In the following, we build on previous work done on higher derivative gravity, in particular Lovelock gravity. The latter is a family of theories in higher space-time dimensions in which interactions involving higher powers of curvature are introduced, but the equations of motion remain second order in derivatives. We develop a new theory involving cubic terms in the curvature. We then show that the equations of motion for graviton fluctuations remain second order. The curvature cubed term is shown not to be a topological object, contrary to the belief that dimensionally extended Euler densities provided the only stable dimensionally continued theories of gravity (Lovelock gravity). Black hole solutions are studied in this new gravitational framework.

I will present the mean curvature flow in Euclidean spaces and the Lagrangian mean curvature flow. We will first study the mean curvature evolution of submanifolds in Euclidean spaces, with an emphasis on the case of hypersurfaces. Along the way we will demonstrate the basic techniques in the study of geometric flows in general (for example, various maximum principles and the treatment of singularities). After that we will move on to the study of Lagrangian mean curvature flows. We will make the relevant definitions and prove the fundamental result that the Lagrangian condition is preserved along the mean curvature flow in Kähler-Einstein manifolds, which started the extensive, and still ongoing, research on Lagrangian mean curvature flows. We will also define special Lagrangian submanifolds as calibrated submanifolds in Calabi-Yau manifolds. Finally, we will study the mean curvature flow of conormal bundles as submanifolds of C^n. Using some tools developed recently, we will show that if a surface has strictly negative curvatures, then away from the zero section, the Lagrangian mean curvature flow starting from a conormal bundle does not develop Type I singularities.

A study of double-variable-curvature microlenses (DVCM) for promoting coupling efficiency between the high-power 980-nm pumping laser diodes and the single-mode fibers has been proposed. In comparison with the previous works on asymmetric fiber microlenses fabricated by the multi-step processes with complicated fabrication, the advantages of the DVCM structure for achieving high coupling are a single-step fabrication, a reproducible process, and a high-yield output. In the fusing procedure, the slight arc fusion was mainly applied for fine polishing merely instead of reshaping for the reason that the fabricated double-variable-curvature fiber endface (DVCFE) was very close to the ideal shape. Hence, the fabrication time was reduced and the yield was promoted due to the withdrawn step of tip elimination. In this study, the geometric center of the fiber was defined through, the cladding diameter and the core diameter, for comparison to measure the offset. The offset measured by the core diameter was more accurate and coincidence with the coupling efficiency in the experiment. In the fabricated 45 DVCMs, to achieve the average coupling efficiencies higher than 84%, the offsets were ought to be controlled in merely less than 0.6£gm with the curvature radii in the minor axis ranged from 2.4 to 2.9£gm (with tolerance of 0.5£gm). Alternatively, the offsets were ought to be controlled in less than 0.3£gm though the curvature radii in the minor axis ranged from 2.4 to 3.7£gm (with larger tolerance of 1.3£gm). However, it was more difficult to control over the offsets than the curvature radii in the minor axis while fabricating the DVCMs. In conclusion, to achieve higher yield, it was relatively practical to control the offsets of fiber microlenses to be less than 0.6£gm with 2.4 to 2.9£gm curvature radius. As a result, the coupling efficiencies were all higher than 80%.

Variation of the center of gravity of a golf club head will influence the initial velocity and rotation of speed of a ball after the golf ball is struck by golf club head. After fixing the weight of 200g of a golf head, the researcher changes the volume of golf head and the horizontal curvature of radius. He also distribute counterpoise to investigates the effect of launching of a golf ball. This thesis summarizes the ball of three-dimensional flight trajectory and offset distance. For the volume of the golf head is 400 cc, the best level of the radius of horizontal curvature is 11 in, in the 430 cc should use a radius of horizontal curvature of 12 in, and the 460 cc head club can chose a radius of horizontal curvature of 13 in. The distribution of counterpoise can effectively improve the play¡¦s habits, so the trajectory of a golf ball can be appropriately adjusted. By finite element method, the physical behavior of a series of the lunching ball can be predicted. The trajectory of golf ball can be measured by substituting the inertial value of ball into the three-dimension equations of motion. According to the trajectory of golf ball flight by this study, this study provides the characteristics for designing a golf club head.

