Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Mesomorphism of Dichotomous Compounds; X-Ray Diffraction Analysis of 4-Chlorophenyl Hexadecyl Ether

Crystallography Reports - The crystal and molecular structures of Cl–C6H4–O–C16H33 (I) have been studied, and its differential scanning calorimetry (DSC) study is performed....     

Application of Synchrotron Radiation to Analyze the Friction-Induced Structural and Phase Transformations of Chrome-Nickel Austenitic Steel

Russian Physics Journal -     

Correction to: Impact of leg bending in the patient-specific computational fluid dynamics of popliteal stenting

Acta Mechanica Sinica - A Correction to this paper has been published: https://doi.org/10.1007/s10409-021-01066-2     

Acridone-Based Host Materials for Green Phosphorescent and Thermally Activated Delayed Fluorescent OLEDs with Low-Efficiency Roll-Offs

By linking the carbazole unit to the nitrogen atom of acridone through phenyl or pyridyl, two compounds, named 10-(4-(9H-carbazol-9-yl)phenyl)acridin-9(10H)-one (AC-Ph-Cz) and 10-(5-(9H-carbazol-9-yl)pyridin-2-yl)acridin-9(10H)-one (AC-Py-Cz) were designed and synthesized. These two materials, characterized with highly twisted and rigid structure, good thermal stability, and balanced carrier-transporting properties, were employed as host materials for green phosphorescent and thermally activated delayed fluorescent organic light-emitting diodes (OLEDs). The carbazole group, despite its small contribution to the highest occupied molecular orbitals (HOMOs) of these two materials, plays an essential role as an intramolecular host in energy delivering and improving the hole transporting ability of these two hosts. The incorporation of the electron-deficient pyridyl group as a linking group slightly improves the electron transporting capability of AC-Py-Cz. The green phosphorescent OLED (PhOLED) based on AC-Py-Cz exhibited excellent device performance with a turn-on voltage of 2.5 V, a maximum power efficiency and an external quantum efficiency (η_ext) of 89.8 lm W⁻¹ and 25.2 %, respectively, benefitting from the better charge-balancing ability of AC-Py-Cz host due to the presence of the pyridyl bridge. More importantly, all the devices based on these two hosts showed low efficiency roll-off at high brightness due to the suppressed non-radiative transition in the emitting layer. In particular, the AC-Py-Cz-hosted green PhOLED exhibited an efficiency roll-off of 1.6 % from the maximum next at a high brightness of 1000 cd m⁻² and a roll-off of 15.9 % at an extremely high brightness of 10000 cd m⁻². This study manifests that acridone-based host materials have great potential in fabricating OLEDs with low efficiency roll-off.     

Effect of Plasmon Resonance of Silver Nanoparticles on the Fluorescent Properties of Doxycycline

Journal of Analytical Chemistry - Silver nanoparticles modified with Eu3+ ions increase the intensity of the fluorescence signal by a factor of 125 in an analytical system containing doxycycline as...     

Comparative Study of LiInSe2 Single Crystals for Thermal-Neutron Detection

Crystallography Reports - Two LiInSe2 single crystals, grown under different conditions, have been studied. Characteristics of these crystals for neutron detection have been compared using...     

Effect of External Factors on the Ferromagnetic Resonance Line Width in Exchange-Biased Structures

Physics of the Solid State - The external factors which influence the ferromagnetic resonance (FMR) line width in bilayer (ferromagnet/antiferromagnet) exchange-biased systems are studied. The...     

Crystallographic Parameters of Special Grain Boundaries in Multicrystalline Silicon

Crystallography Reports - The orientation of grains and the special boundaries formed by them in multicrystalline silicon has been studied by electron backscattered diffraction. It is found that...