We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis on the right-hand side. The input of the hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic interaction of non-diffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the assumed discontinuity of hysteresis. These conditions are formulated in terms of geometry of the manifolds defining the hysteresis thresholds and the spatial profile of the initial data.
Generalized aggregation operators are the tool for aggregation of fuzzy sets. The apparatus was introduced by Takači in \cite{4}. T-extension is a construction method of a generalized aggregation operator and we study it in the paper. We observe the behavior of a T-extension with respect to different order relations and we investigate properties of the construction.
Tagging cells of experimental organisms with genetic markers is commonly used in biomedical research. Insertion of artificial gene constructs can be highly beneficial for research as long as this tagging is functionally neutral and does not alter the tissue function. The transgenic UBC-GFP mouse has been recently found to be questionable in this respect, due to a latent stem cell defect compromising its lymphopoiesis and significantly influencing the results of competitive transplantation assays. In this study, we show that the stem cell defect present in UBC-GFP mice negatively affects T-lymphopoiesis significantly more than B-lymphopoiesis. The production of granulocytes is not negatively affected. The defect in T-lymphopoiesis causes a low total number of white blood cells in the peripheral blood of UBC-GFP mice which, together with the lower lymphoid/myeloid ratio in nucleated blood cells, is the only abnormal phenotype in untreated UBCGFP mice to have been found to date. The defective lymphopoiesis in UBC-GFP mice can be repaired by transplantation of congenic wild-type bone marrow cells, which then compensate for the insufficient production of T cells. Interestingly, the wild-type branch of haematopoiesis in chimaeric UBC-GFP/wild-type mice was more active in lymphopoiesis, and particularly towards production of T cells, compared to the lymphopoiesis in normal wild-type donors.
We consider two families of fuzzy propositional logics obtained by extendirig MTL and IMTL with the n-contraction axiom, for n > 2. These logics - called Cn-MTL and Cn-IMTL - range from Gödel and classical logic (when n = 2) to MTL and IMTL (when n tends to infinity), respectively. We investigate the t-norm based semantics and the proof theory for Cn-MTL and Cn-IMTL. We show standard cornpleteness and suitable analytic hypersequent calculi for theni.
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.