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Let C be the middle-third Cantor set. In this paper, we show that for every x ∈ [ 0 , 4 ] , there exist x 1 , x 2 , x 3 , x 4 ∈ C such that x = x 1 2 + x 2 2 + x 3 2 + x 4 2 , which was conjectured in Athreya et al. (2019) [1] .

Let $A,B\subset\mathbb{R}$. Define $$A\cdot B=\{x\cdot y:x\in A, y\in B\}.$$ In this paper, we consider the following class of self-similar sets with overlaps. Let $K$ be the attractor of the IFS $\{f_1(x)=\lambda x, f_2(x)=\lambda x+c-\lambda,f_3(x)=\lambda x+1-\lambda\}$, where $f_1(I)\cap f_2(I)\neq \emptyset, (f_1(I)\cup f_2(I))\cap f_3(I)=\emptyset,$ and $I=[0,1]$ is the convex hull of $K$. The main result of this paper is $K\cdot K=[0,1]$ if and only if $(1-\lambda)^2\leq c$. Equivalently, we give a necessary and sufficient condition such that for any $u\in[0,1]$, $u=x\cdot y$, where $x,y\in K$., Comment: 12 pages

Isoquinoline alkaloid displays significant anti-gastric cancer effects due to its unique structure, which is attracting more and more attention for the development of anti-gastric cancer drugs. In this study, we explore the active components against gastric cancer from the Tibetan Medicine Corydalis hendersonii Hemsl, which is rich in isoquinoline alkaloids. 14 compounds including 2 previously undescribed natural products were obtained. Interestingly, an new active compound displays potent anti-gastric cancer activity. After accomplishing the total syntheses of the active compound and its derivatives, the anti-gastric cancer activity of the active compound was further investigated. In vitro experiments revealed that the active compound significantly attenuated the proliferative capacity, caused G2/M phase arrest, inhibited the cell migration and invasion, and induced cell apoptosis. Mechanistically, the active compound could increase the Bax/Bcl-2 ratio, elevate cytochrome c in the cytosol, and activate caspase-9/3, along with inactivating the upstream PI3K/Akt/mTOR signaling pathway. In addition, the active compound could also cause gastric cancer cell death by inhibiting topoisomerase I activity. More importantly, the anti-gastric cancer activity of the active compound was confirmed in MGC-803 xenograft nude mice in vivo. This work not only promotes the exploitation of Corydalis hendersonii Hemsl., but also provides some experience for discovering new entities from natural sources.

The extent to which intratumoral heterogeneity of programmed death ligand 1 (PD-L1) expression causes discordance of PD-L1 expression between paired samples remains unclear. Here, PD-L1 status was compared between whole sections from NSCLCs and the corresponding tissue microarrays (TMAs) serving as surrogate biopsy specimens.PD-L1 expression was evaluated by 22C3 immunohistochemistry assay on 190 archival surgical specimens and matched to the TMA results. PD-L1 expression was determined by the tumor proportion score (TPS) and classified as TPS lower than 1%, TPS of 1% to 49%, and TPS of 50% or higher. Agreement statistics were used.The percentage of PD-L1 expression on tumor cells differed greatly between individual TMAs and matched surgical specimens. When PD-L1 TPS was adopted, a total of 36 of 190 discordance cases (18.9%) were observed, with a κ-value of 0.630 between paired samples. The TMAs underestimated or overestimated PD-L1 status in 19 of 36 (52.8%) and 17 of 36 (47.2%) of the matched surgical specimens, respectively (p = 0.118). The discordance rate was much lower in cases with a PD-L1 TPS lower than 1% compared with in cases with a TPS of 1% to 49% and TPS of 50% or higher (18.4% versus 56.7% and 43.3%, p0.001). When a TPS of 50% or higher was used as the cutoff, the discordance rate of PD-L1 TPS less than 50% was further reduced to 7.5%. Such discrepancies were due mainly to intratumoral heterogeneity of PD-L1 expression and nonsignificant association with clinicopathological features.PD-L1 expression in TMAs correlates moderately well with that in the corresponding surgical specimens, indicating that evaluating PD-L1 expression in diagnostic biopsy specimens could be misleading in defining sensitivity to pembrolizumab treatment yet may be reliable as a way to exclude patients with a PD-L1 TPS less than 50% from first-line pembrolizumab treatment.

