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In this paper, we study mixed-type solutions of $${SU(3)}$$ Chern-Simons system (see (1.4) below) on a two dimensional flat torus. Nolasco and Tarantello (Commun Math Phys 213:599-639, ), among other things, Nolasco and Tarantello obtained solutions of (1.4) as minimizers of several functionals closely related to (1.4), and showed that if $${N_1+N_2=1}$$ , then one of those minimizers turns out to be a mixed-type solution, that is, one component tends to $${\ln\frac{1}{2}}$$ pointwise a.e. and the other component converges to a solution of a mean field equation. We call these kinds of solutions mixed-type (I) solutions. In this paper, we prove two main results: (i) the asymptotic analysis of mixed-type (I) solutions with arbitrary configuration of vortex points, and (ii) the existence of mixed-type (I) solutions under a non-degenerate condition. This non-degenerate condition also ensures some uniqueness result. In particular, our results imply that when $${N_1+N_2=1}$$ , there are only two mixed-type (I) solutions of (1.4). [ABSTRACT FROM AUTHOR]

We consider a nonlinear elliptic equation derived from the Chern-Simons gauged $$O(3)$$ sigma model on a flat torus. Recently, it has been conjectured that there might exist a stable nontopological entire solution in $$\mathbb {R}^2$$ under certain conditions. In this paper, we construct bubbling stable solutions on a flat torus which blow up at a vortex point. Our result shows that some global condition on the coefficients in Bartolucci et al. (Ann Inst Henri Poincaré Anal Non Linéaire. doi:, ) is necessary for the equivalence result between stable solutions and topological solutions. Moreover, we investigate other types of bubbling solutions including mountain pass solutions and analyze the asymptotic behavior of general solutions on a flat torus. [ABSTRACT FROM AUTHOR]

The study was designed to examine children's ability with rhythmic duplication in a longitudinal investigation. Participants 0V = 32) were children 6 years old (n = 8), 5 years old (n = 8), 4 years old (n = 8), and 3 years old (n = 8)from a Korean community in a small Midwestern city. Each child was tested on individually duplicating 10 kinds of rhythmic patterns by tapping and chanting. Parents of the participants were interviewed. One year after the first investigation, the phase H was conducted with the same participants (N = 26) and the same test items. Age level was a significant predictor of children's rhythmic development, but gender was not. Children at all age levels could duplicate the rhythmic patterns better by chanting than by tapping. The response mode of the age 3 and age 4 groups did not significantly differ from each other; the same was found for the age 5 through age 7 groups. However, there were significant differences between the age 4 and age 5 groups. An informal observation based on parent interviews indicated that cognitive development, weekly musical exposure time, and family involvement may be variables that need further study. [ABSTRACT FROM AUTHOR]

We are concerned with the mean field equation with singular data on bounded domains. By assuming a singular point to be a critical point of the 1-vortex Kirchhoff-Routh function, we prove local uniqueness and non-degeneracy of bubbling solutions blowing up at a singular point. The proof is based on sharp estimates for bubbling solutions of singular mean field equations and a suitably defined Pohozaev-type identity. [ABSTRACT FROM AUTHOR]

The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence seem to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non-degeneracy assumptions on the associated m-vortex Hamiltonian, the m-point bubbling solutions of the mean field equation are non-degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind. [ABSTRACT FROM AUTHOR]

We consider the self-dual equations arising from the Chern–Simons gauge theory of rank 2 such as the S U ( 3 ) , S O ( 5 ) , and G 2 Chern–Simons model in R 2 . There are three possible types of solutions in these theories, namely, topological, nontopological, and mixed type solutions. The existence of a mixed type solution for an arbitrary configuration of vortex points has been a long-standing open problem. We construct here a family of mixed type solutions ( u 1 , ε , u 2 , ε ) , ε > 0 for an arbitrary configuration of vortex points under a mild non-degeneracy condition. The main new idea of our construction of an approximate solution is to use different scalings for different components. In the process of the finite dimensional reduction, all estimates for this particular construction become rather delicate. [ABSTRACT FROM AUTHOR]

An abstract of the dissertation "Music Practices and Teachers' Needs for Teaching Music in Public Preschools of South Korea," by Youngae Lee is presented.

Background: Epidemiological evidence suggests that particulate matter (PM) exposure can trigger or worsen atopic dermatitis (AD); however, the underlying mechanisms remain unclear. Recently, pregnane X receptor (PXR), a xenobiotic receptor, was reported to be related to skin inflammation in AD., Objectives: This study aimed to explore the effects of PM on AD and investigate the role of PXR in PM-exposed AD., Methods: In vivo and in vitro AD-like models were employed, using BALB/c mice, immortalized human keratinocytes (HaCaT), and mouse CD4 + T cells., Results: Topical application of PM significantly increased dermatitis score and skin thickness in AD-like mice. PM treatment increased the mRNA and protein levels of type 17 inflammatory mediators, including interleukin (IL)-17A, IL-23A, IL-1β, and IL-6, in AD-like mice and human keratinocytes. PM also activated PXR signaling, and PXR knockdown exacerbated PM-induced type 17 inflammation in human keratinocytes and mouse CD4 + T cells. In contrast, PXR activation by rifampicin (a human PXR agonist) reduced PM-induced type 17 inflammation. Mechanistically, PXR activation led to a pronounced inhibition of the nuclear factor kappa B (NF-κB) pathway., Conclusion: In summary, PM exposure induces type 17 inflammation and PXR activation in AD. PXR activation reduces PM-induced type 17 inflammation by suppressing the NF-κB signaling pathway. Thus, PXR represents a promising therapeutic target for controlling the PM-induced AD aggravation., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Lee, Lee, Jang, Oh, Lee and Cho.)

Numerous recent evidence highlights epidemiological connections between rosacea and metabolic disorders. However, the precise path through which metabolic factors impact rosacea risk is still unclear. Therefore, this study aims to investigate the role of adiponectin, a crucial adipokine that regulates metabolic homeostasis, in the pathogenesis of rosacea. We elucidated a detrimental feedback loop between rosacea-like skin inflammation and decreased levels of skin adiponectin. To elaborate, rosacea lesional skin exhibits diminished adiponectin expression compared with nonlesional areas in the same patients. Induction of rosacea-like inflammation reduced adiponectin levels in the skin by generating inflammatory cytokines that suppress adiponectin production from subcutaneous adipocytes. Conversely, complete depletion of adiponectin exacerbated rosacea-like features in the mouse model. Mechanistically, adiponectin deficiency led to heightened S6 phosphorylation, a marker of the mTORC1 signaling pathway, in the epidermis. Adiponectin significantly inhibited S6 phosphorylation in cultured keratinocytes. Notably, replenishing adiponectin whole protein or topically applying an agonist for adiponectin receptor 1 successfully improved rosacea-like features in mice. This study contributes to understanding the role of adiponectin in skin inflammation associated with rosacea pathophysiology, suggesting that restoring adiponectin function in the skin could be a potential therapeutic strategy., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)