ON THE ASYMPTOTIC SPECTRUM OF A TRANSPORT OPERATOR WITH ELASTIC AND INELASTIC COLLISION OPERATORS

In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators(when it exists).The last section of this work is devoted to the properties of the leading eigenvalue(when it exists).So,we discuss the irreducibility of the semigroups generated by these operators.We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.

ON A CHARACTERIZATION OF THE S-ESSENTIAL SPECTRA OF THE SUM AND THE PRODUCT OF TWO OPERATORS AND APPLICATION TO A TRANSPORT OPERATOR

In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L1（[-a,a]×[-1,1]）（a〉0）.

AVERAGE REGULARITY OF THE SOLUTION TO AN EQUATION WITH THE RELATIVISTIC-FREE TRANSPORT OPERATOR

Let u = u(t, x, p) satisfy the transport equation ?u/?t+p/p0 ?u/?x= f, where f =f(t, x, p) belongs to L~p((0, T) × R~3× R~3) for 1 < p < ∞ and ?/?t+p/p0 ?/?x is the relativisticfree transport operator from the relativistic Boltzmann equation. We show the regularity of ∫u(t, x, p)d p using the same method as given by Golse, Lions, Perthame and Sentis. This average regularity is considered in terms of fractional Sobolev spaces and it is very useful for the study of the existence of the solution to the Cauchy problem on the relativistic Boltzmann equation.

The Asymptotic Spectrum and Accumulation of Transport Operator in Slab Geometry

In this paper we investigate the asymptotic spectrum and accumulation of a transport operator A in slab geometry with continuous energy, anisotropic scattering and inhomogeneous medium. In L^p （1 ≤ p 〈 ＋∞） space we show a series of new results for the asymptotic point spectrum and accumulation of A.

Potential Benefits of Increased Public Transit Ridership in Medium Sized Cities: A Case Study

At the beginning of the twentieth century, the United States was leading in the public transit sector, but following World War II, private automobiles became more affordable and gained popularity. Transportation infrastructure investments that increased road capacity further facilitated the increase in automobile use at the expense of reduced public transit ridership. With the increase of dependency on automobiles and the continuing growth of private automobile ownership and use, various problems became major challenges in big cities of USA. These include traffic congestion, air pollution, road and parking infrastructure costs, energy consumption, traffic safety, fewer mobility options for the non-drivers, and a decline in the image and use of public transit. This study uses a medium sized city, Birmingham as a case study to investigate the potential of public transit to reduce automobile trips and in turn improve the overall performance of the road network by addressing the abovementioned challenges. An agent-based simulation model was developed for the Birmingham metropolitan region using the Multi-agent Transport Simulation (MATSim) platform. Three scenarios were considered with gradually increased transit ridership to identify the benefits of increased public transit. Traffic volume, network average speed, and travel times were used as performance measures for the evaluation of the designated scenarios. Results suggest that modal shifts toward public transit and reduction in travel demand for an automobile can result in improvements in speed and travel time for all users. Therefore, investments for improving transit quality and frequency of service, as well as campaigns to improve the image of public transit and make it a mode of choice for transportation users can increase transit ridership and, in turn, improve network operations, thus are deemed worthy for medium sized cities.

Future urban transport management

The incorporation of disruptive innovations into the transportation industry will inevitably cause major upheavals in the transportation sector.However,existing research lacks systematic theories and methodologies to represent the underlying characteristics of future urban transport systems.Furthermore,emerging modes in urban mobility have not been sufficiently studied.The National Natural Science Foundation of China(NSFC)officially approved the Basic Science Center project titled“Future Urban Transport Management”in 2022.The project members include leading scientists and engineers from Beijing Jiaotong University,Beihang University,and Beijing Transport Institute.Based on a wide range of previous projects by the consortium on urban mobility and sustainable cities,this project will encompass transdisciplinary and interdisciplinary research to explore critical issues affecting future urban traffic management.It aims to develop fundamental theories and methods based on social and technological developments in the near future and explores innovative solutions to implement alongside these emerging developments in urban mobility.

Timetable optimization for single bus line based on hybrid vehicle size model

This study proposes a flexible timetable optimization method based on hybrid vehicle size model to tackle the bus demand fluctuations in transit operation. Three different models for hybrid vehicle, large vehicle and small vehicle are built in this study, respectively. With the operation data of Shanghai Transit Route 55 at peak and off-peak hours, a heuristic algorithm was proposed to solve the problem. The results indicate that the hybrid vehicle size model excels the other two modes both in the total time and total cost. The study verifies the rationality of the strategy of hybrid vehicle size model and highlights the importance of the adaptive vehicle size in dealing with the bus demand fluctuation. The main innovation of the study is that unlike traditional timetables, the arrangement of the scheduling interval and the corresponding bus type or size are both involved in the timetable of hybrid vehicle size bus mode, which will be more effective to solve the problem of passenger demand fluctuation. Findings from this research would provide a new perspective to improve the level of regular bus service.