A new proof of some polynomial inequalities related to pseudo-splines

AbstractPseudo-splines of type I were introduced in [I. Daubechies, B. Han, A. Ron, Z. Shen, Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal. 14 (2003) 1–46] and [Selenick, Smooth wavelet tight frames with zero moments, Appl. Comput. Harmon. Anal. 10 (2000) 163–181] and type II were introduced in [B. Dong, Z. Shen, Pseudo-splines, wavelets and framelets, Appl. Comput. Harmon. Anal. 22 (2007) 78–104]. Both types of pseudo-splines provide a rich family of refinable functions with B-splines, interpolatory refinable functions and refinable functions with orthonormal shifts as special examples. In [B. Dong, Z. Shen, Pseudo-splines, wavelets and framelets, Appl. Comput. Harmon. Anal. 22 (2007) 78–104], Dong and Shen gave a regularity analysis of pseudo-splines of both types. The key to regularity analysis is Proposition 3.2 in [B. Dong, Z. Shen, Pseudo-splines, wavelets and framelets, Appl. Comput. Harmon. Anal. 22 (2007) 78–104], which also appeared in [A. Cohen, J.P. Conze, Régularité des bases d'ondelettes et mesures ergodiques, Rev. Mat. Iberoamericana 8 (1992) 351–365] and [I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Series in Applied Mathematics, SIAM, Philadelphia, 1992] for the case l=N−1. In this note, we will give a new insight into this proposition

1-{2-[(2,4-Dichloro­benzyl­idene)amino]eth­yl}-3-methyl­imidazolium hexa­fluoro­phosphate

In the title Schiff base compound, C13H14Cl2N3 +·PF6 −, the dihedral angle between the aromatic ring and imidazole ring in the cation is 6.10 (2)°. Inter­molecular C—H⋯F hydrogen-bonding inter­actions and π–π stacking inter­actions [centoid–centroid distance = 3.7203 (12) Å] help stabilize the crystal packing

Electrical Control of Magnetization in Charge-ordered Multiferroic LuFe2O4

LuFe2O4 exhibits multiferroicity due to charge order on a frustrated triangular lattice. We find that the magnetization of LuFe2O4 in the multiferroic state can be electrically controlled by applying voltage pulses. Depending on with or without magnetic fields, the magnetization can be electrically switched up or down. We have excluded thermal heating effect and attributed this electrical control of magnetization to an intrinsic magnetoelectric coupling in response to the electrical breakdown of charge ordering. Our findings open up a new route toward electrical control of magnetization.Comment: 14 pages, 5 figure

3′,7′,7′-Trimethyl-1′-phenyl-5′,6′,7′,8′-tetra­hydro­spiro­[indoline-3,4′-(1H,4H-pyrazolo­[3,4-b]chromene)]-2,5′-dione

The title spiro­oxindole compound, C26H23N3O3, was prepared by the reaction of isatin, 3-methyl-1-phenyl-2-pyrazolin-5-one and 5,5-dimethyl­cyclo­hexane-1,3-dione in an ethanol solution. The fused cyclo­hexene ring adopts an envelope conformation. The dihedral angle between the aromatic and pyrazoline rings is 23.70 (8)°. An intra­molecular C—H⋯O inter­action occurs. The crystal structure is stabilized by N—H⋯N hydrogen-bonding inter­actions, leading to a zigzag chain along the b axis

Bis(2,6-dichloro­benz­yl)selane

The title mol­ecule, C14H10Cl4Se, features a selenide bridge between two dichloro­benzyl units. The dihedral angle between the two benzene rings is 107.9 (16)°. In the crystal, weak π–π face-to-face aromatic inter­actions are observed [centroid–centroid distance between two adjacent (but crystallographically different) phenyl rings = 3.885 (5) Å], providing some packing stability. Short Cl⋯Cl contacts of 3.41 (2) Å are observed

Epigenetic regulation of CD271, a potential cancer stem cell marker associated with chemoresistance and metastatic capacity.

Cancer stem cells (CSCs) are considered to be the cause of tumor initiation, metastasis and recurrence. Additionally, CSCs are responsible for the failure of chemotherapy and radiotherapy. The isolation and identification of CSCs is crucial for facilitating the monitoring, therapy or prevention of cancer. We aimed to identify esophageal squamous cell carcinoma (ESCC) stem-like cells, the epigenetic mechanism and identify novel biomarkers for targeting ESCC CSCs. Sixty-three paired ESCC tissues and adjacent non-cancerous tissues were included in this study. CD271, which was identified as the CSC marker for melanoma, was assessed using quantitative PCR (qPCR). Using flow cytometry, we isolated CD271+ cells comprising 7.5% of cancer cells from the KYSE70 cell line. Sphere formation and anchorage-independent growth were analyzed in CD271+ and CD271- cancer cells, respectively. qPCR was used to detect stem-related genes and CCK-8 was performed to analyze the sensitivity to chemotherapy in the two groups. Bisulfite genomic sequencing was used to analyze the methylation status. CD271 expression was significantly higher in ESCC tissues than in adjacent non-cancerous tissues. Compared with CD271- cancer cells, CD271+ cancer cells showed a higher ability of sphere and colony formation, a high level expression of stem-related gene, and resistance to chemotherapy. The expression of CD271 was induced by a demethylation agent. In conclusion, CD271+ ESCC cells possess stem-like properties. CD271 can potentially act as a prognostic marker for ESCC, whose expression is regulated epigenetically