Generalized 3G theorem and application to relativistic stable process on non-smooth open sets

Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes.     

A Cu(Ⅱ) Complex with IM-MeImz-к2 N,O Mode in [Cu(IM-MeImz)2]·(SCN)2: Synthesis, Crystal Structure and Magnetic Properties

A new copper(Ⅱ) compound with imino nitroxide radicals [Cu(IM-MeImz)2]·(SCN)2 (IM-meImz =2-(5-methylimidazol-4-yl)-4,4,5,5-tetramethyl-2-imidazoline-1-oxyl) has been synthesized and characterized structurally and magnetically. It crystallizes in monoclinic, space group P21/c with a = 9.3604(7), b = 10.3012(7), c = 16.6684(12) (A), β = 105.0290(10)°, V = 1552.25(19)(A)3, C24H34CuN10O2S2, Mr = 622.27, Z = 2, Dc = 1.331 g/cm3, μ(MoKα) = 0.876 mm-1, F(000) =650, the final R = 0.0374 and wR = 0.1079. X-ray analysis demonstrates that the IM-MeImz ligand is coordinated to the copper(Ⅱ) ion as an unusual didentate chelate with a κ2 N(MeImz),O(IM) mode in the complex. The square-planar coordination sites at Cu(Ⅱ) are occupied by two O and two N atoms from the imino nitroxide radicals. The complex molecules are connected as a onedimensional polymer structure by intermolecular interactions. Magnetic measurements show that there are intramolecular antiferromagnetic interactions between the Cu(Ⅱ) ion and radicals.     

Phosphorescent κ3-(N^C^C)-Gold(III) Complexes: Synthesis,Photophysics, Computational Studies and Application to Solution-Processable OLEDs

Efficient OLED devices have been fabricated using organometallic complexes of platinum group metals. Still, the high material cost and low stability represent central challenges for their application in commercial display technologies. Based on its innate stability, gold(III) complexes are emerging as promising candidates for high-performance OLEDs. Here, a series of alkynyl-, N-heterocyclic carbene (NHC)- and aryl-gold(III) complexes stabilized by a κ³-(N^C^C) template have been prepared and their photophysical properties have been characterized in detail. These compounds exhibit good photoluminescence quantum efficiency (η_PL) of up to 33 %. The PL emission can be tuned from sky-blue to yellowish green colors by variations on both the ancillary ligands as well as on the pincer template. Further, solution-processable OLED devices based on some of these complexes display remarkable emissive properties (η_CE 46.6 cd.A⁻¹ and η_ext 14.0 %), thus showcasing the potential of these motifs for the low-cost fabrication of display and illumination technologies.     

Anti-atherosclerotic activity of Betulinic acid loaded polyvinyl alcohol/methylacrylate grafted Lignin polymer in high fat diet induced atherosclerosis model rats

Betulinic acid is one such natural pentacyclic triterpenoid compound, holding various pharmacological properties but its poor bioavailability is the only limitation. One of the biological macromolecules such as Lignin is a plant-derived aromatic, eco-friendly and low-cost polymer that certainly self-assembles into nano-sized colloids. Therefore, onto the current investigation, we increased the bioavailability of betulinic acid by coating on to a nanopolymer prepared with poly vinyl alcohol, lignins and methyl acrylate. Betulinic acid loaded polyvinyl alcohol/ethylacrylate grafted Lignin polymer (PVA/Lig-g-MA) nanoformulation was characterized using FTIR, XRD, SEM and TEM analysis and also the drug entrapment, in vitro drug releasing capacity was done to examine the efficiency of the nanoformulation of a drug. The MTT assay was evaluated the cytotoxicity of synthesized nanoformulation against normal endothelial cells HUVEC and HAPEC to confirm the side effects of the drug. The anti-atherosclerotic property of the nanoformulation was ascertained in both in vitro condition (with HUVEC and HPAEC) and in vivo studies (with Wistar rats). As a result, the characterization studies and in vitro studies clearly confirmed the Betulinic acid loaded PVA/Lig-g-MA nanoformulation is an ideal nanopolymer and it doesn’t cause any cytotoxic effect in normal endothelial cells. It also decreased the lipopolysaccharides induced inflammation through the down-regulation of NFκB and MAP/JNK signaling molecule expressions. Following in vivo results confirmed the synthesized nanoformulation effectively decreased the hyperchlostremia, inflammation and vasoconstriction, which induced over high fat diet. The results of histopathological analysis of cardiac tissues also confirmed the cardioprotective role of synthesized nanoformulation. Overall, both the in vitro and in vivo studies authentically proven the Betulinic acid loaded PVA/Lig-g-MA nanoformulation would be a potent cost effective anti-atherosclerotic nanodrug.     

