Interpolatory quadrature formulas on the unit circle for Chebyshev weight functions

Summary. In this paper, interpolatory quadrature formulas based upon the roots of unity are studied for certain weight functions. Positivity of the coefficients in these formulas is deduced along with computable error estimations for analytic integrands. A comparison is made with Szeg? quadrature formulas. Finally, an application to the interval [-1,1] is also carried out. Received February 29, 2000 / Published online August 17, 2001     

Preferential Lectin Binding of Cancer Cells upon Sialic Acid Treatment Under Nutrient Deprivation

The terminal monosaccharide of glycoconjugates on a eukaryotic cell surface is typically a sialic acid (Neu5Ac). Increased sialylation usually indicates progression and poor prognosis of most carcinomas. Here, we utilize two human mammary epithelial cell lines, HB4A (breast normal cells) and T47D (breast cancer cells), as a model system to demonstrate differential surface glycans when treated with sialic acid under nutrient deprivation. Under a starved condition, sialic acid treatment of both cells resulted in increased activities of α2→3/6 sialyltransferases as demonstrated by solid phase assay using lectin binding. However, a very strong Maackia amurensis agglutinin I (MAL-I) staining on the membrane of sialic acid-treated T47D cells was observed, indicating an increase of Neu5Acα2→3Gal on the cell surface. To our knowledge, this is a first report showing the utility of lectins, particularly MAL-I, as a means to discriminate between normal and cancer cells after sialic acid treatment under nutrient deprivation. This method is sensitive and allows selective detection of glycan sialylation on a cancer cell surface.     

Development of a Piezoelectric PVDF‐TrFE Fibrous Scaffold to Guide Cell Adhesion,Proliferation, and Alignment

Severe peripheral nervous system injuries currently hold limited therapeutic solutions. Existing clinical techniques such as autografts, allografts, and newer nerve guidance conduits have shown variable outcomes in functional recovery, adverse immune responses, and in some cases low or minimal availability. This can be attributed in part to the lack of chemical, physical, and electrical cues directing both nerve guidance and regeneration. To address this pressing clinical issue, electrospun nanofibers and microfibers composed of piezoelectric polyvinylidene flouride‐triflouroethylene (PVDF‐TrFE) have been introduced as an alternative template for tissue engineered biomaterials, specifically as it pertains to their relevance in soft tissue and nerve repair. Here, biocompatible scaffolds of PVDF‐TrFE are fabricated and their ability to generate an electrical response to mechanical deformations and produce a suitable regenerative microenvironment is examined. It is determined that 20% (w/v) PVDF‐TrFE in (6:4) dimethyl formamide (DMF):acetone solvent maintains a desirable piezoelectric coefficient and the proper physical and electrical characteristics for tissue regeneration. Further, it is concluded that scaffolds of varying thickness promoted the adhesion and alignment of Schwann cells and fibroblasts. This work offers a prelude to further advancements in nanofibrous technology and a promising outlook for alternative, autologous remedies to peripheral nerve damage.     

Electrophilic Bromination of Alkenes,Alkynes, and Aromatic Amines with Iodic Acid/Potassium Bromide Under Mild Conditions

Bromination of alkenes, alkynes, and aromatic amines has efficiently been carried out at room temperature in short reaction times using HIO₃/KBr in CH₂Cl₂/H₂O (1:1) to prepare corresponding brominated compounds in excellent yields.     

Synthesis and characterization of transition metal complexes of thiophene‐2‐methylamine: X‐ray crystal structure of palladium (II) and platinum (II) complexes and use of palladium(II) complexes as pre‐catalyst in Heck and Suzuki cross‐coupling reactions

The reactions of thiophene‐2‐(N‐diphenylphosphino)methylamine, Ph₂PNHCH₂‐C₄H₃S, 1 and thiophene‐2‐[N,N‐bis(diphenylphosphino)methylamine], (Ph₂P)₂NCH₂‐C₄H₃S, 2, with MCl₂(cod) (M = Pd, Pt; cod = 1,5‐cyclooctadiene) or [Cu(CH₃CN)₄]PF₆ yields the new complexes [M(Ph₂PNHCH₂‐C₄H₃S)₂Cl₂], M = Pd 1a, Pt 1b, [Cu(Ph₂PNHCH₂‐C₄H₃S)₄]PF₆, 1c, and [M(Ph₂P)₂NCH₂‐C₄H₃S)Cl₂], M = Pd 2a, Pt 2b, {Cu[(Ph₂P)₂NCH₂‐C₄H₃S]₂}PF₆, 2c, respectively. The new compounds were isolated as analytically pure crystalline solids and characterized by ³¹P‐, ¹³C‐, ¹H‐NMR and IR spectroscopy and elemental analysis. Furthermore, the solid‐state molecular structures of representative palladium and platinum complexes of bis(phosphine)amine, 2a and 2b, respectively, were determined using single crystal X‐ray diffraction analysis. The palladium complexes were tested as potential catalysts in the Heck and Suzuki cross‐coupling reactions. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis of Highly Functionalized Isoxazolinediones from One-pot Reaction of Alkylidene <Emphasis Type="Italic">Meldrum</Emphasis>’s Acid with Alkyl Isocyanides in the Presence of Arylhydroxylamines

Summary. Alkyl isocyanides undergo a smooth reaction with alkylidene Meldrum’s acids in the presence of arylhydroxylamines to produce N ¹-alkyl-2-(3,5-dioxo-2-aryltetrahydro-4-isoxazolyl)alkanamides in high yields.     

The ranks of certain semigroups of partial isometries

Let \(I_{n}\) be the symmetric inverse semigroup on \(X_{n}=\{1,\ldots ,n\}\), and let \(DP_{n}\) and \(ODP_{n}\) be its subsemigroups of partial isometries and of order-preserving partial isometries on \(X_{n}\) under its natural order, respectively. In this paper we find the ranks of the subsemigroups \(DP_{n,r}=\{ \alpha \in DP_{n}:|\mathrm {im\, }(\alpha )|\le r\}\) and \(ODP_{n,r}=\{ \alpha \in ODP_{n}: |\mathrm {im\, }(\alpha )|\le r\}\) for \(2\le r\le n-1\).     

Soliton mechanism of acoustic pulse frequency conversion to the red region

Self-scattering of a transverse acoustic pulse from a longitudinal strain video pulse (induced by an acoustic pulse) in a paramagnetic crystal in a magnetic field is predicted. This effect is accompanied by a continuous frequency shift of the hypersonic pulse to the red region; this shift is proportional to the pulse intensity.