Quantization of virtual Grothendieck rings and their structure including quantum cluster algebras

The quantum Grothendieck ring of a certain category of finite-dimensional modules over a quantum loop algebra associated with a complex finite-dimensional simple Lie algebra $\mathfrak{g}$ has a quantum cluster algebra structure of skew-symmetric type. Partly motivated by a search of a ring corresponding to a quantum cluster algebra of {\em skew-symmetrizable} type, the quantum {\em virtual} Grothendieck ring, denoted by $\mathfrak{K}_q(\mathfrak{g})$, is recently introduced by Kashiwara--Oh \cite{KO23} as a subring of the quantum torus based on the $(q,t)$-Cartan matrix specialized at $q=1$. In this paper, we prove that $\mathfrak{K}_q(\mathfrak{g})$ indeed has a quantum cluster algebra structure of skew-symmetrizable type. This task essentially involves constructing distinguished bases of $\mathfrak{K}_q(\mathfrak{g})$ that will be used to make cluster variables and generalizing the quantum $T$-system associated with Kirillov--Reshetikhin modules to establish a quantum exchange relation of cluster variables. Furthermore, these distinguished bases naturally fit into the paradigm of Kazhdan--Lusztig theory and our study of these bases leads to some conjectures on quantum positivity and $q$-commutativity

The Case for Hypercritical Accretion in M33 X-7

The spin parameter of the black hole in M33 X-7 has recently been measured to be a*=0.77+-0.05 (Liu et al. 2008). It has been proposed that the spin of the 15.65 M_sun black hole is natal. We show that this is not a viable evolutionary path given the observed binary orbital period of 3.45 days since the explosion that would produce a black hole with the cited spin parameter and orbital period would disrupt the binary. Furthermore, we show that the system has to be evolved through the hypercritical mass transfer of about 5 M_sun from the secondary star to the black hole.Comment: 4 page

Implementation of the submarine diving simulation in a distributed environment

ABSTRACTTo implement a combined discrete event and discrete time simulation such as submarine diving simulation in a distributed environment, e.g., in the High Level Architecture (HLA)/Run-Time Infrastructure (RTI), a HLA interface, which can easily connect combined models with the HLA/RTI, was developed in this study. To verify the function and performance of the HLA interface, it was applied to the submarine dive scenario in a distributed environment, and the distributed simulation shows the same results as the stand-alone simulation. Finally, by adding a visualization model to the simulation and by editing this model, we can confirm that the HLA interface can provide user-friendly functions such as adding new model and editing a model

One-dimensional broadband phononic crystal filter with unit cells made of two non-uniform impedance-mirrored elements

A one-dimensional finite-sized phononic crystal(PC) made of a specially-configured unit cell is proposed to realize broad bandpass, high-performance filtering. The unit cell is specially-configured with two elements having mirrored impedance distributions of each other. One element has a non-uniform impedance distribution that is so engineered as to maximize wave transmission in the pass band and to minimize transmission in the adjacent stop band while the other, exactly the mirrored distribution. The mirroring approach naturally yields the overall impedance contrast within the resulting unit cell, necessary to form stop bands in a PC of the unit cells. More importantly, the good transmission performance of the orginally-engineered element can be preserved by the approach because no additional impedance mismatch is introduced along the interface of the two impedance-mirrored elements. Extraordinary performance of the PC filter made of the proposed unit cell, such as high transmission, large bandwidth and sharp roll-off, is demonstrated by using one-dimensional longitudinal elastic wave problems. Copyright 2013 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4790638ope

A Synergistic Anti-Diabetic Effect by Ginsenosides Rb1 and Rg3 through Adipogenic and Insulin Signaling Pathways in 3T3-L1 Cells

