We give some diffusion models which can be used for restoration in image processing. The proposed model is a combination of fast growth with respect to low gradient and slow growth when the gradient is large. The existence theorem for solutions and some numerical results are given.

No abstract

This paper aims to model the impact of retail consumers’ behavior on a new banking dual market featuring both conventional and Islamic banking products. To build the model, we conduct an empirical qualitative and quantitative survey on Moroccan market consumers in order to appraise their preferences with regard to banking products’ attributes. Then, we use conjoint analysis method to determine the consumers’ decision function. We run market simulations on a Multi-Agents Simulation platform and analyze the results. Our findings indicate that in new dual markets, and under a range of assumptions, it is predicted that Islamic banks will face excess liquidity while conventional banks will be exposed to liquidity shortage.

Multiple myeloma (MM) is a genetically complex hematological cancer that is characterized by proliferation of malignant plasma cells in the bone marrow. MM evolves from the clonal premalignant disorder monoclonal gammopathy of unknown significance (MGUS) by sequential genetic changes involving many different genes, resulting in dysregulated growth of multiple clones of plasma cells. The migration, survival, and proliferation of these clones require the direct and indirect interactions with the non-hematopoietic cells of the bone marrow. We develop a hybrid discrete-continuous model of MM development from the MGUS stage. The discrete aspect of the model is observed at the cellular level: cells are represented as individual objects which move, interact, divide, and die by apoptosis. Each of these actions is regulated by intracellular and extracellular processes as described by continuous models. The hybrid model consists of the following submodels that have been simplified from the much more complex state of evolving MM: cell motion due to chemotaxis, intracellular regulation of plasma cells, extracellular regulation in the bone marrow, and acquisition of mutations upon cell division. By extending a previous, simpler model in which the extracellular matrix was considered to be uniformly distributed, the new hybrid model provides a more accurate description in which cytokines are produced by the marrow microenvironment and consumed by the myeloma cells. The complex multiple genetic changes in MM cells and the numerous cell-cell and cytokine-mediated interactions between myeloma cells and their marrow microenviroment are simplified in the model such that four related but evolving MM clones can be studied as they compete for dominance in the setting of intraclonal heterogeneity.