{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.     

On DRC‐covering of Kn by cycles

This paper considers the cycle covering of complete graphs motivated by the design of survivable WDM networks, where the requests are routed on INF‐networks which are protected independently from each other. The problem can be stated as follows: for a given graph G, find a cycle covering of the edge set of K_n, where V(K_n) = V(G), such that each cycle in the covering satisfies the disjoint routing constraint (DRC7rpar;, relatively to G, which can be stated as follows: to each edge of K_n we associate in G a path and all the paths associated to the edges of a cycle of the covering must be vertex disjoint. Here we consider the case where G = C_n, a ring of size n and we want to minimize the number of cycles in the covering. We give optimal solutions for the problem as well as for variations of the problem, namely, its directed version and the case when the cycle length is fixed to 4. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 100–112, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10040     

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.     

Robustness of fat quantification using chemical shift imaging

The purpose of this study was to investigate the effect of parameter changes that can potentially lead to unreliable measurements in fat quantification. Chemical shift imaging was performed using spoiled gradient echo sequences with systematic variations in the following: two-dimensional/three-dimensional sequence, number of echoes, delta echo time, fractional echo factor, slice thickness, repetition time, flip angle, bandwidth, matrix size, flow compensation and field strength. Results indicated no significant (or significant but small) changes in fat fraction with parameter. The significant changes can be attributed to the known effects of T1 bias and two forms of noise bias.     

Mesoporous carbon supported ultrasmall palladium particles as highly active catalyst for Suzuki‐Miyaura reaction

A fast and efficient eco‐friendly two‐step preparation of a palladium‐containing mesoporous carbon catalyst ( C1 ) from green and readily available carbon precursors (phloroglucinol and glyoxal), a porogen template (pluronic F‐127) and PdCl₂ is described. Catalyst C1 contains ultra‐small Pd nanoparticles (1.2 nm) uniformly dispersed in the carbon network and shows an outstanding activity for Suzuki‐Miyaura reactions in pure water: extremely low amounts of palladium (10 μequiv. in most cases) are sufficient to afford almost palladium‐free products (containing <0.25 ppm of precious metal without further purification steps).     

Tetranuclear and Octanuclear Manganese Carboxylate Clusters: Preparation and Reactivity of (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(9)(H(2)O)] and Synthesis of (NBu(n)(4))(2)[Mn(8)O(4)(O(2)CPh)(12)(Et(2)mal)(2)(H(2)O)(2)] with a "Linked-Butterfly" Structure

