On the Exponentials of Some Structured Matrices

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra isomorphism and basic Lie theory. When used in conjunction with structure preserving similarities, such as Givens rotations, these techniques extend to dimensions bigger than four.Comment: 19 page

Isomorphisms between Quantum Group Covariant q-Oscillator Systems Defined for q and 1/q

It is shown that there exists an isomorphism between q-oscillator systems covariant under $SU_q(n)$ and $SU_{q^{-1}}(n)$. By the isomorphism, the defining relations of $SU_{q^{-1}}(n)$ covariant q-oscillator system are transmuted into those of $SU_q(n)$. It is also shown that the similar isomorphism exists for the system of q-oscillators covariant under the quantum supergroup $SU_q(n/m)$. Furthermore the cases of q-deformed Lie (super)algebras constructed from covariant q-oscillator systems are considered. The isomorphisms between q-deformed Lie (super)algebras can not obtained by the direct generalization of the one for covariant q-oscillator systems.Comment: LaTeX 13pages, RCNP-07

Approach to the semiconductor cavity QED in high-Q regimes with q-deformed boson

The high density Frenkel exciton which interacts with a single mode microcavity field is dealed with in the framework of the q-deformed boson. It is shown that the q-defomation of bosonic commutation relations is satisfied naturally by the exciton operators when the low density limit is deviated. An analytical expression of the physical spectrum for the exciton is given by using of the dressed states of the cavity field and the exciton. We also give the numerical study and compare the theoretical results with the experimental resultsComment: 6 pages, 2 figure

Do incoming residents vary in measures of emotional status even prior to residency training?

Objectives: To determine whether Empathy, Emotional Intelligence, and Burnout scores differ by specialty in incoming residents. Methods: This is a single-site, prospective, cross-sectional study. Three validated survey instruments, the Jefferson Scale of Physician Empathy, Maslach Burnout Inventory, and Emotional and Social Competency Inventory, were written into a survey platform as a single 125-question Qualtrics survey. Over three academic years, 2015-2017, 229 incoming residents across all specialties were emailed the survey link during orientation. Residents were grouped by incoming specialty with anonymity assured. A total of 229 responses were included, with 121 (52.8%) identifying as female. Statistical analysis was performed using the Analysis of Variance or Kruskal-Wallis test, Chi-Square or Fisher\u27s Exact test, and Independent Samples t-test or Mann Whitney U test. A Bonferroni correction was applied for pairwise comparisons. Results: Family Medicine had a higher median Jefferson Scale of Physician Empathy score (127) compared to Emergency Medicine (115), (U=767.7, p=0.0330). Maslach Burnout Inventory depersonalization and personal accomplishment subcategory scores showed a significant difference between specialties when omnibus tests were performed, but pairwise comparisons with emergency medicine residents showed no differences. Differences were found in the Maslach Burnout Inventory categories of Depersonalization (χ Conclusions: Differences in measures of well-being exist across specialties, even prior to the start of residency training. The implication for educators of residency training is that some incoming residents, regardless of specialty, already exhibit troublesome features of burnout, and resources to effectively deal with these residents should be developed and utilized