{C \ell{^\ast_3}} Invariance of the Dirac Equation and Electromagnetism

In order to obtain a form invariance of the Dirac wave, the relativistic quantum theory uses ${{\rm SL}(2, \mathbb{C})}$ , a subset of the Clifford algebra C? ₃ of the 3-dimensional physical space. In Dirac theory and electromagnetism, we study a replacement of this invariance group by the full group ${C \ell{^\ast_3}}$ consisting of all invertible elements in C? ₃. We extend this invariance to systems of identical particles. We explain how geometry linked to the Dirac wave implies existence of a second space-time variety, and we review its consequences to particle physics.     

Tri-polarized MIMO systems in real-world channels: Channel investigation and performance analysis

Polarized multi-antenna systems are an effective solution for reducing inter-antenna spacing while still maintaining low inter-antenna correlation. Traditionally, only dual-polarized antenna systems are used for polarized transceivers. In this paper, tri-polarized antenna systems are investigated. Starting from the polarization mechanisms in the wireless propagation channel, it is shown that dual-polarized MIMO systems show high sensitivity to the transmitter and receiver orientation, which may be very critical in practical applications. Tri-polarized MIMO systems are introduced as a solution to obtain a robust MIMO performances, which are independent of the transmitter and receiver orientation. The performances of dual- and tri-polarized MIMO systems are evaluated on real-world measured channels, and the limits of each of these systems is highlighted.     

A boundary-value problem for the stationary vlasov-poisson equations: The plane diode

The stationary Vlasov-Poisson boundary value problem in a spatially one-dimensional domain is studied. The equations describe the flow of electrons in a plane diode. Existence is proved when the boundary condition (the cathode emission distribution) is a bounded function which decays super-linearly or a Dirac mass. Uniqueness is proved for (physically realistic) boundary conditions which are decreasing functions of the velocity variable. It is shown that uniqueness does not always hold for the Dirac mass boundary conditions.     

Enzyme biosensors based on ion-selective field-effect transistors

The key theoretical principles of the work on ion-selective field-effect transistor connected with their application in bioanalytical practice, some specifics of modern microtechnologies for their creation, and measurement schemes with set-ups are discussed. The achievements in the creation of enzyme biosensors based on ion-selective field-effect transistors and prospects for their application are described in detail.     

Electronic structure of Li-intercalated oligopyridines: a comparative study by photoelectron spectroscopy

The role of nitrogen in the charge transfer and storage capacity of lithium-intercalated heterocyclic oligophenylenes was investigated using photoelectron spectroscopy. The development of new occupied states at low binding energies in the valence band region, as well as core level chemical shifts at both carbon and nitrogen sites, demonstrates partial charge transfer from lithium atoms to the organic component during formation of the intercalated compound. In small compounds, i.e., biphenyl and bipyridine derivatives, the position of the nitrogen heteroatom significantly affects the spacing between gap states in the Li-intercalated film; yet it has minimal effects on the charge storage capacity. In larger, branched systems, the presence of nitrogen in the aromatic system significantly enhances the charge storage capacity while the Li-N bond strength at high intercalation levels is significantly weakened relative to the nitrogen-free derivative. These observations have strong implications towards improved deintercalation processes in organic electrodes in lithium-ion batteries.     

Synthesis of pyrazolidine, 1-pyrazoline, 2-pyrazoline derivatives by selenium-induced cyclization of homoallylhydrazines

The PhSeBr-induced cyclization of N′-but-3-en-1-yl ethoxycarbonylhydrazines 1, phenylhydrazines 2 and dimethylhydrazines 3 has been studied. A 5-exo-trig ring closure occurred in each case and phenylselanylmethyl-pyrazolidines 4, 2-pyrazolines 5 and 10, 1-pyrazolines 8 and pyrazolidinium bromides 11 were synthesized. Radical deselenenylation has allowed the preparation of 5-methylpyrazolidines 12 and 5-methyl-2-pyrazolines 13 and 14. Decomposition of the dibromoselenuranes derived from 2-pyrazolines 5 and 10 afforded bromomethyl derivatives. With 1-phenyl-2-pyrazolines 10, an electrophilic p-halogenation of the phenyl nucleus was observed.     

3,5-Bis(ethynyl)pyridine and 2,6-bis(ethynyl)pyridine spanning two Fe(Cp*)(dppe) units: role of the nitrogen atom on the electronic and magnetic couplings

The role of the nitrogen atom on the electronic and magnetic couplings of the mono-oxidized and bi-oxidized pyridine-containing complex models [2,6-{Cp(dpe)Fe-C≡C-}(2)(NC(5)H(3))](n+) and [3,5-{Cp(dpe)Fe-C≡C-}(2)(NC(5)H(3))](n+) is theoretically tackled with the aid of density-functional theory (DFT) and multireference configuration interaction (MR-CI) calculations. Results are analyzed and compared to those obtained for the reference complex [1,3-{Cp*(dppe)Fe-C≡C-)}(2)(C(6)H(4))](n+). The mono-oxidized species show an interesting behavior at the borderline between spin localization and delocalization and one through-bond communication path among the two involving the central ring, is favored. Investigation of the spin state of the dicationic complexes indicates ferromagnetic coupling, which can differ in magnitude from one complex to the other. Very importantly, electronic and magnetic properties of these species strongly depend not only upon the location of the nitrogen atom in the ring versus that of the organometallic end-groups but also upon the architectural arrangement of one terminus, with respect to the other and/or vis-à-vis the central ring. To help validate the theoretical results, the related families of compounds [1,3-{Cp*(dppe)Fe-C≡C-)}(2)(C(6)H(4))](n+), [2,6-{Cp*(dppe)Fe-C≡C-}(2)(NC(5)H(3))](n+), [3,5-{Cp*(dppe)Fe-C≡C-}(2)(NC(5)H(3))](n+) (n = 0-2) were experimentally synthesized and characterized. Electrochemical, spectroscopic (infrared (IR), M?ssbauer), electronic (near-infrared (NIR)), and magnetic properties (electron paramagnetic resonance (EPR), superconducting quantum interference device (SQUID)) are discussed and interpreted in the light of the theoretical data. The set of data obtained allows for many strong conclusions to be drawn. A N atom in the long branch increases the ferromagnetic interaction between the two Fe(III) spin carriers (J > 500 cm(-1)), whereas, when placed in the short branch, it dramatically reduces the magnetic exchange in the di-oxidized species (J = 2.14(5) cm(-1)). In the mixed-valence compounds, when the N atom is positioned on the long branch, the intermediate excited state is higher in energy than the different ground-state conformers and the relaxation process provides exclusively the Fe(II)/Fe(III) localized system (H(ab) ≠ 0). Positioning the N atom on the short branch modifies the energy profile and the diabatic mediating state lies just above the reactant and product diabatic states. Consequently, the LMCT transition becomes less energetic than the MMCT transition. Here, the direct coupling does not occur (H(ab) = 0) and only the coupling through the bridge (c) and the reactant (a) and product (b) diabatic states is operating (H(ac) = H(bc) ≠ 0).     

Plant drug analysis by planar chromatography

Optimal performance laminar chromatography and automated multiple development chromatography are relatively recent techniques of planar chromatography that can be applied with success in plant material analysis. Therefore, these methods are used to study plant extracts and constituents belonging to different chemical classes of secondary metabolism: heterocyclic oxygen compounds (coumarins, flavonoids, and anthocyanins), alkaloids and quaternary ammonium salts, cannabinoids, essential oils, ginsenosides, and cardiac heterosides. Generally, the results obtained with these methods are good, and in most cases they compare with those of thin-layer chromatography.