Using functional analytical and graph theoretical methods, we extend the results of [12] to more general transport processes in networks allowing space dependent velocities and absorption. We characterize asymptotic periodicity and convergence to an equilibrium by conditions on the underlying directed graph and the (average) velocities.2000 Mathematics Subject Classification: 35F25; 34B15.Our aim is-based on the paper [12]-to handle more general transport processes allowing space dependent velocities and absorption in networks. We model the problem by a system of partial di¤erential equations on a directed graph where the vertices serve as linking points between the edges. We show that the flow is (up to §

We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral properties, the problem of unitary equivalence of typical operators, and their embeddability into C 0 -semigroups. Our results provide information on the applicability of Baire category methods in the theory of Hilbert space operators.

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We prove that any finite simple graph can be covered by three of its odd subgraphs, and we construct an infinite sequence of graphs where an edge-disjoint covering by three odd subgraphs is not possible. c

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Mobility as a Service (MaaS) is a new transport concept which integrates, manages, and distributes private and public mobility alternatives by using intelligent digital technologies. Recently, research and implementations have been widely conducted. In order to reveal future implications, it is crucial to analyze the available MaaS services by using systematic methodology. Cluster analysis was applied to create typical groups of MaaS services and to define the common features of the systems, which may highlight future trends. In order to identify the most relevant MaaS initiatives, the typical parameters of the services were taken into account and a dataset was developed. More than 30 MaaS services from 14 countries were investigated, and the features and the functionalities of these services were analyzed. The findings demonstrate that there is potential for the development of the applications in terms of their payment features, their personalization, and the provision of all attainable elements of MaaS. The number of operators is constantly increasing. However, it is uncertain whether public or private MaaS operators will be dominant on the market. Three cluster groups were created with specific features and directions of development. The Route planners group involves a few modes of transport, but it provides an extensive service. While the Third parties group has primarily private MaaS operators, the Public systems group usually includes public MaaS operators. This comprehensive study might be useful to MaaS operators and regulators for understanding the typical features and the development directions of the market.

Infrastructure investments have an important role in a coun IntroductionAs Cost-Benefit Analysis (CBA) is an applied social science, it is mainly based on assumptions. Therefore a CBA can be only as good as its assumptions are. Infrastructure investment projects regularly experience cost and time overruns. Research led by Flyvberg has suggested that misrepresentation and optimism bias are primary causes for overruns [6]. Current researches are mainly focused on new construction and limited attention was devoted to the infrastructure upgrade projects and their impacts on the cost, schedule and traffic. The upgrade works can cause significant disturbance to the existing infrastructure normal operation, especially in rail projects.The objective of this article is to present the current limitations of CBA methodologies applied in Europe [12, 13] using cases in Hungary. It will also collect and summarize the main research and findings in the field of ex-post evaluation.Two Hungarian railway upgrade projects were evaluated economically. In each selected project, the original ex-ante CBA will be recreated and a new ex-post evaluation will be implemented based on the available information. The ex-ante and ex-post results will be compared and further conclusions will be drawn. In addition to the economic analysis, the financial losses were evaluated, since these projects caused significant disturbances for the operations during the construction period.Travel time variability was examined closely. Calculations were made through a case study in order to determine the importance of this impact.A concise literature review of the CBA methodology and the limitation of CBA can be found in earlier studies [10,11], therefore it is not repeated in this article.

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