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Classification of full exceptional collections of line bundles on three blow-ups of
A fullness conjecture of Kuznetsov says that if a smooth projective variety
admits a full exceptional collection of line bundles of length , then
any exceptional collection of line bundles of length is full. In this
paper, we show that this conjecture holds for as the blow-up of
at a point, a line, or a twisted cubic curve, i.e. any
exceptional collection of line bundles of length 6 on is full. Moreover, we
obtain an explicit classification of full exceptional collections of line
bundles on such .Comment: 28 pages. To appear in Journal of the Korean Mathematical Society, A
previous version with a different title appeared as [CGP17025] at
https://cgp.ibs.re.kr/archive/preprints/201
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Electricity-powered artificial root nodule.
Root nodules are agricultural-important symbiotic plant-microbe composites in which microorganisms receive energy from plants and reduce dinitrogen (N2) into fertilizers. Mimicking root nodules using artificial devices can enable renewable energy-driven fertilizer production. This task is challenging due to the necessity of a microscopic dioxygen (O2) concentration gradient, which reconciles anaerobic N2 fixation with O2-rich atmosphere. Here we report our designed electricity-powered biological|inorganic hybrid system that possesses the function of root nodules. We construct silicon-based microwire array electrodes and replicate the O2 gradient of root nodules in the array. The wire array compatibly accommodates N2-fixing symbiotic bacteria, which receive energy and reducing equivalents from inorganic catalysts on microwires, and fix N2 in the air into biomass and free ammonia. A N2 reduction rate up to 6.5βmg N2 per gram dry biomass per hour is observed in the device, about two orders of magnitude higher than the natural counterparts
Genus-, -point, -boundary, -crosscap correlation functions of two-dimensional conformal field theory: Definition and general properties
We propose a systematic definition of genus-, -point, -boundary,
-crosscap correlation functions with
boundary operators, for general two-dimensional conformal field theory. The
are defined as the inner products of the surface
states with the tensor product of asymptotic states, boundary states
and crosscap states, where the defining boundary states carry a total
of boundary operators. The definition implies that
are infinite linear combinations of genus-,
-point functions . A single pole structure is
identified in the expansion coefficients , which is
analogous to the single pole structure in the conformal block decomposition.
This linear property unifies boundary and bulk CFTs. The consistency conditions
of are discussed: conventional upper-half plane
(UHP) and crosscap constraints can be reformulated as extra constraints on a
collection of bulk correlation functions.Comment: 41 pages + references (Minor corrections + references added comparing
to v1
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