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Two conjectures in Ramsey-Tur\'an theory
Given graphs , a graph is -free if
there is a -edge-colouring with no monochromatic
copy of with edges of colour for each . Fix a function
, the Ramsey-Tur\'an function is the
maximum number of edges in an -vertex -free graph with
independence number at most . We determine for and sufficiently small , confirming a
conjecture of Erd\H{o}s and S\'os from 1979. It is known that
has a phase transition at . However, the values of was not
known. We determined this value by proving , answering a question of Balogh, Hu and Simonovits.
The proofs utilise, among others, dependent random choice and results from
graph packings.Comment: 20 pages, 2 figures, 2 pages appendi
Quantum Random Number Generator using Photon-Number Path Entanglement
We report a novel quantum random number generator based on the
photon-numberpath entangled state which is prepared via two-photon quantum
interference at a beam splitter. The randomness in our scheme is of truly
quantum mechanical origin as it comes from the projection measurement of the
entangled two-photon state. The generated bit sequences satisfy the standard
randomness test
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THE COST-EFFECTIVENESS OF ALTERNATIVE EMISSION CONTROL POLICIES IN THE SAN JOAQUIN VALLEY OF CALIFORNIA
This study analyzes the ROG control costs of stationary sources in the San Joaquin Valley of California. The cost-effectiveness of market incentive approaches such as an uniform marketable permit system, localized marketable permit system and an ambient permit system as well as a traditional command-and-control approach are examined.Environmental Economics and Policy,
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