Quasi-Exactly Solvable Schr\"odinger Operators in Three Dimensions

The main contribution of our paper is to give a partial classification of the quasi-exactly solvable Lie algebras of first order differential operators in three variables, and to show how this can be applied to the construction of new quasi-exactly solvable Schr\"odinger operators in three dimensions.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Nodal sets and growth exponents of Laplace eigenfunctions on surfaces

We prove a result, announced by F. Nazarov, L. Polterovich and M. Sodin that exhibits a relation between the average local growth of a Laplace eigenfunction on a closed surface and the global size of its nodal set. More precisely, we provide a lower and an upper bound to the Hausdorff measure of the nodal set in terms of the expected value of the growth exponent of an eigenfunction on disks of wavelength like radius. Combined with Yau's conjecture, the result implies that the average local growth of an eigenfunction on such disks is bounded by constants in the semi-classical limit. We also obtain results that link the size of the nodal set to the growth of solutions of planar Schr\"odinger equations with small potential.Comment: New version to appear in Anal. PDE. (40 pages, 7 figures.

The coexistence of terms to describe the presence of multiple concurrent diseases

Background: Consensus on terminology for multiple diseases is lacking. Because of the clinical relevance and social impact of multiple concurrent diseases, it is important that concepts are clear. Objective: To highlight the diversity of terms in the literature referring to the presence of multiple concurrent diseases/conditions and make recommendations. Design: A bibliometric analysis of English-language publications indexed in the MEDLINE database from 1970 to 2012 for the terms comorbidity, multimorbidity, polymorbidity, polypathology, pluripathology, multipathology, and multicondition, and a review of definitions of multimorbidity found in English-language publications indexed from 1970 to 2012 in the MEDLINE and SCOPUS databases. Results: Comorbidity was used in 67,557 publications, multimorbidity in 434, and the other terms in three to 31 publications. At least 144 publications used the term comorbidity without referring to an index disease. Thirteen general definitions of multimorbidity were identified, but only two were frequently used (91% of publications). The most frequently used definition (48% of publications) was “more than one or multiple chronic or long-term diseases/conditions”. Multimorbidity was not defined in 51% of the publications using the term. Conclusions: Comorbidity was overwhelmingly used to describe any clinical entity coexisting with an index disease under study. Multimorbidity was the term most frequently used when no index disease was designated. Several definitions of multimorbidity were found. However, most authors using the term did not define it. The use of clearly defined terms in the literature is recommended until a general consensus on the terminology of multiple coexistent diseases is reached.Journal of Comorbidity 2013;3(1):4–9 

Wartime China’s Resistance against Japanese Aggression: Changing Interpretations and Perspectives

In 1931, Japan invaded Manchuria and established the puppet state of Manchukuo in northeast China. Hoping to avoid an all-out war with Japan, China pursued a policy of appeasement and did not resist the occupation of China. Nonetheless, in 1937 the Japanese launched a massive attack against Beijing and the eastern coastal cities of China and continued its assault until World War II ended in August 1945. This period, known as the Chinese People’s War of Resistance against Japanese Aggression, has seen many shifts in its historical narrative. After Japan surrendered, a full-fledged civil war broke out between the Communist Party of China (CPC) and the Nationalist/Kuomintang (KMT). The 1949 victory of the CPC and subsequent Mao Zedong era (1949-1976) limited the Chinese memory of the war of against Japanese aggression. However, following the death of Mao, China began a “new remembering” of this war. Our research examines the changing interpretations and perspectives of wartime China in the Mao and post-Mao eras. In addition to academic literature on the subject, our paper draws upon our first-hand exploration of Chinese government-sponsored wartime museums and sites from our research trip to China in June, 2010. Our paper also evaluates the challenges that the Chinese government has encountered as it works to advance a comprehensive history that details the contributions of both the Nationalists and the Communists in the War against Japanese Aggression