In this paper we introduce and study an algebraic structure, namely Grouplike. A grouplike is something between semigroup and group and its axioms are generalizations of the four group axioms. Every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). The first idea of grouplikes comes from b-parts and $b$-addition of real number...

Summa r'y. The number of models for pedestr ian dynamics has grown in the pa.st years, but the experimental data to discriminate between these models is still to a large extent unce rtain and contradictory. To enhance the data base a nd to resolve some discrepancies discussed in the literature over one hundred yean; wc studied the pedestr ian flow through bottlenecks by an experiment performed ...

In this paper, we propose a general way of computing expectation values in the zero-range process, using an exact form of the partition function. As an example, we provide the fundamental diagram (the flux-density plot) of the asymmetric exclusion process corresponding to the zero-range process. We express the partition function for the steady state by the Lauricella hypergeometric function, an...

This paper addresses two shortcomings of the data-driven stochastic fundamental diagram for freeway traffic. The first shortcoming is related to least-squares methods which have been widely used in establishing traffic flow diagrams. We argue that these are not suitable generate percentile-based diagrams, because results generated by represent weighted sample mean, rather than percentile. secon...

One of the usual ways to build up mathematical models corresponding to a wide class of DC–DC converters is by means of piecewise linear differential equations. These models belong to a class of dynamical systems called Variable Structure Systems (VSS). From a classical design point of view, it is of interest to know the dynamical behavior of the system when some parameters are varied. Usually, ...

We analyse the dynamics of the classical optimal velocity model for the case of inhomogeneous drivers and for the case of road works. We introduce a different viewpoint, the so-called rotation solutions, which in case of an additional symmetry leads to the POM solutions. This approach opens the possibility to analytical and numerical bifurcation studies, which show a big variety in the possible...

The Unified Modeling Language (UML) is widely considered as the defacto standard for the design of Object Oriented systems. UML class diagrams are used to depict the static structure of a system with its entities and the relationships between them. The Object Constraint Language (OCL) is a textual language based on first-order logic and can be used to define constraints on the elements of class...