Optical properties of frustrated cholesteric liquid crystals in planar cell

ABSTRACT

We investigated the alignment director of a frustrated cholesteric liquid crystal (CLC) confined in a planar cell. Three cells with different confinement ratio (c?=?d/p) (where p is the pitch and d is the cell thickness) are prepared. Under an electric field, the CLC planar texture is transformed into a cholesteric fingerprint (CF). The results showed that CF contrast depends on c. When c?≈?2, CLC stripes are formed by a periodic CF, with a period equal to the CLC pitch. The CF is developed and slowly extended to the whole cell surface along the rubbing direction and the contrast of the grating stripes keeps unchangeable. Yet, the CLC finger borders have a different light intensity. However, when c?≈?1, the CF contrast increases with time. When c?θ between the polarizer and the CFs.     

Isoperimetric Inequalities for a Wedge-Like Membrane

For a wedge-like membrane, Payne and Weinberger proved in 1960 an isoperimetric inequality for the fundamental eigenvalue which in some cases improves the classical isoperimetric inequality of Faber–Krahn. In this work, we introduce “relative torsional rigidity” for this type of membrane and prove new isoperimetric inequalities in the spirit of Saint-Venant, Pólya–Szeg?, Payne, Payne–Rayner, Chiti, and Talenti, which link the eigenvalue problem with the boundary value problem in a fundamental way.     

Sensitivity and stability analysis on the first and second levels of efficiency score relative to data error

In data envelopment analysis (DEA), efficient decision making units (DMUs) are of primary importance as they define the efficient frontier. The current paper develops a new sensitivity analysis approach for a category DMUs and finds the stability radius for all efficient DMUs. By means of combining some classic DEA models and with the condition that the efficiency scores of efficient DMUs remain unchanged, we are able to determine what perturbations of the data can be tolerated before efficient DMUs become inefficient. Our approach generalizes the conventional sensitivity analysis approach in which the inputs of efficient DMUs increase and their outputs decrease, while the inputs of inefficient DMUs decrease and their outputs increase. We find the maximum quantity of perturbations of data so that all first level efficient DMUs remain at the same level.     

Sulfamic acid immobilized on amino‐functionalized magnetic nanoparticles: A new and active magnetically recoverable catalyst for the synthesis of N‐heterocyclic compounds

Sulfamic acid immobilized on amino‐functionalized magnetic nanoparticles (MNPs/DETA‐SA) was successfully fabricated and characterized using various techniques. Diameters of approximately 15 nm for the MNPs/DETA‐SA were observed from scanning electron microscopy images. The as‐fabricated nanocomposite was applied as an efficient and magnetically reusable catalyst for the synthesis of 2,3‐dihydroquinazoline‐4(1H)‐one and polyhydroquinoline derivatives. All products were obtained in good to excellent yields. Recovery tests confirm that the catalyst can be readily recovered using an external magnet and reused many times without significant loss of its catalytic activity.     

Zirconium oxide complex‐functionalized MCM‐41 nanostructure: an efficient and reusable mesoporous catalyst for oxidation of sulfides and oxidative coupling of thiols using hydrogen peroxide

Zirconium oxide complex‐functionalized mesoporous MCM‐41 (Zr‐oxide@MCM‐41) as an efficient and reusable catalyst is reported for the oxidation of sulfides into sulfoxides using hydrogen peroxide (H₂O₂) as the oxidant, with short reaction times in good to excellent yields at room temperature under solvent‐free conditions. Also, a simple and efficient method is reported for the oxidative coupling of thiols into corresponding disulfides in good to high yields using H₂O₂ as oxidant in the presence of Zr‐oxide@MCM‐41 as recoverable catalyst in ethanol at room temperature. A series of sulfides and thiols possessing functional groups was successfully converted into corresponding products. After completion of reactions the catalyst was easily separated with simple filtration from the reaction mixture and reused for several consecutive runs without significant loss of catalytic efficiency. The mesoporous catalyst was characterized using Fourier transform infrared spectroscopy, Brunauer–Emmett–Teller surface area measurements, X‐ray diffraction, transmission and scanning electron microscopies, energy‐dispersive X‐ray spectroscopy and thermogravimetric analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

A linear programming approach to test efficiency in multi-objective linear fractional programming problems

In a multi-objective linear fractional programming problem (MOLFPP), it is often useful to check the efficiency of a given feasible solution, and if the solution is efficient, it is useful to check strong or weak efficiency. In this paper, by applying a geometrical interpretation, a linear programming approach is achieved to test weak efficiency. Also, in order to test strong efficiency for a given weakly efficient point, a linear programming approach is constructed.     

Green Function Bounds and Parabolic Potentials on a Half-Space

By proving a lower and an upper bound for Green's function of certain parabolic operators with Lipschitz coefficients in 0\} {\text{ and }}0 < T < + \infty $$ " align="middle" border="0"> , we give a characterization of the associated parabolic potentials and we study in a last part the boundary behaviour of these potentials for n=1.     

Thermal buckling of a constrained elastic ring†

The buckling problem of a heated circular elastic ring confined to a uniformly contracting circular boundary is investigated. The buckled configuration is assumed to consist of a shallow detached region with the remainder of the ring in contact with the contracting boundary. The ring is treated as a variational problem with variable end points, by virtue of which, a transversality condition is obtained for the determination of the extent of the detached region. The influence of temperature variation and level of prestressing on the buckling phenomena are studied and a correspondence relationship between the pure contraction and thermal problems is obtained.