Immunohistochemical features of a papillary squamous cell carcinoma of the endometrium with transitional cell differentiation

An 84-year-old woman underwent hysterectomy due to a friable endometrial mass infiltrating almost half way through the myometrial wall. The tumor consisted of papillary structures with thin fibrovascular cores covered by several layers of pleomorphic cells. The deeply located neoplastic cells were ovoid with a pale eosinophilic cytoplasm resembling urothelial cells. A diagnosis of papillary squamous cell carcinoma of the endometrium with transitional cell differentiation was made. Although she recovered well after surgery, she died one year later because of disseminated disease. In an attempt to obtain new insights into the physiopathology of this very rare tumor, an immunohistochemical panel with 32 markers was performed. The neoplastic cells were positive for cytokeratin 5, vimentin, p63, p21, VEGF, Ki67, BAG1, and bcl-2. The expression of BAG-1 and bcl-2 may suggest that anti-apoptotic stimuli are preponderant in this neoplasm.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Pullback exponential attractors for evolution processes in Banach spaces: properties and applications

This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.