Hausdorff dimension of sets with restricted, slowly growing partial quotients in the semi-regular continued fraction

We consider sets of irrational numbers whose partial quotients $a_{\sigma,n}$ in the semi-regular continued fraction expansion obey certain restrictions and growth conditions. Our main result asserts that, for any sequence $\sigma\in\{-1,1\}^\mathbb N$ in the expansion, any infinite subset $B$ of $\mathbb N$ and for any function $f$ on $\mathbb N$ with values in $[\min B,\infty)$ and tending to infinity, the set of irrationals in $(0,1)$ such that $$a_{\sigma,n}\in B,\ a_{\sigma,n}\leq f(n)\text{ for all $n\in\mathbb N$ and }a_{\sigma,n}\to\infty\text{ as }n\to\infty$$ is of Hausdorff dimension $\tau(B)/2,$ where $\tau(B)$ is the exponent of convergence of $B$. We also prove that for any $\sigma\in\{-1,1\}^\mathbb N$ and any $B\subset\mathbb N$, the set of irrationals in $(0,1)$ such that $$a_{\sigma,n}\in B\text{ for all $n\in\mathbb N$ and }a_{\sigma,n}\to\infty\text{ as }n\to\infty$$ is also of Hausdorff dimension $\tau(B)/2$. To prove these results, we construct non-autonomous iterated function systems well-adapted to the given restrictions and growth conditions, and then apply the dimension theory developed by Rempe-Gillen and Urba\'nski.Comment: 14 pages, no figur

Symmetry Breaking in Bose-Einstein Condensates

A gaseous Bose-Einstein condensate (BEC) offers an ideal testing ground for studying symmetry breaking, because a trapped BEC system is in a mesoscopic regime, and situations exist under which symmetry breaking may or may not occur. Investigating this problem can explain why mean-field theories have been so successful in elucidating gaseous BEC systems and when many-body effects play a significant role. We substantiate these ideas in four distinct situations: namely, soliton formation in attractive BECs, vortex nucleation in rotating BECs, spontaneous magnetization in spinor BECs, and spin texture formation in dipolar BECs.Comment: Submitted to the proceedings of International Conference on Atomic Physics 200

Magnons and electromagnons in a spin-lattice-coupled frustrated magnet CuFeO2 as seen via inelastic neutron scattering

We have investigated spin-wave excitations in a four-sublattice (4SL) magnetic ground state of a frustrated magnet CuFeO2, in which `electromagnon' (electric-field-active magnon) excitation has been discovered by recent terahertz time-domain spectroscopy [Seki et al. Phys. Rev. Lett. 105 097207 (2010)]. In previous study, we have identified two spin-wave branches in the 4SL phase by means of inelastic neutron scattering measurements under applied uniaxial pressure. [T. Nakajima et al. J. Phys. Soc. Jpn. 80 014714 (2011) ] In the present study, we have performed high-energy-resolution inelastic neutron scattering measurements in the 4SL phase, resolving fine structures of the lower-energy spin-wave branch near the zone center. Taking account of the spin-driven lattice distortions in the 4SL phase, we have developed a model Hamiltonian to describe the spin-wave excitations. The determined Hamiltonian parameters have successfully reproduced the spin-wave dispersion relations and intensity maps obtained in the inelastic neutron scattering measurements. The results of the spin-wave analysis have also revealed physical pictures of the magnon and electromagnon modes in the 4SL phase, suggesting that collinear and noncollinear characters of the two spin-wave modes are the keys to understand the dynamical coupling between the spins and electric dipole moments in this system.Comment: 8 pages, 6 figure

Estimating Effective Steric and Electronic Impacts of a Ferrocenyl Group in Organophosphines

A series of monodentate ferrocenylphosphines, Fc3P (1a), Fc2PhP (1b), and Fc2ArP (1c; Fc = ferrocenyl, Ar = 3,4-methylenedioxyphenyl), were prepared, and their electronic and steric properties were quantitatively determined. By the IR measurements of their respective Ni(CO)3(phosphine) complexes, the electronic properties of the ferrocenyl group in organophosphines were estimated to be similar to those of primary alkyl groups. The ferrocenyl group is a better electron donor than a methyl group and a poorer donor than an ethyl group. The gold(I) chloride complexes of 1a–c were prepared and their X-ray crystal structures were determined. The %Vbur parameters for 1a–c were calculated using the X-ray structural data, and their ″Tolman cone angles″ were estimated. The steric influence of the ferrocenyl group in organophosphines was clarified to be larger than those of cyclohexyl, tert-butyl, and o-tolyl groups and is comparable to that of a mesityl group

A New Method of Microcatheter Heat-Forming for Cerebral Aneurysmal Coiling Using Stereolithography Three-Dimensional Printed Hollow Vessel Models

[Background] To perform successful coil embolization of cerebral aneurysms, it is crucial to make an appropriately shaped microcatheter tip for an aneurysm and its parent artery. So far, we manually shaped a mandrel by referencing two-dimensional (2D) images of a rotation digital subtraction angiography (DSA) on a computer screen. However, this technique requires a lot of experience, and often involves trial and error. Recently, there have been increasing reports of manual mandrel shaping using a full-scale three-dimensional (3D) model of an aneurysm and its parent artery output by various types of 3D printer. We have further developed this method by producing a hollow model of an aneurysm and its parent artery with a stereolithography 3D printer and inserting a mandrel inside the model to fit and stabilize a microcatheter tip. [Methods] Based on digital imaging and communications in medicine (DICOM) data obtained by rotational DSA, 3D images of an aneurysm and its parent artery were created and converted into standard triangulated language (STL) data. A hollow model was produced by extruding the STL data outward in the normal direction, and then a hole was made at the tip of the aneurysm using these STL data. We output these STL data to a stereolithography 3D printer. After cleaning and sterilizing the model, the mandrel was inserted in the direction of the parent artery through the hole made in the tip of the aneurysm and pushed in, creating the ideal mandrel shape. Twelve cases (14 aneurysms) were included in this study. A microcatheter tip was shaped by this method for patients who were scheduled to undergo coil embolization for an unruptured aneurysm. [Results] In 13 of the 14 aneurysms, the microcatheter was easily guided into the aneurysms in one or two trials, the position of the microcatheter tip in the aneurysm was appropriate, and the stability during coil embolization was high. [Conclusion] Our method differs from the conventional one in that a hollow model made of resin is produced with a stereolithography 3D printer and that the mandrel is shaped by inserting it retrogradely into the hollow model. Using our new method, it will be possible to shape the tip of a microcatheter suitable for safe and stable coil embolization without relying on an operator’s experience

ドイツ第二帝政期における一般兵役義務と軍事言説 1871-1914

早大学位記番号:新7594早稲田大

Effect of Pt Addition on the Formation of Ni-Pt Porous Layer

A Ni-Pt alloy porous layer was formed by electrodepositing Pt using Ni as the substrate sample, followed by Al-depositing and Al-dissolving. The Pt was electrolyzed using an aqueous solution as the medium, and the Al-depositing and Al-dissolving were treated using a molten salt as the medium. The molten salt used was NaCl-KCl with 3.5 mol% AlF3 added. It was found that Pt electrodeposition formed on the surface had a finer structure. Furthermore, it was clarified that the lower the electrodeposition potential, the thicker the Ni-Pt alloy porous layer. The cathode polarization curve was measured in KOH solution, and the hydrogen gas was determined when a constant voltage electrolysis was performed with a hydrogen detection gas sensor using a tubular yttria-stabilized zirconia (8 mol% Y2O3-ZrO2)