Some conservative nonlinear integral operators

Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Primary cancer-associated fibroblasts exhibit high heterogeneity among breast cancer subtypes

Background: Cancer-associated fibroblasts (CAFs) are a diverse subset of cells, that is recently gaining in popularity and have the potential to become a new target for breast cancer therapy; however, broader research is required to understand their mechanisms and interactions with breast cancer cells. The goal of the study was to isolate CAFs from breast cancer tumour and characterise isolated cell lines. We concentrated on numerous CAF biomarkers that would enable their differentiation.  Materials and methods: Flow cytometry, immunofluorescence, and reverse transcription quantitative real-time polymerase chain reaction (RT-qPCR) were used to phenotype the primary CAFs. Conclusions: According to our findings, there was no significant pattern in the classification of cancer-associated fibroblasts. The results of biomarkers expression were heterogeneous, thus no specific subtypes were identified. Furthermore, a comparison of cancer-associated fibroblasts derived from different BC subtypes (luminal A and B, triple-negative, HER2 positive) did not  reveal any clear trend of expression

Variable exponent Besov-Morrey spaces

In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.publishe

Review: L. A. Steen; Mathematics today - twelwe informal essays

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Orlicz spaces and modular spaces

Includes index