Positivity and periodicity of QQ-systems in the WZW fusion ring

We study properties of solutions of $Q$-systems in the WZW fusion ring obtained by the Kirillov-Reshetikhin modules. We make a conjecture about their positivity and periodicity and give a proof of it in some cases. We also construct a positive solution of the level $k$ restricted $Q$-system of classical types in the fusion rings. As an application, we prove some conjectures of Kirillov and Kuniba-Nakanishi-Suzuki on the level $k$ restricted $Q$-systems.Comment: 29 pages;Table 1 reproduced from arXiv:math/9812022 [math.QA]; v2 : no changes in main results, paper reorganized, introduction rewritten, notations polished, typos corrected, references added; v3 : typos corrected; v4 : minor change

A Proof of the KNS conjecture : DrD_r case

We prove the Kuniba-Nakanishi-Suzuki (KNS) conjecture concerning the quantum dimension solution of the $Q$-system of type $D_r$ obtained by a certain specialization of classical characters of the Kirillov-Reshetikhin modules. To this end, we use various symmetries of quantum dimensions. As a result, we obtain an explicit formula for the positive solution of the level $k$ restricted $Q$-system of type $D_r$ which plays an important role in dilogarithm identities for conformal field theories.Comment: 13 pages, v3. published version, minor update (references added, typos corrected

Nahm's conjecture and Y-systems

Nahm's conjecture relates $q$-hypergeometric modular functions to torsion elements in the Bloch group. An interesting class of such functions can be (conjecturally) obtained from a pair $(X,X')$ of diagrams, each of which is either a Dynkin diagram of type $ADE$ or a diagram of type $T$. Using properties of Y-systems, we prove that for a matrix of the form $A=\mathcal{C}(X)\otimes \mathcal{C}(X')^{-1}$ where $\mathcal{C}(X)$ and $\mathcal{C}(X')$ are the corresponding Cartan matrices, every solution of the equation $\mathbf{x}=(1-\mathbf{x})^A$ gives rise to a torsion element of the Bloch group.Comment: 11 pages, v4. published version, minor update (typos corrected, references added

Parity-violating πNN\pi NN coupling constant from the flavor-conserving effective weak chiral Lagrangian

We investigate the parity-violating pion-nucleon-nucleon coupling constant $h^1_{\pi NN}$, based on the chiral quark-soliton model. We employ an effective weak Hamiltonian that takes into account the next-to-leading order corrections from QCD to the weak interactions at the quark level. Using the gradient expansion, we derive the leading-order effective weak chiral Lagrangian with the low-energy constants determined. The effective weak chiral Lagrangian is incorporated in the chiral quark-soliton model to calculate the parity-violating $\pi NN$ constant $h^1_{\pi NN}$. We obtain a value of about $10^{-7}$ at the leading order. The corrections from the next-to-leading order reduce the leading order result by about 20~\%.Comment: 12 page

Tribological Characteristics of Smart Materials (Magneto-Rheological Fluids and Elastomers) and Their Applications

Magneto-rheological fluids (MRFs) and magneto-rheological elastomers (MREs), as smart materials, have been widely studied in various engineering fields to address vibration issues because the mechanical properties are controllable under the strength of a magnetic field. Their tribological characteristics are also important to be evaluated, as applications using MRFs and MREs contain various contact interfaces under reciprocating and rotating working conditions. The performance and durability of these materials are related to their tribological characteristics. Therefore, various working conditions and environmental conditions are taken into consideration, and their tribological characteristics are experimentally examined. In addition, applications using MRFs and MREs are introduced, and the tribological performances of these materials are evaluated