Function-valued Padé-type approximant via E-algorithm and its applications in solving integral equations

The function-valued Padé-type approximant (FPTA) was defined in the inner product space [8]. In this work, we choose the coefficients in the Neumann power series to make the inner product with both sides a function-valued system of equations to yield a scalar system. Then we express an FPTA in the determinant form. To avoid the direct computation of the determinants, we present the E-algorithm for FPTA based on the vector-valued E-algorithm given by Brezinski [4]. The method of FPTA via E-algorithm (FPTAVEA) not only includes all previous methods but overcomes their essential difficulties. The numerical experiment for a typical integral equation [1] illustrates that the method of FPTAVEA is simpler and more effective for obtaining the characteristic values and the characteristic functions than all previous methods. In addition, this method is also applicable to other Fredholm integral equations of the second kind without explicit characteristic values and characteristic functions. A corresponding example [12] is given and the numerical result is the same as that in [12].     

Some Paradoxes in Special Relativity and the Resolutions

The special theory of relativity is the foundation of modern physics, but its unusual postulate of invariant vacuum speed of light results in a number of plausible paradoxes. This situation leads to radical criticisms and suspicions against the theory of relativity. In this paper, from the perspective that the relativity is nothing but a geometry, we give a uniform resolution to some famous and typical paradoxes such as the ladder paradox, the Ehrenfest’s rotational disc paradox. The discussion shows that all the paradoxes are caused by misinterpretation of concepts. We misused the global simultaneity and the principle of relativity. As a geometry of Minkowski space-time, special relativity can never result in a logical contradiction.     

Nonlinear buckling behavior of 3D-braided composite cylindrical shells subjected to internal pressure loads in thermal environments

The nonlinear buckling behavior of a 3D-braided composite cylindrical shell of finite length subjected to internal pressure in thermal environments is considered. According to a new micromacromechanical model, a 3D-braided composite may be treated as a cell system where the geometry of each cell strongly depends on its position in the cross section of the cylindrical shell. The material properties of the epoxy matrix are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear deformation theory of shells with a von Karman–Donnell-type kinematic nonlinearity and include thermal effects. The singular perturbation technique is employed to determine the buckling pressure and the postbuckling equilibrium paths of the shell.     

Asymptotical optimality of WSEPT for stochastic online scheduling on uniform machines

We study the stochastic online scheduling on m uniform machines with the objective to minimize the expected value of total weighted completion times of a set of jobs that arrive over time. For each job, the processing time is a random variable, and the distribution of processing time is unknown in advance. The actual processing time could be known only when the job is completed. For the problem, we propose a policy which is proved to be asymptotically optimal when the processing times and weights are uniformly bounded, i.e. the relative error of the solution achieved by our policy approaches zero as the number of jobs increases to infinity.     

Direct observation of lithium staging in partially delithiated LiFePO4 at atomic resolution

Lithium ions in LiFePO(4) were observed directly at atomic resolution by an aberration-corrected annular-bright-field scanning transmission electron microscopy technique. In addition, it was found in partially delithiated LiFePO(4) that the remaining lithium ions preferably occupy every second layer, along the b axis, analogously to the staging phenomenon observed in some layered intercalation compounds. This new finding challenges previously proposed LiFePO(4)/FePO(4) two-phase separation mechanisms.     

Large-scale synthesis of uniform and extremely small-sized iron oxide nanoparticles for high-resolution T1 magnetic resonance imaging contrast agents

Uniform and extremely small-sized iron oxide nanoparticles (ESIONs) of < 4 nm were synthesized via the thermal decomposition of iron-oleate complex in the presence of oleyl alcohol. Oleyl alcohol lowered the reaction temperature by reducing iron-oleate complex, resulting in the production of small-sized nanoparticles. XRD pattern of 3 nm-sized nanoparticles revealed maghemite crystal structure. These nanoparticles exhibited very low magnetization derived from the spin-canting effect. The hydrophobic nanoparticles can be easily transformed to water-dispersible and biocompatible nanoparticles by capping with the poly(ethylene glycol)-derivatized phosphine oxide (PO-PEG) ligands. Toxic response was not observed with Fe concentration up to 100 μg/mL in MTT cell proliferation assay of POPEG-capped 3 nm-sized iron oxide nanoparticles. The 3 nm-sized nanoparticles exhibited a high r(1) relaxivity of 4.78 mM(-1) s(-1) and low r(2)/r(1) ratio of 6.12, demonstrating that ESIONs can be efficient T(1) contrast agents. The high r(1) relaxivities of ESIONs can be attributed to the large number of surface Fe(3+) ions with 5 unpaired valence electrons. In the in vivo T(1)-weighted magnetic resonance imaging (MRI), ESIONs showed longer circulation time than the clinically used gadolinium complex-based contrast agent, enabling high-resolution imaging. High-resolution blood pool MR imaging using ESIONs enabled clear observation of various blood vessels with sizes down to 0.2 mm. These results demonstrate the potential of ESIONs as T(1) MRI contrast agents in clinical settings.     

