An approach for metric space with a convex combination operation and applications

In this paper, we embed metric space endowed with a convex combination operation, named convex combination space, into a Banach space and the embedding preserves the structures of metric and convex combination. For random element taking values in this kind of space, applications of embedding are also established. On the one hand, some nice properties of expectation such as representation of expected value through continuous affine mappings, the linearity of expectation will be given. On the other hand, the notion of conditional expectation will be also introduced and discussed. Thanks to embedding theorem, we establish some basic properties of conditional expectation, Jensen's inequality, convergences of martingales and ergodic theorem.Comment: 17 page

INNOVATION AND INSTITUTIONAL QUALITY ON ECONOMIC GROWTH IN ASIA

When looking at the different effects of institutional quality on economic development, namely control of corruption, there are two different hypotheses that explain such effects. One is the “grease the wheel” hypothesis, which predicts that corruption is beneficial for growth, and the other one is the “sand the wheel” hypothesis, which says the opposite. Corruption is normally blamed for the slow economic growths in some countries, but some Asian countries’ exponential growths have proven the “grease the wheel” hypothesis otherwise. The “Asian experience”1 phenomenon occurs when corruption does not seem to hamper business activities in some Asian countries. This research will focus on finding how institutional quality variables, such as corruption control and government effectiveness, can correlate with innovation variables to contribute to economic growth. Using data and examples from Asian countries, this study finds a positive correlation between corruption and economic growth in some developed countries, such as China and South Korea

Red-emitting Ba2Si5N8Eu2+ conversion phosphor: A new selection for enhancing the optical performance of the in-cup packaging MCW-LEDs

In this research, the influence of the red-emitting Ba2Si5N8Eu2+ convention phosphor on the optical performance of the 7,000K and 7,700K in-cup packaging multi-chip white LEDs (MCW-LEDs) is investigated. The effect of the red-emitting Ba2Si5N8Eu2+ convention phosphor is demonstrated based on Mie Theory by Mat Lab and Light Tools software. The research results indicated that the optical performance of MCW-LEDs was crucially affected by the red-emitting Ba2Si5N8Eu2+ phosphor's concentration. This paper provides an essential recommendation for selecting and developing the phosphor materials for MW-LEDs manufacturing.Web of Science51art. no. 148615