Let [ a,b ] be a finite real interval and ( S ,‖·‖) a complete random normed module endowed with the ( e , λ )-topology. We first introduce the …
Let [ a,b ] be a finite real interval and ( S ,‖·‖) a complete random normed module endowed with the ( e , λ )-topology. We first introduce the Riemann integral for abstract-valued functions from [ a,b ] to S and give a sufficient condition for such a continuous function with the almost surely bounded range to be Riemannintegrable. Then we investigate the relation between random spectral measures and ordinary random measures. Finally, based on the above two preliminaries, we establish the Stone’s representation theorem of a group of random unitary operators on complete complex random inner product modules.
This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the …
This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the agent's fuzzy preference in the consumption set. We set up a new fuzzy binary relation on the consumption set to evaluate the fuzzy preferences. Also, we prove that there exists a continuous fuzzy order-preserving function in the consumption set under certain conditions. The existence of a fuzzy competitive equilibrium for the PXE-FP is confirmed through a new result on the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games. The payoffs of all strategy profiles for any agent are fuzzy numbers in fuzzy non-cooperative games. Finally, we show that the fuzzy competitive equilibrium could be characterized as a solution to an associated quasi-variational inequality, giving rise to an equilibrium solution.
We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy …
We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the $r$-power of the measure. We show in a uniformed manner that the generalized monogamy and polygamy relations are transitive to other powers of the measure in weighted forms. We demonstrate that our weighted monogamy and polygamy relations are stronger than recently available relations. Comparisons are given in detailed examples which show that our results are stronger in both situations.
We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy …
We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the $r$-power of the measure. We show in a uniformed manner that the generalized monogamy and polygamy relations are transitive to other powers of the measure in weighted forms. We demonstrate that our weighted monogamy and polygamy relations are stronger than recently available relations. Comparisons are given in detailed examples which show that our results are stronger in both situations.
This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the …
This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the agent's fuzzy preference in the consumption set. We set up a new fuzzy binary relation on the consumption set to evaluate the fuzzy preferences. Also, we prove that there exists a continuous fuzzy order-preserving function in the consumption set under certain conditions. The existence of a fuzzy competitive equilibrium for the PXE-FP is confirmed through a new result on the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games. The payoffs of all strategy profiles for any agent are fuzzy numbers in fuzzy non-cooperative games. Finally, we show that the fuzzy competitive equilibrium could be characterized as a solution to an associated quasi-variational inequality, giving rise to an equilibrium solution.
Let [ a,b ] be a finite real interval and ( S ,‖·‖) a complete random normed module endowed with the ( e , λ )-topology. We first introduce the …
Let [ a,b ] be a finite real interval and ( S ,‖·‖) a complete random normed module endowed with the ( e , λ )-topology. We first introduce the Riemann integral for abstract-valued functions from [ a,b ] to S and give a sufficient condition for such a continuous function with the almost surely bounded range to be Riemannintegrable. Then we investigate the relation between random spectral measures and ordinary random measures. Finally, based on the above two preliminaries, we establish the Stone’s representation theorem of a group of random unitary operators on complete complex random inner product modules.