Face algebras and unitarity of SU(N)_L-TQFT

Using face algebras (i.e. algebras of L-operators of IRF models), we construct modular tensor categories with positive definite inner product, whose fusion rules and S-matrices are the same as (or slightly different from) those obtained by $U_q (\frak{sl}_{N})$ at roots of unity. Also we obtain state-sums of ABF models on framed links which give quantum SU(2)-invariants of corresponding 3-manifolds.Comment: AMS-LaTeX, 36 pages, to appear in Commun. Math. Phy

Compressive Sampling for Remote Control Systems

In remote control, efficient compression or representation of control signals is essential to send them through rate-limited channels. For this purpose, we propose an approach of sparse control signal representation using the compressive sampling technique. The problem of obtaining sparse representation is formulated by cardinality-constrained L2 optimization of the control performance, which is reducible to L1-L2 optimization. The low rate random sampling employed in the proposed method based on the compressive sampling, in addition to the fact that the L1-L2 optimization can be effectively solved by a fast iteration method, enables us to generate the sparse control signal with reduced computational complexity, which is preferable in remote control systems where computation delays seriously degrade the performance. We give a theoretical result for control performance analysis based on the notion of restricted isometry property (RIP). An example is shown to illustrate the effectiveness of the proposed approach via numerical experiments

Topological strings and 5d T_N partition functions

We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau threefolds. The theories include certain non-Lagrangian theories such as the T_N theory. The refined topological vertex computation generically contains contributions from decoupled M2-branes which are not charged under the 5d gauge symmetry engineered. We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function. We explicitly check this for the T_3 theory as well as Sp(1) gauge theories with N_f = 2, 3, 4 flavors. In particular, our method leads to a new expression of the Sp(1) Nekrasov partition functions without any contour integrals. We also develop prescriptions to calculate the partition functions of theories obtained by Higgsing the T_N theory. We compute the partition function of the E_7 theory via this prescription, and find the E_7 global symmetry enhancement. We finally discuss a potential application of the refined topological vertex to non-toric web diagrams.Comment: 79 pages, 27 figures; v2: minor improvements, references adde

Defect detection using quasi-scholte wave for plate loaded with water on single surface

Ultrasonic guided waves achieve non-destructive inspection of thin plates. However, issues such as large energy leakage and attenuation often plague guided wave inspection of storage tanks and pipes filled with fluid. This study experimentally investigated the non-destructive testing of a water-loaded flat aluminum alloy plate through the application of a quasi-Scholte (QS) wave that propagated along the fluid-plate interface without experiencing attenuation due to leakage. A QS wave was confirmed as having been generated and propagated in a plate loaded with water on the bottom surface using ultrasonic incidence and detection at the top water-free surface. Two-dimensional Fourier transform images of the waveforms revealed refiection of the QS wave from a defect as well as a forward incident QS wave. The visualization results experimentally confirmed-via measurements of waves in water using a laser Doppler vibrometer-that QS waves propagated along a plate surface, while scattered waves were generated by defects

Mode extraction technique for guided waves in a pipe

Guided waves propagating in a pipe consist of many modes with different velocities and dispersions. To analyze these complex guided waves through a normal mode expansion technique, that is the fundamental theory on guided waves, we must first extract guided wave modes from received signals. In this study, we develop a mode extraction technique in which many received signals at different circumferential positions can be processed based on the fact that guided wave modes have different displacement distributions in the circumferential direction. After discussing the relevant theory, we verify our mode extraction technique experimentally using eight signals at eight different circumferential positions. Moreover, we show that the circumferential position of an excitation transducer, as well as the distance between an excitation transducer and a receiver in a pitch-catch configuration can be identified using the mode extraction technique. © 2005 Taylor & Francis Ltd.This is an Accepted Manuscript of an article published by Taylor & Francis in Nondestructive Testing and Evaluation on 19 Aug 2006, available at http://wwww.tandfonline.com/10.1080/10589750500062771