We investigate the regularity of solutions to linear elliptic equations in both divergence and non-divergence forms, particularly when the principal coefficients have Dini mean oscillation. We show that if a solution u to a divergence-form equation satisfies Du(x(o))=0 at a point, then the second derivative D(2)u(x(o)) exists and satisfies sharp continuity estimates. As a consequence, we obtain "C-2,C-alpha regularity" at critical points when the coefficients of L are C-alpha. This result refines a theorem of Teixeira (Math. Ann. 358 (2014), no. 1-2, 241-256) in the linear setting, where both linear and nonlinear equations were considered. We also establish an analogous result for equations in the non-divergence form.

We show that spatial zero extension across the boundary may fail in parabolic Sobolev spaces ℋ^1_p((0,T) × Ω), which can also be characterized as L_p(0,T;W^1_p(Ω))∩ W^1_p(0,T; W^-1_p(Ω)). More precisely, for any p∈ [1, ∞), we construct a function u∈ℋ^1_p((0,T)×ℝ^d_+) whose zero extension does not belong to ℋ^1_p((0,T)×ℝ^d). The obstruction occurs even for a flat boundary and is caused by a self-similar boundary layer concentrated at the initial-boundary corner, which produces a boundary supported normal flux defect after zero extension. We also discuss the suitability of various Sobolev-type spaces as solution spaces for parabolic equations in divergence form.

We investigate the regularity of elliptic equations in double divergence form, where the leading coefficients satisfy the Dini mean oscillation condition. We prove that the solutions are differentiable on the zero level set and derive a pointwise bound for the derivative. As an application, we establish global pointwise estimates for the Green's function of second-order uniformly elliptic operators in non-divergence form, assuming Dini mean oscillation coefficients in bounded C1,alpha domains.

We establish the existence, uniqueness, and various estimates for Green functions of mixed Dirichlet-conormal derivative problems for the stationary Stokes system with measurable coefficients in a two-dimensional Reifenberg flat domain with a rough separation.

AbstractIncreased production of reactive oxygen species (ROS) leads to oxidative stress, with its damaging effect extending to the mitochondria and plasma membrane. Further, prolonged inflammation can result in chronic disease development. The marine microdiatom Odontella aurita is recognized for its potential in food and pharmaceutical development. Moreover, it contains antioxidant and anti-inflammatory properties. However, studies regarding the efficacy of their varying extract forms and their underlying mechanisms remain scarce. Therefore, this study aims to explore the antioxidant and anti-inflammatory effects of Odontella aurita extracts obtained using various extraction methods (hot water, 70% ethanol, and chloroform:methanol (CM)). Among the three Odontella aurita extracts, the CM extract demonstrated superior efficacy in protecting RAW 264.7 cells from H2O2-induced cytotoxicity. It significantly lowered the levels of ROS and enhanced the expression of superoxide dismutase and glutathione peroxidase. Furthermore, the CM extract outperformed other extracts in inhibiting LPS-induced nitric oxide production, reducing mRNA levels in nitric oxide synthase, cyclooxygenase, and the proinflammatory cytokines interleukin IL-1β, IL-6, TNFα. Additionally, CM extract effectively suppressed the activation of NF-κB/IκBα and JAK2-STAT3 in LPS-induced RAW 264.7 cells. HPLC–UV analysis revealed a remarkable 33-fold higher fucoxanthin content in CM compared to the ethanol extract. GC–MS analysis identified elevated levels of cholest-5-en-3-ol, phytol, eicosapentaenoic acid methyl ester, methyl palmitate, palmitoleic acid methyl ester, and neophytadiene in the CM extract. These findings suggest that Odontella aurita CM extract is a promising antioxidant candidate for preventing or treating inflammatory diseases, consequently emphasizing its potential for further development. Graphical Abstract

