A new quadratic nonconforming finite element on rectangles

A new quadratic nonconforming finite element on rectangles (or parallelograms) is introduced. The nonconforming element consists of P₂ ⊕ Span{x²y,xy²} on a rectangle and eight degrees of freedom. Our element is essentially of seven degrees of freedom since the degree of freedom associated with the integration on rectangle is essentially of bubble‐function nature. Global basis functions are constructed for both Dirichlet and Neumann type of problems; accordingly the corresponding dimensions are counted. The local and global interpolation operators are defined. Error estimates of optimal order are derived in both broken energy and L²(Ω) norms for second‐order of elliptic problems. Brief numerical results are also shown to confirm the optimality of the presented quadratic nonconforming element. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Microporous manganese formate: a simple metal-organic porous material with high framework stability and highly selective gas sorption properties

Novel microporous metal-organic framework material composed of Mn(II) and formate ions displays permanent porosity, high thermal stability, and size-selective gas sorption behavior. The framework is stable enough to maintain single crystallinity after the complete guest removal at 150 degrees C under a reduced pressure. Most importantly, it selectively adsorbs H2 and CO2 but not N2 and other gases with larger kinetic diameters, which appears to be due to the small aperture of the channels. Despite a moderate H2 storage capacity, which is however still higher than that of any zeolite, its H2 surface coverage is one of the highest among the known microporous materials. Thus this new zeolite-like material made of a simple organic building block may find useful applications in gas separation and sensor.     

Simultaneous quantitation of 17 female sex hormones in illegal products by validated liquid chromatography-high resolution mass spectrometry and liquid chromatography-tandem mass spectrometry methods

The consumption of food and drugs adulterated with female sex hormones can have an extremely adverse effect on human health. Therefore, developing appropriate monitoring methods for the identification of various exogenous female sex hormones is crucial for minimizing and eliminating the related health risks. Herein, 17 female hormones categorized into two groups: estrogen and progestin, were analyzed using reversed-phase liquid chromatography coupled to Orbitrap or triple quadrupole mass spectrometry. The fragmentation patterns for all compounds were discovered, and fragmented structures were also derived from them through liquid chromatography–high-resolution mass spectrometry followed by qualitative sample analysis. In addition, a quantitative analysis of 67 samples of illicit drugs and dietary supplements was performed using the validated liquid chromatography-tandem mass spectrometry method. Female hormone components were detected in two samples of an unauthorized injectable solution and a tablet-type drug. Medroxyprogesterone was detected in the samples in the range of 96.4–206 ng/g. Notably, eight components similar in structure to steroids were simultaneously detected as male sex hormones by confirming their fragmentation ion patterns using liquid chromatography–high-resolution mass spectrometry. The developed methods thus offer a dependable and practically applicable approach for the screening and detection of exogenous female sex hormones in real food and drug samples to ensure public health.     

Uniqueness in a frequency-domain inverse problem of a stratified uniaxial bianisotropic medium

An inverse problem for a stratified uniaxial bianisotropic slab is considered in the frequency domain. The problem is treated as an analytic factorization problem in the frequency complex plane. Uniqueness in the parameter reconstruction is discussed and illustrated under a particular choice of a priori information.     

Nonconforming Galerkin methods for the Helmholtz equation

Nonconforming Galerkin methods for a Helmholtz‐like problem arising in seismology are discussed both for standard simplicial linear elements and for several new rectangular elements related to bilinear or trilinear elements. Optimal order error estimates in a broken energy norm are derived for all elements and in L² for some of the elements when proper quadrature rules are applied to the absorbing boundary condition. Domain decomposition iterative procedures are introduced for the nonconforming methods, and their convergence at a predictable rate is established. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 475–494, 2001     

Anion-directed self-organization of thermotropic liquid crystalline materials containing a guanidinium moiety

New wedge-shaped thermotropic liquid crystalline materials containing a guanidinium moiety at the apex organize into various supramolecular structures such as hexagonal columnar, rectangular columnar and Pm3n cubic mesophases depending on anions illustrating guest-directed self-organization in mesophases.     

Discotic liquid crystalline materials for potential nonlinear optical applications: synthesis and liquid crystalline behavior of 1,3,5-triphenyl-2,4,6-triazine derivatives containing achiral and chiral alkyl chains at the periphery

As a novel approach to nonlinear optical materials, new octupolar discotic liquid crystalline materials 1,3,5-triphenyl-2,4,6-triazine derivatives containing achiral alkyl chains (5a) and chiral alkyl chains (5b) at the periphery were synthesized. The former exhibits an ordered hexagonal columnar mesophase, whereas the latter displays a rectangular columnar mesophase. The negative exciton splitting observed in the CD spectrum of a thin film of 5b suggests that it has a left-handed helical structure within the column.