For ordinary flops, the correspondence defined by the graph closure is shown to give equivalence of Chow motives and to preserve the Poincaré pairing. In the case of simple ordinary flops, this correspondence preserves the big quantum cohomology ring after an analytic continuation over the extended Kähler moduli space.For Mukai flops, it is shown that the birational map for the local models is deformation equivalent to isomorphisms. This implies that the birational map induces isomorphisms on the full quantum rings and all the quantum corrections attached to the extremal ray vanish.(1) Is there a canonical correspondence between the cohomology groups of K-equivalent smooth varieties?(2) Is there a modified ring structure which is invariant under the K-equivalence relation?The following conjecture was advanced by Y. Ruan [24] and the third author [26] in response to these questions.Conjecture 0.4. K-equivalent smooth varieties have canonically isomorphic quantum cohomology rings over the extended Kähler moduli spaces.

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Hydrochloric acid (HCl) and caustic (NaOH) are among the most widely used chemicals by the water industry. Direct anodic electrochemical HCl production by water electrolysis has not been successful as current commercially available electrodes are prone to chlorine formation. This study presents an innovative technology simultaneously generating HCl and NaOH from NaCl using a Mn0.84Mo0.16O2.23 oxygen evolution electrode during water electrolysis. The results showed that protons could be anodically generated at a high Coulombic efficiency (i.e. ≥ 95%) with chlorine formation accounting for 3 ~ 5% of the charge supplied. HCl was anodically produced at moderate strengths at a CE of 65 ± 4% together with a CE of 89 ± 1% for cathodic caustic production. The reduction in CE for HCl generation was caused by proton cross-over from the anode to the middle compartment. Overall, this study showed the potential of simultaneous HCl and NaOH generation from NaCl and represents a major step forward for the water industry towards on-site production of HCl and NaOH. In this study, artificial brine was used as a source of sodium and chloride ions. In theory, artificial brine could be replaced by saline waste streams such as Reverse Osmosis Concentrate (ROC), turning ROC into a valuable resource.

We show that the generating functions of Gromov-Witten invariants with ancestors are invariant under a simple flop, for all genera, after an analytic continuation in the extended Kähler moduli space. This is a sequel to [14].