Extension theorems for paraboloids in the finite field setting

In this paper we study the L ^p ? L ^r boundedness of the extension operators associated with paraboloids in ${{\mathbb F}_{q}^{d}}In this paper we study the L ^p − L ^r boundedness of the extension operators associated with paraboloids in \mathbb F_q^d{{\mathbb F}_{q}^{d}} , where \mathbbF_q{\mathbb{F}_{q}} is a finite field of q elements. In even dimensions d ≥ 4, we estimate the number of additive quadruples in the subset E of the paraboloids, that is the number of quadruples (x,y,z,w) ? E⁴{(x,y,z,w) \in E^4} with x + y = z+w. As a result, in higher even dimensions, we obtain the sharp range of exponents p for which the extension operator is bounded, independently of q, from L ^p to L ⁴ in the case when −1 is a square number in \mathbbF_q{\mathbb{F}_{q}} . Using the sharp L ^p −L ⁴ result, we improve upon the range of exponents r, for which the L ² − L ^r estimate holds, obtained by Mockenhaupt and Tao (Duke Math 121:35–74, 2004) in even dimensions d ≥ 4. In addition, assuming that −1 is not a square number in \mathbbF_q{\mathbb{F}_{q}}, we extend their work done in three dimension to specific odd dimensions d ≥ 7. The discrete Fourier analytic machinery and Gauss sum estimates make an important role in the proof.     

Magnetic iron oxide nanoparticles for biorecognition: evaluation of surface coverage and activity

Modifying the surfaces of magnetic nanoparticles (MNPs) by the covalent attachment of biomolecules will enable their implementation as contrast agents for magnetic resonance imaging or as media for magnetically assisted bioseparations. In this paper we report both the surface coverage and the activity of IgG antibodies on MNPs. The antibodies were immobilized on gamma-Fe2O3 nanoparticles by conventional methods using aminopropyltriethoxy silane and subsequent activation by glutaraldehyde. Novel fluorescence methods were used to provide a quantitative evaluation of this well-known approach. Our results show that surface coverage can be stoichiometrically adjusted with saturated surface coverage occurring at approximately 36% of the theoretical limit. The saturated surface coverage corresponds to 34 antibody molecules bound to an average-sized MNP (32 nm diameter). We also show that the immobilized antibodies retain approximately 50% of their binding capacity at surface-saturated levels.     

Triode field emitters with planar carbon-nanoparticle cathodes

We designed and fabricated three different types of triode field emitters with planar carbon-nanoparticle (CNP) cathodes such as a normal-gate structure, a double-gate structure, and a well-structure. A normal-gate structure CNP triode emitter showed good field emission properties. The field emission started at the gate-voltage of 45 V, and the anode current reached the level of 120 nA at the gate-voltage of 60 V. However, in general, normal-gate structure suffered from large gate current. Using the double-gate structure, we successfully reduced the gate current to the level less than 4% of anode currents up to the anode current of 250 nA. To simplify fabrication process while maintaining the gate current reduction effect of the double-gate structure, a triode emitter with a well-structure cathode was fabricated via reactive-ion etching of a heavily doped n-type silicon wafer. The triode emitter with a well-structure cathode and a recessed gate structure showed negligible gate current.     

An Upper Bound for the Total Restrained Domination Number of Graphs

Let G be a graph with vertex set V. A set ${D \subseteq V}$ is a total restrained dominating set of G if every vertex in V has a neighbor in D and every vertex in ${V \setminus D}$ has a neighbor in ${V \setminus D}$ . The minimum cardinality of a total restrained dominating set of G is called the total restrained domination number of G, and is denoted by γ _tr (G). In this paper, we prove that if G is a connected graph of order n ≥ 4 and minimum degree at least two, then ${\gamma_{tr}(G) \leq n-\sqrt[3]{n \over 4}}$ .     

Mesogenic Schiff base esters with benzothiazole core: synthesis and phase transition studies

A series of new rod-shaped mesomorphic compounds, 6-ethoxy-2-(4-alkanoyloxybenzylidenamino)benzothiazoles, consisting of a 2,6-disubstituted benzothiazole core and a Schiff base central linkage, were synthesized and their structures were ascertained via elemental analysis and spectroscopic techniques. Their mesomorphic properties were studied using differential scanning calorimetry (DSC), polarized optical microscopy (POM) and X-ray diffraction (XRD) analysis. All compounds showed enantiotropic mesomorphism. Whilst the lower members of the series, hexanoyloxy and octanoyloxy derivatives exhibited nematic phase, the higher members (decanoyloxy, dodecanoyloxy, tetradecanoyloxy, hexadecanoyloxy and octadecanoyloxy derivatives) exhibited nematic and smectic C phases.     

