41,768 research outputs found

    Mutual Fund Theorem for continuous time markets with random coefficients

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    We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving Brownian motion, and they are supposed to be currently observable. It is shown that some weakened version of Mutual Fund Theorem holds for this market for general class of utilities; more precisely, it is shown that the supremum of expected utilities can be achieved on a sequence of strategies with a certain distribution of risky assets that does not depend on risk preferences described by different utilities.Comment: 17 page

    Flavor Mixing in the Gauge-Higgs Unification

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    Gauge-Higgs unification is the fascinating scenario solving the hierarchy problem without supersymmetry. In this scenario, the Standard Model (SM) Higgs doublet is identified with extra component of the gauge field in higher dimensions and its mass becomes finite and stable under quantum corrections due to the higher dimensional gauge symmetry. On the other hand, Yukawa coupling is provided by the gauge coupling, which seems to mean that the flavor mixing and CP violation do not arise at it stands. In this talk, we discuss that the flavor mixing is originated from simultaneously non-diagonalizable bulk and brane mass matrices. Then, this mechanism is applied to various flavor changing neutral current (FCNC) processes via Kaluza-Klein (KK) gauge boson exchange at tree level and constraints for compactification scale are obtained.Comment: 5 pages, prepared for the proceedings of the International Workshop on Grand Unified Theories (GUT2012) held at Yukawa Institute for Theoretical Physics, March 15-17 2012, Kyoto, Japa

    Modeling and control of flexible space stations (slew maneuvers)

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    Large orbiting space structures are expected to experience mechanical vibrations arising from several disturbing forces such as those induced by shuttle takeoff or docking and crew movements. The problem is considered of modeling and control of large space structures subject to these and other disturbing forces. The system consists of a (rigid) massive body, which may play the role of experimental modules located at the center of the space station and flexible configurations, consisting of several beams, forming the space structure. A complete dynamic model of the system was developed using Hamilton's principle. This model consists of radial equations describing the translational motion of the central body, rotational equations describing the attitude motions of the body and several beam equations governing the vibration of the flexible members (platform) including appropriate boundary conditions. In summary, the dynamics of the space structure is governed by a complex system of interconnected partial and ordinary differential equations. Using Lyapunov's approach the asymptotic stability of the space structure is investigated. For asymptotic stability of the rest state (nominal trajectory), feedback controls are suggested. In the investigation, stability of the slewing maneuvers is also considered. Several numerical results are presented for illustration of the impact of coupling and the effectiveness of the stabilizing controls. Some insight is provided into the complexity of modeling, analysis and stabilization of actual space structures

    Convex relaxation of mixture regression with efficient algorithms

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    We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data

    Practical application of CFD for wind loading on tall buildings

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    This paper is concerned with assessing the scope of appicabiity for computational fluid dynamics(CFD) in the field of structural engineering, with a particular reference to tall buildings. Modern design trends and advances in engineering materials have encouraged the demand for taller and more slender structures. This pattern induces inherent structural flexibility; these cases exceed the limitations of the quasi-static method offered by current codes of practice. Wind tunnel testing is the traditional solution for such dynamically sensitive structures. However, even this scaled modelling approach is clouded by some uncertainties, including scaling the Reynolds number and assuming damping values for the aeroelastic model. While CFD cannot be used as a replacement for wind tunnel testing, there are results within the literature to suggest it has the potential to act as a complimentary tool - provided it is used within its capabilities. The paper outlines the various turbulence models that are available and summarises the extent of their application in a practical structural engineering sense. It also details the user-defined criteria that must be satisfied and discusses the potential for simplified models in tall building CFD analyses, with a view to promoting more efficient and practical solutions
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