Counting matchings via capacity-preserving operators

The notion of the capacity of a polynomial was introduced by Gurvits around 2005, originally to give drastically simplified proofs of the van der Waerden lower bound for permanents of doubly stochastic matrices and Schrijver’s inequality for perfect matchings of regular bipartite graphs. Since this seminal work, the notion of capacity has been utilised to bound various combinatorial quantities and to give polynomial-time algorithms to approximate such quantities (e.g. the number of bases of a matroid). These types of results are often proven by giving bounds on how much a particular differential operator can change the capacity of a given polynomial. In this paper, we unify the theory surrounding such capacity-preserving operators by giving tight capacity preservation bounds for all nondegenerate real stability preservers. We then use this theory to give a new proof of a recent result of Csikvári, which settled Friedland’s lower matching conjecture.

Physical modeling of an automated ship’s list control system

In order to implement and demonstrate all the processes associated with the real stability trial system on vessels, a ship’s model was made. The developed model consists of electrical and hardware parts. It is concluded that the model is applicable for the study of issues of automatic control of the ship’s list, simulating various loading options. Scalable loading studies of various types and sizes of cargo were carried out. The results of the study showed the correct operation of the model according to a specified algorithm. To work with the microcontroller and to code, the mathematical modeling environment Matlab/Simulink was used. The results of the study showed that the created control system is able to secure the vessel during various types of loading operations, speed up the loading process, thus reducing the time spent at the port stay and save port costs.

Hydrate—A Mysterious Phase or Just Misunderstood?

Hydrates that form during transport of hydrocarbons containing free water, or water dissolved in hydrocarbons, are generally not in thermodynamic equilibrium and depend on the concentration of all components in all phases. Temperature and pressure are normally the only variables used in hydrate analysis, even though hydrates will dissolve by contact with pure water and water which is under saturated with hydrate formers. Mineral surfaces (for example rust) play dual roles as hydrate inhibitors and hydrate nucleation sites. What appears to be mysterious, and often random, is actually the effects of hydrate non-equilibrium and competing hydrate formation and dissociation phase transitions. There is a need to move forward towards a more complete non-equilibrium way to approach hydrates in industrial settings. Similar challenges are related to natural gas hydrates in sediments. Hydrates dissociates worldwide due to seawater that leaks into hydrate filled sediments. Many of the global resources of methane hydrate reside in a stationary situation of hydrate dissociation from incoming water and formation of new hydrate from incoming hydrate formers from below. Understanding the dynamic situation of a real hydrate reservoir is critical for understanding the distribution characteristics of hydrates in the sediments. This knowledge is also critical for designing efficient hydrate production strategies. In order to facilitate the needed analysis we propose the use of residual thermodynamics for all phases, including all hydrate phases, so as to be able to analyze real stability limits and needed heat supply for hydrate production.

Geotechnical and Numerical analysis of Bcharreh Landslide stability

The aim of this study is to shed light on a real stability problem within the region of Bcharreh located in North of Lebanon where roads have no protection against landslides. An attempt for landslide assessment that occurred in November 2016 is presented in order to analyse the different factors behind the landslide and find the trigger factor affecting the stability of the slope. The characterization of soil properties along the slope is done based on geotechnical investigation, and data collection. The first part of work consists of site inspection and geotechnical investigation followed by a series of laboratory tests to evaluate the mechanical properties constituting the slope, in addition to collection of topographical and hydrogeological data. The second part presents the numerical analysis where a finite element model simulating the slope conditions is generated using Plaxis 2D in order to reproduce the process of landslides, to assess slope stability and determine the overall factor of safety in both dry and wet conditions. The contribution of each causal factor in prompting soil movement is then demonstrated and explained.

King-Type Derivative-Free Iterative Families: Real and Memory Dynamics

A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties.