Extension of the LP-Newton method to conic programming problems via semi-infinite representation

Numerical Algorithms - The LP-Newton method solves linear programming (LP) problems by repeatedly projecting a current point onto a certain relevant polytope. In this paper, we extend the...     

New Fluorescence Domain “Excited Multimer” Formed upon Photoexcitation of Continuously Stacked Diaroylmethanatoboron Difluoride Molecules with Fused π‐Orbitals in Crystals

The crystal‐packing structures of seven derivatives of diaroylmethanatoboron difluoride ( 1 a – gBF₂ ) are characterized by no overlap of the π‐conjugated main units of two adjacent molecules (type I), overlap of the benzene ring π‐orbitals of two adjacent molecules (type II), and overlap of the benzene and dihydrodioxaborinine rings π‐orbitals of adjacent molecules (type III). The crystal‐packing structures govern the fluorescence (FL) properties in the crystalline states. The FL domain that is present in type I crystals, in which intermolecular orbital interactions are absent, leads to excited monomer‐like FL properties. In the case of the type II crystals, the presence of intermolecular overlap of the benzene rings π‐orbitals generates new FL domains, referred to as “excited multimers”, which possess allowed S₀–S₁ electronic transitions and, as a result, similar FL lifetimes at longer wavelengths than the FL of the type I crystals. Finally, intermolecular overlap of the benzene and dihydrodioxaborinine ring π‐orbitals in the type III crystals leads to “excited multimer” domains with forbidden S₀–S₁ electronic transitions and longer FL lifetimes at similar wavelengths as that in type I crystals.     

A vanadium-based oxide-phosphate-pyrophosphate framework as a 4 V electrode material for K-ion batteries

K-ion batteries (KIBs) are promising for large-scale electrical energy storage owing to the abundant resources and the electrochemical specificity of potassium. Among the positive electrode materials for KIBs, vanadium-based polyanionic materials are interesting because of their high working voltage and good structural stability which dictates the cycle life. In this study, a potassium vanadium oxide phosphate, K₆(VO)₂(V₂O₃)₂(PO₄)₄(P₂O₇), has been investigated as a 4 V class positive electrode material for non-aqueous KIBs. The material is synthesized through pyrolysis of a single metal–organic molecular precursor, K₂[(VOHPO₄)₂(C₂O₄)] at 500 °C in air. The material demonstrates a reversible extraction/insertion of 2.7 mol of potassium from/into the structure at a discharge voltage of ∼4.03 V vs. K. Operando and ex situ powder X-ray diffraction analyses reveal that the material undergoes reversible K extraction/insertion during charge/discharge via a two-phase reaction mechanism. Despite the extraction/insertion of large potassium ions, the material demonstrates an insignificant volume change of ∼1.2% during charge/discharge resulting in excellent cycling stability without capacity degradation over 100 cycles in a highly concentrated electrolyte cell. Robustness of the polyanionic framework is proved from identical XRD patterns of the pristine and cycled electrodes (after 100 cycles).

Highly pure K₆(VO)₂(V₂O₃)₂(PO₄)₄(P₂O₇), synthesized from the oxalatophosphate precursor, demonstrates a reversible potassium extraction/insertion capacity of 59 mA h g⁻¹ with a single discharge voltage plateau at 4.0 V at room temperature.     

Enantioselective synthesis of near enantiopure compound by asymmetric autocatalysis triggered by asymmetric photolysis with circularly polarized light

Right- and left-handed circularly polarized light (CPL) has been proposed as one of the origins of homochirality of biomolecules. However, the enantiomeric excess induced by CPL has been only very low (<2% ee). We found the unprecedented example of asymmetric autocatalysis triggered directly by a chiral physical factor, that is, right- and left-handed CPL, leading to a near enantiopure compound. Asymmetric photolysis of racemic pyrimidyl alkanol by r-CPL irradiation followed by asymmetric autocatalysis affords (R)-pyrimidyl alkanol with >99.5% ee. On the other hand, irradiation with l-CPL affords (S)-pyrimidyl alkanol with >99.5% ee. Thus, chiral physical power, such as CPL, in conjunction with asymmetric autocatalysis, provides a highly enantioenriched compound.     

3,14‐Bis(p‐nitrophenyl)‐17,17‐dipentyltetrabenzo[a,c,g,i]‐fluorene: A New Fluorophore Displaying Both Remarkable Solvatochromism and Crystalline‐Induced Emission

A series of 17,17‐dialkyl‐3,14‐diaryltetrabenzofluorenes were efficiently prepared by using Suzuki–Miyaura cross‐coupling reactions of the corresponding 3,14‐dibromo derivatives. Studies of the unique fluorescence properties of these compounds showed that they display intense blue to yellow fluorescence with high quantum yields in the solution state and blue to orange fluorescence with moderate quantum yields in the solid state. In addition, the fluorescence wavelength of the bis(p‐nitrophenyl) derivative is remarkably solvent‐dependent in a manner that correlates with the solvent polarity parameter E_T(30). The results of density function theory calculations suggest that the intramolecular charge‐transfer character of the HOMO–LUMO transition is responsible for the large solvent effect. Moreover, addition of water to a tetrahydrofuran (THF) solution of this compound leads to quenching of the yellow fluorescence owing to an increase in the solvent polarity. However, when the amount of water fraction exceeds 70 %, a new fluorescence band appears at the same orange‐red emission wavelength as that of the solid‐state fluorescence. This observation suggests the occurrence of a crystallization‐induced emission (CIE) phenomenon in highly aqueous THF.     

Positive definite matrix approximation with condition number constraint

Positive definite matrix approximation with a condition number constraint is an optimization problem to find the nearest positive definite matrix whose condition number is smaller than a given constant. We demonstrate that this problem can be converted to a simpler one when we use a unitary similarity invariant norm as a metric. We can especially convert it to a univariate piecewise convex optimization problem when we use the Ky Fan p-k norm. We also present an analytical solution to the problem whose metric is the spectral norm and the trace norm.