Universal inequalities for eigenvalues of a system of elliptic equations of the drifting Laplacian

Let \(\Omega \) be a bounded domain in a n-dimensional Euclidean space \(\mathbb {R}^{n}\). We study eigenvalues of an eigenvalue problem of a system of elliptic equations of the drifting Laplacian

$$\begin{aligned} \left\{ \begin{array}{ll} \mathbb {L_{\phi }}\mathbf{{u}} + \alpha (\nabla (\mathrm {div}{} \mathbf{{u}}) - \nabla \phi \mathrm {div}{} \mathbf{{u}})= -\bar{\sigma }\mathbf{{u}}, &{} \hbox {in} \,\Omega ; \\ \mathbf{{u}}|_{\,\partial \Omega }=0. \end{array} \right. \end{aligned}$$

Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, a universal inequality for lower order eigenvalues of the problem is also derived. Finally, we prove an universal inequality type Ashbaugh and Benguria for the drifting Laplacian on Riemannian manifold immersed in an unit sphere or a projective space.

     

Biimidazole and bis(amide)bipyridine molybdenum carbonyl complexes as anions receptors

Compounds [Mo(CO)4(N-N)] (N-N = 4,4'-bis((4-methylphenyl)carbamoyl)-2,2'-bipyridine, bipy', 1; or 2,2'-biimidazole, H2biim, 2), [MoCl(eta3-methallyl)(CO)2(N-N)] (N-N = bipy', 3; H2biim, 4), and [Mo(eta3-methallyl)(CNtBu)(CO2)(N-N)]BAr'4 (Ar' = 3,5-bis(trifluoromethyl)phenyl; N-N= bipy', 5; H2biim, 6) were synthesized and characterized, and their behavior toward anions was investigated in solution (IR and 1H NMR) and in solid state (X-ray diffraction).     

Enantioselective synthesis of sphingadienines and aromatic ceramide analogs

A new approach to the synthesis of sphingoid bases has been developed. The strategy is based on Sonogashira coupling of a chiral acetylenic carbamate that can be prepared in enantiomerically enriched form from 2,3-epoxy-4-pentyn-1-ol, which is readily accessible by Sharpless asymmetric epoxidation. Several N-Boc-sphingadienines and aromatic ceramide analogs have been synthesized.     

Imidazole to NHC rearrangements at molybdenum centers: an experimental and theoretical study

Both manganese and rhenium complexes of the type [M(bipy)(CO)(3)(N-RIm)](+) (bipy=2,2'-bipyridine) undergo deprotonation of the central CH group of the N-alkylimidazole (N-RIm) ligand when treated with a strong base. However, the outcome of the reaction is very different for either metal. For Mn, the addition of the equimolar amount of an acid to the product of the deprotonation affords an N-heterocyclic carbene (NHC) complex, whereas for Re, once the deprotonation of the central imidazole CH group has occurred, the bipy ligand undergoes a nucleophilic attack on an ortho carbon, affording the C-C coupling product. The extension of these studies to pseudo-octahedral [Mo(η(3)-allyl)(bipy)(CO)(2)(N-RIm)](+) complexes has allowed us to isolate cationic NHC complexes (Mn(I)-type behavior), as well as their neutral imidazol-2-yl precursors. Theoretical studies of the reaction mechanisms using DFT computations were carried out on the deprotonation of [Mn(bipy)(CO)(3)(N-PhIm)](+), [Re(bipy)(CO)(3) (N-MesIm)](+), and [Mo(η(3)-C(4)H(7))(bipy)(CO)(2) (N-MesIm)](+) complexes (Mes=mesityl) at the B3LYP/6-31G(d) (LANL2DZ for Mn, Re, and Mo) level of theory. Our results explain why different products have been found experimentally for Mn, Mo, and Re complexes. For Re, the process leading to a C-C coupling product is clearly more favored than those forming an imidazol-2-yl product. In contrast, for Mn and Mo complexes, the lower stabilizing interaction between the central imidazole and ortho bipy C atoms, along with the higher lability of the ligands, make the formation of an NHC-type product kinetically more accessible, in good agreement with experimental findings.     

Handling occlusion in object tracking in stereoscopic video sequences

In this paper, we study simple algorithms for three-dimensional tracking objects in a stereo video sequence, by combining optical flow and stereo vision. This method is not able to handle the occlusion of the moving objects when they disappear due to an obstacle. To improve the performance of this method, we propose the use of adaptive filters and neural networks to predict the expected instantaneous velocities of the objects. In the previous works, this system has been successfully proved in two-dimensional tracking.     

A totally stereocontrolled route to N-methyl-γ-amino-β-hydroxy acids: Asymmetric synthesis of the amino acid component of hapalosin

A new approach to the synthesis of N-methyl-γ-amino-β-hydroxy acids, compounds that are essential components of several depsipeptides exhibiting highly interesting therapeutic profiles, is presented. Relevant steps in the synthetic sequence involve the totally stereoselective preparation of a protected aminoalkyl epoxide from a highly enantiopure 2,3-epoxy alcohol, efficient N-methylation and three-step conversion to the desired N-methyl amino acid. The method is exemplified by the enantioselective synthesis of (3R,4S)-4-(N-methylamino)-3-hydroxy-5-phenylpentanoic acid in two differently protected forms.     

Two‐electron atomic systems confined within spheroidal boxes

The direct variational method is used to estimate some interesting physical properties of the He atom and the Li⁺ ion confined within impenetrable spheroidal boxes. A comparative investigation of the ground‐state energy, pressure, polarizability, dipole, and quadrupole moments with those of the He atom inside boxes with paraboloidal walls is made. The overall results show a similar qualitative behavior. However, for Li⁺ there are quantitative differences on such properties due to its major nuclear charge, as expected. The trial wave function is constructed as a product of two hydrogenic wave functions adapted to the geometry of the confining boxes. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 509–515, 2000     

Activation of Aromatic C−C Bonds of 2,2’‐Bipyridine Ligands

4,4’‐Disubstituted‐2,2′‐bipyridine ligands coordinated to Mo^II and Re^I cationic fragments become dearomatized by an intramolecular nucleophilic attack from a deprotonated N‐alkylimidazole ligand in cis disposition. The subsequent protonation of these neutral complexes takes place on a pyridine carbon atom rather than at nitrogen, weakening an aromatic C?C bond and affording a dihydropyridyl moiety. Computational calculations allowed for the rationalization of the formation of the experimentally obtained products over other plausible alternatives.