We suggest a simple grand unified theory where the fifth dimensional coordinate is compactified on an S1/(Z2 × Z ′ 2) orbifold. This model is based on the supersymmetric flipped SU(5) × U(1) grand unified theory, which can realize not only the triplet-doublet splitting but also the natural fermion mass hierarchies. The triplet-doublet splitting is realized by S1/(Z2 × Z ′ 2) orbifolding, which ...

With the growing interest in service-oriented architectures, achieving seamless interoperability between heterogeneous middleware technologies has become increasingly important. While much work investigating functional interoperability between different middleware architectures has been reported, little practical work has been done on providing a unified and/or interoperable view of security be...

We suggest a simple grand unified theory where the fifth dimensional coordinate is compactified on an S1/(Z2 × Z ′ 2) orbifold. This model is based on the supersymmetric flipped SU(5) × U(1) grand unified theory, which can realize not only the triplet-doublet splitting but also the natural fermion mass hierarchies. The triplet-doublet splitting is realized by S1/(Z2 × Z ′ 2) orbifolding, which ...

Image translation, size scaling and rotation can be analyzed from a unified standpoint. Let for and denote a discrete destination image that is created by geometrical modification of a discrete source image for and . In this derivation, the source and destination images may be different in size. Geometrical image transformations are usually based on a Cartesian coordinate system representation ...

This paper presents theories and algorithms for 3-D root canal model construction from 2-D X-ray images in a clinically practical way: (1) the geometrical rectification algorithm for correcting distorted 2-D X-ray images, (2) the transformation algorithms from 2-D X-ray image coordinate system to unified 3-D reference coordinate system, (3) the merging algorithms and theory for obtaining spatia...

In this paper a novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace methods and is derived from both ordinary coordinate representations and camera matrices and from a so...

A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in cyclotomic rings and cyclotomic fields in that most arithmetic operations are done on vectors. From this formulation we can generate optimized algorithms for m...

Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading to static correlation error. These two conditions are now unified and extended to states with both fractional charge and fractional spin to give a much more ...

It has been known since the early 1970s that the Hessian matrices in quasi– Newton methods can be updated by variational means, in several different ways. The usual formulation of these variational problems uses a coordinate system, and the symmetry of the Hessian matrices are enforced as explicit constraints. As a result, the variational problems seem complicated. In this paper, we give a very...

Determining the conformational rearrangements of large macromolecules is challenging experimentally and computationally. Case in point is the ribosome; it has been observed by high-resolution crystallography in several states, but many others are known only from low-resolution methods including cryo-electron microscopy. Combining these data into dynamical trajectories that may aid understanding...