We discuss in some detail certain gaps and open problems in the recent paper by E. T. Tomboulis, which claims to give a rigorous proof of quark confinement in 4D lattice Yang-Mills theory for all values of the bare coupling. We also discuss what would be needed to fill the gaps in his proof.

We provide an extension of the perfect sampling algorithm of Fill (1998) to general chains, and describe how use of bounding processes can ease computational burden. Along the way, we unearth a simple connection between the Coupling From The Past (CFTP) algorithm originated by Propp and Wilson (1996) and our extension of Fill’s algorithm.

共振型ワイヤレス電力伝送では，送受電器として非放射形の共振器を用いることにより，高力率かつ高効率な中距離の電力伝送を実現する．しかし，我々の生活環境中は実験環境とは異なり，金属や水，人体など様々な物体が存在するため，それらの影響により共振周波数に変動が生じる．動作環境への適応能力を有し，必要な電力を安定的に給電可能なワイヤレス電力伝送システムの構築に向けて，可変リアクタによる共振周波数補正機構が求められている．本論文では，可変リアクタによる共振周波数補正の原理について概説した上で，現在研究が進められている可変リアクタをその動作原理に基づき分類し，それぞれの特徴を比較する．中でもフィードバックレスで力率補正が可能なFET ブリッジ形可変リアクタについて深く掘り下げ，その動作原理を図説するとともに，6.78 MHz 動作における性能と課題について筆者が実施した実機実験の結果も踏まえて解説...

The Gas Metal Arc Welding Process is characterized by many important process outputs, all of which should be controlled to ensure consistent high performance joints. However, application of multivariable control methods is confounded by the strong physical coupling of typical outputs of bead shape and thermal properties. This coupling arises form he three dimensional thermal diffusion processes...

A high-performance and compact fiber-to-waveguide binary blazed subwavelength grating coupler was designed based on silicon-on-insulator. By the appropriate choice of waveguide/grating parameters, including thicknesses, periods, height, and fill factor, to optimize the mode matching, a relatively high coupling efficiency was obtained for the fiber and waveguide interface. Moreover, perfectly ve...

In this paper we return to a model with domain wall fermions in a waveguide. This model contains a Yukawa coupling y which is needed for gauge invariance. A previous paper left the analysis for large values of this coupling incomplete. We fill the gap by developing a systematic expansion suitable for large y, and using this, we gain an analytic understanding of the phase diagram and fermion spe...

Measurements of the specific heat of liquid helium confined in all three spatial dimensions shows an anomalous behavior that suggests a coupling of individual regions of superfluid. This coupling is thought to occur through the shallow channels used to fill the boxes used as confinement structures. This may be evidence of a proximity effect where helium in the larger boxes modifies the behavior...