Nyasol은 Anemarrhena asphodeloides Bunge로부터 분리된 리그난 계열의 화합물로 강력한 티로시나아제 억제, 해열, 심장강화, 이뇨, 항균 및 항산화 활성을 지닌 것으로 알려졌다. 본 연구에서는 이 화합물의 항산화 특성을 체계적으로 설명하기 위해 B3LYP 하이브리드 함수 및 6–311+G(d,p) 기저함수를 사용한 밀도범함수 이론(DFT)에 기반한 이론적 계산을 수행하였다. Omega2를 사용하여 생성된 24개의 초기 구조를 Gaussian 16으로 최적화한 후, 추가적인 계산을 위하여 서로 다른 세 개의 conformer를 선택하였다. 전자적 성질들의 계산 결과는 nyasol이 라디칼 소거능을 가지며 4

We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two-dimensional Reifenberg flat domain.

The Gfo/Idh/MocA family enzyme DgpA was known to catalyze the regiospecific oxidation of puerarin to 3”-oxo-puerarin in the presence of 3-oxo-glucose. Here, we discovered that D3dgpA, dgpA cloned from the human gut bacterium Dorea sp. MRG-IFC3, catalyzed the regiospecific oxidation of various C-/O-glycosides, including puerarin, in the presence of methyl β-D-3-oxo-glucopyranoside. While C-glycosides were converted to 3”- and 2”-oxo-products by D3dgpA, O-glycosides resulted in the formation of aglycones and hexose enediolone from the 3”-oxo-products. From DFT calculations, it was found that isomerization of 3”-oxo-puerarin to 2”-oxo-puerarin required a small activation energy of 9.86 kcal/mol, and the O-glycosidic bond cleavage of 3”-oxo-products was also thermodynamically favored with a small activation energy of 3.49 kcal/mol. In addition, the reaction mechanism of D3dgpA was discussed in comparison to those of Gfo/Idh/MocA and GMC family enzymes. The robust reactivity of D3dgpA was proposed as a new general route for derivatization of glycosides.

Puerarin, daidzein C -glucoside, was known to be biotransformed to daidzein by human intestinal bacteria, which is eventually converted to ( S )-equol. The metabolic pathway of puerarin to daidzein by DgpABC of Dorea sp. PUE strain was reported as puerarin ( 1 ) → 3’’-oxo-puerarin ( 2 ) → daidzein ( 3 ) + hexose enediolone ( C ). The second reaction is the cleavage of the glycosidic C–C bond, supposedly through the quinoid intermediate ( 4 ). In this work, the glycosidic C–C bond cleavage reaction of 3’’-oxo-puerarin ( 2 ) was theoretically studied by means of DFT calculation to elucidate chemical reaction mechanism, along with biochemical energetics of puerarin metabolism. It was found that bioenergetics of puerarin metabolism is slightly endergonic by 4.99 kcal/mol, mainly due to the reaction step of hexose enediolone ( C ) to 3’’-oxo-glucose ( A ). The result implied that there could be additional biochemical reactions for the metabolism of hexose enediolone ( C ) to overcome the thermodynamic energy barrier of 4.59 kcal/mol. The computational study focused on the C–C bond cleavage of 3’’-oxo-puerarin ( 2 ) found that formation of the quinoid intermediate ( 4 ) was not accessible thermodynamically, rather the reaction was initiated by the deprotonation of 2’’C–H proton of 3’’-oxo-puerarin ( 2 ). The 2’’C-dehydro-3’’-oxo-puerarin ( 2a2C ) anionic species produced hexose enediolone ( C ) and 8-dehydro-daidzein anion ( 3a8 ), and the latter quickly converted to daidzein through the daidzein anion ( 3a7 ). Our study also explains why the reverse reaction of C -glycoside formation from daidzein ( 3 ) and hexose enediolone ( C ) is not feasible.

