1,597 research outputs found
Yang-Baxter Equations, Computational Methods and Applications
Computational methods are an important tool for solving the Yang-Baxter
equations(in small dimensions), for classifying (unifying) structures, and for
solving related problems. This paper is an account of some of the latest
developments on the Yang-Baxter equation, its set-theoretical version, and its
applications. We construct new set-theoretical solutions for the Yang-Baxter
equation. Unification theories and other results are proposed or proved.Comment: 12 page
On transcendental numbers
Transcendental numbers play an important role in many areas of science. This
paper contains a short survey on transcendental numbers and some relations
among them. New inequalities for transcendental numbers are stated in Section 2
and proved in Section 4. Also, in relationship with these topics, we study the
exponential function axioms related to the Yang-Baxter equation.Comment: 6 page
On transcendental numbers: new results and a little history
Attempting to create a general framework for studying new results on
transcendental numbers, this paper begins with a survey on transcendental
numbers and transcendence, it then presents several properties of the
transcendental numbers and , and then it gives the proofs of new
inequalities and identities for transcendental numbers. Also, in relationship
with these topics, we study some implications for the theory of the Yang-Baxter
equations, and we propose some open problems.Comment: 8 page
Executive Pay and Firm Performance: Methodological Considerations and Future Directions
This paper is an investigation of the pay-for-performance link in executive compensation. In particular we document main issues in the pay-performance debate and explain practical issues in setting pay as well as data issues including how pay is disclosed and how that has changed over time. We also provide a summary of the state of CEO pay levels and pay mix in 2009 using a sample of over 2,000 companies and describe main data sources for researchers. We also investigate what we believe to be at the root of fundamental confusion in the literature across disciplines β methodological issues. In exploring methodological issues, we focus on empirical specifications, causality, fixed-effects, first- differencing and instrumental variables issues. We then discuss two important but not yet well explored areas; international issues and compensation in nonprofits. We conclude by examining a series of research areas where further work can be done, within and across disciplines
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