Representations and classification of traveling wave solutions to Sinh-G{\"o}rdon equation

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to Sinh-G{\"o}rdon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method aren't true. In final, we prove that our solutions to Sinh-G{\"o}rdon equation include all solutions obtained in the paper[Fu Z T et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.Comment: 12 pages. accepted by Communications in theoretical physics (Beijing

Design Management Capability in Entrepreneurship: A Case Study of Xiaomi

In recent years, entrepreneurship has become a popular topic and attracted many young people to start their own companies. In entrepreneurship, design was generally viewed as essential to innovation, replacing the conventional role of the engineer. Unlike traditional businesses, which generally take a longer time to become established in the more stable economic context of mass-production, current start-ups have to face fierce competition and have the tendency to expand rapidly and accommodate the dynamic business environment. Consequently, design management is considered to be crucial to business growth, since it contributes to both competitive advantages and strategic flexibility. However, start-up companies are well-known for their high failure ratio. This triggered our initial research question: what is the role of design in a start-up to support it in achieving success? Through a case study of Xiaomi, a well-known successful entrepreneurship in China, the new capabilities of entrepreneurial design management were reported. It was further classified into three key topics in line with the three stages of entrepreneurial business development. Difference with design management capabilities reported in previous studies, the new capabilities show the dynamic nature of entrepreneurial design management

The classification of traveling wave solutions and superposition of multi-solutions to Camassa-Holm equation with dispersion

Under the traveling wave transformation, Camassa-Holm equation with dispersion is reduced to an integrable ODE whose general solution can be obtained using the trick of one-parameter group. Furthermore combining complete discrimination system for polynomial, the classifications of all single traveling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More general, an implicit linear structure in Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion

Universe Models with a Variable Cosmological "Constant" and a "Big Bounce"

We present a rich class of exact solutions which contains radiation-dominated and matter-dominated models for the early and late universe. They include a variable cosmological ``constant'' which is derived from a higher dimension and manifests itself in spacetime as an energy density for the vacuum. This is in agreement with observational data and is compatible with extensions of general relativity to string and membrane theory. Our solutions are also typified by a non-singular ``big bounce'' (as opposed to a singular big bang), where matter is created as in inflationary cosmology.Comment: 17 pages, 2 figures, AASTEX. To appear in Ap