본 연구는 범부채의 뿌리에 존재하는 이소플라보노이드들의 항산화 활성을 in vitro 시험법으로 평가하고 이론적 계산을 통하여 항산화 기작을 조사하기 위하여 수행되었다. 먼저, UPLC-PDA-MS를 활용하여 얻은 질량 스펙트럼들과 UV 스펙트럼들을 기존에 발표된 결과와 비교하여 5종의 주요 화합물, 즉 iridin, irigenin, tectoridin, tectorigenin 그리고 irisflorentin을 확인하였다. DPPH 라디칼 소거능 평가에서 메탄올 추출물과 iridin, irigenin 그리고 tectorigenin은 항산화 활성을 보였다. 반면에, tectoridin과 irisflorentin의 활성은 확인할 수 없었다. 이소플라보노이드에 대하여 hydrogen atom transfer (HAT), single electron transfer followed by proton transfer (SET-PT) 그리고 sequential proton loss electron transfer (SPLET)의 잘 알려진 항산화 기작을 밝히고자 기상과 액상(에탄올과 물)에서 B3LYP/6-311++g(d,p) 수준에서 범밀도함수를 적용하였다. 계산결과를 바탕으로 세 개의 기작과 관계되어 있는 다섯의 반응 엔탈피들을 분석하였다. 분석 결과, iridin과 irigenin은 다른 이소플라보노이들에 비하여 좀 더 높은 항산화 활성을 가질 것으로 예측되었다. 또한 기상에서는 항산화기작으로 HAT이 좀 더 가능성이 높고 에탄올과 물에서는 HAT뿐만 아니라 SPLET가 우세할 것으로 판단되었다.

Anemarrhena asphodeloides Bunge (A. asphodeloides Bunge) root extract contains nyasol as its main ingredient. Nyasol was extracted and prepared as a cosmetic raw material in 95% ethanol. To identify nyasol as a marker compound qualitative analysis was performed using ultra-performance liquid chromatographyi coupled with electrospray ionization–tandem mass spectrometry. Below a nyasol content of 12 μg/mL, the root extract exhibited negligible cytotoxicity. In this concentration range, melanin production in B16F10 mouse melanoma cells decreased as the concentration of nyasol increased, indicating a skin-whitening effect. In addition, an antiwrinkling effect was confirmed by evaluating the inhibition of MMP-1 protein expression in TNF-α-treated HaCaT cells by either A. asphodeloides Bunge root extract (>0.31 μg/mL) or nyasol (>0.25 μg/mL). High-performance liquid chromatography-coupled with a photodiode detector array was used to show that our extract contained 5.06 ± 0.01% nyasol. Furthermore, when this analysis method was applied for the quality control of a cream product containing 2 wt.% of A. asphodeloides Bunge root extract, the measured content of nyasol (0.1%) was over 90% of the nominal quantity. Therefore, the product was deemed to be within the required quality standards.

We obtain the regularity of solutions in Sobolev spaces for the mixed Dirichlet-conormal problem for parabolic operators in cylindrical domains with time-dependent separations, which is the first of its kind. Assuming the boundary of the domain to be Reifenberg-flat and the separation to be locally sufficiently close to a Lipschitz function of $m$ variables, where $m=0,\ldots,d-2$, with respect to the Hausdorff distance, we prove the unique solvability for $p\in (2(m+2/(m+3),2(m+2)/(m+1)))$. In the case when $m=0$, the range $p\in(4/3,4)$ is optimal in view of the known results for Laplace equations.

We establish L_q,p -estimates and solvability for mixed Dirichlet–conormal problems for parabolic equations in a cylindrical Reifenberg-flat domain with a rough time-dependent separation.

The demand for flexible displays (e.g. foldable and rollable displays) has recently increased, thus necessitating the development of various component technologies. An anisotropic conductive film, which is a conventional surface mount technology, is deemed more necessary than soldering for the implementation of a flexible display. However, it is still difficult to secure the electrical conductivity and reliability of the conductive ball used in the anisotropic conductive film. In this paper, a copper conductive ball having a lower resistance than the conventional conductive ball was fabricated. It has a lower contact resistance than nickel and gold, and the reliability issue, which is a disadvantage of copper, is secured by blocking the reaction with oxygen and coating a thin corrosive solution.

