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.     

Tuning Optical and Electron Donor Properties by Peripheral Thio–Aryl Substitution of Subphthalocyanine: A New Series of Donor–Acceptor Hybrids for Photoinduced Charge Separation

Subphthalocyanine (SubPc), a unique ring‐reduced member of the common phthalocyanines family, although known for its higher absorptivity, reveals narrow absorption with peak maxima around 570 nm thus limiting its utility in light‐energy‐harvesting applications. In the present study, by peripheral thio–aryl substitution of SubPc macrocycle, the spectral properties have been modulated to extend the absorption and emission well into the visible/near‐IR region. Additionally, for α‐ring‐substituted derivatives, facile oxidation of SubPc was witnessed, thus making these derivatives better electron donors. Next, the preparation of donor–acceptor dyads containing the well‐known electron acceptor C₆₀ connected to the central boron atom of SubPc was accomplished by making use of the 1,3‐dipolar cycloaddition reaction. Control experiments and free‐energy calculations using the redox and spectral data suggested that the observed fluorescence quenching of SubPc in these dyads is due to electron transfer. Accordingly, transient spectral studies performed both in polar and nonpolar solvents conclusively proved electron transfer to be the quenching mechanism in these dyads. The measured rate constants by fitting kinetic data revealed efficient charge separation and charge recombination processes, suggesting that these dyads could be useful materials for the construction of light‐to‐electricity or light‐to‐fuel production devices.     

New families of balanced symmetric functions and a generalization of Cusick,Li and Stǎnicǎ’s conjecture

In this paper we provide new families of balanced symmetric functions over any finite field. We also generalize a conjecture of Cusick, Li, and Stǎnicǎ about the non-balancedness of elementary symmetric Boolean functions to any finite field and prove part of our conjecture.     

Synthesis and pharmacological characterization at glutamate receptors of erythro- and threo-tricholomic acid and homologues thereof

The erythro- and threo-amino-(3′-hydroxy-4′,5′-dihydro-isoxazol-5′-yl)-acetic acids, stereoisomers of tricholomic acid, were synthesized along with the corresponding higher homologues erythro- and threo-amino-(3′-carboxy-4′,5′-dihydro-isoxazol-5′-yl)-acetic acids. The target compounds were prepared via the 1,3-dipolar cycloaddition of a suitable nitrile oxide to (±)-2-tert-butoxycarbonylamino-3-buten-1-ol. Such a strategy allowed the synthesis of the two stereoisomeric amino acids in comparable amounts. The pharmacological activity of these compounds was investigated at ionotropic and metabotropic glutamate receptors (iGluRs and mGluRs) by means of receptor binding assays to rat cortical membranes, electrophysiological tests and second messenger assays at cloned receptors expressed in CHO cells. Their pharmacological profiles were compared to those of l-glutamate and of the previously described selective NMDA receptor antagonists 5-(2-amino-2-carboxyethyl)-4,5-dihydroisoxazole-3-carboxylic acids in order to highlight the effect of increasing/reducing the distance between the amino acid moiety and the distal acid group, which represent the two pharmacophoric entities.     

Voie d'accès aux amino-3(5) pyrazoles substitués en 4 par un groupement SEt

Reaction of hydrazine with bromoderivatives $\text{1}$, obtained from aldehydes, gives almost quantitatively 3(5)-aminopyrazoles $\text{2}$. An approach of the structure of $\text{2}$ is attempted by ¹³C NMR.     

Uniqueness of the inversive plane of order 5

It is proved that any inversive plane of order 5 must be isomorphic with the Miquelian plane. The proof is given in some detail: a companion paper will assert that the same arguments can be applied to a plane of order 7.     

Nonstationary Wavelets on them-Sphere for Scattered Data

We construct classes of nonstationary wavelets generated by what we callspherical basis functions,which comprise a subclass of Schoenberg's positive definite functions on them-sphere. The wavelets are intrinsically defined on them-sphere and are independent of the choice of coordinate system. In addition, they may be orthogonalized easily, if desired. We will discuss decomposition, reconstruction, and localization for these wavelets. In the special case of the 2-sphere, we derive an uncertainty principle that expresses the trade-off between localization and the presence of high harmonics—or high frequencies—in expansions in spherical harmonics. We discuss the application of this principle to the wavelets that we construct.