We consider an isothermal gas flowing through a straight pipe and study the effects of a two-way electronic valve on the flow. The valve is either open or closed according to the pressure gradient and is assumed to act without any time or reaction delay. We first give a notion of coupling solution for the corresponding Riemann problem; then, we highlight and investigate several important properties for the solver, such as coherence, consistence, continuity on initial data and invariant domains. In particular, the notion of coherence introduced here is new and related to commuting behaviors of valves. We provide explicit conditions on the initial data in order that each of these properties is satisfied. The modeling we propose can be easily extended to a very wide class of valves

Abstract. We solve problems concerning the coefficients of functions in the class T (λ) of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: |a4 − a2a3| and |a2a4 − a3 2 |. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in T (λ). Furthermore, we find the upper and the lower bounds of functionals of Fekete-Szegö type. Finally, we present some conclusions for the classes T and T (1/2).Mathematics Subject Classification. 30C50.

The application of methods using graphs to model a variety of engineering issues has been known for several decades, but the application of graph algorithms to model the urban water management issues is a completely new approach. The article reviews the scientific literature on integrated urban water management systems in terms of the use of graph theory algorithms in this topic. Such a review has not been done before and constitutes a completely novel study. Some of the algorithms presented are directly derived from graph theory, while others were developed from other sciences, including environmental engineering or genetics, to solve specific engineering problems. The paper presents a general scheme and a brief description of the most important components of an integrated urban water management system. The necessary concepts of graphs were defined, the origin and the principle of graph algorithms used in modeling water management issues (Loop-By-Loop Cutting Algorithm, Hanging Gardens Algorithm, Tree Growth Algorithm, Dijkstra's Algorithm, Genetic Algorithm, and Bayesian Networks Algorithm) were described. Their use in modeling the issues in stormwater, sanitary sewage and water distribution system was described. A complete list of scientific literature in this field was provided.

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