We present a simple, differentiation-free, integrationfree, trigonometryfree, direct and elementary proof of the Fundamental Theorem of Algebra. “The final publication (in The Mathematical Intelligencer, 33, No. 2 (2011), 1-2) is available at www.springerlink.com: http://www.springerlink.com/content/l1847265q2311325/”

In this paper we give irrationality results for numbers of the form ∑∞ n=1 an n! where the numbers an behave like a geometric progression for a while. The method is elementary, not using differentiation or integration. In particular, we derive elementary proofs of the irrationality of π and em for Gaussian integers m 6= 0.

Rat embryos explanted at early head-fold stage and grown in vitro by improved culture methods were compared with littermates in vivo. Very similar rates of growth and differentiation were obtained over a period of 48 h, while the embryos developed to around the 25-somite stage.

Athreya, Goldenfeld, and Dantzig [Phys. Rev. E 74, 011601 (2006)] claim that the current implementation of the renormalization-group method neglects the proper ordering of renormalization and differentiation. Their analysis is, however, based on the wrong multiple-scales method results.

Although epidemiological data provide evidence that early life experience plays a critical role in human development, the mechanism of how this works remains in question. Recent data from human and animal literature suggest that epigenetic changes, such as DNA methylation, are involved not only in cellular differentiation but also in the modulation of genome function in response to early life e...

BACKGROUND New blood vessels formation is a critical step in tumor progression. Vascular density affects the clinical outcome and prognosis of malignant tumors. The aim of this study was to investigate the relation between the Vascular Endothelial Growth Factor (VEGF) expression and vascular density with the clinical and histopathologic features in oral squamous cell carcinoma (OSCC). METHODS...

The grading of cancer is a histological method intended to help predict prognosis based on specific morphological features. It typically is based on architectural or cytological features (nuclear grade or number of mitoses), or in some cases, a combination of both. Grading is usually broken down into a spectrum from well differentiated (grade 1) to the most poorly differentiated (grade 3 or 4)....

Despite many years of research, a method to precisely and quantitatively determine cancer disease state remains elusive. Current practice for characterizing solid tumors involves the use of varying systems of tumor grading and staging and thus leaves diagnosis and clinical staging dependent on the experience and skill of the physicians involved. Although numerous disease markers have been ident...

BACKGROUND The impact of histopathologic tumor invasion of the superior mesenteric vein (SMV)/portal vein (PV) on prognosis in patients with pancreatic ductal adenocarcinoma (PDAC) after pancreatectomy remains controversial. A meta-analysis was performed to assess this issue. RESULTS Eighteen observational studies comprising 5242 patients were eligible, of whom 2199 (41.9%) patients received ...