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The standard model of particle physics is generalized with a horizontal symmetry so that all its results are successfully reproduced without inducing any unphysical modes of existence. Two stage breakdowns of symmetries result in mass matrices of Majorana and Dirac types for fundamental fermions and predict rich physical modes of boson fields, some of which might be observed by the LHC experiment.

Using the four best measured moduli of the flavor mixing matrix (|V_ud|, |V_us|, |V_cd|, |V_cs|), the Jarlskog invariant J(V), and the quark masses at M_Z energy scale as experimental constraints, a statistical comparison of three different types of quark mass matrices in the physical basis is performed. The mass matrices in question are the Chaturvedi–Gupta–Sánchez-Colón (CGS), the Fritzsch and the Gupta–Rajpoot types. With nine parameters the best fits are obtained using a Gupta–Rajpoot-type matrix while with seven parameters the best fits are obtained using the CGS-type matrix. The stability of our analysis with respect to evolution of the quark masses is also presented.

A comparative study is performed for the direct and iterative methods for updating the structural matrices based on measured data. The former was derived from the orthogonality constraints by replacing the modal vector of concern by the modal matrix in computing the correction matrices. ¹ The iterative method used is the improved inverse eigensenstivity method. ² Through the numerical studies, it was demonstrated that both methods yield good results. However, the direct updating method is found to be more suitable for engineering applications due to its ease in treating multi-modes and higher efficiency, especially for complicated structures.

Low-cost robotic welding and wide availability of high strength steel plates of grades over 500MPa make the use of tapered members an economical alternative to conventional prismatic members for modern steel structures, as experienced by the authors in some practical projects in Hong Kong and Macau. This paper proposes a new and efficient numerical method for modal and elastic time-history analysis of the frames with tapered sections. A series of non-prismatic elements is derived on the basis of analytical expressions, and the exact consistent mass and tangent stiffness matrices are formulated. Five common types of tapered sections for practical applications, namely the circular solid, circular hollow, rectangular solid, rectangular hollow and doubly symmetric-I sections, are studied. Contrary to the conventional method using the approximate assumptions for the section properties along the member length, this research analytically expresses the flexural rigidity and cross-sectional area for the stiffness and mass matrices of an element. Further, the techniques for obtaining the dynamic performances, such as natural vibrations and time-history responses, of non-prismatic members are investigated. Finally, three examples are conducted for validating and verifying the accuracy of the proposed formulations. The present work can be used in the dynamic response analysis of frame structures with tapered sections in seismic zones.

Simple engineering analysis based on stress and momentum correspondence principles and the Rayleigh quotient approximation is used to derive error convergence rates and estimates for dynamic beam models based on the Timoshenko beam theory. These predictions are verified by carrying out numerical computations.

We propose a MATLAB implementation of the $P^1$ finite element method for the numerical solutions of the Poisson problem and the linear elasticity problem in two-dimensional (2D) and three-dimensional (3D). The code consists of vectorized (and short) assembling functions for the matrices (mass and stiffness) and the right-hand sides. Since for the $P^1$ finite element, the element mass matrix and right-hand side are simple, the implementation uses only the MATLAB function sparse on the elements volume. For the stiffness matrix, to obtain a MATLAB implementation close to the standard form, cell-arrays are used to store the gradients of the element basis functions. The assembling procedure can then use matrix/vector products on small size cell-arrays. Numerical experiments show that our implementation is fast, scalable with respect to time, and outperforms existing vectorized MATLAB FEM codes.

The lepton-charge (L_e, L_μ, L_τ) nonconserving interaction leads to the mixing of the electron, muon and tau neutrinos, which manifests itself in spatial oscillations of a neutrino beam, and also to the mixing of the electron, negative muon and tau lepton, which, in particular, may be the cause of the "forbidden" radiative decay of the negative muon into the electron and γ quantum. Under the assumption that the nondiagonal elements of the mass matrices for neutrinos and ordinary leptons, connected with the lepton charge nonconservation, are the same, and by performing the joint analysis of the experimental data on neutrino oscillations and experimental restriction for the probability of the decay μ^- → e^- + γ per unit time, the following estimate for the lower bound of neutrino mass has been obtained: .

Gauge field theory of a horizontal symmetry of the group G_H = SU(2)_H × U(1) is developed so as to generalize the standard model of particle physics. All fermion and scalar fields are assumed to belong to doublets and singlets of the group in high energy regime. Mass matrices with four texture zeros of Dirac and Majorana types are systematically derived. In addition to seven scalar particles, the theory predicts existence of one peculiar vector particle which seems to play important roles in astrophysics and particle physics.