Lagrangian mean curvature flow for entire Lipschitz graphs II

We prove longtime existence and estimates for smooth solutions to a fully nonlinear Lagrangian parabolic equation with locally $C^{1,1}$ initial data $u_0$ satisfying either (1) $-(1+\eta ) I_n\le D^2u_0 \le (1+\eta )I_n$ for some positive dimensional constant $\eta $ , (2) $u_0$ is weakly convex everywhere, or (3) $u_0$ verifies a large supercritical Lagrangian phase condition.     

Functional magnetic resonance (fMR) imaging of a rat brain tumor model: implications for evaluation of tumor microvasculature and therapeutic response

Functional MR (fMR) imaging techniques based on blood oxygenation level dependent (BOLD) effects were developed and applied to a rat brain tumor model to evaluate the potential utility of the method for characterizing tumor growth and regression following treatment. Rats bearing 9L brain tumors in situ were imaged during inhalation of room air and after administration of 100% oxygen + acetazolamide (ACZ) injected 15 mg/kg intravenously. Pixel-to-pixel fMR maps of normalized signal intensity change from baseline values were calculated from T2 weighted spin echo (SE) images acquired pre- and post- oxygen + ACZ administration. Resultant fMR maps were then compared to gross histological sections obtained from corresponding anatomical regions. Regions containing viable tumor with increased cellular density and localized foci of necrotic tumor cells consistent with hypoxia were visualized in the fMR images as regions with decreased signal intensities, indicating diminished oxyhemoglobin concentration and blood flow as compared to normal brain. Histological regions having peritumor edema, caused by increased permeability of tumor vasculature, were visualized in the fMR images as areas with markedly increased signal intensities. These results suggest that fMR imaging techniques could be further developed for use as a non-invasive tool to assess changes in tumor oxygenation/hemodynamics, and to evaluate the pharmacologic effect of anti-neoplastic drugs.     

Free radical polymerization of caffeine‐containing methacrylate monomers

The incorporation of acrylic functionality into caffeine enables the preparation of a vast array of novel thermoplastics and thermosets. A two‐step derivatization provided a novel caffeine‐containing methacrylate monomer capable of free radical polymerization. Copolymers of 2‐ethylhexyl methacrylate and caffeine methacrylate (CMA) allowed for a systematic study of the effect of covalently bound caffeine on polymer properties. ¹H NMR and UV‐vis spectroscopy confirmed caffeine incorporation at 5 and 13 mol %, and SEC revealed the formation of high molecular weight (co)polymers (>40,000 g/mol). CMA incorporation resulted in a multistep degradation profile with initial mass loss closely correlating to caffeine content. Differential scanning calorimetry, rheological, and thermomechanical analysis demonstrated that relatively low levels of CMA increased the glass transition temperature, resulting in higher moduli and elucidating the benefits of incorporating caffeine into polymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2829–2837     

Ligand Control of Palladium-Catalyzed Site-Selective α- and γ-Arylation of α,β-Unsaturated Ketones with (Hetero)aryl Halides

This study describes the first palladium-catalyzed, site-selective α- and γ-arylation of α,β-unsaturated ketones with (hetero)aryl halides. A wide range of hetero(aryl)halides coupled with α,β-unsaturated ketones, and transformation into the arylated products proceeded with excellent to good yields. The site selectivity of the reaction is switchable by simply changing the phosphine ligand to access either α-arylated or γ-arylated products in good to excellent yields by using a low catalyst loading, and the method demonstrates good functional-group compatibility.     

Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.     

Diels-Alder reactions of three fused nitrogen-containing bicyclic enones: an efficient method toward novel nitrogen-containing angular tricyclic skeletons

The syntheses of three fused bicyclic enones, including 1,2,6,6a-tetrahydro-1-tosyl-cyclopenta[b]pyrrol-3(5H)-one, 1,2,3,6,7,7a-hexahydro-4H-1-tosyl-cyclopenta[b]pyridin-4-one and 1,2,5,6,7,7a-hexahydro-3H-1-tosyl-indol-3-one, via anionic cyclization and Diels-Alder reactions with various dienes to construct novel nitrogen-containing angular tricyclic skeletons are described.     

