Existence of competitive equilibrium in economies with multi-member households

This paper focuses on the existence of a competitive equilibrium in the general equilibrium model with multi-member households introduced by Haller (2000). Two main results are obtained: the first is based on the assumption of ``budget exhaustion,'' which is also used in the existence theorem by Gersbach and Haller (1999). The second is based on the assumption that every household has at least one member whose preference is nonsatiated with respect to feasible household consumption, and this is applicable to the case in which budget exhaustion does not hold.Multi-member households, Competitive equilibrium, nonsatiation

Some sufficient conditions for the existence of a competitive equilibrium in economies with satiated consumers

It is well known that a competitive equilibrium may fail to exist when consumers' preferences are possibly satiated. In this paper, we provide three new sufficient conditions for the existence of a competitive equilibrium in the standard Arrow-Debreu pure exchange economy with satiated consumers. We first consider a condition that restricts the behavior of the excess demand correspondence on the boundary of a certain subset of the price domain. Another two sufficient conditions are obtained by using the existence result under this condition.satiation

Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: Minimization

We construct embedded Willmore tori with small area constraint in Riemannian three-manifolds under some curvature condition used to prevent M\"obius degeneration. The construction relies on a Lyapunov-Schmidt reduction; to this aim we establish new geometric expansions of exponentiated small symmetric Clifford tori and analyze the sharp asymptotic behavior of degenerating tori under the action of the M\"obius group. In this first work we prove two existence results by minimizing or maximizing a suitable reduced functional, in particular we obtain embedded area-constrained Willmore tori (or, equivalently, toroidal critical points of the Hawking mass under area-constraint) in compact 3-manifolds with constant scalar curvature and in the double Schwarzschild space. In a forthcoming paper new existence theorems will be achieved via Morse theory.Comment: 41 pages. Final version to appear in the Proceedings of the London Math. Societ

The real photon structure functions in massive parton model in NLO

We investigate the one-gluon-exchange ($\alpha \alpha_s$) corrections to the real photon structure functions $W_{TT}$, $W_{LT}$, $W_{TT}^{a}$ and $W_{TT}^\tau$ in the massive parton model. We employ a technique based on the Cutkosky rules and the reduction of Feynman integrals to master integrals. We show that a positivity constraint, which is derived from the Cauchy-Schwarz inequality, is satisfied among the unpolarized and polarized structure functions $W_{TT}$, $W_{TT}^a$ and $W_{TT}^\tau$ calculated up to the next-to-leading order in QCD.Comment: arXiv admin note: text overlap with arXiv:1110.262

Higgs Production in Two-Photon Process and Transition Form Factor

The Higgs production in the two-photon fusion process is investigated where one of the photons is off-shell while the other one is on-shell. This process is realized in either electron-positron collision or electron-photon collision where the scattered electron or positron is detected (single tagging) and described by the transition form factor. We calculate the contributions to the transition form factor of the Higgs boson coming from top-quark loops and W-boson loops. We then study the $Q^2$ dependence of each contribution to the total transition form factor and also of the differential cross section for the Higgs production.Comment: 4pages, 6figur