Equations of curvature

This fourth volume of the Mathematical Papers of Sir William Rowan Hamilton completes the project begun, in 1925, by the instigators and ®rst Editors: Arthur William Conway (1875±1950) and John Lighton Synge (1897±1995). It contains Hamilton's published papers on geometry, analysis, astronomy, probability and ®nite differences, and a miscellany of publications including several addresses.
847p camchuong_1 10122012 37 5 Download

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Qcurvature under generic assumptions. The problem amounts to solving a fourthorder nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minmax schemes, jointly with the compactness result of [35]. 1.
48p dontetvui 17012013 38 6 Download

This paper considers a trapped characteristic initial value problem for the spherically symmetric EinsteinMaxwellscalar ﬁeld equations. For an open set of initial data whose closure contains in particular ReissnerNordstr¨m data, o the future boundary of the maximal domain of development is found to be a lightlike surface along which the curvature blows up, and yet the metric can be continuously extended beyond it. This result is related to the strong cosmic censorship conjecture of Roger Penrose. ...
55p tuanloccuoi 04012013 33 5 Download

For the complex parabolic GinzburgLandau equation, we prove that, asymptotically, vorticity evolves according to motion by mean curvature in Brakke’s weak formulation. The only assumption is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen. Introduction In this paper we study the asymptotic analysis, as the parameter ε goes to zero, of the complexvalued parabolic GinzburgLandau equation for functions uε :
128p noel_noel 17012013 30 5 Download

In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the MongeAmp`re equation when the inhomogee neous term is only assumed to be H¨lder continuous. As a consequence of our o approach, we also establish the existence and uniqueness of globally smooth solutions to the second boundary value problem for the aﬃne maximal surface equation and aﬃne mean curvature equation.
38p dontetvui 17012013 31 5 Download

The former leads to a ”microscopic” cosmological model with Hubble expansion. Due to interaction of a Higgslike cosmological potential, the original timespace symmetry is spontaneously broken, inducing a strong timelike curvature and a weak spacelike deviation curve. In the result, the wavelike solution leads to KleinGordonFock equation which would serve an explicit approach to the problem of consistency between quantum mechanics and general relativity.
12p thuyliebe 08102018 3 0 Download

R Huang worked the pelastic in a Riemannian manifold with constant sectional curvature. In this work, we solve the EulerLagrange equation by quadrature and study the Frenet equation of the pelastica by using the Killing field in the three dimensional Lorentzian space forms.
9p danhdanh27 07012019 1 0 Download

Seismic Design of Reinforced Concrete Bridges 38.1 Introduction TwoLevel PerformanceBased Design • Elastic vs. Ductile Design • Capacity Design Approach 38 38.2 Typical Column Performance Characteristics of Column Performance • Experimentally Observed Performance 38.3 Flexural Design of Columns Earthquake Load • Fundamental Design Equation • Design Flexural Strength • Moment–Curvature Analysis • Transverse Reinforcement Design 38.4 Shear Design of Columns Fundamental Design Equation • Current Code Shear Strength Equation • Reﬁned Shear Strength Equations 38.
24p naunho 27122010 64 15 Download

Average depth model has a variety of applications in hydraulic engineering, especially in applications that flow depth is much smaller than the width of the flow. In this method the vertical variation is negligible and the hydraulic variables average integrated from channel bed to the surface free for the vertical axis. in equations arising management, pure hydrostatic pressure is assumed that not really valid in the case of flow in the bed is curved and can not be described curvature effects of the bed.
127p gauhaman123 17112011 75 13 Download

This book is based on lectures delivered over the years by the author at the Universit´e Pierre et Marie Curie, Paris, at the University of Stuttgart, and at City University of Hong Kong. Its twofold aim is to give thorough introductions to the basic theorems of differential geometry and to elasticity theory in curvilinear coordinates. The treatment is essentially selfcontained and proofs are complete.
215p kimngan_1 06112012 40 1 Download

Based on an extended spacetime symmetry a new attempt to search for links between general relativity and quantum mechanics is proposed. A simplified cylindrical model of gravitational geometrical dynamics leads to a microscopic geodesic description of strongly curved extradimensional spacetime which implies a duality between an emission law of microscopic gravitational waves and the quantum mechanical equations of free elementary particles. Consequently, the Heisenberg indeterminism would originate from the timespace curvatures.
9p thuyliebe 09102018 10 0 Download

Next, a few words about our strategy. It is well recognized now that one has to go beyond the EinsteinHilbert action for gravity, both from the experimental viewpoint (eg.,because of Dark Energy) and from the theoretical viewpoint (eg., because of the UV incompleteness of quantized Einstein gravity, and the need of its uniﬁcation with the Standard Model of Elementary Particles). In our approach, the origin of inﬂation is purely geometrical, ie. is closely related to spacetime and gravity.
0p lulaula 25102012 33 8 Download

These lectures intend to give a selfcontained exposure of some techniques for computing the evolution of plane curves. The motions of interest are the socalled motions by curvature. They mean that, at any instant, each point of the curve moves with a normal velocity equal to a function of the curvature at this point. This kind of evolution is of some interest in differential geometry, for instance in the problem of minimal surfaces.
187p camchuong_1 04122012 39 7 Download

This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian me chanics and with a view to controltheoretical applications. The basic methodology is that of geometric mechanics applied to the Lagranged’Alembert formulation, generalizing the use of connections and momentum maps associated with a given symmetry group to this case.
79p loixinloi 08052013 21 1 Download