A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.     

Fixed Points,Continuous Selections,and Existence of Solution of Optimization-Related Problems

We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations.     

X-ray diffraction study of mesogenic 4-methoxyphenyl-4′-n-nonyloxybenzoate

4-methoxyphenyl-4′-n-nonyloxybenzoate have been investigated by single crystal X-ray structural analysis. Crystal packing of the compounds does not represent a precursor of the mesophse although the typical for liquid crystal compounds separation of crystal packing on aromatic and aliphatic areas is observed here. Possible reason for monotropic properties are discussed.     

含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理，本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件，并通过数值算例验证了理论结果的有效性.