Preparation of dibromopyridines having -(CH2)m-SO3Na groups as monomers for new polypyridines

Dibromopyridines or dibromopyridone with -(CH₂)_m-SO₃Na group(s) has been prepared via the reactions of the corresponding dibromopyridines with -OH and -NH₂ groups with sultone. These compounds were converted into polymers with the -(CH₂)_m-SO₃H groups via organometallic polycondensation. The polymer showed proton conducting properties and high stability toward oxidation.     

Continuous Synthesis of Aryl Amines from Phenols Utilizing Integrated Packed-Bed Flow Systems

Aryl amines are important pharmaceutical intermediates among other numerous applications. Herein, an environmentally benign route and novel approach to aryl amine synthesis using dehydrative amination of phenols with amines and styrene under continuous-flow conditions was developed. Inexpensive and readily available phenols were efficiently converted into the corresponding aryl amines, with small amounts of easily removable co-products (i.e., H₂O and alkanes), in multistep continuous-flow reactors in the presence of heterogeneous Pd catalysts. The high product selectivity and functional-group tolerance of this method allowed aryl amines with diverse functional groups to be selectively obtained in high yields over a continuous operation time of one week.     

Thickening of crystals during rapid heating. II. Crosslinked polyethylene and methoxymethylated nylon 6

The effect of modification of polymer chains on crystal thickening during heating was investigated with an apparatus devised for rapid measurement of small-angle x-ray diffraction. Thickening of crystals still occurred even at a heating rate of 18°C/min in polyethylene irradiated with gamma ray doses of 30–300 Mrad, and the melting point was depressed. These results showed that the melting point depression due to irradiation is not due to a restriction on crystal thickening but rather to crystal lattice distortion. On the other hand, although methoxymethylation of nylon 6 completely inhibits crystal thickening, the melting point increases or decreases depending on the temperature of annealing preceding methoxymethylation. From these results we are led to conclude that irradiation and methoxymethylation are not effective means of obtaining the relation between melting point and crystal thickness.     

2d–4d connection between q-Virasoro/W block at root of unity limit and instanton partition function on ALE space

We propose and demonstrate a limiting procedure in which, starting from the q-lifted version (or K-theoretic five-dimensional version) of the (W)AGT conjecture to be assumed in this paper, the Virasoro/W block is generated in the r-th root of unity limit in q   in the 2d side, while the same limit automatically generates the projection of the five-dimensional instanton partition function onto that on the ALE space R⁴/_Zr${\mathbb{R}}^4/{\mathbb{Z}}_r$. This circumvents case-by-case conjectures to be made in a wealth of examples found so far. In the 2d side, we successfully generate the super-Virasoro algebra and the proper screening charge in the q→−1$q\to -1$, t→−1$t\to -1$ limit, from the defining relation of the q-Virasoro algebra and the q  -deformed Heisenberg algebra. The central charge obtained coincides with that of the minimal series carrying odd integers of the N=1$N=1$ superconformal algebra. In the r-th root of unity limit in q in the 2d side, we give some evidence of the appearance of the parafermion-like currents. Exploiting the q-analysis literatures, q  -deformed su(n)$\mathit{su}(n)$ block is readily generated both at generic q,t$q,t$ and the r  -th root of unity limit. In the 4d side, we derive the proper normalization function for general (n,r)$(n,r)$ that accomplishes the automatic projection through the limit.     

Separability criterion for quantum effects

Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability criteria have been proposed to determine whether a given state is entangled. In this Letter, we propose a separability criterion for specific quantum effects (binary observables) that can be regarded as a dual version of the Bell–Clauser–Horne–Shimony–Holt (Bell–CHSH) inequality for quantum states. The violation of the dual version of the Bell–CHSH inequality is confirmed by using IBM's cloud quantum computer. As a consequence, the violation of our inequality rules out the maximal tensor product state space, that satisfies information causality and local tomography. As an application, we show that an entangled observable which violates our inequality is useful for quantum teleportation.     

Einstein equations and Lagrangians on symmetry-restricted phase spaces

When Lagrangians are restricted to subspaces of the phase space satisfying certain symmetry conditions, they do not always yield the correct Einstein equations. An example was found by Hawking in the Lagrangian for spatially homogeneous universes. First we show that this problem is not limited to general relativity. Then we visualize certain terms which do not appear in Lagrangians on symmetry-restricted phase spaces but which nevertheless contribute to the Euler-Lagrange derivatives. We apply our general formula to the Schwarzschild metric, the Friedmann universes, and spatially homogeneous universes.     

Continuous Synthesis of Aryl Amines from Phenols Utilizing Integrated Packed‐Bed Flow Systems

Aryl amines are important pharmaceutical intermediates among other numerous applications. Herein, an environmentally benign route and novel approach to aryl amine synthesis using dehydrative amination of phenols with amines and styrene under continuous‐flow conditions was developed. Inexpensive and readily available phenols were efficiently converted into the corresponding aryl amines, with small amounts of easily removable co‐products (i.e., H₂O and alkanes), in multistep continuous‐flow reactors in the presence of heterogeneous Pd catalysts. The high product selectivity and functional‐group tolerance of this method allowed aryl amines with diverse functional groups to be selectively obtained in high yields over a continuous operation time of one week.     

Separability of Dirac equation in higher dimensional Kerr–NUT–de Sitter spacetime

It is shown that the Dirac equations in general higher dimensional Kerr–NUT–de Sitter spacetimes are separated into ordinary differential equations.     

Nickel-Catalyzed Reductive Allyl−Aryl Cross-Electrophile Coupling via Allylic C−F Bond Activation

Nickel-catalyzed reductive cross-coupling of allylic difluorides with aryl iodides was achieved via allylic C−F bond activation. Based on this protocol, a series of γ-arylated monofluoroalkenes were synthesized in moderate to high yields with high Z-selectivities. Mechanistic studies suggest that the C−I bonds of the aryl iodides and the C−F bonds of the allylic difluorides were cleaved via oxidative addition and β-fluorine elimination, respectively, where the oxidative addition of less reactive C−F bonds was avoided to permit their transformation.