Quantum Cluster Variables via Serre Polynomials

For skew-symmetric acyclic quantum cluster algebras, we express the quantum $F$-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. As byproducts, we obtain the existence of counting polynomials for these varieties and the positivity conjecture with respect to acyclic seeds. These results complete previous work by Caldero and Reineke and confirm a recent conjecture by Rupel.Comment: minor corrections, reference added, example 4.3 added, 38 page

Repetitive higher cluster categories of type A_n

We show that the repetitive higher cluster category of type A_n, defined as the orbit category D^b(mod kA_n)/(tau^{-1}[m])^p, is equivalent to a category defined on a subset of diagonals in a regular p(nm+1)-gon. This generalizes the construction of Caldero-Chapoton-Schiffler, which we recover when p=m=1, and the work of Baur-Marsh, treating the case p=1, m>1. Our approach also leads to a geometric model of the bounded derived category D^b(mod kA_n)

Ab initio calculation of the KRb dipole moments

The relativistic configuration interaction valence bond method has been used to calculate permanent and transition electric dipole moments of the KRb heteronuclear molecule as a function of internuclear separation. The permanent dipole moment of the ground state $X^1\Sigma^+$ potential is found to be 0.30(2) $ea_0$ at the equilibrium internuclear separation with excess negative charge on the potassium atom. For the $a^3\Sigma^+$ potential the dipole moment is an order of magnitude smaller (1 $ea_0=8.47835 10^{-30}$ Cm) In addition, we calculate transition dipole moments between the two ground-state and excited-state potentials that dissociate to the K(4s)+Rb(5p) limits. Using this data we propose a way to produce singlet $X^1\Sigma^+$ KRb molecules by a two-photon Raman process starting from an ultracold mixture of doubly spin-polarized ground state K and Rb atoms. This Raman process is only allowed due to relativistic spin-orbit couplings and the absence of gerade/ungerade selection rules in heteronuclear dimers.Comment: 16 pages, 7 figure

p-wave phase shift and scattering length of 6^6Li

We have calculated the p-wave phase shifts and scattering length of $^6$Li. For this we solve the $p$ partial wave Schr\"odinger equation and analyze the validity of adopting the semiclassical solution to evaluate the constant factors in the solution. Unlike in the $s$ wave case, the semiclassical solution does not provide unique value of the constants. We suggest an approximate analytic solution, which provides reliable results in special cases. Further more, we also use the variable phase method to evaluate the phase shifts. The p-wave scattering lengths of $^{132}$Cs and $^{134}$Cs are calculated to validate the schemes followed. Based on our calculations, the value of the $p$ wave scattering length of $^6$Li is $-45a_o$.Comment: 10 figure

Global analysis of data on the spin-orbit coupled A1Σu+A^{1}\Sigma_{u}^{+} and b3Πub^{3}\Pi_{u} states of Cs2

We present experimentally derived potential curves and spin-orbit interaction functions for the strongly perturbed $A^{1}\Sigma_{u}^{+}$ and $b^{3}\Pi_{u}$ states of the cesium dimer. The results are based on data from several sources. Laser-induced fluorescence Fourier transform spectroscopy (LIF FTS) was used some time ago in the Laboratoire Aim\'{e} Cotton primarily to study the $X ^{1}\Sigma_{g}^{+}$ state. More recent work at Tsinghua University provides information from moderate resolution spectroscopy on the lowest levels of the $b^{3}\Pi_{0u}^{\pm}$ states as well as additional high resolution data. From Innsbruck University, we have precision data obtained with cold Cs$_{2}$ molecules. Recent data from Temple University was obtained using the optical-optical double resonance polarization spectroscopy technique, and finally, a group at the University of Latvia has added additional LIF FTS data. In the Hamiltonian matrix, we have used analytic potentials (the Expanded Morse Oscillator form) with both finite-difference (FD) coupled-channels and discrete variable representation (DVR) calculations of the term values. Fitted diagonal and off-diagonal spin-orbit functions are obtained and compared with {\it ab initio} results from Temple and Moscow State universities

Acute mesenteric ischaemia in refractory shock on veno-arterial extracorporeal membrane oxygenation

Background: Acute mesenteric ischaemia is a severe complication in critically ill patients, but has never been evaluated in patients on veno-arterial extracorporeal membrane oxygenation (V-A ECMO). This study was designed to determine the prevalence of mesenteric ischaemia in patients supported by V-A ECMO and to evaluate its risk factors, as well as to appreciate therapeutic modalities and outcome. Methods: In a retrospective single centre study (January 2013 to January 2017), all consecutive adult patients who underwent V-A ECMO were included, with exclusion of those dying in the first 24 hours. Diagnosis of mesenteric ischaemia was performed using digestive endoscopy, computed tomography scan or first-line laparotomy. Results: One hundred and fifty V-A ECMOs were implanted (65 for post-cardiotomy shock, 85 for acute cardiogenic shock, including 39 patients after refractory cardiac arrest). Overall, median age was 58 (48-69) years and mortality 56%. Acute mesenteric ischaemia was suspected in 38 patients, with a delay of four (2-7) days after ECMO implantation, and confirmed in 14 patients, that is, a prevalence of 9%. Exploratory laparotomy was performed in six out of 14 patients, the others being too unstable to undergo surgery. All patients with mesenteric ischaemia died. Independent risk factors for developing mesenteric ischaemia were renal replacement therapy (odds ratio (OR) 4.5, 95% confidence interval (CI) 1.3-15.7, p=0.02) and onset of a second shock within the first five days (OR 7.8, 95% CI 1.5-41.3, p=0.02). Conversely, early initiation of enteral nutrition was negatively associated with mesenteric ischaemia (OR 0.15, 95% CI 0.03-0.69, p=0.02). Conclusions: Acute mesenteric ischaemia is a relatively frequent but dramatic complication among patients on V-A ECMO