Principal component directed partial least squares analysis for combining nuclear magnetic resonance and mass spectrometry data in metabolomics: application to the detection of breast cancer

Nuclear magnetic resonance (NMR) spectroscopy and mass spectrometry (MS) are the two most commonly used analytical tools in metabolomics, and their complementary nature makes the combination particularly attractive. A combined analytical approach can improve the potential for providing reliable methods to detect metabolic profile alterations in biofluids or tissues caused by disease, toxicity, etc. In this paper, (1)H NMR spectroscopy and direct analysis in real time (DART)-MS were used for the metabolomics analysis of serum samples from breast cancer patients and healthy controls. Principal component analysis (PCA) of the NMR data showed that the first principal component (PC1) scores could be used to separate cancer from normal samples. However, no such obvious clustering could be observed in the PCA score plot of DART-MS data, even though DART-MS can provide a rich and informative metabolic profile. Using a modified multivariate statistical approach, the DART-MS data were then reevaluated by orthogonal signal correction (OSC) pretreated partial least squares (PLS), in which the Y matrix in the regression was set to the PC1 score values from the NMR data analysis. This approach, and a similar one using the first latent variable from PLS-DA of the NMR data resulted in a significant improvement of the separation between the disease samples and normals, and a metabolic profile related to breast cancer could be extracted from DART-MS. The new approach allows the disease classification to be expressed on a continuum as opposed to a binary scale and thus better represents the disease and healthy classifications. An improved metabolic profile obtained by combining MS and NMR by this approach may be useful to achieve more accurate disease detection and gain more insight regarding disease mechanisms and biology.     

Simultaneous LC?CMS?CMS Determination of HM30181A, [2-(2-{4-[2-(6,7-Dimethoxy-3,4-dihydro-1H-isoquinolin-2-yl)-ethyl]-phenyl}-2H-tetrazol-5-yl)-4,5-dimethoxyphenyl]amide, as a new P-Glycoprotein Inhibitor and Its Two Metabolites, M1 and M2, in Human Plasma: Application to a Pharmacokinetic Study

A simultaneous simple, rapid, and sensitive LC?CMS?CMS method was developed and validated for the determination of HM30181A, [2-(2-{4-[2-(6,7-dimethoxy-3,4-dihydro-1H-isoquinolin-2-yl)-ethyl]-phenyl}-2H-tetrazol-5-yl]-4,5-dimethoxy-phenyl]amide, as a P-glycoprotein inhibitor and its two metabolites, M1 and M2, in human plasma using docetaxel as an internal standard (IS). The analytes were extracted from 200???L of biological sample by liquid?Cliquid extraction using 1?mL of methyl-t-butyl ether. Chromatographic separation was carried on a Luna C8 column at 30???C with mobile phase consisting of distilled water with 0.1% formic acid and acetonitrile (75:25, v/v) at a flow rate of 0.7?mL?min^?1 for human plasma samples. The method was linear over concentration ranges of 0.5?C50, 0.1?C10, and 0.1?C10?ng?mL^?1 for HM30181A, M1, and M2, respectively, in human plasma. The values of coefficient variation for the assay precision were <12.5, <9.10, and <9.96% for HM30181A, M1, and M2, respectively, in human plasma. The values of accuracy were 93.0?C108, 94.7?C104%, and 95.7?C105% for HM30181A, M1, and M2, respectively, in human plasma. This method is simple, sensitive, and applicable for the pharmacokinetic studies of HM30181A and its metabolites in humans.     

Synthesis, cytotoxicities and DNA-binding affinities of benzofuran-3-ols and their fused analogs

A series of benzofuropyrazoles 2a-i were synthesized in 10-92% from the reaction of 2-aroylbenzofuran-3-ols 1a-i with hydrazine hydrate, and screened for their antitumor activities toward four human solid tumor cell lines, including gastric carcinoma cells MKN45, hepatocellular carcinoma cells HepG2, breast cancer cells MCF-7, and lung cancer cells A549. The results indicated that both compounds 1a-i and 2a-i displayed moderate antitumor activities. Among them, compound 2e exhibited potent inhibitory activity toward all the four tumor cell lines. In addition, compounds 1e and 2e showed strong DNA-binding affinities, and induced an increase in the viscosity of calf-thymus DNA, suggesting that they might act as an intercalator.     

Determination of Pilocarpine in Human Plasma by LC�CAPCI�CMS�CMS and Application to a Pharmacokinetic Study

A sensitive, specific and rapid high performance liquid chromatography?Catmospheric pressure chemical ionization source-tandem mass spectrometry (LC-APCI-MS-MS) method for the determination of pilocarpine in human plasma was developed and validated. The method is based on liquid?Cliquid extraction, followed by a reversed-phase liquid chromatographic separation, and detected by means of tandem mass spectrometry. The linear calibration curve covered a concentration range of 2?C500 ??g L^?1. The intra- and inter-day precisions for pilocarpine were <10% and the accuracies were between 90 and 110%. The method was applied successfully to a pharmacokinetic study involving 20 healthy Chinese male volunteers after oral administration of 6 mg pilocarpine.