Convenient preparation of N-8-quinolinyl benzenesultams as novel NF-κB inhibitors

An efficient synthesis of a series of N-8-quinolinyl benzenesultams as novel NF-κB inhibitors was described via diazotization-induced cyclization of easily accessible N-8-quinolinyl-2-aminobenzenesulfonamides.     

New biphenantherene and nervogenic acid derivatives from Liparis regnieri Finet and their inhibitory activities against NF-κB activation

A phytochemical investigation of the whole plant of Liparis regnieri Finet led to the isolation of one new biphenantherene (1) and ten new nervogenic acid derivatives (2–11), together with nine known compounds. Their structures were elucidated mainly by extensive analyses of 1D and 2D NMR spectroscopic data and chemical reactions. Additionally, for the first time a previously unreported biphenantherene was discovered to effectively suppress TNF-α induced expression of NF-κB-Luc in Hela cells with the IC₅₀ value of 1.80 μM and the structure-activity relationshipwas also discussed.     

Studies on nano suspensions of silver sol and redispersed nanocrystallite silver in aqueous and alcoholic media

Nanocrystallite silver and silver sol were prepared and characterized by UV-visible spectra, XRD, TEM and HRTEM. The crystallite silver is re-dispersed in two different media, namely, water and alcohol and sonicated before ultrasonic investigation. The silver sol was used as such. Three different models for the propagation of ultrasound through two phase media are compared in these three different types of nano suspensions. Effect of particle size and medium on ultrasonic velocity (U), compressibility (κ) impedance (Z) and viscous relaxation time (τ) is studied. The particle concentration range was 0.2-1 v/v. Density and viscosity of the dispersion and sol are measured at different particle volume fractions. Effective density and ultrasonic velocity are computed by Urick, Kuster and Toksöz and Urick and Ament models and compared with experimental velocities. Values of effective density obtained by using Urick and Urick and Ament equations closely agree with experimental results of density while Urick's equation prediction of velocity is in close agreement with the experimental velocities. This comes as a surprise in view of the large density difference between the medium and suspended particle and suggests the possibility of the balancing effect of the inertial and viscous forces operating in the suspension.     

拟绝对-*-κ-仿正规算子的谱性质

引入了拟绝对-*-k-仿正规算子,获得了拟绝对-*-k-仿正规算子的一个充要条件.并证明了拟绝对-*-k-仿正规算子在0≤k≤1上是有限上升的,作为此性质的应用,证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则Weyl谱和本质近似点谱的谱映射定理成立.最后证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则σ_(ja)(T)\{0}=σ_a(T)\{0}.     

Resonance Interaction Energy in κ-Minkowski Spacetime

If gravity is quantized, one of the consequences may be that the spacetime coordinates are quantized and become noncommutative. The κ-Minkowski spacetime is such kind of noncommutative spacetime. In this paper, the resonance interaction energy of a two-atom system coupled with a fluctuating vacuum scalar field in the κ-Minkowski spacetime is studied. It is found that the resonance interaction energy is dependent on the interatomic separation, the transition wavelength of the atoms, and the spacetime non-commutativity. When the interatomic separation is small compared with a characteristic length determined by the spacetime non-commutativity parameter and the transition wavelength, the resonance interaction energy is that in the Minkowski spacetime plus a correction due to the spacetime non-commutativity. When the interatomic separation is comparable to or larger than the characteristic length, the resonance interaction energy cannot be organized in the form of a Minkowski term plus a correction, which indicates that the long-range behavior of the vacuum in the κ-Minkowski spacetime is fundamentally different from that in the Minkowski spacetime.