The reaction of Mn(O(2)CPh)(2).2H(2)O and PhCO(2)H in EtOH/MeCN with NBu(n)(4)MnO(4) gives (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(9)(H(2)O)] (4) in high yield (85-95%). Complex 4 crystallizes in monoclinic space group P2(1)/c with the following unit cell parameters at -129 degrees C: a = 17.394(3) ?, b = 19.040(3) ?, c = 25.660(5) ?, beta = 103.51(1) degrees, V = 8262.7 ?(3), Z = 4; the structure was refined on F to R (R(w)) = 9.11% (9.26%) using 4590 unique reflections with F > 2.33sigma(F). The anion of 4 consists of a [Mn(4)(&mgr;(3)-O)(2)](8+) core with a "butterfly" disposition of four Mn(III) atoms. In addition to seven bridging PhCO(2)(-) groups, there is a chelating PhCO(2)(-) group at one "wingtip" Mn atom and terminal PhCO(2)(-) and H(2)O groups at the other. Complex 4 is an excellent steppingstone to other [Mn(4)O(2)]-containing species. Treatment of 4 with 2,2-diethylmalonate (2 equiv) leads to isolation of (NBu(n)(4))(2)[Mn(8)O(4)(O(2)CPh)(12)(Et(2)mal)(2)(H(2)O)(2)] (5) in 45% yield after recrystallization. Complex 5 is mixed-valent (2Mn(II),6Mn(III)) and contains an [Mn(8)O(4)](14+) core that consists of two [Mn(4)O(2)](7+) (Mn(II),3Mn(III)) butterfly units linked together by one of the &mgr;(3)-O(2)(-) ions in each unit bridging to one of the body Mn atoms in the other unit, and thus converting to &mgr;(4)-O(2)(-) modes. The Mn(II) ions are in wingtip positions. The Et(2)mal(2)(-) groups each bridge two wingtip Mn atoms from different butterfly units, providing additional linkage between the halves of the molecule. Complex 5.4CH(2)Cl(2) crystallizes in monoclinic space group P2(1)/c with the following unit cell parameters at -165 degrees C: a = 16.247(5) ?, b = 27.190(8) ?, c = 17.715(5) ?, beta = 113.95(1) degrees, V = 7152.0 ?(3), Z = 4; the structure was refined on F to R (R(w)) = 8.36 (8.61%) using 4133 unique reflections with F > 3sigma(F). The reaction of 4 with 2 equiv of bpy or picolinic acid (picH) yields the known complex Mn(4)O(2)(O(2)CPh)(7)(bpy)(2) (2), containing Mn(II),3Mn(III), or (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(7)(pic)(2)] (6), containing 4Mn(III). Treatment of 4 with dibenzoylmethane (dbmH, 2 equiv) gives the mono-chelate product (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(8)(dbm)] (7); ligation of a second chelate group requires treatment of 7 with Na(dbm), which yields (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(7)(dbm)(2)] (8). Complexes 7 and 8 both contain a [Mn(4)O(2)](8+) (4Mn(III)) butterfly unit. Complex 7 contains chelating dbm(-) and chelating PhCO(2)(-) at the two wingtip positions, whereas 8 contains two chelating dbm(-) groups at these positions, as in 2 and 6. Complex 7.2CH(2)Cl(2) crystallizes in monoclinic space group P2(1) with the following unit cell parameters at -170 degrees C: a = 18.169(3) ?, b = 19.678(4) ?, c = 25.036(4) ?, beta = 101.49(1) degrees, V = 8771.7 ?(3), Z = 4; the structure was refined on F to R (R(w)) = 7.36% (7.59%) using 10 782 unique reflections with F > 3sigma(F). Variable-temperature magnetic susceptibility studies have been carried out on powdered samples of complexes 2 and 5 in a 10.0 kG field in the 5.0-320.0 K range. The effective magnetic moment (&mgr;(eff)) for 2 gradually decreases from 8.61 &mgr;(B) per molecule at 320.0 K to 5.71 &mgr;(B) at 13.0 K and then increases slightly to 5.91 &mgr;(B) at 5.0 K. For 5, &mgr;(eff) gradually decreases from 10.54 &mgr;(B) per molecule at 320.0 K to 8.42 &mgr;(B) at 40.0 K, followed by a more rapid decrease to 6.02 &mgr;(B) at 5.0 K. On the basis of the crystal structure of 5 showing the single Mn(II) ion in each [Mn(4)O(2)](7+) subcore to be at a wingtip position, the Mn(II) ion in 2 was concluded to be at a wingtip position also. Employing the reasonable approximation that J(w)(b)(Mn(II)/Mn(III)) = J(w)(b)(Mn(III)/M(III)), where J(w)(b) is the magnetic exchange interaction between wingtip (w) and body (b) Mn ions of the indicated oxidation state, a theoretical chi(M) vs T expression was derived and used to fit the experimental molar magnetic susceptibility (chi(M)) vs T data. The obtained fitting parameters were J(w)(b) = -3.9 cm(-)(1), J(b)(b) = -9.2 cm(-)(1), and g = 1.80. These values suggest a S(T) = (5)/(2) ground state spin for 2, which was confirmed by magnetization vs field measurements in the 0.5-50.0 kG magnetic field range and 2.0-30.0 K temperature range. For complex 5, since the two bonds connecting the two [Mn(4)O(2)](7+) units are Jahn-Teller elongated and weak, it was assumed that complex 5 could be treated, to a first approximation, as consisting of weakly-interacting halves; the magnetic susceptibility data for 5 at temperatures >/=40 K were therefore fit to the same theoretical expression as used for 2, and the fitting parameters were J(w)(b) = -14.0 cm(-)(1) and J(b)(b) = -30.5 cm(-)(1), with g = 1.93 (held constant). These values suggest an S(T) = (5)/(2) ground state spin for each [Mn(4)O(2)](7+) unit of 5, as found for 2. The interactions between the subunits are difficult to incorporate into this model, and the true ground state spin value of the entire Mn(8) anion was therefore determined by magnetization vs field studies, which showed the ground state of 5 to be S(T) = 3. The results of the studies on 2 and 5 are considered with respect to spin frustration effects within the [Mn(4)O(2)](7+) units. Complexes 2 and 5 are EPR-active and -silent, respectively, consistent with their S(T) = (5)/(2) and S(T) = 3 ground states, respectively.     

