On generalized recurrent Riemannian manifolds

The object of the present paper is to study a type of Riemannian manifolds called generalized recurrent manifolds. We have constructed two concrete examples of such a manifold whose scalar curvature is non-zero non-constant. Some other properties have been considered. Among others it is shown that on a generalized recurrent manifold with constant scalar curvature, Weyl-semisymmetry and semisymmetry are equivalent. Sufficient condition for a generalized recurrent manifold to be a special quasi Einstein manifold is obtained.     

Development of Lactose Biosensor Based on β‐Galactosidase and Glucose Oxidase Immobilized into Gelatin

In this article, we describe the preparation of a new lactose biosensor based on electrode coating with β‐galactosidase and glucose oxidase immobilized gelatin. For this purpose, β‐galactosidase and glucose oxidase enzymes were immobilized onto gelatin by crosslinking with glutaraldehyde. Properties of the immobilized β‐galactosidase and glucose oxidase enzymes electrode have been studied. The effects of glutaraldehyde concentration, temperature and pH variations and reusability were among the subjects analyzed. Lactose biosensors were subjected to continuous repeated use in order to observe reusability and shelf life; where standard lactose and milk samples were used as substrate solutions. Continuous reuse experiments showed that most of the lactose biosensors activities were retained even after the 10th use in a period of 30 days.     

Applied electric field effect on light-scattering birefringence of dye-doped liquid crystal molecule and consistent neural network empirical physical formula construction for scattering intensities

In this paper, we realized two objectives. Firstly, birefringence of azo and anthraquinone dye-doped nematic liquid crystal (NLC) molecules was investigated by applied electric field dependent laser scattering intensities. The birefringence was essentially calculated from ordinary and extraordinary ray phase difference, which is determined from the measured intensities corresponding to parallel and perpendicular orientations of analyzer to polarizer. The birefringence was found to be dependent on both applied voltage and the kind of the doping dye. As the second objective, by nonlinear universal function approximator layered feedforward neural network (LFNN), we constructed explicit form of empirical physical formulas (EPFs) for experimentally measured dye-doped NLC nonlinear scattering intensities. Excellent LFNN test set predictions over yet-to-be measured experimental data proved that the constructed LFNN-EPFs estimated the measured intensities consistently. The correlation coefficients assessing the goodness of predictions were about r = 0.998for all cases. The LFNN-EPFs also extracted the intensity dependency on the kind of dye used. When theoretical and LFNN-EPFs intensities are compared, we conclude that given certain experimental conditions, theoretical and LFNN-EPFs predictions are in excellent agreement. In this sense, we can say that the physical laws embedded in the birefringence scattering data can be consistently extracted by LFNN. Therefore, judging from the consistent extraction of the molecular dependencies of pure and doped NLC intensities, we predict that the LFNN-EPFs can help to identify unknown molecular structural parameters in liquid crystal extracts. More concretely, by suitable mathematical operations such as differentiation, integration, minimization on these intensity LFNN-EPFs, some useful information into the charge distributions of the LC molecules can be gained.     

A coupled WC-TL SPH method for simulation of hydroelastic problems

A coupled weakly compressible (WC) and total Lagrangian (TL) smoothed particle hydrodynamics (SPH) method is developed for simulating hydroelastic problems. The fluid phase is simulated using WCSPH method, while the structural dynamics are solved using TLSPH method. Fluid and solid components of the method are validated separately. A sloshing water tank problem is solved to test the WCSPH method while oscillation of a thin plate and large deformation of a cantilever beam are simulated to test the TLSPH method. After validating each component, the coupled WC-TL SPH scheme is used to simulate two benchmark hydroelastic problems. The first test case shows the evolution of water column with an elastic boundary gate, and the second one investigates the breaking water column impact on elastic structures. The agreement between WC-TL SPH results and literature data shows the ability of the proposed method in simulating hydroelastic phenomena.     

Cyclic codes over <Emphasis Type="Italic">R</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript>

Cyclic codes over an infinite family of rings are defined. The general properties of cyclic codes over these rings are studied, in particular nontrivial one-generator cyclic codes are characterized. It is also proved that the binary images of cyclic codes over these rings under the natural Gray map are binary quasi-cyclic codes of index 2 ^k . Further, several optimal or near optimal binary codes are obtained from cyclic codes over R _k via this map.