Generating vector solitary waves of Bose-Einstein Condensates in optical lattices

We describe the process of formation of vector solitary waves in Bose-Einstein Condensates located in optical lattices. The two components of the vector correspond to the envelope of the condensate mean field wavefunction in the Wannier basis of the first and second bands.     

An internal language for autonomous categories

We present an internal language for symmetric monoidal closed (autonomous) categories analogous to the typed lambda calculus as an internal language for cartesian closed categories. The language we propose is the term assignment to the multiplicative fragment of Intuitionistic Linear Logic, which possesses exactly the right structure for an autonomous theory. We prove that this language is an internal language and show as an application the coherence theorem of Kelly and Mac Lane, which becomes straightforward to state and prove. Finally, we extend the language with the natural numbers and show that this corresponds to a weak Natural Numbers Object in an autonomous category.     

Stepwise hapticity changes in sequential one-electron redox reactions of indenyl-molybdenum complexes: combined electrochemical, ESR, X-ray, and theoretical studies.

Reduction of the dication [(eta5-Ind)(Cp)Mo[P(OMe)3]2]2+ (1(2+)) and oxidation of the neutral complex (eta3-Ind)(Cp)Mo[P(OMe)3]2 (1) proceed through a one-electron intermediate, 1+. The structures of 1(2+) and 1 have been determined by X-ray diffraction studies, which show the slip-fold distortion angle, Omega, of the indenyl ring increasing from 4.1 degrees in 1(2+) to 21.7 degrees in 1. Cyclic voltammetry and bulk electrolysis were employed to define the thermodynamics and heterogeneous charge-transfer kinetics of reactions 1(2+) + e(-) <==> 1+ and 1+ + e(-) <==> 1: DeltaE1/2 = 113 mV in CH3CN and 219 mV in CH2Cl2/0.1 M [NBu4][PF6]; k(s) = 0.4 cm x s(-1) for 1(2+)/1+ couple, 1.0 cm x s(-1) for 1+/1 couple in CH3CN. ESR spectra of 1+ displayed a surprisingly large hyperfine splitting (7.4 x 10(-4) x cm(-1)) from a single 1H nucleus, and spectra of the partially deuterated indenyl analogue confirmed assignment of a(H) to the H2 proton of the indenyl ring. The related eta5 18-electron complexes [(eta5-Ind)(Cp)Mo(dppe)]2+ (2(2+)) (dppe = diphenylphosphinoethane) and (eta5-Ind)(Cp)Mo(CN)2 (3) may also be reduced in two successive one-electron steps; ESR spectra of the radicals 2+ and 3- showed a similarly large a(H2) (8.7 x 10(-4) and 6.4 x 10(-4) x cm(-1), respectively). Molecular orbital calculations (density functional theory, DFT, and extended Hückel, EH) predict metal-indenyl bonding in 1+ that is approximately midway between that of the eta5 and eta3 hapticities (e.g., Omega = 11.4 degrees ). DFT results show that the large value of a(H2) arises from polarization of the indenyl-H2 by both inner-sphere orbitals and the singly occupied molecular orbital (SOMO) of 1+. The measured ks values are consistent with only minor inner-sphere reorganizational energies being necessary for the electron-transfer reactions, showing that a full eta5/eta3 hapticity change may require only small inner-sphere reorganization energies when concomitant with a pair of stepwise one-electron-transfer processes. The indenyl ligand in 1+ is best described as donating approximately four pi-electrons to Mo by combining a traditional eta3 linkage with two "half-strength" Mo-C bonds.     

Finding borders between coding and noncoding DNA regions by an entropic segmentation method

We present a new computational approach to finding borders between coding and noncoding DNA. This approach has two features: (i) DNA sequences are described by a 12-letter alphabet that captures the differential base composition at each codon position, and (ii) the search for the borders is carried out by means of an entropic segmentation method which uses only the general statistical properties of coding DNA. We find that this method is highly accurate in finding borders between coding and noncoding regions and requires no "prior training" on known data sets. Our results appear to be more accurate than those obtained with moving windows in the discrimination of coding from noncoding DNA.     

