing in productive classroom discussions: A case for teacher learning

In this paper, we contrast two mathematical arguments that occurred during an algebra lesson to illustrate the importance of relevant framings in the ensuing arguments. The lesson is taken from a graduate course for elementary teachers who are enrolled in a mathematics specialist program. We use constructs associated with enthnography of argumentation to characterize the framings for warrants and backings that supported the ensuing arguments. Our findings suggest that teachers fully participated in argumentations that were framed by problem situations that were familiar to them, ones that were couched in elementary, fundamental mathematical ideas, and that these types of argumentations were arguably more productive in terms of opportunities for learning.     

Some arguments against intentionalism

Recently, many have argued that phenomenal content supervenes on representational content; i.e. that the phenomenal character of an experience is wholly determined (metaphysically, not causally) by the representational content of that experience. This paper it identifies many counter-examples to intentionalism. Further, this paper shows that, if intentionalism were correct, that would require that an untenable form of representational atomism also be correct. Our argument works both against the idea that phenomenal content supervenes on “conceptual” content and also against the idea that it supervenes on “non-conceptual” content. It is also shown that the distinction between conceptual and non-conceptual content has been wrongly conceived as distinction between different kinds of information: in fact, it is a distinction between ways of packaging information that is, in itself, neither conceptual or non-conceptual.     

Lower bound on size of branch-and-bound trees for solving lot-sizing problem

We show that there exists a family of instances of the lot-sizing problem, such that any branch-and-bound tree that solves them requires an exponential number of nodes, even in the case when the branchings are performed on general split disjunctions. This result is of interest since there exists dynamic programming algorithm that solves lot-sizing in polynomial-time. To the best of our knowledge, this is the first study that shows that dynamic programming can be exponentially faster than branch-and-bound.     

Sturmian substitutions on two letters, cutting paths and their projections

We study the structure of projections of finite cutting paths that correspond to a Sturmian substitution with incidence matrix that has determinant 1. We show that such projections can be seen as two-letter words, and that there exists another Sturmian substitution that generates these words.     

On the existence of a specified cycle in digraphs with constraints on degrees

We prove that Woodall's and Ghouila-Houri's conditions on degrees which ensure that a digraph is Hamiltonian, also ensure that it contains the analog of a directed Hamiltonian cycle but with one edge pointing the wrong way; that is, it contains two vertices that are connected in the same direction by both an edge and a Hamiltonian path.