On the Marginal Cost Approach in Maintenance

In this paper we investigate the conditions under which the marginal cost approach of Refs. 1–3 holds. As observed in Ref. 4, the validity of the marginal cost approach gives rise to a useful framework of single-component maintenance optimization models, which covers almost all models used in practice. For the class of unimodal finite-valued marginal cost functions, we show that these optimization models are easy to solve.     

On the Marginal Automorphisms of a Group

Let W be a nonempty subset of a free group. We call an automorphism α of a group G a marginal automorphism if x ^?1α(x) ∈ W*(G) for each x ∈ G, where W*(G) is the marginal subgroup of G. In this article, we give some results on marginal automorphisms of a group.     

On Krull's Separation Lemma

We show that Krull's Separation Lemma for arbitrary rings and a certain lattice-theoretical generalization of it are equivalent to the classical Prime Ideal Theorem for Boolean algebras. As an application, we derive the intersection theorem for Baer radicals from choice principles weaker than the Axiom of Choice. A central tool for our considerations are Scott-openm-filters in quantales.     

具有平稳增量的自相似过程的边缘分布

设Ｘ＝（Ｘ\-t）\-\{t≥0\} 是指数Ｈ（＞０）型的具有平稳增量的自相似过程，该文给出了Ｘ\-１的边缘分布的一些结果。对于Ｈ≠１，log\++Ｘ\-１的压缩函数有一个只依赖于Ｈ的界；对于Ｈ＞０，Ｘ\-１除了一些平凡的情形外是非原子的；而对于Ｈ＞１，Ｘ\-１的尾分布的下界也给出了；文章的最后对Ｘ\-１的支撑的连通性给予了讨论并给出了一些结果。     

On Results' Accuracy at Two‐Dimensional Transonic Wind Tunnel Testing

The principal factors which influence the accuracy of two‐dimensional wind tunnel test results are analyzed. The influences of Reynolds number, Mach number and wall interference with reference to solid and flow blockage (blockage of wake) as well as the influence of side‐wall boundary layer control are analyzed.     

Transonic wind tunnel test sections

Zusammenfassung Um von Windkanalversuchen auf die Verhältnisse beim freien Flug schliessen zu können, müssen die Einflüsse der Kanalwände auf die Geschwindigkeitsverteilung am Modell berücksichtigt werden. Bei schallnaher Strömung sind diese Einflüsse an Modellen üblicher Grösse so stark, dass sie die Messungen vollständig verfälschen.Die hier beschriebenen Methoden beruhen auf der Berechnung von 4 Arten von Interferenzen in einem Punkt des Modells. Von diesen werden auf einfache Art die Interferenzgeschwindigkeiten in den anderen Punkten des Modells abgeleitet.Ausgehend von einer gemittelten Grenzbedingung werden die Interferenzgeschwindigkeiten für teilweise offene Kanalwände berechnet. Durch die Wahl verschiedener Wandkonstruktionen können einzelne Interferenzen eliminiert werden. Die Tabellen 1 und 2 zeigen eine Zusammenstellung der Möglichkeiten für verschiedene Arten von teilweise offenen Kanalwänden.

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This work was sponsored by the Office of Scientific Research of the Air Research and Development Command of the United States Air Force.     

On Separation Index of Heegaard Splittings

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｏｎｃｅｐｔｏｆｒｅｄｕｃｉｂｌｅＨｅｅｇａａｒｄｓｐｌｉｔｉｎｇｓｗａｓｆｉｒｓｔｄｅｖｅｌｏｐｅｄｂｙＨａｋｅｎ［１］．Ｉｔｓｒｅｌａ－ｔｉｏｎｔｏｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇ３－ｍａｎｉｆｏｌｄｓｃｏｎ...     

The Solution of Isentropic Transonic Flow

A general method for analysing mixed subsonic-supersonic flowshas been developed. It has been applied to the case of chokedisentropic flow in a convergent-divergent nozzle and the resultshave been compared with existing series solutions for simplegeometries; very good agreement has been found throughout theflow field. Good agreement has also been found with experimentalresults for the flow in nozzles of more complicated geometry.Some extensions of the method are mentioned such as the inclusionof boundary layer development and the analysis of flows withfree boundaries.     

Marginal Material Stability

Marginal stability plays an important role in nonlinear elasticity because the associated minimally stable states usually delineate failure thresholds. In this paper we study the local (material) aspect of marginal stability. The weak notion of marginal stability at a point, associated with the loss of strong ellipticity, is classical. States that are marginally stable in the strong sense are located at the boundary of the quasi-convexity domain and their characterization is the main goal of this paper. We formulate a set of bounds for such states in terms of solvability conditions for an auxiliary nucleation problem formulated in the whole space and present nontrivial examples where the obtained bounds are tight.     

On a Separation Principle for Nonconvex Sets

In this paper, we relate the nonconvex separation principle (SP) established in Zheng and Ng (Math Program Series A, 104:69–90, 2005) with the known extremal principle (EP), Ekeland variational principle (EVP) and the completeness of the underlying space. In particular, we show that (SP) is equivalent to the completeness in a normed linear space setting. Moreover, as an application, an extension of the strict convex separation theorem is presented for Banach space.     

On Global Optimality Conditions via Separation Functions

The paper examines some axiomatic definitions of separation functions that can be employed fruitfully in the analysis of side-constrained extremum problems. A study of their general properties points out connections with abstract convex analysis and recent generalizations of Lagrangian approaches to duality and exact penalty methods. Many concrete examples are brought out.     

On Dense Subspaces Satisfying Stronger Separation Axioms

We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace. We show that there exists a Tychonoff space without dense normal subspaces and give other examples of spaces without "good" dense subsets.     

Transonic viscous inviscid interactions in narrow channels

Unsteady as well as steady transonic flows through channels which are so narrow that the classical boundary layer approach fails are considered. As a consequence the properties of the inviscid core and the viscosity dominated boundary layer region can no longer be determined in subsequent steps but have to be calculated simultaneously. The resulting interaction problem for laminar flows is formulated for both perfect and dense gases under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes one-dimensional in the leading order approximation. The latter allows an interpretation of the flow in the core region by means of the theory of one-dimensional transonic inviscid flow through a Laval nozzle while preserving the essential features of the interaction problem associated with the internal structure of pseudoshocks. The sensitivity of a separation bubble caused by a pseudoshock of sufficient strength to perturbations under the condition of choked flow will be demonstrated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transonic flow on an axially symmetric torus

On a Riemannian manifold the existence (and uniqueness) of subsonic gas flows with prescribed circulation has been previously established (Acta Math.125 1970, 57–73). If the manifold is a torus of revolution then the gas dynamics equation reduces to a nonlinear ordinary differential equation and the flow can be described explicitly. We show that, as the circulations are increased, one obtains a complete family of solutions: smooth subsonic, smooth transonic, transonic with shocks, and smooth supersonic flows.     

Marginal AMP chain graphs

We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not only subsume AMP chain graphs but also multivariate regression chain graphs. We describe global and pairwise Markov properties for MAMP chain graphs and prove their equivalence for compositional graphoids. We also characterize when two MAMP chain graphs are Markov equivalent.For Gaussian probability distributions, we also show that every MAMP chain graph is Markov equivalent to some directed and acyclic graph with deterministic nodes under marginalization and conditioning on some of its nodes. This is important because it implies that the independence model represented by a MAMP chain graph can be accounted for by some data generating process that is partially observed and has selection bias. Finally, we modify MAMP chain graphs so that they are closed under marginalization for Gaussian probability distributions. This is a desirable feature because it guarantees parsimonious models under marginalization.