Explicit eigenvalues of certain scaled trigonometric matrices

In a very recent paper "\emph{On eigenvalues and equivalent transformation of trigonometric matrices}" (D. Zhang, Z. Lin, and Y. Liu, LAA 436, 71--78 (2012)), the authors motivated and discussed a trigonometric matrix that arises in the design of finite impulse response (FIR) digital filters. The eigenvalues of this matrix shed light on the FIR filter design, so obtaining them in closed form was investigated. Zhang \emph{et al.}\ proved that their matrix had rank-4 and they conjectured closed form expressions for its eigenvalues, leaving a rigorous proof as an open problem. This paper studies trigonometric matrices significantly more general than theirs, deduces their rank, and derives closed-forms for their eigenvalues. As a corollary, it yields a short proof of the conjectures in the aforementioned paper.Comment: 7 pages; fixed Lemma 2, tightened inequalitie

Toward Sovereignty: Zhang Zhidong’s Military Strengthening of China, 1884-1901

The conventional history of China’s late nineteenth-century Self-Strengthening movement charted a failure of military reforms. My research explores this period through the perspective of the prominent governor-general Zhang Zhidong. From 1884-1901, Zhang consistently pursued new military academies and western-style armies aiming to secure the nation against foreign imperialist incursion. At the same time, the governor’s understanding of regional differences as well as his increasing experience in military affairs distinctly shaped his effective new military institutions. At the turn of the century, Zhang Zhidong’s military apparatus was arguably one of the best in China. In the wider analysis of Chinese military history, the governor’s career contrasted with other historical figures by its peripatetic nature and its continuity through the Sino-Japanese War and Boxer Rebellion. Zhang’s many jurisdictions showed not only his consistent dedication to military power as a means to national sovereignty, but also created numerous military institutions for study. More importantly, the continuity in the governor’s effective military reforms underlined fundamental historical misunderstandings about the nature of late-Qing China. First, Zhang’s successful military institutions contended with China’s deterioration narrative from 1895 to the dynastic fall in 1911. Second, the reason for historical misinterpretation stemmed from the obscuring of both late-Qing historians’ and the historical actors’ perceptions by the influences of western imperialism. Ultimately, the study of Zhang Zhidong’s military reforms shows a discontinuity in the conventional historical narrative, and thus creates space for increased Chinese agency in their own history

On the Renormalization of the Kardar-Parisi-Zhang equation

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally subtracted perturbation expansion about d = 2. For the KPZ roughening transition in dimensions d > 2, this renormalization group yields the dynamic exponent z* = 2 and the roughness exponent chi* = 0, which are exact to all orders in epsilon = (2 - d)/2. The expansion becomes singular in d = 4, which is hence identified with the upper critical dimension of the KPZ equation. The implications of this perturbation theory for the strong-coupling phase are discussed. In particular, it is shown that the correlation functions and the coupling constant defined in minimal subtraction develop an essential singularity at the strong-coupling fixed point.Comment: 21 pp. (latex, now texable everywhere, no other changes), with 2 fig

Penas Ibáñez, Mª Azucena y Xiaohan Zhang (2012): Polisemia funcional de SER y ESTAR en español y en chino. Las locuciones verbales del diccionario DCLEA. Una contribución al estudio del español como lengua 2 (ELE) [Reseña]

[Resumen] Reseña de Penas Ibáñez, Mª Azucena y Xiaohan Zhang (2012): Polisemia funcional de SER y ESTAR en español y en chino. Las locuciones verbales del diccionario DCLEA. Una contribución al estudio del español como lengua 2 (ELE)

Zhang Yimou's 'Blood simple':cannibalism, remaking and translation in world cinema

Zhang Yimou’s A Woman, A Gun and A Noodle Shop (2009) remakes the Coen brothers’ Blood Simple (1984) in a way that re-imagines the earlier film in a Chinese setting, adapting and recreating the narrative, but the film cannot be regarded as being aimed solely at a Chinese audience, as it was also released in the United States and United Kingdom. Drawing from translation studies and film studies, this article analyses how Zhang’s film adapts its source material, particularly its tendency to make explicit elements that were left implicit in the source text. The idea of cannibalization, from Brazilian modernist theory, helps explain the ambiguous orientation of the remake as both homage to and localization of the source text. This hybridity was not well received by American audiences and shows how the movie’s connection to both Zhang and the Coens leads to a dual voice in the film. The analysis demonstrates how translation and cross-cultural adaptation enrich ideas of world cinema

Senior Development Fellowship Report (Zhang Xiulan)

In this report, an outline of the experiences and achievements of each Senior International Associate follows a general discussion of the programme. Professor Zhang was selected because of her wide experience as an analyst of Chinese social and health policy and her close collaboration with policymakers in that country. In addition, the School of Social Development and Public Policy, of which she is a Director, has already established a postgraduate course on development studies for students from a variety of low and middle income countries.DFI