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We study cooperative games in which some of the coalitions are not viable and in addition, there are externalities among the feasible coalitions. These games are called here restricted partition function form games. For this class of games, two extensions of the Shapley value are proposed and characterized. [ABSTRACT FROM AUTHOR]

In the classical approach of von Neumann and Morgenstern to cooperative games, it was assumed that the worth of all coalitions must be given. However, in real-world problems, the worth of some coalitions may be unknown. Therefore, in this study, we consider the Shapley value for convex partially defined games using two approaches. Firstly, we introduce a polytope that includes the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. The elements of this polytope are said to be the Shapley payoff vectors. Secondly, we obtain the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. Moreover, we axiomatize the proposed two values. [ABSTRACT FROM AUTHOR]

The object of this paper is to study restricted cooperative games, that is, cooperative games for which the worth of some coalitions is unknown. We consider a value for these restricted cooperative games whose definition is based on the Harsanyi's dividends approach, and can therefore be seen as an extension of the Shapley value. We provide a characterization of this value with three axioms: Carrier, Symmetric-partnership and Additivity, which are similar to those proposed by Shapley (in: Kuhn and Tucker (eds) Contributions to the theory of games, Princeton University Press, Princeton, 1953). In addition, we characterize this value on the subclass of restricted cooperative simple games. Finally, we apply this value for restricted cooperative games to analyze the power distribution of the Catalonian Parliament in 1980 and compare the results with those of the coalitional value in Carreras and Owen (Math Soc Sci 15:87–92, 1988). [ABSTRACT FROM AUTHOR]

Abstract Dislocations in chemical vapor deposited (111) single crystal diamond were studied by synchrotron X-ray topography. By analyzing X-ray topography images with various g vectors using the contrast extinction criterion, mixed dislocations with b = a/2 [011] and edge dislocations with b = a/2 [0 1 ¯ 1] are determined. Then, etch pits were formed using O 2 /H 2 plasma; observations by X-ray topography and atomic force microscopy revealed that etch pits formed on the dislocations. Hence, we investigated the relationship between the types of dislocations structure and the formation of etch pits. The results showed that the etch pits were larger in diamond samples with mixed dislocations than in those of edge dislocations. Graphical abstract Unlabelled Image Highlights • Dislocations and etch pits in chemical vapor deposited (111) single crystal diamond were studied. • Dislocations are determined as pure edge dislocation and mixed dislocations. • Etch pits on mixed dislocations are larger than in those of edge dislocations. [ABSTRACT FROM AUTHOR]

Stacking faults (SFs) in a (111) single crystal diamond grown on a (111) seed crystal were investigated by taking synchrotron X-ray topography images with various diffraction vector g conditions. We found that the SFs on the {111} plane of fault vector f were a/3 [11 1 ̅ ] , a/3 [ 1 ̅ 11] , and a/3 [1 1 ̅ 1] . Subsequently, we analyzed these images in terms of the b·g extinction criteria and determined that the partial dislocations of the SFs were Shockley partial dislocations with Burgers vector b = a/6 <211>. Then, we determined that the SFs are Shockley type faults. Therefore, we propose that these SFs were generated by decomposition of one perfect dislocation with b = a/2 < 1 ¯ 10 > . [ABSTRACT FROM AUTHOR]

The effects of thermal annealing on stacking faults and dislocations in single-crystal diamonds with a low defect density were investigated by synchrotron X-ray topography. We compared the X-ray topography images before and after annealing under various diffraction conditions. We found that the stacking faults disappeared after annealing, and new dislocations appeared at the edges of disappeared stacking faults. These results indicate that the stacking faults were Shockley type, and they were sandwiched between two Shockley partial dislocations. Therefore, we concluded that the Shockley stacking faults disappeared as a result of the movement of the Shockley partial dislocations. Before annealing, the perfect dislocations were straight along the [2 1 ¯ 1] direction; annealing caused these dislocations to bend along the [1 1 ¯ 0] and [101] directions. We identified two dislocation shapes; upper bending and lower bending dislocations. An analysis based on contrast extinction criterion; indicated that the bending direction depends on the Burgers vector, for example, a dislocation with b = a/2[101] moved along the [0 11 ¯ ] direction, and a dislocation with b = a/2[1 1 ¯ 0] moved along the [011] direction. [ABSTRACT FROM AUTHOR]

This paper considers a cooperative fuzzy game withnplayers andralternatives called a multi-alternative fuzzy game. Considering the non-homogeneity among players, we pro-pose a new value function on a class of these games, which means evaluation values for the game by players. Furthermore an axiom system is proposed on which the new value function is based. Finally we give a numerical example in which the new value is compared with traditional values. [ABSTRACT FROM PUBLISHER]

Killer defects are responsible for leakage current and breakdown in β-gallium oxide (β-Ga2O3) Schottky barrier diodes, which are crucial for power device applications. We have found that stacking faults in the halide vapor phase epitaxial (HVPE) (001) layer are killer defects. One type of defect is found to consist of (111) and (1 1 ¯ 1) stacking faults. The leakage current is 50 nA/defect at − 200 V. This defect appears as a heart-shaped etch pit. Another type of defect is found to be a sequence of stacking faults from microparticles, which are formed at low gas flow rate during HVPE growth. The leakage current is 0.11–0.49 μA/defect at − 200 V. This defect appears as a group of bullet-shaped etch pits. [ABSTRACT FROM AUTHOR]

Abstract From transmission electron microscope (TEM) observation, a 25 nm thick amorphous layer was confirmed at the diamond/Si bonding interface without annealing, the amorphous layer thickness decreased with the annealing temperature. No cracking even in nanometer scale occurred even after high-temperature annealing at 800 °C. From in-situ micro-Raman monitoring, the compressed stress was observed in the Si of the bonding interface without annealing with respect to the bonding Si substrate. A tensile stress relaxation was observed in the diamond of the bonding interface with respect to the polished diamond. These results were attributed to the large load applied to the diamond and Si substrates during bonding process. After annealing at 400 °C, the residual stress in the Si of the bonding interface decreased, while the residual stress in the diamond of the bonding interface increased, which should be due to the residual stress caused by the applied load was released by annealing process. The residual stress in the Si and diamond of the bonding interface increased and decreased, respectively, as the annealing temperature increased from 400 to 1000 °C. The main reason was due to the structure change of the amorphous layer and the tensile stress relaxation in the diamond of the bonding interface. Graphical abstract Unlabelled Image Highlights • Diamond/Si bonding interface could withstand a load of high temperature as high as 800 °C. • The amorphous layer observed at the bonding interface decreased with annealing temperature. • The residual stress released in the diamond of the bonding interface decreased with annealing temperature. • The residual stress formed in the bonding interface annealed at 1000˚C is much smaller than that of diamond grown on Si. [ABSTRACT FROM AUTHOR]