Stripes on rectangular tilings

We consider a class of cut-and-project sets \Lambda = \Lambda_F \times \zahl in the plane. Let $L=\Lambda+w\real$, $w\in\real^2$, be a countable union of parallel lines. Then either (1) $L$ is a discrete family of lines, (2) $L$ is a dense subset of $\real^2$, or (3) each connected component of the closure of $L$ is homeomorphic to $[0,1] \times \real$.Comment: 6 pages, 2 figure

Separated right and left ventricular excitation during right ventricular septal pacing in a patient with narrow QRS wave: A case report

Introduction. Right ventricular septal pacing is thought to be better than right ventricular apical pacing for shortening the QRS duration and for preserving left ventricular function. However, right ventricular septal pacing may not be effective in all cases. In this case report, we present a rare case in which right ventricular septal pacing induced thoroughly separated right and left ventricular excitation despite the presence of a relatively narrow QRS wave during atrium-only pacing. Case presentation. We report a case of 63-year-old Japanese man with cardiomyopathy with an implantable cardioverter defibrillator placement for ventricular tachycardia. Three years after implantation, he developed second-degree atrio-ventricular block. Therefore, atrio-ventricular sequential pacing was started; then his heart failure was much worsened. His electrocardiogram showed a dissociated biphasic QRS wave during right ventricular high-septal pacing, despite the presence of a non-fragmented QRS morphology during atrium-only pacing. An activation map during right ventricular high-septal pacing showed that right ventricular conduction started at the pacing site and ended at the right ventricular basal inferior site. Subsequently after a 10ms interval, left ventricular conduction started at the left ventricular posteroseptum and ended at the left ventricular lateral wall. These data indicate that during right ventricular high-septal pacing, the first component of the QRS wave supposedly reflects only right ventricular excitation and the second component only left ventricular excitation. Also due to the intracardiac electrograms, it was assumed that this phenomenon was caused by transversely limited severe transseptal conduction disturbance. Conclusion: It should be noted that even ventricular septal pacing could evoke harmful interventricular dyssynchrony due to transversely limited severe septal conduction disturbance, despite the presence of a relatively narrow QRS wave. © 2014 Yaegashi et al.; licensee BioMed Central Ltd

非線形離散可積分系の新展開

"Novel Development of Nonlinear Discrete Integrable Systems". September 2～4, 2013. edited by Junta Matsukidaira. The papers presented in this volume of RIMS Kokyuroku Bessatsu are in final form and refereed