Annotations of two examples about Markov process

In this paper, we discuss an incorrect example that a Markov process does not satisfy strong Markov property, and analyzes the reason of mistake. In the end, we point out it is not reasonable to define strong Markov property by using transition probability functions since transition probability functions might not be one and only

On non-abelian extensions of 3-Lie algebras

In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed.Comment: 17 page

Pharyngeal and Cervical Cancer Incidences Significantly Correlate with Personal UV Doses Among Whites in the United States

Because we found UV-exposed oral tissue cells have reduced DNA repair and apoptotic cell death compared with skin tissue cells, we asked if a correlation existed between personal UV dose and the incidences of oral and pharyngeal cancer in the United States. We analyzed the International Agency for Research on Cancer\u27s incidence data for oral and pharyngeal cancers by race (white and black) and sex using each state\u27s average annual personal UV dose. We refer to our data as ‘white’ rather than ‘Caucasian,’ which is a specific subgroup of whites, and ‘black’ rather than African-American because blacks from other countries around the world reside in the U.S. Most oropharyngeal carcinomas harboured human papilloma virus (HPV), so we included cervical cancer as a control for direct UV activation. We found significant correlations between increasing UV dose and pharyngeal cancer in white males (p=0.000808) and females (p=0.0031) but not in blacks. Shockingly, we also found cervical cancer in whites to significantly correlate with increasing UV dose (p=0.0154). Thus, because pharyngeal and cervical cancer correlate significantly with increasing personal UV dose in only the white population, both direct (DNA damage) and indirect (soluble factors) effects may increase the risk of HPV-associated cancer