Global information balance in quantum measurements

We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a tight and general entropic information-disturbance trade-off, and explains the physical mechanism underlying it. Finally, the single-outcome case, that is, the case of measurements with posts election, is briefly discussed.     

Geometric analysis of spatial distortion in projection-type integral imaging

In projection-type integral imaging, positional errors in elemental images and elemental lenses affect three-dimensional (3D) image quality. We analyzed the relationships between the geometric distortion in elemental images caused by a projection lens and the spatial distortion in the reconstructed 3D image. As a result, we clarified that 3D images that were reconstructed far from the lens array were largely affected, and that the reconstructed images were significantly distorted in the depth direction at the corners of the displayed images.     

Density-matrix renormalization group study of trapped imbalanced Fermi condensates

The density-matrix renormalization group is employed to investigate a harmonically trapped imbalanced Fermi condensate based on a one-dimensional attractive Hubbard model. The obtained density profile shows a flattened population difference of spin-up and spin-down components at the center of the trap, and exhibits phase separation between the condensate and unpaired majority atoms for a certain range of the interaction and population imbalance P. The two-particle density matrix reveals that the sign of the order parameter changes periodically, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov phase. The minority spin atoms contribute to the quasicondensate up to at least P approximately 0.8. Possible experimental situations to test our predictions are discussed.     

Total Synthesis and Structure Elucidation of JBIR‐39: A Linear Hexapeptide Possessing Piperazic Acid and γ‐Hydroxypiperazic Acid Residues

The total synthesis and stereochemical structural elucidation of JBIR‐39, containing four nonproteinogenic piperazic acid (Piz) residues, is reported. The synthesis includes Sc(OTf)₃‐catalyzed acylation of a Piz(γ‐OTBS) derivative with piperazic acid chloride, providing the desired Piz‐Piz(γ‐OTBS) dipeptide in high yield without epimerization. After assembling two additional Piz moieties and (S)‐isoleucic acid at the N‐terminus, amidation with the (R)‐α‐methylserine ester at the C‐terminus, and deprotection afforded the desired (2R,8S)‐hexapeptide, which is the assumed structure of JBIR‐39. Although the spectral data of the (2R,8S)‐hexapeptide was not identical to JBIR‐39, further synthesis of three stereoisomers confirmed the stereochemical structure of JBIR‐39 to be (2S,6S,8S,11R,16S,21R,26S,27S).     

Iridium‐Catalyzed Sequential Silylation and Borylation of Heteroarenes Based on Regioselective C−H Bond Activation

An iridium‐catalyzed regioselective sequential silylation and borylation of heteroarenes was developed, which represents a rare example of unsymmetrical intermolecular C?H bond difunctionalization through the introduction of two different functionalities during a one‐pot transformation. Although the substrate scope for the dehydrogenative silylation of heteroarenes has been limited mainly to electron‐rich five‐membered rings, the current reaction proceeds with both electron‐rich and electron‐deficient heteroarenes with the aid of heteroatom‐directing C?H bond activation. The regioselectivity of the second borylation was controlled by both steric factors and the electronic effect of the silyl group installed in the first step. In combination with the classic cross‐coupling reaction, this method provides rapid access to multisubstituted heteroarenes.     

Copper-catalyzed addition reactions of aromatics and ketones to 2-aza-2,4-cyclopentadienone: facile and efficient transformation of carbonyl-ene-nitriles to 1H-pyrrolin-2(5H)-ones

Copper-catalyzed reactions of carbonyl-ene-nitriles with carbon nucleophiles, such as aromatics and ketones, afforded pyrrolin-2-ones (gamma-lactam) in excellent yield. The reaction mechanism involves addition reactions with a ketimine moiety of the 2-aza-2,4-cyclopentadienone intermediate, which is formed via hydration of a nitrile moiety followed by dehydrative cyclization.     

Internal delivery of soft chlorine and bromine atoms: stereoselective synthesis of (E)-beta-halogenovinyl(aryl)-lambda3-iodanes through domino lambda3-iodanation-1,4-halogen shift-fluorination of alkynes

4-(Difluoroiodo)toluene-induced domino lambda(3)-iodanation-1,4-halogen shift-ring enlargement-fluorination reaction of 5-halopentynes with a four-, five-, or six-membered carbocycle afforded the ring-expanded (E)-delta-fluoro-beta-halovinyl-lambda3-iodanes stereoselectively in high yields, probably via the intermediacy of five-membered halonium ions. Use of internal alkynes makes it possible to synthesize tetrasubstituted beta-halovinyl-lambda(3)-iodanes with defined stereochemistry.     

Critical Blowup for Systems of Semilinear Wave Equations in Low Space Dimensions

We consider the Cauchy problem for systems of semilinear wave equations in two and three space dimensions with small initial data. Del Santo et al. [“Geometric Optics and Related Topics” (F. Colombini and N. Lerner, Eds.), Progress in Nonlinear Differential Equations and Their Applications, Vol. 32, pp. 117–140, Birkhauser, Boston, 1997] have studied the existence and nonexistence of global classical solutions of the Cauchy problem except for the critical case. In this paper we study the critical case, and we show the nonexistence of global classical solutions and also give the upper bounds of the life span.