A new characterization of Sobolev spaces on $${\mathbb{R}^{n}}$$

In this paper we present a new characterization of Sobolev spaces on . Our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of Euclidean space. An interesting feature of our condition is that depends only on the metric of and the Lebesgue measure, so that one can define Sobolev spaces of any order of smoothness on any metric measure space.     

Hyperbolic polygons of minimal perimeter with given angles

We prove that, among all convex hyperbolic polygons with given angles, the perimeter is minimized by the unique polygon with an inscribed circle. The proof relies on work of Schlenker (Trans Am Math Soc 359(5): 2155–2189, 2007).     

Linear Frameworks for Block Ciphers

Inthis paper we generalize the structure of the ciphers Shark, Square, BKSQ, Crypton and Rijndael. We show that the linearcomponents play an essential role in the effect of the nonlinearS-boxes in providing resistance against differential and linearcryptanalysis and provide upper bounds for the probability ofdifferential characteristics and the correlation of linear approximationsfor the general structure. We show how good linear componentscan be constructed efficiently from Maximum-Distance Separablecodes. The presented block cipher structure can make optimaluse of a wide range of processor word lengths and its parallelismallows very fast dedicated hardware implementations. Cipherswith variable block length can be constructed by varying certainparameters in the presented structure.     

Synthesis,crystal structures and magnetic behaviors of two dicyanamide bridged di- and polynuclear complexes of cobalt(II) derived from 2,4,6-tris(2-pyridyl)1,3,5-triazine and imidazole

Two new dicyanamido-bridged di- and polynuclear complexes of Co(II), [Co(dca)(tptz)(H₂O)]₂·2(ClO₄) (1) and [Co(dca)₂(imz)₂]_n (2) [dca, dicyanamide; tptz, 2,4,6-tris(2-pyridyl)1,3,5-triazine; and imz, imidazole] have been synthesized and characterized structurally, as well as magnetically. The X-ray single crystal structure determination of complex 1 shows that two symmetry related octahedral Co(II) ions are separated by dca ligand and other coordination sites are satisfied by tptz and aquo ligands. Each dinuclear unit is associated with each other by intramolecular hydrogen bonding interactions, giving rise to a 1D chain structure. On the other hand complex 2 is a 1D coordination polymer having [Co(II)(imz)₂] units connected by double bridging dca ligands. These 1D chains interact through face-to-face π–π stacking interactions of the imz rings extending the dimensionality to a 2D supramolecular network. The variable temperature (300–2 K) magnetic measurements of both compounds reveal that dicyanamide exhibits a weak antiferromagnetic interaction between the metal centers.     

Syntheses,structural analyses,and magneto-structural correlations of three polymeric Fe(II) complexes with azide ligand

Three new metal-organic polymeric complexes, [Fe(N(3))(2)(bpp)(2)] (1), [Fe(N(3))(2)(bpe)] (2), and [Fe(N(3))(2)(phen)] (3) [bpp = (1,3-bis(4-pyridyl)-propane), bpe = (1,2-bis(4-pyridyl)-ethane), phen = 1,10-phenanthroline], have been synthesized and characterized by single-crystal X-ray diffraction studies and low-temperature magnetic measurements in the range 300-2 K. Complexes 1 and 2 crystallize in the monoclinic system, space group C2/c, with the following cell parameters: a = 19.355(4) A, b = 7.076(2) A, c = 22.549(4) A, beta = 119.50(3) degrees, Z = 4, and a = 10.007(14) A, b = 13.789(18) A, c = 10.377(14) A, beta = 103.50(1) degrees, Z = 4, respectively. Complex 3 crystallizes in the triclinic system, space group P(-)1, with a = 7.155(12) A, b = 10.066(14) A, c = 10.508(14) A, alpha = 109.57(1) degrees, beta = 104.57(1) degrees, gamma = 105.10(1) degrees, and Z = 2. All coordination polymers exhibit octahedral Fe(II) nodes. The structural determination of 1 reveals a parallel interpenetrated structure of 2D layers of (4,4) topology, formed by Fe(II) nodes linked through bpp ligands, while mono-coordinated azide anions are pendant from the corrugated sheet. Complex 2 has a 2D arrangement constructed through 1D double end-to-end azide bridged iron(II) chains interconnected through bpe ligands. Complex 3 shows a polymeric arrangement where the metal ions are interlinked through pairs of end-on and end-to-end azide ligands exhibiting a zigzag arrangement of metals (Fe-Fe-Fe angle of 111.18 degrees) and an intermetallic separation of 3.347 A (through the EO azide) and of 5.229 A (EE azide). Variable-temperature magnetic susceptibility data suggest that there is no magnetic interaction between the metal centers in 1, whereas in 2 there is an antiferromagnetic interaction through the end-to-end azide bridge. Complex 3 shows ferro- as well as anti-ferromagnetic interactions between the metal centers generated through the alternating end-on and end-to-end azide bridges. Complex 1 has been modeled using the D parameter (considering distorted octahedral Fe(II) geometry and with any possible J value equal to zero) and complex 2 has been modeled as a one-dimensional system with classical and/or quantum spin where we have used two possible full diagonalization processes: without and with the D parameter, considering the important distortions of the Fe(II) ions. For complex 3, the alternating coupling model impedes a mathematical solution for the modeling as classical spins. With quantum spin, the modeling has been made as in 2.     

