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In this paper, we obtain monotonicity of Steklov eigenvalues on graphs which as a special case on trees extends the results of He and Hua (Steklov flows on trees and applications. ) to higher Steklov eigenvalues and gives affirmative answers to two problems proposed in He and Hua (). As applications of the monotonicity of Steklov eigenvalues, we obtain some estimates for Steklov eigenvalues on trees generalizing the isodiametric estimate for the first positive Steklov eigenvalues on trees in He and Hua (Calc Var Partial Differ Equ 61(3):101, 2022. ). [ABSTRACT FROM AUTHOR]

In this short note, by using a general three circles theorem, we show the rigidity of the sharp Bezout estimate first found by Gang Liu on nonnegatively curved Riemann surfaces. [ABSTRACT FROM AUTHOR]

In this paper, we extend Gang Liu's three circle theorem for Kähler manifolds to almost Hermitian manifolds. As applications of the three circle theorem, we obtain sharp dimension estimates for spaces of holomorphic functions of polynomial growth and rigidity for the estimates, Liouville theorems for pluri-subharmonic functions of sub-logarithmic growth and Liouville theorems for holomorphic functions of Cheng-type, and fundamental theorem of algebra on almost Hermitian manifolds with slightly negative holomorphic sectional curvature. The results are generalization of Liu's results and some of them are new even for the Kähler case. We also discuss the converse of the three circle theorem on Hermitian manifolds which turns out to be rather different with the Kähler case. In order to obtain the three circle theorem on almost Hermitian manifolds, we also establish a general maximum principle in the spirit of Calabi's trick so that a general three circle theorem is a straightforward consequence of the general maximum principle. The general maximum principle and three circle theorem established may be of independent interests. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a Lichnerowicz-type estimate for the first positive Steklov eigenvalues on graphs and discuss its rigidity. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs and discuss its rigidity. As applications of the comparison of eigenvalues, we obtain Lichnerowicz-type estimates and some combinatorial estimates for Steklov eigenvalues on graphs. [ABSTRACT FROM AUTHOR]

In this paper, we consider affine self-similar solutions for the affine curve shortening flow in the Euclidean plane. We obtain the equations of all affine self-similar solutions up to affine transformations and solve the equations or give descriptions of the solutions for the degenerate case. Some new special solutions for the affine curve shortening flow are found. [ABSTRACT FROM AUTHOR]

In this short note, we show the rigidity of a trace estimate for Steklov eigenvalues with respect to functions in our previous work (Shi and Yu (2016) [13]). Namely, we show that equality of the estimate holds if and only if the manifold is a direct product of a round ball and a closed manifold. The key ingredient in the proof is a splitting theorem for flat and totally geodesic Riemannian submersions which may be of independent interests. [ABSTRACT FROM AUTHOR]

Let f : M m → N n be a smooth map between two differential manifolds with N connected, f ( M ) closed and f ( M ) ≠ N . In this short note, we show that either all the points of M are critical points of f or the dimension the collection of all critical points of f is not less than n − 1 . Some consequences of this result for surjectivity of mappings are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we show the rigidity of isometric immersions for a Riemannian manifold of dimension n − 1 into the light cone of n + 1 dimensional Minkowski, de Sitter and anti-de Sitter spacetimes for n ≥ 3 . [ABSTRACT FROM AUTHOR]

The authors obtain a complex Hessian comparison for almost Hermitian manifolds, which generalizes the Laplacian comparison for almost Hermitian manifolds by Tossati, and a sharp spectrum lower bound for compact quasi Kähler manifolds and a sharp complex Hessian comparison on nearly Kähler manifolds that generalize previous results of Aubin, Li Wang and Tam-Yu. [ABSTRACT FROM AUTHOR]

Let p : R → R be a given function, and let A p be the set of smooth functions f such that f ( p ( ⋅ ) + c ) is smooth for any c ∈ R . We show that if p is not smooth, then either every element of A p is constant, or there is a nonzero constant d such that A p is equal to the set of smooth functions of periodicity d . [ABSTRACT FROM AUTHOR]

