Finite Generation of Canonical Ring by Analytic Method

In the 80th birthday conference for Professor LU Qikeng in June 2006 I gave a talk on the analytic approach to the finite generation of the canonical ring for a compact complex algebraic manifold of general type. This article is my contribution to the proceedings of that conference from my talk. In this article I give an overview of the analytic proof and focus on explaining how the analytic method handles the problem of infinite number of interminable blow-ups in the intuitive approach to prove the finite generation of the canonical ring. The proceedings of the LU Qikeng conference will appear as Issue No. 4 of Volume 51 of Science in China Series A: Mathematics (www.springer.com/math/applications/journal/11425)

Effective algebraic degeneracy

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}

On Alexander Wylie’s Jottings on the Science of the Chinese Arithmetic

Oral Presentation(Theme 2): R102Starting from August of 1852 the British Protestant missionary and sinologist, Alexander Wylie (1815–1887), published in nine instalments an account Jottings on the Science of the Chinese Arithmetic in the newspaper North China Herald. He explained clearly the purpose of his account at the beginning: ‘The object of the following desultory notes, made from time to time, in the course of some researches entered upon, with another purpose in view, is to draw attention to the state of the arithmetical science in China, a subject which has not been so fully explored as it might with advantage, and on which some erroneous statements have been current in modern publications.’ Alexander Wylie is a well-known figure in the last quarter of the Qing Dynasty for his contribution in transmitting Western science into China during the latter half of the 19th century. In mathematics he was known for translating three treatises in collaboration with the Qing mathematician Li Shanlan (1811–1882) — Supplementary Elements of Geometry in 1856 but published in 1865 (believed to be based on the English translation of Book VII to XV of Elements by Henry Billingsley in 1570), Treatise of Algebra in 1859 (based on Elements of Algebra by Agustus De Morgan in 1835) and Analytical Geometry and Differential and Integral Calculus Step by Step in 1859 (based on Elements of Analytical Geometry and of the Differential and Integral Calculus of Elias Loomis in 1850). He was also the author of Compendium of Arithmetic published in 1853. This presentation will discuss the knowledge of Chinese science and mathematics which most European sinologists of the 18th and 19th centuries possessed and the low regard they held it in, but the viewpoint of which was critically examined by Wylie in his account.published_or_final_versio

Banach Analytic Sets and a Non-Linear Version of the Levi Extension Theorem

We prove a certain non-linear version of the Levi extension theorem for meromorphic functions. This means that the meromorphic function in question is supposed to be extendable along a sequence of complex curves, which are arbitrary, not necessarily straight lines. Moreover, these curves are not supposed to belong to any finite dimensional analytic family. The conclusion of our theorem is that nevertheless the function in question meromorphically extends along an (infinite dimensional) analytic family of complex curves and its domain of existence is a pinched domain filled in by this analytic family.Comment: 19 pages, This is the final version with significant corrections and improvements. To appear in Arkiv f\"or matemati

Bilateral Anterior Shoulder Dislocation

Introduction: Unilateral anterior shoulder dislocation is one of the most common problems encountered in orthopedic practice. However, simultaneous bilateral anterior dislocation of the shoulders is quite rare. Case Presentation: We report a case of a 75-year-old woman presented with simultaneous bilateral anterior shoulder dislocation following a trauma, complicated with a traction injury to the posterior cord of the brachial plexus. Conclusions: Bilateral anterior shoulder dislocation is very rare. The excessive traction force during closed reduction may lead to nerve palsy. Clear documentation of neurovascular status and adequate imaging before and after a reduction should be performed

Cyclin F Is Degraded during G2-M by Mechanisms Fundamentally Different from Other Cyclins

Cyclin F, a cyclin that can form SCF complexes and bind to cyclin B, oscillates in the cell cycle with a pattern similar to cyclin A and cyclin B. Ectopic expression of cyclin F arrests the cell cycle in G2/M. How the level of cyclin F is regulated during the cell cycle is completely obscure. Here we show that, similar to cyclin A, cyclin F is degraded when the spindle assembly checkpoint is activated and accumulates when the DNA damage checkpoint is activated. Cyclin F is a very unstable protein throughout much of the cell cycle. Unlike other cyclins, degradation of cyclin F is independent of ubiquitination and proteasome-mediated pathways. Interestingly, proteolysis of cyclin F is likely to involve metalloproteases. Rapid destruction of cyclin F does not require the N-terminal F-box motif but requires the COOH-terminal PEST sequences. The PEST region alone is sufficient to interfere with the degradation of cyclin F and confer instability when fused to cyclin A. These data show that although cyclin F is degraded at similar time as the mitotic cyclins, the underlying mechanisms are entirely distinct

Application of the Spiritual Intelligence Self-Report Inventory (SISRI-24) Among Hong Kong University Students

The aim of this study was to examine the psychometric properties of the Chinese version of the Spiritual Intelligence Self-Report Inventory (SISRI-24). Two hundred thirteen undergraduate students in Hong Kong completed the Chinese SISRI-24, the Meaning of Life Questionnaire, the Metapersonal Self-Construal Scale, and the Satisfaction with Life Scale to allow examination of internal reliability and construct validity. Confirmatory factor analysis was also performed to examine whether the model of King and DeCicco (2009) fit our data. Our results indicated that the full scale of the Chinese SISRI-24 and its four subscales had acceptable internal reliability. The results also showed a positive relationship between spiritual intelligence and metapersonal self-construal. However, no significant relationship was reported between spiritual intelligence and life satisfaction. As such, construct validity was low to moderate. This study can be considered a foundation for understanding and measuring spiritual intelligence among undergraduate students in Hong Kong. Future research directions are suggested

Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum computation. In this paper we completely characterize the class of boolean functions computable by unitary two-qubit matchgate circuits with some probability of success. We show that this class precisely coincides with that of the linear threshold gates. The latter is a fundamental family which appears in several fields, such as the study of neural networks. Using the above characterization, we further show that the power of matchgate circuits is surprisingly trivial in those cases where the computation is to succeed with high probability. In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions depending on only a single bit of the input