Hong Kong is an impact crater: Proof from the geomorphological and geological evidence

Hong Kong is a city in southern China. The urban districts of Hong Kong, Kowloon, and Victoria Harbour are situated within Hong Kong. Hong Kong is surrounded by mountains with a diameter of 11 km. Three million people live inside the basin. The round structure of the mountains in Hong Kong has been describd as a granite dome that is deeply eroded (batholith). The circularity of the mountains, the existence of a central hill, the inner slope of the mountains being greater than the outer slope, the presence of deep layer rock inside the basin, and the depth-to-diameter ratio were studied. All this evidence shows that the Hong Kong structure satisfies the geomorphological requirement of an impact crater. Some shock metamorphic phenomena of the rocks in Hong Kong such as planar features, microspherilitic silica glass (lechaterlierite), fused margins of rock fragments, concussion fractures, impact glass in which some schlierens are consistent with pyroxene spiculites, etc., were first discovered in Oct. 1990. In Hong Kong Island, an impact melt sheet was observed from the Victoria Peak to the southern shore. Quenching fractures of quartz in Kowloon fine-grained granite was also discovered. In our work, the K-Ar age (83.34 + 1.26 m.y.) of the impact melt rock, which is younger in comparison to the K-Ar age (117 m.y.) in Hong Kong and Kowloon granite, was measured, and the phenomena indicate that after the granite body formed, there was another geologic event. Maybe it is the Hong Kong cratering event

Immediately algebraically closed fields

We consider two overlapping classes of fields, IAC and VAC, which are defined using valuation theory but which do not involve a distinguished valuation. Rather, each class is defined by a condition that quantifies over all possible valuations on the field. In his thesis, Hong asked whether these two classes are equal (Hong, 2013, Question 5.6.8). In this paper, we give an example that negatively answers Hong's question. We also explore several situations in which the equivalence does hold with an additional assumption, including the case where every $K'\equiv K$ is IAC.Comment: 12 pages, based on results from a chapter of the author's thesis, under the supervision of Professor Deirdre Haskel

The Lueders Postulate and the Distinguishability of Observables

The Lueders postulate is reviewed and implications for the distinguishability of observables are discussed. As an example the distinguishability of two similar observables for spin-1/2 particles is described. Implementation issues are briefly analyzed.Comment: Submitted to the proceedings of ICFNCS, Hong Kong, 200

Polynomial Retracts and the Jacobian Conjecture

Let $K[x, y]$ be the polynomial algebra in two variables over a field $K$ of characteristic $0$. A subalgebra $R$ of $K[x, y]$ is called a retract if there is an idempotent homomorphism (a {\it retraction}, or {\it projection}) $\varphi: K[x, y] \to K[x, y]$ such that $\varphi(K[x, y]) = R$. The presence of other, equivalent, definitions of retracts provides several different methods of studying them, and brings together ideas from combinatorial algebra, homological algebra, and algebraic geometry. In this paper, we characterize all the retracts of $K[x, y]$ up to an automorphism, and give several applications of this characterization, in particular, to the well-known Jacobian conjecture. Notably, we prove that if a polynomial mapping $\varphi$ of $K[x,y]$ has invertible Jacobian matrix {\it and } fixes a non-constant polynomial, then $\varphi$ is an automorphism

Automorphisms fixing a variable of K<x,y,z>

We study automorphisms of the free associative algebra K over a field K which fix z and such that the images of x, y are linear with respect to x, y. We prove that some of these automorphisms are wild in the class of all automorphisms fixing z, including the well known automorphism discovered by Anick, and show how to recognize the wild ones. This class of automorphisms induces tame automorphisms of the polynomial algebra K[x,y,z]. For n>2 the automorphisms of K which fix z and are linear in the x's are tame.Comment: 8 page

Intermediaries in Entrepot Trade: Hong Kong Re-Exports of Chinese Goods

In this paper, we examine Hong Kong's role in intermediating trade between China and the rest of the world. Hong Kong distributes a large fraction of China's exports. Net of customs, insurance, and freight charges, re-exports of Chinese goods are much more expensive when they leave Hong Kong than when they enter. Hong Kong markups on re-exports of Chinese goods are higher for differentiated products, products with higher variance in export prices, products sent to China for further processing, and products shipped to countries which have less trade with China. These results are consistent with quality-sorting models of intermediation and with the outsourcing of production tasks from Hong Kong to China. Additional results suggest that Hong Kong traders price discriminate across destination markets and use transfer pricing to shift income from high-tax countries to Hong Kong.