No description available.

No description available.

No description available.

Thesis (Ph. D.)--John Hopkins University, 1912. / "Reprinted from American journal of mahtematics, vol. XXXVI, no. 1." Biographical.

This thesis presents a computational study to examine lateral impact behavior of pressurized pipelines and to determine influence of internal pressure on the impact behaviors of pipelines. More than 300 numerical simulations were carried out on mild steel pipe models with different internal pressure levels and were struck at the mid-span and at the one quarter span positions. The computational results for the first time systematically revealed the effects of internal pressure, impact position, and outside diameter on the lateral impact behavior of the pipeline models. It inspects effects of important parameters such as the outside diameter and internal pressure. Quartic polynomial functions are applied to formulate the maximum crushing force (F), permanent displacement (W), and absorbed energy (E) of the pressurized pipelines during the impact problem. Response surfaces are plotted based on the generated quartic polynomial functions and the quality (accuracy) of those functions are verified through several techniques.

No description available.

Water and methanol are common solvents used in liquid chromatographic (LC) separations. It is highly desirable to model .the interactions of these solvents in order to better understand the nature of analyte solvation and its effect on retention. Therefore, structure and frequencies of complexes of these solvent molecules have been studied from a theoretical perspective as a first step in this direction. Specifically, cluster structures have been optimized at the RHF and MP2 levels in various flexible basis sets and with the counterpoise correction for basis set superposition error, and trends in the structure and binding energies of several clusters are described. Good agreement wasobtained for the water dimer with the experimental value for the binding energy of D20 using MP2 energies from 6-3 11G**/6-3 l+G** basis sets in conjunction with counterpoise optimizations and full counterpoise corrections. In this investigation harmonic frequencies have been calculated and corrected for the effects of anharmonicity by several methods, two of which are original. The first new method fits a Morse potential function to the energy computed along each normal mode. A second new method is based on fitting a quartic polynomial to energies computed along each normal mode. In cases where the quartic potential function is not very different from the harmonic well, a second order perturbation formula provides a reasonable approximation to the anharmonic vibrational frequencies. When the quartic potential is very far from the harmonic potential, a variational treatment of the vibrations is required. We find that the Morse method delivers reasonable estimates of frequencies of anharmonic motions at lower cost than multi-point potential mapping/multiple geometry optimization/Taylor series methods, and is more successful at predicting intermolecular frequencies than the anharmonic VSCF methods found in GAMESS software. Variational calculations using the quartic polynomials produce estimates of frequencies comparable to the more costly VSCF method. Both the Morse method and polynomial method are very fast computationally relative to these and other methods found in the literature.

Neste trabalho consideramos extensões do Modelo Padrão contendo vértices quárticos anômalos parametrizados por operadores efetivos de dimensão oito. Estes alteram o comportamento das amplitudes do tipo VV VV , onde V pode ser o fóton, o bóson Z, o bóson W ou o Higgs. Para essa extensão ser consistente, ela tem que obedecer o teorema ótico. Entretanto, as amplitudes geradas por estes operadores efetivos tendem a aumentar conforme a energia do centro de massa aumenta. Estudaremos o comportamento dessas amplitudes e determinaremos se há violação de unitariedade. Para isso utilizamos também o formalismo da base de helicidade. / In this work we consider Standard Model extensions containing anomalous quartic vertex parametrized by effective dimension-eight operators. These modify the behaviour of the scat- tering amplitudes VV VV , where V can be photon, Z boson, W boson and Higgs. To this extension be consistent, it has to obey the optical theorem. However, the amplitudes generated by these effective operators tends to grow as the center of mass energy increase. We will study the behaviour of these amplitudes and we will determine if there is unitarity violation. For this it was also used the helicity base formalism.

On compact Riemann surfaces, the Laplacian $\Delta$ has a discrete, non-negative spectrum of eigenvalues $\{\lambda_{i}\}$ of finite multiplicity. The spectrum is intrinsically linked to the geometry of the surface. In this work, we consider surfaces of constant negative curvature with a large symmetry group. It is not possible to explicitly calculate the eigenvalues for surfaces in this class, so we combine group theoretic and analytical methods to derive results about the spectrum. In particular, we focus on the Bolza surface and the Klein quartic. These have the highest order symmetry groups among compact Riemann surfaces of genera 2 and 3 respectively. The full automorphism group of the Bolza surface is isomorphic to $\mathrm{GL}_{2}(\mathbb{Z}_{3})\rtimes\mathbb{Z}_{2}. We analyze the irreducible representations of this group and prove that the multiplicity of $\lambda_{1}$ is 3, building on the work of Jenni, and identify the irreducible representation that corresponds to this eigenspace. This proof relies on a certain conjecture, for which we give substantial numerical evidence and a hopeful method for proving. We go on to show that $\lambda_{2}$ has multiplicity 4.

Neste trabalho consideramos extensões do Modelo Padrão contendo vértices quárticos anômalos parametrizados por operadores efetivos de dimensão oito. Estes alteram o comportamento das amplitudes do tipo VV VV , onde V pode ser o fóton, o bóson Z, o bóson W ou o Higgs. Para essa extensão ser consistente, ela tem que obedecer o teorema ótico. Entretanto, as amplitudes geradas por estes operadores efetivos tendem a aumentar conforme a energia do centro de massa aumenta. Estudaremos o comportamento dessas amplitudes e determinaremos se há violação de unitariedade. Para isso utilizamos também o formalismo da base de helicidade. / In this work we consider Standard Model extensions containing anomalous quartic vertex parametrized by effective dimension-eight operators. These modify the behaviour of the scat- tering amplitudes VV VV , where V can be photon, Z boson, W boson and Higgs. To this extension be consistent, it has to obey the optical theorem. However, the amplitudes generated by these effective operators tends to grow as the center of mass energy increase. We will study the behaviour of these amplitudes and we will determine if there is unitarity violation. For this it was also used the helicity base formalism.