Structural modification of fullerene thin films by highly charged iron ions

In this paper, the results of structural modification of fullerene thin films bombarded by highly charged iron ions (Fe⁶⁺) are presented. The properties of as-deposited and irradiated fullerene thin films have been investigated by Raman spectroscopy, UV/Vis spectrophotometry and atomic force microscopy (AFM). The results of Raman spectroscopy have indicated structural changes of irradiated thin films depending on fluences. It was found that iron doped fullerene films are dominated by sp³ rather than sp² after bombardment which might be due to formation of nanodiamond structures. AFM analysis showed that the ion beam had destroyed the surface ordering. The optical band gap was found to be in the range of 0.6 to 1.4 eV for irradiated films by Fe⁶⁺ ions at the highest fluences. PACS 61.48.+c; 78.30.-j; 79.20.Rf     

Transition metal coordination compounds with the dithiooxalate ligand. Synthesis,spectroscopic studies,crystal structure,and bonding of (C5H5NH)2[Ni(S2C2O2)2]

Several new compounds belonging to the family of bis(dithiooxalato)-nickelate(II) complex anion with the general formula (BH)₂[Ni(S₂C₂O₂)₂], where B=pyridine, 3-methylpyridine, 3-ethylpyridine, 4-methylpyridine, and 4-ethylpyridine (hereafter abbreviated as PYNIDT, M3NIDT, E3NIDT, M4NIDT, and E4NIDT, respectively) have been prepared. PYNIDT, M3NIDT, and E3NIDT are isostructural between them and different from the two other compounds, M4NIDT and E4NIDT, which are also isostructural. All of these compounds crystallize in the monoclinic system, space groupP2₁/n withZ=2. Crystal parameters for PYNIDT are:a=5.793(3),b=14.280(5),c=11.222(3) Å,=97.29(4)°,V=920.8(9) ų,F(000)=468,D _x =1.66,D _o=1.65(1) Mg m^–3,R=0.048, andR _w =0.057 for 1236 observed reflections. The IR and UV-V spectra show that the organic bases are protonated and the anion presents the well-known spectrum for the bis(dithiooxalato)-nickelate(II) anions. Thermogravimetric studies indicate that the compounds are anhydrous. The structure solution of PYNIDT confirms that this compound contains discrete quasi-planar complex [Ni(S₂C₂O₂)₂]^2– anions and (C₅H₅NH)⁺ planar cations linked through hydrogen bonds. The structure stacks into layers where the ions are associated into cationanioncation entities through bifurcated hydrogen bonds.     

Chemical Reaction Monitoring using Zero-Field Nuclear Magnetic Resonance Enables Study of Heterogeneous Samples in Metal Containers

We demonstrate that heterogeneous/biphasic chemical reactions can be monitored with high spectroscopic resolution using zero-field nuclear magnetic resonance spectroscopy. This is possible because magnetic susceptibility broadening is negligible at ultralow magnetic fields. We show the two-step hydrogenation of dimethyl acetylenedicarboxylate with para-enriched hydrogen gas in conventional glass NMR tubes, as well as in a titanium tube. The low frequency zero-field NMR signals ensure that there is no significant signal attenuation arising from shielding by the electrically conductive sample container. This method paves the way for in situ monitoring of reactions in complex heterogeneous multiphase systems and in reactors made of conductive materials while maintaining resolution and chemical specificity.     

On some characterizations of preinvex fuzzy mappings

Jeyakumar (Methods Oper. Res. 55:109–125, 1985) and Weir and Mond (J. Math. Anal. Appl. 136:29–38, 1988) introduced the concept of preinvex function. The preinvex functions have some interesting properties. For example, every local minimum of a preinvex function is a global minimum and nonnegative linear combinations of preinvex functions are preinvex. Invex functions were introduced by Hanson (J. Math. Anal. Appl. 80:545–550, 1981) as a generalization of differentiable convex functions. These functions are more general than the convex and pseudo convex ones. The type of invex function is equivalent to the type of function whose stationary points are global minima. Under some conditions, an invex function is also a preinvex function. Syau (Fuzzy Sets Syst. 115:455–461, 2000) introduced the concepts of pseudoconvexity, invexity, and pseudoinvexity for fuzzy mappings of one variable by using the notion of differentiability and the results proposed by Goestschel and Voxman (Fuzzy Sets Syst. 18:31–43, 1986). Wu and Xu (Fuzzy Sets Syst 159:2090–2103, 2008) introduced the concepts of fuzzy pseudoconvex, fuzzy invex, fuzzy pseudoinvex, and fuzzy preinvex mapping from \(\mathbb{R}^{n}\) to the set of fuzzy numbers based on the concept of differentiability of fuzzy mapping defined by Wang and Wu (Fuzzy Sets Syst. 138:559–591, 2003). In this paper, we present some characterizations of preinvex fuzzy mappings. The necessary and sufficient conditions for differentiable and twice differentiable preinvex fuzzy mapping are provided. These characterizations correct and improve previous results given by other authors. This fact is shown with examples. Moreover, we introduce additional conditions under which these results are valid.     

The Maximum Number of Edges in Geometric Graphs with Pairwise Virtually Avoiding Edges

Let G be a geometric graph on n vertices that are not necessarily in general position. Assume that no line passing through one edge of G meets the relative interior of another edge. We show that in this case the number of edges in G is at most 2n?3.