It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner’s little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted also that, while the rotational degree of freedom for a massless particle leads to i...

Einstein's E = mc 2 unifies the momentum-energy relations for massive and massless particles. According to Wigner, the internal space-time symmetries of massive and massless particles are isomorphic to O(3) and E(2) respectively. According to Inonu and Wigner, O(3) can be contracted to E(2) in the large-radius limit. It is noted that the O(3)-like little group for massive particles can be contr...

B = signed Boolean matrix C = damping matrix f = vector of external forces G = matrix of associated modes g = vector of connecting forces K = stiffness matrix L = Boolean localization matrix M = mass matrix q = vector of unique degrees of freedom R = reduction matrix r = vector of residual forces t = time u = vector of degrees of freedom Y = receptance matrix Z = dynamic stiffness matrix = vect...

A method is derived to detect and localize linear damage in a structure using the measured modal vibration parameters. This method is applicable when the vibration strain energy is stored in the axial or torsional modes, which differentiates it from previously derived strain-energy-based methods. The new method is compared to the previously derived flexibility-change method for comparison. Both...

We extend the algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei by combining the eikonal approximation for the scattering with a description of odd-mass nuclei in terms of the interacting boson-fermion model. We derive closed expressions for the transition matrix elements for one of the dynamical symmetries and discuss the interplay between collective and single...

We discuss the localized tachyon condensation in the non-supersymmetric orbifold theories by taking the cosmological constant as the measure of degrees of freedom. We show that both localized and delocalized degrees of freedom encode information on the process of localized tachyon condensation: the former encodes in the c-function given by the lightest tachyon mass, and the latter in the g-func...

The graviton is pictured as a bound state of a fermion and antifermion with the spacetime metric assumed to be a composite object of spinor fields, based on a globally Lorentz invariant action proposed by Hebecker and Wetterich. The additional degrees of freedom beyond those of the graviton are described by Goldstone boson gravitational degrees of freedom. If we assume that the fermion is a lig...

freedom is one of the greatest and highest human values and of necessities of life and evolution that all nations have wanted its realization. the word freedom dates back to human history and it has found criterion and rate through indicators such as truth-seeking, justice and human's existential growth and defines its own limits and is manifested in literature of different nations in vari...

A MATLAB-based software tool, called the Solar Sail Control Toolbox, has been developed for solar sail analysis, design and simulation. The toolbox includes functions for multibody dynamic modeling, attitude control systems design, thrust vector control design, orbit analysis, solar sail mission analysis, thermal analysis and power subsystem analysis. Sailcraft models can be created, analyzed a...