In this study, a sexaxial figure of the Earth was created using randomly distributed 6400 control points on geoid, which generated by EGM2008 gravity model. The shape ellipsoid is defined its six orthogonal axes. To construct new geometric figure, eight triaxial ellipsoids were fitted to Cartesian coordinates in each octant geoid least squares method. Its origin constrained coincide with centre...

The effective description of molecular geometry is important for theoretical studies of intermolecular interactions. Here we introduce a new translation-rotation-internal coordinate (TRIC) system which explicitly includes the collective translations and rotations of molecules, or parts of molecules such as monomers or ligands, as degrees of freedom. The translations are described as the centroi...

Solutions to tensor, vector, and scalar linear inhomogeneous partial differential equations can be obtained by discrete Fourier inversion of the linear system. The inverse (Green’s function) problem can be cast into sets of single, double, and triple summation/integration expressions by using transcendental eigenfunction expansions in certain three-dimensional triply-orthogonal geometries whose...

geospatial information system (gis) has emerged as a very powerful tool for capturing, storing, analyzing, managing, and presenting data that is linked to location. the location information, which is usually obtained from existing maps or the global positioning systems (gps), refers to different coordinate and map projection systems. therefore, unification of the coordinate and mapping systems ...

We propose a reaction path‐based Hamiltonian in terms of the reaction coordinate, the curvature coordinate, the remaining 3N−8 transverse normal coordinates (whose directions are orthogonal to the path tangent and curvature vectors), and their conjugate momenta, for an Natomic reaction system. The 3N−8 transverse vibrational modes are independent of the motion along the reaction path, although ...

Soybean lipoxygenase-1 (SLO-1) is a paradigmatic enzyme system for studying the contribution of hydrogen tunneling to enzymatic proton-coupled electron transfer processes. In this study, the impact of pairs of double mutants on the properties of SLO-1 is presented. Steady-state rates and their deuterium kinetic isotope effects (KIEs) have been measured for the bimolecular reaction of enzyme wit...

A 3D numerical model with orthogonal curvilinear coordinate in the horizontal direction and sigma coordinate in the vertical direction has been developed. This model is based on POM (the Princeton Ocean Model). In this model a second moment turbulence closure sub-model is embedded, and the stratification caused by salinity and temperature is considered. Furthermore, in order to adapt to estuary...

It is known that by employing space-time-frequency codes (STFCs) to frequency selective MIMO-OFDM systems, all the three diversity viz spatial, temporal and multipath can be exploited. There exists space-time-frequency block codes (STFBCs) designed using orthogonal designs with constellation precoder to get full diversity (Z.Liu, Y.Xin and G.Giannakis IEEE Trans. Signal Processing, Oct. 2002). ...