Construction of Markov processes and associated multiplicative functionals from given harmonic measures

Let E be a noncompact locally compact second countable Hausdorff space. We consider the question when, given a family of finite nonzero measures on E that behave like harmonic measures associated with all relatively compact open sets in E (i.e. that satisfy a certain consistency condition), one can construct a Markov process on E and a multiplicative functional with values in [0, ∞) such that the hitting distributions of the process “inflated” by the multiplicative functional yield the given harmonic measures. We achieve this construction under weak continuity and local transience conditions on these measures that are natural in the theory of Markov processes, and a mild growth restriction on them. In particular, if the space E equipped with the measures satisfies the conditions of a harmonic space, such a Markov process and associated multiplicative functional exist. The result extends in a new direction the work of many authors, in probability and in axiomatic potential theory, on constructing Markov processes from given hitting distributions (i.e. from harmonic measures that have total mass no more than 1).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47657/1/440_2005_Article_BF01192513.pd

Construction of markov processes from hitting distributions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47648/1/440_2004_Article_BF00538487.pd

From antiferromagnetism to d-wave superconductivity in the 2D t-J model

We have found that the two dimensional t-J model, for the physical parameter range J/t = 0.4 reproduces the main experimental qualitative features of High-Tc copper oxide superconductors: d-wave superconducting correlations are strongly enhanced upon small doping and clear evidence of off diagonal long range order is found at the optimal doping \delta ~ 0.15. On the other hand antiferromagnetic long range order, clearly present at zero hole doping, is suppressed at small hole density with clear absence of antiferromagnetism at \delta >~ 0.1.Comment: 4 pages, 5 figure

Antiferromagnetism and superconductivity of the two-dimensional extended t–J model

The mechanism of high-temperature superconductivity (HTS) and the correlation between the antiferromagnetic long-range order (AFLRO) and superconductivity (SC) phases are the central issues of the study of HTS theory. SC and AFLRO of the hole-doped two-dimensional extended t- J model are studied by the variational Monte Carlo method. The results show that SC is greatly enhanced by the long-range hopping terms t' and t" for the optimal and overdoped cases. The phase of coexisting SC and AFM in the t-J model disappears when t and t" are included. It is concluded that the extended t-J model provides a more accurate description for HTS than the traditional t-J model does. The momentum distribution function n(k) and the shape of Fermi surface play critical roles for establishing the phase diagram of HTS materials

The breakdown of the Nagaoka phase in the 2D t-J model

In the limit of weak exchange, J, at low hole concentration, the ground state of the 2D t-J model is believed to be ferromagnetic. We study the leading instability of this Nagaoka state, which emerges with increasing J. Both exact diagonalization of small clusters, and a semiclassical analytical calculation of larger systems show that above a certain critical value of the exchange, Nagaoka's state is unstable to phase separation. In a finite-size system a bubble of antiferromagnetic Mott insulator appears in the ground state above this threshold. The size of this bubble depends on the hole concentration and scales as a power of the system size, N

Spatially homogeneous ground state of the two-dimensional Hubbard model

We investigate the stability with respect to phase separation or charge density-wave formation of the two-dimensional Hubbard model for various values of the local Coulomb repulsion and electron densities using Green-function Monte Carlo techniques. The well known sign problem is particularly serious in the relevant region of small hole doping. We show that the difference in accuracy for different doping makes it very difficult to probe the phase separation instability using only energy calculations, even in the weak-coupling limit ($U=4t$) where reliable results are available. By contrast, the knowledge of the charge correlation functions allows us to provide clear evidence of a spatially homogeneous ground state up to $U=10t$.Comment: 7 pages and 5 figures. Phys. Rev. B, to appear 200

Phase separation and stripe formation in the 2D t-J model: a comparison of numerical results

We make a critical analysis of numerical results for and against phase separation and stripe formation in the t-J model. We argue that the frustrated phase separation mechanism for stripe formation requires phase separation at too high a doping for it to be consistent with existing numerical studies of the t-J model. We compare variational energies for various methods, and conclude that the most accurate calculations for large systems appear to be from the density matrix renormalization group. These calculations imply that the ground state of the doped t-J model is striped, not phase separated.Comment: This version includes a revised, more careful comparison of numerical results between DMRG and Green's function Monte Carlo. In particular, for the original posted version we were accidentally sent obsolete data by Hellberg and Manousakis; their new results, which are what were used in their Physical Review Letter, are more accurate because a better trial wavefunction was use

The Narrative Frame of Daniel: A Literary Assessment

This paper presents a fuzzy multicriteria group decision making approach for evaluating and selecting information systems projects. The inherent subjectiveness and imprecision of the evaluation process is modeled by using linguistic terms characterized by triangular fuzzy numbers. A new algorithm based on the concept of the degree of dominance is developed to avoid the complex and unreliable process of comparing fuzzy numbers usually required in fuzzy multicriteria decision making. A multicriteria decision support system is proposed to facilitate the evaluation and selection process. An information systems project selection problem is presented to demonstrate the effectiveness of the approach

A Study of the Compilation, Influence, and Documentary Value of the Questions and Answers between Zhu Xi and Cheng Xun

《朱程問答》是朱熹與程洵往來的書信集，其中保存朱熹寫給程洵的信件，以及程洵的回信。為了要瞭解這部著作的價值何在，本文分為三部分討論。首先探討的是此書的編纂背景。此書在明代由程氏家族的養子程資編輯，並且出資刊刻，其中最特殊的資料是家族中保存的先世遺墨，這批資料之所以受到重視，與程氏家族在明代刻意標榜以朱子學為家學有關。其次，此書為明代程曈纂寫《新安學繫錄》中的程洵傳記，提供第一手的資料，並且，清代夏炘也利用此書中所保存的信件，提出朱學三變之說。兩人都是為著建構徽州地區的朱子學傳承歷史而作。然而他們對於資料的使用，仍有值得商榷之處。第三，由於此書中，收錄朱熹的佚文以及程洵的書信，因此能夠提供更完整的線索，考訂兩人論學書信的編年問題，說明朱熹與林用中及葉仁的交往過程，以及朱熹早年對於《正蒙》和〈西銘〉的觀點，進而對照出朱熹和程洵在思想上的差異。The Questions and Answers between Zhu Xi and Cheng Xun records the personal correspondence between Zhu Xi and Cheng Xun, including the letters Zhu Xi wrote to Cheng Xun and Cheng Xun’s replies. In trying to fully understand the value of this collection, this article is divided into three sections. First investigated is the background to the compilation of this collection. It was compiled and funded during the Ming dynasty by Cheng Zi, an adopted child of the Cheng family. One of the most interesting types of documents in this collection is the ancestors’ manuscripts preserved within the family. These documents were highly valued because the Cheng family in the Ming dynasty put a lot of emphasis on Zhu Xi’s studies as their family teachings. Second, the collection provided first-hand information for Cheng Tong’s compilation of Cheng Xun’s biography in The Intellectual Lineage of Xin’an in the Ming dynasty. Also, Qing scholar Xia Xin used the correspondence preserved in the collection to support his observation of three changes in Zhu Xi’s theories. Both scholars made an effort to construct the heritage of Zhu Xi’s studies in the Huizhou area, but how they used the documents has problems. Third, since the collection includes Zhu Xi’s lost works and Cheng Xun’s letters, it provides historical evidence for reconstructing the chronology of these scholarly communications. It validates Zhu Xi’s association with Lin Yong-Zhong and Ye Ren, verifies Zhu Xi’s earlier views on Zhang Zai’s Rectifying the Ignorant and The Western Inscription, and reflects the ideological differences between Zhu Xi and Cheng Xun