Partial data inverse problems for Maxwell equations via Carleman estimates

In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim–Uhlmann and Kenig–Sjöstrand–Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.     

Temperature characteristics of nonaqueous Li–O2 batteries

Discharge/charge characteristics of Li–O₂ batteries at a test temperature of 343 K, using Super P carbon electrodes, have been explored in this paper based on ether-based electrolytes. Compared with ambient temperature, high temperature significantly influences the discharge/charge process of Li–O₂ batteries since discharging capacity increases at about 80 % and charging voltage plateau decreases from 4.2 to 3.5 V. The stability of stainless steel mesh with electrolyte at 343 K has been researched using cyclic voltammetry. This paper lays the bases for further research on Li–O₂ batteries in high-temperature areas.     

Substitution of Lithium for Magnesium,Zinc, and Aluminum in Li15Si4: Crystal Structures,Thermodynamic Properties,as well as 6Li and 7Li NMR Spectroscopy of Li15Si4 and Li15−xMxSi4 (M=Mg,Zn, and Al)

An investigation into the substitution effects in Li₁₅Si₄, which is discussed as metastable phase that forms during electrochemical charging and discharging cycles in silicon anode materials, is presented. The novel partial substitution of lithium by magnesium and zinc is reported and the results are compared to those obtained for aluminum substitution. The new lithium silicides Li₁₄MgSi₄ ( 1 ) and Li_14.05Zn_0.95Si₄ ( 2 ) were synthesized by high‐temperature reactions and their crystal structures were determined from single‐crystal data. The magnetic properties and thermodynamic stabilities were investigated and compared with those of Li_14.25Al_0.75Si₄ ( 3 ). The substitution of a small amount of Li in metastable Li₁₅Si₄ for more electron‐rich metals, such as Mg, Zn, or Al, leads to a vast increase in the thermodynamic stability of the resulting ternary compounds_. The ^6,7Li NMR chemical shift and spin relaxation time T₁‐NMR spectroscopy behavior at low temperatures indicate an increasing contribution of the conduction electrons to these NMR spectroscopy parameters in the series for 1 – 3 . However, the increasing thermal stability of the new ternary phases is accompanied by a decrease in Li diffusivity, with 2 exhibiting the lowest activation energy for Li mobility with values of 56, 60, and 62 kJ mol^?1 for 2 , Li_14.25Al_0.75Si₁₄, and 1 , respectively. The influence of the metastable property of Li₁₅Si₄ on NMR spectroscopy experiments is highlighted.     

Toward an Octonionic World

In order to obtain a consistent formulation ofoctonionic quantum mechanics (OQM), we introduceleft/right-barred operators. Such operators enable us tofind the translation rules between octonionic numbers and 8 × 8 real matrices (a translation isalso given for 4 × 4 complex matrices). The use ofa complex geometry allows us to overcome the hermiticityproblem and define an appropriate momentum operator within OQM. As an application of our results,we develop an octonionic relativistic free waveequation, linear in the derivatives. Even if the wavefunctions are only one-component, we show that fourindependent solutions, corresponding to those of the Diracequation, exist.     

Elastic electron tunneling study of the metal-insulator transition in TTF-TCNQ

Using a single crystal of TTF-TCNQ as a moving electrode and by approaching to to an oxidized Al counter-electrode we realized tunnel junctions in the temperature range of about 30 to 295 K. By selecting junctions with minimum thermionic background current and measuring the tunnel conductance by a standard constant voltage lock-in detection we observed a deepening of the zero bias conductance abruptly reaching zero at about 53 K. We suggest that this reflects a progressive depletion of the electron density of states at the Fermi level and gives a direct image of the opening of a Peierls gap at the transition temperature.     

Purification of alpha-L-fucosidase from various sources by affinity chromatography.

An affinity column for alpha-L-fucosidases was constructed by linking p-amino-phenyl 1-thio-alpha-L-fucopyranoside to Sepharose 4B through linkers of succinyl 3,3'-diamino-dipropylamine. Excellent purification of alpha-L-fucosidase from rat epididymis, Clostridium perfringens and Limulus polyphemus (horse shoecrab) could be effected inone step with good yield. An affinity column purification step can be introduced at any point in published purification procedures. The purified enzyme is essentially free of other glycosidases and proteolytic enzymes. The column material is stable and can be reused for at least two years.     

Valence Isomerism in Selected Heterocyclic Systems

Valence isomerization and the phenomenologically related principle of valence tautomerism, as they apply to several nitrogen-containing heterocyclic systems, are discussed herein. Attention is called first to 1H-azepines and the reluctance of such substances to isomerize to azanorcaradienes. The role of homo-1H-azepines in this context is then briefly outlined. Azocines (azacyclooctatetraenes) are seen to occupy an interesting position in the sense that pronounced shifts in the position of equilibrium (from almost entirely monocyclic to virtually completely bicyclic) occur with substitutional alterations of various types. The capability of azabullvalenes for degenerate valence isomerization is the next presented, and contrast is made with the properties of benzazabullvalenes and an azasemibullvalene derivative.     

Quaternionic electroweak theory and Cabibbo-Kobayashi-Maskawa matrix

We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex numbers to quaternions, the calculation of the real-valued parameters of the Cabibbo-Kobayashi-Maskawa matrix drastically changes. We aim to explain thisquaternionic puzzle.