Mechanisms of micellization and rheology of PEO-PPO-PEO triblock copolymers with various architectures

Micelle formation was followed by micro-DSC and rheology for aqueous solutions of two copolymers of PEO-PPO-PEO, the Pluronic F127 (from BASF) and the EG56 (from PolymerExpert), a branched copolymer built with three chains of F127 type. It is shown that micellization is endothermic and that, for both polymers, the enthalpy of formation/melting is proportional to total concentration. The rheology of the solutions was carefully analyzed, before gelation for F127, and it reveals firstly the progressive changes of solubility of the unimers (decease of relative solution viscosity), followed by micelle formation over a 10 degrees C range. In this range, the micelle concentration dependence on temperature was deduced from enthalpy measurements and the corresponding volume fractions were derived. Viscosity was interpreted within the framework of well-known theories for hard sphere suspensions (Krieger-Dougherty or Quemada) based on an analogy between micelles and nanosized hairy grain suspensions. The gel state is achieved due to formation of the colloidal crystal. For EG56, the rheology is quite different; as the aggregation increases with temperature, a progression is observed from Newtonian to visco-elastic liquid. The characteristic frequency, defined by the relation G(') = G('), for EG56 varies with temperature and the corresponding times increase by two orders of magnitude according to an Arrhenius law. The frequency dependence of G(') and G(') at different temperatures can be superposed with a horizontal shift factor and a small amplitude adjustment. There is no elastic solid formation in this case. The "gelation" of these two copolymers is compared to the physical gelation of cold-set gels (gelatin).     

Analytical comparison of different parts of Radix Angelicae Sinensis by gas chromatography coupled with mass spectrometry

The three parts of Radix Angelicae Sinensis (Danggui) were reported to have different therapeutic effects. In order to investigate their chemical compositions of different parts of Danggui, gas chromatography-mass spectrometry (GC-MS) combined with chemometrics data analysis was applied to provide a more detailed study. Subwindow factor analysis (SFA) and a modified augmented evolving window orthogonal projection (AEWOP) method were used to resolve the batch GC-MS data sets from the Danggui samples. Then, t-test, Wilcoxon rank sum test, and principal component analysis (PCA) were applied to carry out the comparison job. The results indicate which components are found to have significant differences among the three parts. These findings may be helpful for further research of the pharmacological activities of Danggui.     

An ab initio study of the low-lying electronic states of YO2 and Franck-Condon simulation of the first photodetachment band of YO2(-)

A variety of density functional theory and ab initio methods, including B3LYP, B98, BP86, CASSCF, CASSCF/RS2, CASSCF/MRCI, BD, BD(T), and CCSD(T), with ECP basis sets of up to the quintuple-zeta quality for Y, have been employed to study the X(2)B2 state of YO2 and the X(1)A1 state of YO2(-). Providing that the Y 4s(2)4p(6) outer-core electrons are included in the correlation treatment, the RCCSD(T) method gives the most consistent results and is concluded to be the most reliable and practical computational method for YO2 and YO2(-). In addition, RCCSD(T) potential energy functions (PEFs) of the X(2)B2 state of YO2 and the X(1)A1 state of YO2(-) were computed, employing the ECP28MDF_aug-cc-pwCVTZ and aug-cc-pVTZ basis sets for Y and O, respectively. Franck-Condon factors, which include allowance for Duschinsky rotation and anharmonicity, were calculated using the computed RCCSD(T) PEFs and were used to simulate the first photodetachment band of YO2(-). The simulated spectrum matches very well with the corresponding experimental 355 nm photodetachment spectrum of Wu, H.; Wang, L.-S. J. Phys. Chem. A 1998, 102, 9129, confirming the reliability of the RCCSD(T) PEFs used. Further calculations on low-lying electronic states of YO2 gave T(e)'s and T(vert)'s of the A(2)A1, B(2)B1, and C(2)A2 states of YO2, as well as EAs and VDEs to these states from the X(1)A1 state of YO2(-). On the basis of the ab initio VDEs obtained in the present study, previous assignments of the second and third photodetachment bands of YO2(-) have been revised.     

Chemical constituents from the leaves of Manglietia phuthoensis and their effects on osteoblastic MC3T3-E1 cells

Two new phenyl glycosides, mangliesides A and B (1, 2), a new ionol glycoside, manglieside C (3), two new lignan glycosides, mangliesides D and E (4, 5), were isolated from the leaves of Manglietia phuthoensis, along with two known lignans, 3-methoxymagnolol (6) and obovatol (7). Their structures were established by means of 1D and 2D NMR, electrospray ionization (ESI)-MS and HR-ESI-MS experiments. Among them, compounds 2 and 5 significantly (p<0.05) increased the growth and differentiation of osteoblastic MC3T3-E1 cells in vitro.