Bifurcation of limit cycles from a 4-dimensional center in 1:n resonance

We study the bifurcation of limit cycles from the periodic orbits of a linear differential system in R⁴ in resonance 1:n perturbed inside a class of piecewise linear differential systems, which appear in a natural way in control theory. Our main result shows that at most 1 limit cycle can bifurcate using expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed.     

Simultaneous optically sectioned fluorescence and optical coherence microscopy with full-field illumination

Full-field optical coherence microscopy (FF-OCM) and optically sectioned fluorescence microscopy are two imaging techniques that are implemented here in a novel dual modality instrument. The two imaging modalities use a broad field illumination to acquire the entire field of view without raster scanning. Optical sectioning is achieved in both imaging modalities owing to the coherence gating property of light for FF-OCM, and a structured illumination setup for fluorescence microscopy. Complementary image data are provided by the dual modality instrument in the context of biological tissue screening. FF-OCM imaging modality shows the tissue microarchitecture, while fluorescence microscopy highlights specific tissue features with cellular-level resolution by using targeting contrast agents. Complementary tissue morphology and biochemical features could potentially improve the understanding of cellular functions and disease diagnosis.     

Recent Advancements in the Development of Anti-Breast Cancer Synthetic Small Molecules

Among all cancer types, breast cancer (BC) still stands as one of the most serious diseases responsible for a large number of cancer-associated deaths among women worldwide, and diagnosed cases are increasing year by year worldwide. For a very long time, hormonal therapy, surgery, chemotherapy, and radiotherapy were used for breast cancer treatment. However, these treatment approaches are becoming progressively futile because of multidrug resistance and serious side effects. Consequently, there is a pressing demand to develop more efficient and safer agents that can fight breast cancer belligerence and inhibit cancer cell proliferation, invasion and metastasis. Currently, there is an avalanche of newly designed and synthesized molecular entities targeting multiple types of breast cancer. This review highlights several important synthesized compounds with promising anti-BC activity that are categorized according to their chemical structures.