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1.
Robert L. Jerrard Halil Mete Soner 《Calculus of Variations and Partial Differential Equations》2002,14(2):151-191
We study the Ginzburg-Landau functional
for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation
of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional.
Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001 相似文献
2.
Piermarco Cannarsa Fausto Gozzi Halil Mete Soner 《Applied Mathematics and Optimization》1991,24(1):197-220
We study a Hamilton-Jacobi equation in infinite dimensions arising in optimal control theory for problems involving both exit times and state-space constraints. The corresponding boundary conditions for the Hamilton-Jacobi equation, of mixed nature, have been derived and investigated in [19], [2], [5], and [15] in the finite-dimensional case. We obtain a uniqueness result for viscosity solutions of such a problem and then prove the existence of a solution by showing that the value function is continuous.The work of P. Cannarsa was partially supported by the Italian National Project Equazioni Differenziali e Calcolo delle Variazioni. H. M. Soner's work was supported by National Science Foundation Grant DMS-90-02249. 相似文献
3.
Seongsin M.Kim William Baughman David S.Wilbert Lee Butler Michael Bolus Soner Balci Patrick Kung 《中国光学快报(英文版)》2011,(11):46-49
We demonstrate two distinct emerging terahertz (THz) biomedical imaging techniques.One is based on the use of a new single frequency THz quantum cascade laser and the other is based on broadband THz time domain spectrocopy.The first method is employed to derive a metastasis lung tissue imaging at 3.7 THz with clear contrast between cancerous and healthy areas.The second approach is used to study an osseous tissue under several imaging modalities and achieve full THz spectroscopic imaging based on the freque... 相似文献
4.
This article is concerned with Markov chains on m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic. 相似文献
5.
6.
This paper considers a deterministic flow inn-dimensional space, perturbed by a Markov jump process with small variance. Asymptotic expansions are obtained for certain functionals of Feynman—Kac type, in powers of a small parameter representing a noise intensity. The methods are analytical rather than probabilistic.The research of the first author was partly supported by AFOSR under Contract No. 91-0116-0, by ONR under Contract No. N0014-83-K-0542, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR. The second author's research was partly supported by NSF under Contract No. DMS-8702537, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR. 相似文献
7.
We consider the problem of hedging a European contingent claim in a Bachelier model with temporary price impact as proposed by Almgren and Chriss (J Risk 3:5–39, 2001). Following the approach of Rogers and Singh (Math Financ 20:597–615, 2010) and Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), the hedging problem can be regarded as a cost optimal tracking problem of the frictionless hedging strategy. We solve this problem explicitly for general predictable target hedging strategies. It turns out that, rather than towards the current target position, the optimal policy trades towards a weighted average of expected future target positions. This generalizes an observation of Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b) from their homogenous Markovian optimal investment problem to a general hedging problem. Our findings complement a number of previous studies in the literature on optimal strategies in illiquid markets as, e.g., Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b), Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), Rogers and Singh (Math Financ 20:597–615, 2010), Almgren and Li (Option hedging with smooth market impact. Preprint, 2015), Moreau et al. (Math Financ. doi: 10.1111/mafi.12098, 2015), Kallsen and Muhle-Karbe (High-resilience limits of block-shaped order books. Preprint, 2014), Guasoni and Weber (Mathematical Financ. doi: 10.1111/mafi.12099, 2015a; Nonlinear price impact and portfolio choice. Preprint, 2015b), where the frictionless hedging strategy is confined to diffusions. The consideration of general predictable reference strategies is made possible by the use of a convex analysis approach instead of the more common dynamic programming methods. 相似文献
8.
Robert Leon Jerrard Halil Mete Soner 《Archive for Rational Mechanics and Analysis》1998,142(2):99-125
(Accepted August 19, 1996) 相似文献
9.
We study a Merton type optimization problem under a reallocation constraint. Under this restriction, the stock holdings can
not be liquidated faster than a certain rate. This is a common restriction in certain type of investment firms. Our main objective
is to study the large time optimal growth rate of the expected value of the utility from wealth. We also consider a discounted
infinite horizon problem as a step towards understanding the first problem. A numerical study is done by solving the dynamic
programming equations. Under the assumption of a power utility function, an appropriate dimension reduction argument is used
to reduce the original problem to a two dimensional one in a bounded domain with convenient boundary conditions. Computation
of the optimal growth rate introduces additional numerical difficulties as the straightforward approach is unstable. In this
direction, new analytical results characterizing the growth rate as the limit of a sequence of finite horizon problems with
continuously derived utility are proved. 相似文献
10.
Ce1?xErxO2 and Ce1?2xErxGdxO2 co-doped ceria electrolyte nanopowder materials were successfully prepared by sol–gel method. Depending on the temperature, the crystal structure changes were analyzed by X-ray diffraction. It was observed that the crystal size of the electrolytes decreased depending on the temperature and the time. X-ray diffraction results confirmed cubic fluorite structure in the samples. The microstructural properties of the samples were analyzed by scanning electron microscopy, and thermal stability measurement was performed by thermogravimetric and differential thermal analyses. The total electrical conductivity of the nanopowder electrolytes was determined by the dc four-point probe technique in air at temperatures ranging from room temperature to 1373 K. The four-probe conductivity results revealed that Ce0.8Er0.1Gd0.1O2 has a higher ionic conductivity compared to Ce0.83Er0.17O2 at 1123 K. The four-probe conductivity results show that both Ce1?xErxO2 and Ce1?2xErxGdxO2 solid electrolytes have potential application to oxide ionic conductor for solid oxide fuel cells. 相似文献