Algebraic Montgomery-Yang problem and smooth obstructions

Let $S$ be a rational homology complex projective plane with quotient singularities. The algebraic Montgomery-Yang problem conjectures that the number of singular points of $S$ is at most three if its smooth locus is simply-connected. In this paper, we leverage results from the study of smooth 4-manifolds, including the Donaldson diagonalization theorem and Heegaard Floer correction terms, to establish additional conditions for $S$. As a result, we eliminate the possibility of a rational homology complex projective plane of specific types with four singularities. Moreover, we identify large families encompassing infinitely many types of singularities that satisfy the orbifold BMY inequality, a key property in algebraic geometry, yet are obstructed from being a rational homology complex projective plane due to smooth conditions. Additionally, we discuss computational results related to this problem, offering new insights into the algebraic Montgomery-Yang problem.Comment: 26 pages, 14 figures, minor revisions for the purpose of correcting typos and refining the languag

Synergistic multi-doping effects on the Li7La3Zr2O12 solid electrolyte for fast lithium ion conduction.

Here, we investigate the doping effects on the lithium ion transport behavior in garnet Li7La3Zr2O12 (LLZO) from the combined experimental and theoretical approach. The concentration of Li ion vacancy generated by the inclusion of aliovalent dopants such as Al(3+) plays a key role in stabilizing the cubic LLZO. However, it is found that the site preference of Al in 24d position hinders the three dimensionally connected Li ion movement when heavily doped according to the structural refinement and the DFT calculations. In this report, we demonstrate that the multi-doping using additional Ta dopants into the Al-doped LLZO shifts the most energetically favorable sites of Al in the crystal structure from 24d to 96 h Li site, thereby providing more open space for Li ion transport. As a result of these synergistic effects, the multi-doped LLZO shows about three times higher ionic conductivity of 6.14 × 10(-4) S cm(-1) than that of the singly-doped LLZO with a much less efforts in stabilizing cubic phases in the synthetic condition

Dynamics from open innovation to evolutionary change

We created conceptual models that people may use to analyze and forecast the dynamic effects of open innovation, which we applied to the smartphone sector using a model-based analysis approach. In addition, we built an open innovation simulation model for the smartphone sector. The dynamic model of open innovation linked logic and concepts relating to open innovation, complex adaptive systems, and evolutionary change. The model can be used to analyze the dynamic effects of open innovation strategies and open innovation simulation for the selection of future strategies.1

Sustainability Condition of Open Innovation: Dynamic Growth of Alibaba from SME to Large Enterprise

Research Question: Open innovation and the open business model exaggerate complexity (a transaction cost) in addition to the realization of emergence and its lock-in. Within a short period, Alibaba has become one of the global top e-commerce companies with several open innovation business models. Our research question was: How could Alibaba become a global top e-commerce company in China in such a short time? Research Method: We chose a deep interview method, participatory observation, and meta-analysis to answer this research question. Research Result: Alibaba has applied global, creative e-commerce business models through open innovation in a short time. In addition, it has overcome complexity-i.e., the cost of open innovation and the force that breaks down a company-through an open innovation-friendly culture. This is a Jack-Ma style consumer confidence and new Guanxi culture, a new and strong Chinese corporate culture. Alibaba has also undergone the expansion of its open business model feedback loop platform. This study investigated the expanded open business model feedback loop platform, the continuously strengthened open-innovation-friendly culture, and complexity, with the latter being the cost of open innovation, which was controlled by an open-innovation-friendly culture and open business model feedback loop. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.1

Open Innovation and Serial Entrepreneurs

With the advent of the Fourth Industrial Revolution, the role of entrepreneurs has become more crucial than ever. As a result, an open innovation model is suggested here that can promote serial entrepreneurs by answering the following question: How does the serial entrepreneur in open innovation conditions continuously identify business opportunities? This question is answered through an in-depth case study of Medison from 1985 to 2016, as Medison is not only a representative Korean medical device company, but is also a representative example of serial entrepreneurship in Korea. First, we examined the diverse open innovation channels, such as spin-offs, venture investment, and joint venture, used by Medison before it was merged with Samsung. Second, we examined the open innovation serial entrepreneurs of Medison and then analyzed the direct serial entrepreneurs of Medison. Fourth, we built a causal loop model of Medison open innovation with emergence and complexity combined. Finally, a sustainable open innovation strategy and an approach to sustainable serial entrepreneurship was formulated. The foundation of this research is as follows. First, an open innovation strategy can be a strong motivator for serial entrepreneurs. Second, a balance between emergence and complexity is required to trigger sustainable serial entrepreneurs of open innovation. © 2019 by the authors.1

How to Respond to the Fourth Industrial Revolution, or the Second Information Technology Revolution? Dynamic New Combinations between Technology, Market, and Society through Open Innovation

How can we respond to the Fourth Industrial Revolution in terms of technology?&rdqu