In this paper, we show that the Chen-Nester-Tung (CNT) quasi-local energy with 4D isometric matching references is closely related to the Wang–Yau (WY) quasi-local energy. As a particular example, we compute the second variation of the CNT quasi-local energy for axially symmetric Kerr-like spacetimes with axially symmetric embeddings at the obvious critical point ( 0 , 0 ) and find that it is a saddle critical point in most of the cases. Also, as a byproduct, we generalize a previous result about the coincidence of the CNT quasi-local energy and Brown–York mass for axially symmetric Kerr-like spacetimes by Tam and the first author Liu and Tam (2016) to general spacetimes. [ABSTRACT FROM AUTHOR]

CD36 signal transduction modulates the uptake of oxidized low-density lipoprotein (oxLDL) and foam cell formation. We previously observed that 7-ketocholesteryl-9-carboxynonanoate (oxLig-1), the lipid moiety of oxLDL, activates the CD36-Src-JNK/ERK1/2 signalling pathway. In this study, we assessed the role of the ω-carboxyl group in the binding of oxLig-1 to CD36 and investigated whether the binding of the ω-carboxyl group to CD36 triggers CD36-mediated signalling, thereby resulting in the upregulation of caveolin-1 expression. Our results showed that oxLig-1 bound to CD36 and that the ω-carboxyl group was critical for this binding. Furthermore, immunoprecipitation and Western blot analyses showed that interaction between the ω-carboxyl group of oxLig-1 and CD36 triggered intracellular Src-JNK/ERK1/2 signal transduction. Moreover, the binding of the ω-carboxyl group to CD36 induced caveolin-1 expression and translocation to the membrane in macrophages. Additionally, inhibitors of Src, JNK and ERK and siRNA targeting CD36 and NF-κB significantly suppressed the enhanced caveolin-1 expression induced by oxLig-1. In conclusion, these observations suggest that oxLig-1 is a critical epitope of oxLDL that mediates the binding of oxLDL to CD36 and activates downstream Src-JNK/ERK1/2-NF-κB signal transduction, resulting in upregulation of caveolin-1 expression in macrophages. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the Hersch–Payne–Schiffer inequality for Steklov eigenvalues to higher dimensional case by extending the trick used by Hersch, Payne and Schiffer to higher dimensional manifolds. More precisely, we show that, for a compact oriented Riemannian manifold with boundary of dimension n , the multiplication of a Steklov eigenvalue for functions and a Steklov eigenvalue for differential ( n − 2 ) -forms can be controlled from above by a certain eigenvalue of the Laplacian operator on the boundary. [ABSTRACT FROM AUTHOR]

This is a continuation of our previous work (Y. Shi and C. Yu, 2016 [21] ) on the trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch–Payne–Schiffer [13] , Brock [2] , Raulot–Savo [21] and Dittmar [5] . [ABSTRACT FROM AUTHOR]

We present a microfabricated quantum dot-linked immuno-diagnostic assay (μQLIDA) biosensor with an embedded mixing element. We adapted our previous capillary-based system into a microfabricated planar microchannel, which has been integrated with an active, electrothermal mixing component. With the active mixing element, the detection time was significantly reduced from about 3.5 h to 30 min in a case study of detecting myeloperoxidase (MPO). MPO is an inflammatory biomarker that is over-expressed in inflammatory conditions including inflammatory bowel disease and cardiovascular disease. The μQLIDA biosensor presented here is a low-cost, rapid immunofluorescence sensor that can detect nanomolar concentrations of MPO, with a working volume of 2 μl. [ABSTRACT FROM AUTHOR]

In this paper, we give a classification of almost Hermitian metrics with nonpositive holomorphic bisectional curvature on a product of compact almost complex manifolds. This generalizes previous results of Zheng [ Ann. of Math. (2), 137(3), 671-673 (1993)] and the author [ Proc. Amer. Math. Soc., 139(4), 1469-1472 (2011)]. [ABSTRACT FROM AUTHOR]