Two New Antiferromagnetic Nickel(II) Complexes Bridged by Azido Ligands in the Cis Position. Effect of the Counteranion on the Crystal Structure and Magnetic Properties

Two new nickel(II) end-to-end azido-bridged compounds, cis-catena-[NiL(2)(&mgr;-N(3))](n)()(ClO(4))(n)().nH(2)O (1) and [Ni(2)L(4)(&mgr;-N(3))(2)](PF(6))(2) (2), were synthesized and characterized; L is 2-(aminoethyl)pyridine. The crystal structures of 1 and 2 were solved. Complex 1: monoclinic system, space group P2(1)/a, a = 8.637(2) ?, b = 18.9995(7) ?, c = 12.3093(7) ?, beta = 105.92(2) degrees, Z = 4. Complex 2: triclinic system, space group P&onemacr;, a = 9.139(7) ?, b = 10.124(3) ?, c = 12.024(2) ?, alpha = 70.407(14) degrees, beta = 84.19(2) degrees, gamma = 67.67(4) degrees, Z = 1. In the two complexes the nickel atom is situated in a similarly distorted octahedral environment. The two complexes are different; 1 is a one-dimensional helicoidal complex with the two L ligands and the two end-to-end azido bridges in a cis arrangement while complex 2 is a dinuclear system with two end-to-end azido bridges, indicating the extreme importance of the counteranion present (ClO(4)(-) for 1 and PF(6)(-) for 2). The magnetic properties of the two compounds were studied by susceptibility measurements vs temperature. The chi(M) vs T plot for 1 shows the shape for a weakly antiferromagnetically coupled nickel(II) one-dimensional complex without a maximum until 4 K. In contrast, for complex 2 the shape of the chi(M) vs T curve shows a maximum near 40 K, indicating medium antiferromagnetic coupling. From the spin Hamiltonian -J(ij)()S(i)()S(j)(), J values for 1 and 2 were less than -1 and -29.1 cm(-)(1), respectively. The magnetic behavior for 1 and 2 may be explained in terms of the overlap between magnetic orbitals, taking into account the torsion of the Ni(II) atoms and azido-bridging ligands in the two structures.     

Extending colorings of locally planar graphs

Suppose G is a graph embedded in S_g with width (also known as edge width) at least 264(2^g−1). If P ⊆ V(G) is such that the distance between any two vertices in P is at least 16, then any 5‐coloring of P extends to a 5‐coloring of all of G. We present similar extension theorems for 6‐ and 7‐chromatic toroidal graphs, for 3‐colorable large‐width graphs embedded on S_g with every face even‐sided, and for 4‐colorable large‐width Eulerian triangulations. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 105–116, 2001     

Time shift correction in second-order liquid chromatographic data with iterative target transformation factor analysis

When the generalized rank annihilation method (GRAM) is applied to liquid chromatographic data with diode-array detection, an important problem is the time shift of the peak of the analyte in the test sample. This problem leads to erroneous predictions. This time shift can be corrected if a time window is selected so that the chromatographic profile of the analyte in the test sample is trilinear with the peak of the analyte in the calibration sample. In this paper we present a new method to determine when this condition is met. This method is based on the curve resolution with iterative target transformation factor analysis (ITTFA). The calibration and test matrices are independently decomposed into profiles and spectra, and aligned before GRAM is applied. Here we study two situations: first, when the calibration matrix has one analyte and second, when it has two analytes. When the calibration matrix has two analytes, we selectively determine the time window for the analyte to be quantified. There were considerably fewer prediction errors after correction.     

Determination of S-containing drug metabolites from in vitro and in vivo metabolism studies by using LC-ICP/MS

Recently, liquid chromatography coupled to inductively coupled plasma mass spectrometry (LC-ICP/MS) has been introduced to deal with some applications in the field of pharmaceutical, biomedical, and clinical analysis. In the case of drug research, the number of drugs and their metabolites containing detectable elements is quite limited. In this paper, LC-ICP/MS has been demonstrated to be suitable for the determination of S-containing drugs and their metabolites. In order to minimize the interference of polyatomic oxygen (m/z 32), the indirect detection of S, by means of the SO(+) ion (m/z 48), was optimized. For quantification purposes, it has been encountered that the percentage of organic solvent in the mobile phase strongly affects the sensitivity. Here, corrective strategies based on calibration curves established at different solvent concentrations (solvent-zone quantification) and post-column gradient compensation have been proposed to circumvent sensitivity variations. Results obtained have shown that suitable calibration models have been built for any compound regardless of the solvent percentage at which it is eluted from the chromatographic column. To prove the applicability of this methodology, the metabolism of ethacrynic acid and tiotropium bromide has been studied in vitro and in vivo. In the first case, ethacrynic acid does not contain S in its structure, however, the major route of metabolism for this compound consists of the formation of glutathione adduct and its further degradation. In the second case, tiotropium bromide contains two S atoms in its structure.