Currently, as the next-generation of display progresses—with high performance and high integration—the surface mounting technology of components is very important. In particular, in the case of flexible displays, such as rollable and bendable displays, ACF that connects wires to any curvature is essential. However, the conductive ball used inside the ACF has had problems with particle size and non-uniform metal coating. It was confirmed that the presence of solvent and oxygen, which are used in polymer synthesis, affects the sphere formation of polymer beads. By optimizing the factors affecting the polymer beads, a perfect spherical polymer bead was manufactured. In addition, the conductive ball manufacturing process was optimized by confirming the factors affecting the metal coating. The metal coating on the surface of the polymer bead was applied with a uniform thickness by considering the specific surface area and concentration of the conductive balls, and, through this optimized process, conductive balls for anisotropic conductive films with uniform size and metal thickness were obtained.

We study stationary Stokes systems in divergence form with piecewise Dini mean oscillation (DMO) coefficients and data in a bounded domain containing a finite number of subdomains with $C^{1,{Dini}}$ boundaries. We prove that if $(u, p)$ is a weak solution of the system, then $(Du, p)$ is bounded and piecewise continuous. The corresponding results for stationary Navier--Stokes systems are also established, from which the Lipschitz regularity of the stationary $H^1$-weak solution in dimensions $d=2,3,4$ is obtained. Our results can be applied to stationary Stokes systems and Navier--Stokes systems with the second-order term $\operatorname{div} (\tau \mathcal{S}u)$, where $\mathcal{S}u=\frac{1}{2}(Du+(Du)^{\top})$ is the strain tensor and $\tau$ is a positive piecewise DMO scalar function.

. We establish existence and uniqueness of Green functions for flow velocity of stationary Stokes systems, under a continuity assumption of weak solutions to the system, in a bounded domain such that the divergence equation is solvable there. We also obtain pointwise bounds of the Green functions.

We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We construct the Green function when coefficients are merely measurable in one direction and have Dini mean oscillation in the other directions, and $\Omega$ is such that the divergence equation is solvable there. We also establish global pointwise bounds for the Green function and its derivatives when coefficients have Dini mean oscillation and $\Omega$ has a $C^{1,\rm{Dini}}$ boundary. Green functions for the flow velocity of Stokes systems are also considered.

The market for next-generation flexible displays is rapidly expanding with the launch of foldable electronic products. Consequently, the flexible electronic material and device industries are continuously growing. Specifically, the cover window used in foldable displays is a very important component that must have excellent optical, physical, and mechanical characteristics while withstanding high external stresses caused by the bending radius, unlike the existing rigid-type cover windows. Considerable research efforts have been dedicated toward improving their performance. In this study, a cover window substrate for a foldable display having high flexibility was developed. To this end, ultra-thin glass (UTG) with excellent flexibility and transparency was used to overcome the low surface hardness of the typical polymer substrate used in existing foldable substrates. In addition, for efficient stress control, the design of the multilayer structure was optimized by generating multiple neutral planes through the use of an optical clear adhesive (OCA) buffer layer. The structure of the cover window was designed using the finite element simulation technique, and actual samples of the cover window with the optimized structure were produced to evaluate their physical, mechanical, and optical characteristics. As a result, the optimized foldable cover window showed a surface hardness of 9 H and a light transmittance of 90 %; especially, it exhibited an excellent bending reliability with 200000 bending repetitions without failure at the small bending radius of 1.5 R.

Recent display technology has changed substantially from flat-type displays to bended displays. As a result, the lamination process for bonding the panel substrates and bended window glass has become difficult due to the changes in display shape, and the use of optically clear adhesive (OCA) makes it impossible to rework defective substrates due to residue problems. Therefore, it is necessary to research and develop a substrate-surface treatment that maintains the initial adhesion and is reusable via the complete removal of impurities during delamination in order to enable rework. In this paper, the possibility of maintaining adhesive force and reusing substrates was confirmed through the surface treatment of substrates and OCA using various materials. We found that a surface coating and a cooling treatment of additional substrates completely removed the impurities that remained on the substrates during reworking. These results could contribute to improving lamination-process technology and the productivity of the various forms of next-generation displays that are currently under development.