Recently, quasi-two-dimensional RP(Ruddlesden-Popper)-based perovskite solar cells have attracted a wide range of research interest. However, two-dimensional layered perovskites have disordered phase distribution and multi-quantum well structure that are adversely to charge transport and extraction, resulting in the inability to obtain relatively satisfactory photoelectric conversion efficiency (PCE). Here, we fabricated an 2D RP perovskite solar cell with reversely graded phase arrangement by friendly antisolvent method, and obtained the PCE of 14.45%. The dependence of efficiency on device architecture according to the vertical growth direction is further revealed and discussed. To investigate the effect of different antisolvents on crystal orientation and phase arrangement of GA-based 2D RP perovskites, we applied IPA as antisolvent and found that IPA not only significantly improved the surface roughness, quality and crystallinity of 2D perovskites but also reduce or even eliminate lower-n (n = 1, 2) phases and improve the vertical orientation of 2D phases in perovskites films, thereby improving charge transport and extraction. In the end, we achieved a champion PCE of 15.80%. These findings provide an effective guidance for developing GA-based organic spacers toward highly efficient and stable 2D PSCs with less quantum confinement. [Display omitted] • It has been proved that the GA-based 2D RP perovskite films deposited by the anti-solvent method have a reverse phase gradient distribution, which is more conducive to the transfer of electrons to the bottom and hinders their transfer to the top (metal electrode direction). • Compared with EA, IPA can reduce the rate of removing solvent DMF and DMSO during the spin coating process, resulting in relatively low supersaturated state and highly vertically growing 2D perovskite films with reduced resistance to the efficient carrier transmission. • Compared with EA-treated films, the small n (n = 1,2) values phases at the top of IPA-treated films disappear, which reduces the quantum confinement assisted recombination and facilitates the charge extraction. • 15.8% PCE of n-i-p device based on the IPA-treated GA 2 MA 4 Pb n I 3n+1 (n = 5) was obtained. [ABSTRACT FROM AUTHOR]

We obtain supremum of the $$k$$ -th normalized Steklov eigenvalues of all rotationally symmetric conformal metrics on $$[0,T]\times \mathbb {S}^1$$ , $$k>1$$ . This generalizes the corresponding result of Fraser and Schoen for the case $$k=1$$ . We give geometric description in terms of minimal surfaces for metrics attaining the supremum. We obtain some results on the comparison of the normalized Steklov eigenvalues of rotationally symmetric metrics and general conformal metrics on $$[0,T]\times \mathbb {S}^1$$ . We also construct an example of a conformal metric on $$[0,T]\times \mathbb {S}^1$$ whose first normalized Steklov eigenvalue is larger than that of the corresponding rotationally symmetric conformal metric. [ABSTRACT FROM AUTHOR]

Aim Lectin-like oxidized low-density lipoprotein receptor-1 (LOX-1), a specific membrane receptor for oxidized low-density lipoprotein (oxLDL), plays a crucial role in atherosclerosis progression. The aim of this study was to elucidate the role of 7-ketocholesteryl-9-carboxynonanoate (oxLig-1), a lipid component of oxLDL, in the binding of oxLDL to LOX-1 and to determine whether oxLig-1 binding to LOX-1 is involved in the upregulation of ABCA1 expression. Main methods OxLig-1 binding to LOX-1 was analysed by AutoDock 4.2.6 and confirmed by fluorescence immunocytochemistry and enzyme-linked immunosorbent assays (ELISAs). LOX-1, LXRα and ABCA1 protein expression induced by oxLig-1 or methylated oxLig-1 was measured by western blotting. In addition, PPARγ activation was investigated using a dual-luciferase reporter system. Furthermore, the signalling cascade involved in oxLig-1-induced ABCA1 expression was assessed using inhibitors for PPARγ and LXRα and specific siRNAs against LOX-1, PPARγ and LXRα. Key findings Docking, fluorescence immunocytochemistry and ELISA analyses showed that oxLig-1 bound LOX-1 and that the ω-carboxyl group was critical for this binding. Moreover, oxLig-1, but not methylated oxLig-1, increased LOX-1, LXRα, and ABCA1 expression. Luciferase reporter assays indicated that oxLig-1 activated PPARγ in the presence of LOX-1. Additionally, the inhibitor and siRNA experiments showed that oxLig-1 triggered the PPARγ-LXRα signalling pathway, leading to upregulation of ABCA1, and that this process required the participation of LOX-1. Significance Our observations indicate that oxLig-1 is a critical epitope of oxLDL that mediates the binding of oxLDL to LOX-1 and initiates PPARγ signal transduction to upregulate the expression of ABCA1. [ABSTRACT FROM AUTHOR]