5‐(3,4‐Dimethoxybenzyl)‐7‐isopropyl‐1,3,5‐triazepane‐2,6‐dione acetonitrile solvate refined using a multipolar atom model

The crystal structure of the title compound, C₁₆H₂₃N₃O₄·CH₃CN, was refined using a multipolar atom model transferred from an experimental electron‐density database. The refinement showed some improvement in crystallographic statistical indices compared with the independent atom model. The triazepane ring adopts a twist‐boat conformation. In the crystal structure, the molecule forms intermolecular contacts with 14 different neighbours. There are two N—H...O and one C—H...O intermolecular hydrogen bond.     

1H, 13C, and 73Ge NMR spectral analysis of substituted aryltrimethylgermanes

NMR chemical shifts of 1H, 13C, and 73Ge are reported for a series of monosubstituted aromatic trimethylgermanes of the type XC6H4Ge(CH3)3; X = p-N(CH3)2, p-OCH3, p-OC2H5, p-C(CH3)3, p-Si(CH3)3, p-Ge(CH3)3, p-Sn(CH3)3, p-CH3, m-CH3, -H, m-OCH3, p-Cl, p-Br, m-F, m-CF3, p-CF3, o-OCH3, and o-CH3. The relatively narrow 73Ge resonances show a strong correlation with Hammett sigma constants, with a correlation coefficient of 0.976 and 0.876 for 73Ge chemical shifts in meta- and para-substituted derivatives, respectively. The 13C chemical shifts of the methyl carbons bonded to germanium also display a relationship, with correlation coefficients of 0.904, 0.993, and 0.911 for para-, meta- and all derivatives, respectively. Comparisons of the Hammett plots for the homologous series XC6H4M(CH3)3; M = C, Si, Ge, Sn, show that, in general, correlation coefficients decrease while slopes increase significantly down the group, presumably reflecting the corresponding increase in chemical shift range of the group 14 atom. The Hammett constant derived for the p-Ge(CH3)3 group of +0.13 compares with the NMR-derived constants of -0.12 for p-C(CH3)3, +0.14 for p-Si(CH3)3, and -0.14 for p-Sn(CH3)3. The indication of electron release by carbon and tin can be rationalized through traditional hyperconjugative arguments for carbon and by the low electronegativity and consequent inductive effect of tin. The small electron attraction suggested by the positive constants for silicon and germanium can be simply, and perhaps naively, attributed to pi-acceptor interactions with the benzene ring.     

Testimony of the Correlation Between the Reactive Histidine Residue and the Arginase Catalytic Mechanism Using a Biochromatographic Concept and Mutagenesis Experiments

In a previous paper (Bagnost et al., J Chromatogr B Analyt Technol Biomed Life Sci 853:38–46, 2007), an arginase chromatographic support was developed to study the association mechanism of arginase (an enzyme which can reduce endothelial dysfunction and blood pressure rising in spontaneously hypertensive rats) with nor-NOHA a potential inhibitor of its activity. In this report mutagenesis experiments associated with this biochromatographic approach confirmed that the active-site residue Hist 141 is protonated as imidazolium cation. Hist 141 could function as a general acid to protonate the leaving amino group of l-ornithine during catalysis.