The Effect of a Finite Interaction Cross-Section on the Hanle Signal

Hanle technique is used for the lifetime measurement of the atomic excited states. Field dependent Hanle signal is Lorentzian under ideal conditions. Any departure from ideal situation is reflected in the shape of the Hanle signal resulting in erroreous measurements. The effect of one such factor, a finite interaction cross section, is discussed here.     

Idempotents in a compact ring

In this paper we investigate stable range conditions by virtue of elements in 2-dimensional general linear groups. Also we give the substitutions of modules over rings with stable range conditions. As an application, we prove that 2-fold stable condition is left-right symmetric.     

Strain‐Induced Isomerization in One‐Dimensional Metal–Organic Chains

The ability to use mechanical strain to steer chemical reactions creates completely new opportunities for solution‐ and solid‐phase synthesis of functional molecules and materials. However, this strategy is not readily applied in the bottom‐up on‐surface synthesis of well‐defined nanostructures. We report an internal strain‐induced skeletal rearrangement of one‐dimensional (1D) metal–organic chains (MOCs) via a concurrent atom shift and bond cleavage on Cu(111) at room temperature. The process involves Cu‐catalyzed debromination of organic monomers to generate 1,5‐dimethylnaphthalene diradicals that coordinate to Cu adatoms, forming MOCs with both homochiral and heterochiral naphthalene backbone arrangements. Bond‐resolved non‐contact atomic force microscopy imaging combined with density functional theory calculations showed that the relief of substrate‐induced internal strain drives the skeletal rearrangement of MOCs via 1,3‐H shifts and shift of Cu adatoms that enable migration of the monomer backbone toward an energetically favorable registry with the Cu(111) substrate. Our findings on this strain‐induced structural rearrangement in 1D systems will enrich the toolbox for on‐surface synthesis of novel functional materials and quantum nanostructures.     

Modulation of Foreign Body Reaction against PDMS Implant by Grafting Topographically Different Poly(acrylic acid) Micropatterns

The surface of poly(dimethylsiloxane) (PDMS) is grafted with poly(acrylic acid) (PAA) layers via surface‐initiated photopolymerization to suppress the capsular contracture resulting from a foreign body reaction. Owing to the nature of photo‐induced polymerization, various PAA micropatterns can be fabricated using photolithography. Hole and stripe micropatterns ≈100‐µm wide and 3‐µm thick are grafted onto the PDMS surface without delamination. The incorporation of PAA micropatterns provides not only chemical cues by hydrophilic PAA microdomains but also topographical cues by hole or stripe micropatterns. In vitro studies reveal that a PAA‐grafted PDMS surface has a lower proliferation of both macrophages (Raw 264.7) and fibroblasts (NIH 3T3) regardless of the pattern presence. However, PDMS with PAA micropatterns, especially stripe micropatterns, minimizes the aggregation of fibroblasts and their subsequent differentiation into myofibroblasts. An in vivo study also shows that PDMS samples with stripe micropatterns polarized macrophages into anti‐inflammatory M2 macrophages and most effectively inhibits capsular contracture, which is demonstrated by investigation of inflammation score, transforming‐growth‐factor‐β expression, number of macrophages, and myofibroblasts as well as the collagen density and capsule thickness.     

Inhibitory Effects of Cucurbitane-Type Triterpenoids from Momordica charantia Fruit on Lipopolysaccharide-Stimulated Pro-Inflammatory Cytokine Production in Bone Marrow-Derived Dendritic Cells

The bitter melon, Momordica charantia L., was once an important food and medicinal herb. Various studies have focused on the potential treatment of stomach disease with M. charantia and on its anti-diabetic properties. However, very little is known about the specific compounds responsible for its anti-inflammatory activities. In addition, the in vitro inhibitory effect of M. charantia on pro-inflammatory cytokine production by lipopolysaccharide (LPS)-stimulated bone marrow-derived dendritic cells (BMDCs) has not been reported. Phytochemical investigation of M. charantia fruit led to the isolation of 15 compounds (1−15). Their chemical structures were elucidated spectroscopically (one- and two-dimensional nuclear magnetic resonance) and with electrospray ionization mass spectrometry. The anti-inflammatory effects of the isolated compounds were evaluated by measuring the production of the pro-inflammatory cytokines interleukin IL-6, IL-12 p40, and tumor necrosis factor α (TNF-α) in LPS-stimulated BMDCs. The cucurbitanes were potent inhibitors of the cytokines TNF-α, IL-6, and IL-12 p40, indicating promising anti-inflammatory effects. Based on these studies and in silico simulations, we determined that the ligand likely docked in the receptors. These results suggest that cucurbitanes from M. charantia are potential candidates for treating inflammatory diseases.