Cheng Equation: A Revisit Through Symmetry Analysis

The symmetry analysis of the Cheng Equation is performed. The Cheng Equation is reduced to a first-order equation of either Abel's Equations, the analytic solution of which is given in terms of special functions. Moreover, for a particular symmetry the system is reduced to the Riccati Equation or to the linear nonhomogeneous equation of Euler type. Henceforth, the general solution of the Cheng Equation with the use of the Lie theory is discussed, as also the application of Lie symmetries in a generalized Cheng equation.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae journa

Note on the paper of Fu and Wong on strictly pseudoconvex domains with K\"ahler--Einstein Bergman metrics

It is shown that the Ramadanov conjecture implies the Cheng conjecture. In particular it follows that the Cheng conjecture holds in dimension two

The Policies of State Succession: Harmonizing Self-Determination and Global Order in the Twenty-First Century Tai-Heng Cheng, State Succession and Commercial Obligations

I differ with Cheng\u27s appraisal of certain events and think that we need a more sophisticated analysis of the twin policy goals he identifies and embraces--self-determination and global order--before they can offer real policy guidance. But State Succession and Commercial Obligations stands out as a rigorously researched, original, and insightful effort to understand this quite confused and opaque body of international law. Cheng\u27s work will both enable and encourage a more candid, reasoned, and constructive debate about the global policies at stake each time “a state fundamentally changes its structures of power and authority, and an authoritative international response is needed to manage disruptions to international arrangements that may result from that change.” Briefly, I find Cheng\u27s analysis of the dynamics of State succession relative to commercial obligations sophisticated, pragmatic, descriptively comprehensive, and, for the most part, normatively compelling. But it may be too ambitious. Defining disruptions to global commerce as the principal indicia of State succession tends to inflect, and at times to bias, the general analysis of the diverse phenomena that fall within the rubric of State succession. This commercial focus can obscure or normatively predispose our understanding and appraisal of equally vital, but non-economic, dimensions of State succession, including the core policy goals--self-determination and global order--that Cheng identifies and recommends. And to a certain extent, this compromises the work\u27s descriptive accuracy and normative appeal

Value and selfhood: pragmatism, Confucianism, and phenomenology

This article articulates a dialogue between Edward Casey, Cheng Chung‐ying, and me that began at the Eastern Division annual meeting in Philadelphia of the American Philosophical Association, in a session sponsored by the International Society for Chinese Philosophy. There, we read brief versions of the papers presented in this issue and commented on one another. Casey represented Continental phenomenology, Cheng the Chinese tradition as he has developed it into onto‐generative hermeneutics, and I the melding of American pragmatic and Confucian traditions that I have been developing

Algebra diagrams: a HANDi introduction

A diagrammatic notation for algebra is presented – Hierarchical Al- gebra Network Diagrams, HANDi. The notation uses a 2D network notation with systematically designed icons to explicitly and coherently encode the fun- damental concepts of algebra. The structure of the diagrams is described and the rules for making derivations are presented. The key design features of HANDi are discussed and compared with the conventional formula notation in order demonstrate that the new notation is a more logical codification of intro- ductory algebra

A note on the Almost Schur lemma on smooth metric measure spaces

In this paper, we prove almost Schur Lemma on closed smooth metric measure spaces, which implies the results of X. Cheng and De Lellis-Topping whenever the weighted function f is constant.Comment: 15 page