In this thesis, a pursuit-evasion game, in which the pursuer moves with simple motion whereas the evader moves at a fixed speed but with a curvature constraint, is investigated. The game is the inverse of the usual homicidal chauffeur game. Square of the distance between the pursuer and the evader when the game is terminated is selected as the cost function. To solve such a zero-sum game, the variational approach will be employed to solve the problem. An algorithm will be proposed to determine a saddle point and the value of the game under consideration

To find a relationship between moment versus curvature in a traction-free ovine artery, a pure moment was applied to a radially cut ovine artery (length 50.23 mm). The curvature of the segment opposite the cut was calculated and used to calculate the pre-stresses using a Fung type model. The pre-stresses were then used to calculate the moment. The moment applied during the experiment was calculated by recording the twist applied and the stiffness of the wire applying the moment. The artery was sutured symmetrically with a custom jig, and then sutured to two blocks, one fixed and one subject to the pure moment. The axial strain was assumed unity. The Fung model yielded a linear moment versus curvature relationship, as well as the moment versus curvature relationship for the experiment. Despite both small and large stretches, the strains felt by the artery were not influential enough to display a non-linear correlation for moment vs curvature.

A strategy was proposed to make machining rate stable and the machining precision achieved by properly tool dwelling time when surface still has form error after previously machining. Using computer simulation to plan tool dwelling time and to estimate practicability of this strategy. As a result of curvatures are different on the every points of the work piece surface. Normal vectors that between tool and work pieces surface are not stable in polishing process.HDP conditions and film thickness will be changed by curvature radius of work pieces.So HDP conditions must be controlled when the planning of tool motion. Analyzing all of different aspheric surfaces to make sure this strategy can be used. The different thing that between axially symmetric and axially non-symmetric is tool dwelling time should be a linear function the product of the depth function of profile and the radius for symmetric work pieces, but that of axially non-symmetric work pieces only should be linearly proportional to the depth function of profile.

Thèse : Analyse : Faculté des sciences de Paris : 1856. Thèse : Astronomie : Faculté des sciences de Paris : 1856. / Titre provenant de l'écran-titre.

Thesis (doctoral)--Westfälischen Wilhelms-Universität zu Münster, 1911. / Cover title. Vita. Includes bibliographical references.

Classical field curvature theory emphasizes the Petzval theorem, which models field curvature aberration to the 4th order. However, modern lens designs use aspheric surfaces. These surfaces strongly induce higher order field curvature aberration which is not accounted for Petzval field curvature. This dissertation focuses on developing higher order field curvature theories that are applied to highly aspheric designs. Three new theories to control field curvature aberration are discussed. Theory 1: an aspheric surface that is close to the image and has two aspheric terms sharply reduces field curvature by 85%. Theory 2: an aspheric surface that is farther from the image plane induces astigmatism to balance Petzval field curvature. Theory 3: oblique spherical aberration can be induced to balance Petzval field curvature. All three theories are applied to real design examples including the following lenses: cellular phone, wide angle, fast photographic, and zoom lenses. All of the analyses results are consistent with the theories. Moreover, two types of novel aspheric surfaces are proposed to control field curvature. Neither of the surfaces are polynomial-type surfaces. Examples show that the novel aspheric surfaces are equivalent to even aspheric surfaces with two aspheric coefficients in terms of field curvature correction. The study on field curvature correction using aspheric surfaces provides an alternative method to use when aspheres are accessible. Overall, this dissertation advances the theory of field curvature aberration, and it is particularly valuable to evaluate highly aspheric designs when Petzval theory is inapplicable.