Although ginsenosides Rb1 and Rg3 have been identified as the significant ginsenosides found in red ginseng that confer anti-diabetic actions, it is unclear whether insulin-sensitizing effects are mediated by the individual compounds or by their combination. To determine the effect of ginsenosides Rb1 and Rg3 on adipocyte differentiation, 3T3-L1 preadipocytes were induced to differentiate the standard hormonal inducers in the absence or presence of ginsenosides Rb1 or Rg3. Additionally, we determined the effects of Rb1, Rg3, or their combination on the expression of genes related to adipocyte differentiation, adipogenic transcription factors, and the insulin signaling pathway in 3T3-L1 cells using semi-quantitative RT-PCR. Rb1 significantly increased the expression of CEBP alpha, PPAR gamma, and aP2 mRNAs. However, Rg3 exerted its maximal stimulatory effect on these genes at 1 mu M concentration, while a high concentration (50 mu M) showed inhibitory effects. Similarly, treatment with Rb1 and Rg3 (1 mu M) increased the expression of IRS-1, Akt, PI3K, GLUT4, and adiponectin. Importantly, co-treatment of Rb1 and Rg3 (9:1) induced the maximal expression levels of these mRNAs. Our data indicate that the anti-diabetic activity of red ginseng is, in part, mediated by synergistic actions of Rb1 and Rg3, further supporting the significance of minor Rg3

(1,2-Dicarba-closo-dodeca­boran­yl)trimethyl­methanaminium iodide

The title compound, [1-(CH3)3NCH2-1,2-C2B10H11]+·I− or C6H22B10N+·I−, was obtained by the reaction of (1,2-dicarba-closo-dodeca­boran­yl)dimethyl­methanamine with methyl iodide. The asymmetric unit contains two iodide anions and two (o-carboran­yl)tetra­methyl­ammonium cations. The bond lengths and angles in the carborane cage are within normal ranges, but the N—Cmethyl­ene—Ccage angle is very large [120.2 (2)°] because of repulsion between the carborane and tetra­methyl­ammonium units. In the crystal, ions are linked through C—H⋯I hydrogen bonds

Enhancing the rate-hardness of haptic interaction: Successive force augmentation approach

© 1982-2012 IEEE. There have been numerous approaches that have been proposed to enlarge the impedance range of haptic interaction while maintaining stability. However, enhancing the rate-hardness of haptic interaction while maintaining stability is still a challenging issue. The actual perceived rate-hardness has been much lower than what the users expect to feel. In this paper, we propose the successive force augmentation (SFA) approach, which increases the impedance range by adding a feed-forward force offset to the state-dependent feedback force rendered using a low stiffness value. This allows the proposed approach to display stiffness of up to 10 N/mm with Phantom Premium 1.5. It was possible to further enhance the rate-hardness by using the original value of virtual environment stiffness for feedback force calculation during the transient response followed by normal SFA. Experimental evaluation for multi-DoF virtual environment exhibited a much higher displayed stiffness and rate-hardness compared to conventional approaches. Two user studies revealed that the increase of rate-hardness due to SFA allowed the participants to have a faster reaction time to an unexpected collision with a virtual wall and accurately discriminate between four virtual walls of different stiffness

Association of Epidermal Growth Factor Receptor Mutations with Metastatic Presentations in Non-Small Cell Lung Cancer

We performed this retrospective study to assess the association of epidermal growth factor receptor (EGFR) with metastatic presentations in advanced non-small cell lung cancer (NSCLC). The data from 125 patients with stage III or IV NSCLC were analyzed. We detected EGFR mutations in 36 NSCLC patients. EGFR mutations were predominant in never-smokers (P < .001), patients with adenocarcinomas (P < .001), and female patients (P < .001). When the metastatic sites were analyzed, pleural metastases were associated with a high incidence of EGFR mutations (P = .028). Particularly, pleural metastases with minimal effusion (PMME) were associated with EGFR mutational status (P = .001). Patients with N3 lesions were less likely to harbor EGFR mutations (P = .033). On multivariate analysis, N3 lesions (P = .017) and PMME (P < .001) remained significant factors for EGFR mutations. EGFR mutations may be associated with different presentations of pleural and N3 nodal metastases