Models for capacitated lot-sizing problem with backlogging,setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.     

An [(NHC)(NHCEWG)RuCl2(CHPh)] Complex for the Efficient Formation of Sterically Hindered Olefins by Ring‐Closing Metathesis

NHC with EWGs for RCM : Ruthenium complexes with two N‐heterocyclic carbenes (NHCs), one of them substituted with electron‐withdrawing groups (EWGs), are highly efficient (pre)catalysts for the synthesis of tetrasubstituted olefins and trisubstituted olefins by ring‐closing metathesis reactions (RCM, see scheme).

     

Electron paramagnetic resonance structure investigation of copper complexation in a hemicarcerand

The double-bridged hemicarcerand [A,B-(CH2OH)2-cavitand]-(CH2NHCH2)2-[A,B-(CH2OH)2-cavitand] 23 (and several other related compounds) was synthesized by the condensation of the two complementary precursors A,B-(CH2NH2)2(CH2OH)2-cavitand and A,B-(CH2Br)2(CH2OAc)2-cavitand followed by hydrolysis of the acetate groups. This hemicarcerand has nitrogen and oxygen donor atoms located on the interior of the spherical cavity and thus allows endohedral coordination of metal ions. The cavity has a volume of approximately 0.12 nm3, a value obtained by calculating a Connolly-type contact surface and the molecular electrostatic potential. The Cu2+ complex of hemicarcerand 23 was studied in detail by EPR and DFT calculations at the UB3LYP/6-31G level to verify the anticipated endohedral nature of the metal complex. It could be shown that the copper ion is coordinated to four oxygen donor atoms and no deviation from axial symmetry at the copper site could be detected. No direct coordination to nitrogen atoms of the hemicarcerand could be observed; however, complexation with DMF solvent molecules was detected by ESEEM and HYSCORE experiments. The closed structure of the hemicarcerand was also confirmed by an evaluation of proton-copper distances. Results from DFT calculations are in accord with the EPR results, and further support suggested coordination of the Cu(II) within the hemicarcerand cavity by four oxygen donor atoms.     

On the experimental feasibility of continuous-variable optical entanglement distillation

Entanglement distillation aims at preparing highly entangled states out of a supply of weakly entangled pairs, using local devices and classical communication only. In this note we discuss the experimentally feasible schemes for optical continuous-variable entanglement distillation that have been presented in [D.E. Browne, J. Eisert, S. Scheel, and M.B. Plenio, Phys. Rev. A 67, 062320 (2003)] and [J. Eisert, D.E. Browne, S. Scheel, and M.B. Plenio, Annals of Physics (NY) 311, 431 (2004)]. We emphasize their versatility in particular with regards to the detection process and discuss the merits of the two proposed detection schemes, namely photo-detection and homodyne detection, in the light of experimental realizations of this idea becoming more and more feasible. The text was submitted by the authors in English.     

Entanglement cost under positive-partial-transpose-preserving operations

We study the entanglement cost under quantum operations preserving the positivity of the partial transpose (PPT operations). We demonstrate that this cost is directly related to the logarithmic negativity, thereby providing the operational interpretation for this entanglement measure. As examples we discuss general Werner states and arbitrary bipartite Gaussian states. Then we prove that for the antisymmetric Werner state PPT cost and PPT entanglement of distillation coincide. This is the first example of a truly mixed state for which entanglement manipulation is asymptotically reversible, which points towards a unique entanglement measure under PPT operations.     

Logarithmic negativity: a full entanglement monotone that is not convex

It is proven that logarithmic negativity does not increase on average under a general positive partial transpose preserving operation (a set of operations that incorporate local operations and classical communication as a subset) and, in the process, a further proof is provided that the negativity does not increase on average under the same set of operations. Given that the logarithmic negativity is not a convex function this result is surprising, as it is generally considered that convexity describes the local physical process of losing information. The role of convexity and, in particular, its relation (or lack thereof) to physical processes is discussed and importance of continuity in this context is stressed.     

Classical information and distillable entanglement

We establish a quantitative connection between the amount of lost classical information about a quantum state and the concomitant loss of entanglement. Using methods that have been developed for the optimal purification of mixed states, we find a class of mixed states with known distillable entanglement. These results can be used to determine the quantum capacity of a quantum channel which randomizes the order of transmitted signals.     

Conditions for the local manipulation of Gaussian states

We present a general necessary and sufficient criterion for the possibility of a state transformation from one mixed Gaussian state to another of a bipartite continuous-variable system with two modes. The class of operations that will be considered is the set of local Gaussian completely positive trace-preserving maps.