Let $(\mathcal{M}, c_k, n_k,\kappa)$ be a class of homogeneous Moran sets. Suppose $f(x,y)\in C^3$ is a function defined on $\mathbb{R}^2$. Given $E_1, E_2\in(\mathcal{M}, c_k, n_k,\kappa) $, in this paper, we prove, under some checkable conditions on the partial derivatives of $f(x,y)$, that $$f(E_1,E_2)=\{f(x,y):x\in E_1,y\in E_2\}$$ is exactly a closed interval or a union of finitely many closed intervals. Similar results for the homogeneous self-similar sets with arbitrary overlaps can be obtained. Further generalization is available for some inhomogeneous self-similar sets if we utilize the approximation theorem., Comment: To appear in JMAA

Nine new lignans (1-8, 13) and five known ones (9-12, 14) have been isolated from the roots of Schisandra sphenanthera and were tested for their capacity to scavenge 2,2-diphenyl-1-Picryl-hydrazyl (DPPH). Of these lignans tested, compounds 1, 7, 8 and 13 exhibited noteworthy antioxidant activity with IC50 values of 92, 115, 35 and 48 μg/mL, respectively. The anti-oxidative haemolysis of human red blood cells (RBCs) activity of the most active compound 8, which is similar to that of vitamin C, was evaluated.

Summary CD4+ T helper (Th) differentiation is regulated by diverse inputs, including the vitamin A metabolite retinoic acid (RA). RA acts through its receptor RARα to repress transcription of inflammatory cytokines, but is also essential for Th-mediated immunity, indicating complex effects of RA on Th specification and the outcome of the immune response. We examined the impact of RA on the genome-wide transcriptional response during Th differentiation to multiple subsets. RA effects were subset-selective and were most significant in Th9 cells. RA globally antagonized Th9-promoting transcription factors and inhibited Th9 differentiation. RA directly targeted the extended Il9 locus and broadly modified the Th9 epigenome through RARα. RA-RARα activity limited murine Th9-associated pulmonary inflammation, and human allergic inflammation was associated with reduced expression of RA target genes. Thus, repression of the Th9 program is a major function of RA-RARα signaling in Th differentiation, arguing for a role for RA in interleukin 9 (IL-9) related diseases.

The enhancer regions of the myogenic master regulator MyoD give rise to at least two enhancer RNAs. Core enhancer eRNA (CEeRNA) regulates transcription of the adjacent MyoD gene, whereas DRReRNA affects expression of Myogenin in trans. We found that DRReRNA is recruited at the Myogenin locus, where it colocalizes with Myogenin nascent transcripts. DRReRNA associates with the cohesin complex, and this association correlates with its transactivating properties. Despite being expressed in undifferentiated cells, cohesin is not loaded on Myogenin until the cells start expressing DRReRNA, which is then required for cohesin chromatin recruitment and maintenance. Functionally, depletion of either cohesin or DRReRNA reduces chromatin accessibility, prevents Myogenin activation, and hinders muscle cell differentiation. Thus, DRReRNA ensures spatially appropriate cohesin loading in trans to regulate gene expression.

The adsorption characteristics of heavy metals: Cu(II), Pb(II), Zn(II) and Cd(II) ions on tourmaline were studied. Adsorption equilibrium was established. The adsorption isotherms of all the four metal ions followed well Langmuir equation. Tourmaline was found to remove heavy metal ions efficiently from aqueous solution with selectivity in the order of Pb(II)>Cu(II)>Cd(II)>Zn(II). The adsorption of metal ions by tourmaline increased with the initial concentration of metal ions increasing in the medium. Tourmaline could also increase pH value of metal solution. -The maximum heavy metal ions adsorbed by tourmaline was found to be 78.86, 154.08, 67.25, and 66.67 mg/g for Cu(II), Pb(II), Zn(II) and Cd(R), respectively. The temperature (25-55 degrees C) had a small effect on the adsorption capacity of tourmaline. Competitive adsorption of Cu(II), Pb(II), Zn(II) and Cd(II) ions was also studied. The adsorption capacity of tourmaline for single metal decreased in the order of Pb>Cu>Zn >Cd and inhibition dominance observed in two metal systems was Pb>Cu, Pb>Zn, Pb>Cd, Cu>Zn, Cu>Cd, and Cd>Zn.

Host defense requires the specification of CD4+ helper T (Th) cells into distinct fates, including Th1 cells that preferentially produce interferon-γ (IFN-γ). IFN-γ, a member of a large family of anti-pathogenic and anti-tumor IFNs, induces T-bet, a lineage-defining transcription factor for Th1 cells, which in turn supports IFN-γ production in a feed-forward manner. Herein, we show that a cell-intrinsic role of T-bet influences how T cells perceive their secreted product in the environment. In the absence of T-bet, IFN-γ aberrantly induced a type I IFN transcriptomic program. T-bet preferentially repressed genes and pathways ordinarily activated by type I IFNs to ensure that its transcriptional response did not evoke an aberrant amplification of type I IFN signaling circuitry, otherwise triggered by its own product. Thus, in addition to promoting Th1 effector commitment, T-bet acts as a repressor in differentiated Th1 cells to prevent abberant autocrine type I IFN and downstream signaling.