A note on the spectral mapping theorem of quantum walk models

We discuss the description of eigenspace of a quantum walk model $U$ with an associating linear operator $T$ in abstract settings of quantum walk including the Szegedy walk on graphs. In particular, we provide the spectral mapping theorem of $U$ without the spectral decomposition of $T$. Arguments in this direction reveal the eigenspaces of $U$ characterized by the generalized kernels of linear operators given by $T$.Comment: 17 page

Quantum walks on simplicial complexes

We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in the case of the Grover walk on lattices. Moreover, our numerical simulation suggests that localization of our quantum walks reflects not only topological but also geometric structures. On the other hand, our proposing quantum walk contains an intrinsic problem concerning exhibition of non-trivial behavior, which is not seen in typical quantum walks such as Grover walks on graphs. © 2016 Springer Science+Business Media New YorkEmbargo Period 12 month

CFD-based Design of Multi-tube Heat Exchange Type Compact Reactor

The production capacity of compact reactors with micrometer or millimeter-scale channels or tubes is increased by numbering-up. In previous studies, a multi-channel plate type reactor and a multi-tube type reactor (MTR) were developed and applied to extraction and reaction operations. Fluid distribution has often been evaluated to design these reactors, but temperature control, which is critical to the reaction, has not been fully considered. It is important to solve this problem and establish a design method. In this study, computational fluid dynamics (CFD)-based design was performed so as to achieve the uniform flow and temperature distributions among the reaction tubes in the MTR, where an exothermic reaction proceeds in each tube with an immobilized catalyst and the reaction temperature is controlled by a coolant flowing outside the tubes. Effects of multi-tube arrangement of lattice, concentric circles and single circle, shell cross-sectional shape of circle, rectangle and ring, and reaction tubes with or without catalyst-free inert sections on the reactor performance were investigated by CFD. The usefulness of a two-step approach of designing the MTR after designing the double-tubular reactor was confirmed through a case study on parallel reactions

Irinotecan Hydrochloride (CPT-11) in Dialysis Patients with Gastrointestinal Cancer

We investigated changes in drug disposition and toxicities with CPT-11 in 15 dialysis patients with gastrointestinal cancers to clarify whether CPT-11 could be administered safely in such patients. For comparison, the same parameters were also investigated in 10 cancer patients not undergoing dialysis. Items investigated included (1) plasma concentrations of SN-38, SN-38G and CPT-11 at 0, 1, 12, 24, 36, 48 and 72h after administration, together with a comparison of mean AUC values for 3 dose levels of CPT-11 (50, 60 and 70mg/m2) in dialysis patients and controls;and (2) occurrence of adverse events. Several findings emerged from this study:(1) No significant difference was observed in the AUC for SN-38 or CPT-11 between the dialysis and control groups;(2) The AUC for SN-38G at each dose was significantly higher in dialysis patients;and (3) Grade 1-4 leucopenia was observed in 11 of the dialysis patients. One patient developed grade 4 leucopenia and died due to sepsis. Anorexia, diarrhea, nausea, alopecia and interstitial pneumonia occurred in 6 dialysis patients. We found changes in drug dispositions of CPT-11, SN-38 and SN-38G in dialysis patients, suggesting that hepatic excretion, especially that of SN-38G, was increased. No significant difference in occurrence of adverse events was observed between the 2 groups. This indicates that CPT-11 can be administered safely in patients on dialysis.</p

Quantum search on simplicial complexes

金沢大学理工学域 数物科学系 名誉教授In this paper, we propose an extension of quantum searches on graphs driven by quantum walks to simplicial complexes. To this end, we define a new quantum walk on simplicial complex which is an alternative of preceding studies by authors. We show that the quantum search on the specific simplicial complex corresponding to the triangulation of n-dimensional unit square driven by this new simplicial quantum walk works well, namely, a marked simplex can be found with probability 1+o(1) 1+o(1) within a time O(N − − √ ) O(N), where N is the number of simplices with the dimension of marked simplex.Embargo Period 12 month

Magnetic phase diagram of antiferroquadrupole ordering in HoB2C2

The magnetic phase diagram for antiferro-quadrupole (AFQ) ordering in tetragonal HoB$_2$C$_2$ has been investigated by measurements of elastic constants $C_{11}$, $C_{44}$ and $C_{66}$ in fields along the basal $x$-$y$ plane as well as the principal [001]-axis. The hybrid magnet (GAMA) in Tsukuba Magnetic Laboratory was employed for high field measurements up to 30 T. The AFQ phase is no longer observed above 26.3 T along the principal [001] axis in contrast to the relatively small critical field of 3.9 T in fields applied along the basal [110] axis. The quadrupolar intersite interaction of $O_{xy}$ and/or $O_2^2$ is consistent with the anisotropy in the magnetic phase diagram of the AFQ phase in HoB$_2$C$_2$.Comment: Phys. Rev. B. (2005) in press. approx 8 pages, 10 figure