On the minimum and maximum selective graph coloring problems in some graph classes

Given a graph together with a partition of its vertex set, the minimum selective coloring problem consists of selecting one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is minimum. The contribution of this paper is twofold. First, we investigate the complexity status of the minimum selective coloring problem in some specific graph classes motivated by some models described in Demange et al. (2015). Second, we introduce a new problem that corresponds to the worst situation in the minimum selective coloring; the maximum selective coloring problem aims to select one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is maximum. We motivat

Le gisement tungstifère de Leucamp (Cantal, France) : contrôle géologiques et minéralisations

Le gisement de Leucamp (district de la Châtaigneraie : Cantal, France) est constitué de filons de quartz à wolframite associés spatialement à un granite carbonifère et encaissés dans des schistes épimétamorphiques d'âge inconnu. La structure complexe du champ filonien peut s'expliquer par la réouverture et le remplissage simultanés, sans doute sous l'action des fluides, de toutes les structures planaires crées par la tectonique souple polyphasée antérieure à la mise en place du granite. Les filons sont ultérieurement hachés par des failles normales, elles-même scellées par différentes venues éruptives. Le remplissage des filons minéralisés peut être décomposé en une venue à tourmaline suivie, après fracturation, par une venue de quartz; après une nouvelle fracturation, le remplissage se termine par la minéralisation principale (pyrite et wolframite associées à des minéraux mineurs de Bi, As, Zn et Au). La minéralisation princale est remaniée dans les veines tardive

Improved Seals for High Temperature Airframe Applications

Current thermal barrier seals, such as those used on the Space Shuttle, are insufficient to fully meet the demands of future hypersonic vehicles and reentry spacecraft. Previous investigations have demonstrated limited usage temperatures, as evidenced by a decreased ability to maintain sealing effectiveness at high temperatures (i.e., inadequate resiliency). In order to improve resiliency at elevated temperatures, Rene 41 (Allvac) was substituted for Inconel X-750 (Special Metals Corp.) as the spring tube material in the existing seal design. A seal construction incorporating the Rene 41 spring tube was fabricated and tested against the baseline Inconel X-750 spring tube seal. Although resiliency improvements were not as dramatic as in previous tests with the spring tubes alone, seals incorporating the Rene 41 spring tube exhibited an average 20 percent resiliency enhancement up to 1750 F when compared to seals containing the Inconel spring tube. In addition, the seals with the Rene 41 spring tubes showed less reduction in resiliency as temperatures increased above 1200 F. Results also indicated the Saffil (Saffil Ltd.) insulation in the core of the seal contributed more to resiliency than previously thought. Leakage data did not demonstrate an improvement with the seal containing the Rene 41 spring tube. However, based upon resiliency results, one could reasonably expect the Rene 41 version of the seal to track gap openings over a wider range. Therefore it would exhibit lower leakage than the Inconel X-750 version as the seal gap opens during a typical mission

Performance Evaluations of Ceramic Wafer Seals

Future hypersonic vehicles will require high temperature, dynamic seals in advanced ramjet/scramjet engines and on the vehicle airframe to seal the perimeters of movable panels, flaps, and doors. Seal temperatures in these locations can exceed 2000 F, especially when the seals are in contact with hot ceramic matrix composite sealing surfaces. NASA Glenn Research Center is developing advanced ceramic wafer seals to meet the needs of these applications. High temperature scrub tests performed between silicon nitride wafers and carbon-silicon carbide rub surfaces revealed high friction forces and evidence of material transfer from the rub surfaces to the wafer seals. Stickage between adjacent wafers was also observed after testing. Several design changes to the wafer seals were evaluated as possible solutions to these concerns. Wafers with recessed sides were evaluated as a potential means of reducing friction between adjacent wafers. Alternative wafer materials are also being considered as a means of reducing friction between the seals and their sealing surfaces and because the baseline silicon nitride wafer material (AS800) is no longer commercially available

Biorthogonal quantum mechanics

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems. © 2014 IOP Publishing Ltd

Coreness of Cooperative Games with Truncated Submodular Profit Functions

Coreness represents solution concepts related to core in cooperative games, which captures the stability of players. Motivated by the scale effect in social networks, economics and other scenario, we study the coreness of cooperative game with truncated submodular profit functions. Specifically, the profit function $f(\cdot)$ is defined by a truncation of a submodular function $\sigma(\cdot)$: $f(\cdot)=\sigma(\cdot)$ if $\sigma(\cdot)\geq\eta$ and $f(\cdot)=0$ otherwise, where $\eta$ is a given threshold. In this paper, we study the core and three core-related concepts of truncated submodular profit cooperative game. We first prove that whether core is empty can be decided in polynomial time and an allocation in core also can be found in polynomial time when core is not empty. When core is empty, we show hardness results and approximation algorithms for computing other core-related concepts including relative least-core value, absolute least-core value and least average dissatisfaction value

Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences

Advanced Ceramic Wafer Seals Demonstrated at 2000 deg. F

Durable, high-temperature sliding seals are required in advanced hypersonic engines and around movable control surfaces on future vehicles. These seals must operate at temperatures of 2000 to 2500 F, limit hot gas flow, remain resilient for multiple cycles, and resist scrubbing damage against rough surfaces. Current seal designs do not meet these demanding requirements, so the NASA Glenn Research Center is developing advanced seals and preload devices to overcome these shortfalls. An advanced ceramic wafer seal design and two silicon nitride compression spring designs were evaluated in a series of compression, scrub, and flow tests

Matching structure and bargaining outcomes in buyer–seller networks

We examine the relationship between the matching structure of a bipartite (buyer-seller) network and the (expected) shares of the unit surplus that each connected pair in this network can create. We show that in different bargaining environments, these shares are closely related to the Gallai-Edmonds Structure Theorem. This theorem characterizes the structure of maximum matchings in an undirected graph. We show that the relationship between the (expected) shares and the tructure Theorem is not an artefact of a particular bargaining mechanism or trade centralization. However, this relationship does not necessarily generalize to non-bipartite networks or to networks with heterogeneous link values

Quantum catastrophes: a case study

The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it ad hoc} choice of the inner product in the physical Hilbert space of quantum bound states (i.e., via an {\it ad hoc} construction of the so called metric). The name of quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e., to the scenario in which we leave domain D along such a path that at the boundary of D, an N-plet of bound state energies degenerates and, subsequently, complexifies. At any fixed $N \geq 2$, this process is simulated via an N by N benchmark effective matrix Hamiltonian H. Finally, it is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement.Comment: 23 p