Z2×Z2 \mathbb{Z}_2 \times \mathbb{Z}_2 generalizations of N=1{\cal N} = 1 superconformal Galilei algebras and their representations

We introduce two classes of novel color superalgebras of $\mathbb{Z}_2 \times \mathbb{Z}_2$ grading. This is done by realizing members of each in the universal enveloping algebra of the ${\cal N}=1$ supersymmetric extension of the conformal Galilei algebra. This allows us to upgrade any representation of the super conformal Galilei algebras to a representation of the $\mathbb{Z}_2 \times \mathbb{Z}_2$ graded algebra. As an example, boson-fermion Fock space representation of one class is given. We also provide a vector field realization of members of the other class by using a generalization of the Grassmann calculus to $\mathbb{Z}_2 \times \mathbb{Z}_2$ graded setting.Comment: 17 pages, no figur

Adiabatic thermostatistics of the two parameter entropy and the role of Lambert's W-function in its applications

A unified framework to describe the adiabatic class of ensembles in the generalized statistical mechanics based on Schwammle-Tsallis two parameter (q, q') entropy is proposed. The generalized form of the equipartition theorem, virial theorem and the adiabatic theorem are derived. Each member of the class of ensembles is illustrated using the classical nonrelativistic ideal gas and we observe that the heat functions could be written in terms of the Lambert's W-function in the large N limit. In the microcanonical ensemble we study the effect of gravitational field on classical nonrelativistic ideal gas and a system of hard rods in one dimension and compute their respective internal energy and specific heat. We found that the specific heat can take both positive and negative values depending on the range of the deformation parameters, unlike the case of one parameter Tsallis entropy.Comment: 26 pages, Accepted for Publication in Physica

Super-Jordanian Quantum Superalgebra Uh(osp(2/1)){\cal U}_{h}(osp(2/1))

A triangular quantum deformation of $osp(2/1)$ from the classical $r$-matrix including an odd generator is presented with its full Hopf algebra structure. The deformation maps, twisting element and tensor operators are considered for the deformed $osp(2/1)$. It is also shown that its subalgebra generated by the Borel subalgebra is self-dual.Comment: 18 Page

Arrhythmia induction using isoproterenol or epinephrine during electrophysiology study for supraventricular tachycardia

Background Electrophysiology study (EPS) is an important part of the diagnosis and workup for supraventricular tachycardia (SVT). Provocative medications are used to induce arrhythmias, when they are not inducible at baseline. The most common medication is the β1‐specific agonist, isoproterenol, but recent price increases have resulted in a shift toward the nonspecific agonist, epinephrine. Objective We hypothesize that isoproterenol is a better induction agent for SVT during EPS than epinephrine. Methods We created a retrospective cohort of 131 patients, who underwent EPS and required medication infusion with either isoproterenol or epinephrine for SVT induction. The primary outcome was arrhythmia induction. Results Successful induction was achieved in 71% of isoproterenol cases and 53% of epinephrine cases (P = 0.020). Isoproterenol was significantly better than epinephrine for SVT induction during EPS (odds ratio [OR], 2.35; 95% confidence interval [CI], 1.14‐4.85; P = 0.021). There was no difference in baseline variables or complications between the two groups. Other variables associated with successful arrhythmia induction included a longer procedure duration and atrioventricular nodal re‐entry tachycardia as the clinical arrhythmia. In a multivariable model, isoproterenol remained significantly associated with successful induction (OR, 2.57; 95% CI, 1.002‐6.59; P = 0.05). Conclusions Isoproterenol was significantly better than epinephrine for SVT arrhythmia induction. However, epinephrine was safe and successfully induced arrhythmias in the majority of patients who received it. Furthermore, when atropine was added in epinephrine‐refractory cases, in a post hoc analysis there was no difference in arrhythmia induction between medications. Cost savings could thus be significant without compromising safety

Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U_q[osp(1/2)] and the corresponding supergroup OSp_q(1/2). The classical q-->1 limit of this universal T-matrix yields the group element of the undeformed OSp(1/2) supergroup. The finite dimensional representations of the quantum supergroup OSp_q(1/2) are readily constructed employing the said universal T-matrix and the known finite dimensional representations of the dually related deformed U_q[osp(1/2)] superalgebra. Proceeding further, we derive the product law, the recurrence relations and the orthogonality of the representations of the quantum supergroup OSp_q(1/2). It is shown that the entries of these representation matrices are expressed in terms of the little Q-Jacobi polynomials with Q = -q. Two mutually complementary singular maps of the universal T-matrix on the universal R-matrix are also presented.Comment: 21pages, no figure; final form for publicatio