Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation

Set-Valued and Variational Analysis - R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or...     

Synthesis,spectral, electrochemical and magnetic properties of new asymmetric dicopper(II) complexes bearing chemically distinct coordination sites

Two new unsymmetrical binucleating ligands, 2-[bis(3-N, N-dimethylaminopropyl)-aminomethyl]-6-[prolin-1-yl)methyl]-4-bromophenol [H ₂L¹] and 2-[bis(3-N, N -dimethylaminopropyl)aminomethyl]-6-[prolin-1-yl)methyl]-4-methylphenol [H₂L²], and their dicopper(II) complexes with different exogenous bridging motifs (OAc, Br and Cl) have been prepared and characterized by spectral, electrochemical, magnetic and e.p.r. studies. Electrochemical studies indicate the presence of two irreversible reduction peaks in the cathodic region. Variable temperature magnetic susceptibility studies of the complexes show that the extent of antiferromagnetic coupling increases in the order: OAc^–< Cl^–< Br^–. Broad isotropic or axial symmetric spectral features are observed in powder e.p.r. spectra of the complexes at 77K. A comparison of the electrochemical and magnetic behaviour of the complexes derived from the ligands is discussed on the basis of an exogenous bridge as well as the substituent at the para position of the phenolic ring.     

New unsymmetrical μ-phenoxo bridged binuclear copper(II) complexes

A series of binuclear Cu^II complexes [Cu₂XL] ⁿ⁺ having two copper(II) ions bridged by different motifs (X = OH^–, MeCO₂ ^–, or Cl^–) have been prepared using the ligands: H₂L¹ = 4-methyl-2-[N-(2-{dimethylamino}ethyl-N-methyl)aminomethyl]-6-[(prolin-1-yl)methyl]phenol, H₂L² = 4-nitro-2-[N-(2-{dimethylamino}ethyl-N-methyl)aminomethyl]-6-[(prolin-1-yl)methyl]phenol, H₂L³ = 4-methyl-2-[N-(2-{diethylamino}ethyl-N-ethyl)aminomethyl]-6-[(prolin-1-yl)methyl]phenol and H₂L⁴ = 4-nitro-2-[N-(2-{diethylamino}ethyl-N-ethyl)aminomethyl]-6-[(prolin-1-yl)methyl]phenol. The complexes have been characterized by spectroscopic, analytical, magnetic and electrochemical measurements. Cryomagnetic investigations (80–300 K) revealed anti-ferromagnetic exchange between the Cu^II ions (–2J in the range –50 to –182 cm^–1). The strength of anti-ferromagnetic coupling lies in the order: OAc > OH > Cl. Cyclic voltammetry revealed the presence of two redox couples, assigned to Cu^II/Cu^II/Cu^II/Cu^I/Cu^I/Cu^I. The first reduction potential is sensitive to electronic effects from the aromatic ring substituents and steric effect on the donor nitrogens (side arm) of the ligand systems.     

A novel discrete dinuclear copper(II)–gadolinium(III) complex derived from a Schiff base ligand [Cu(salbn)Gd(NO3)3·H2O] (salbn): N,N′-butylenebis(salicylideaminato)

The synthesis, X-ray and e.p.r. spectral studies of a 3d–4f couple are described here. The crystal structure of [Cu(salbn)Gd(NO₃)₃·H₂O], (2), salbn = N,N-butylenebis(salicylideaminato), has been determined by X-ray crystallography. Compound (2) crystallizes in the monoclinic system, space group p21/n, with a = 9.025(1), b = 22.912(1), c = 12.790(1) Å, = 99.36(1), Z = 4. The deviations of the four coordinating atoms (O(1)O(2)N(1) and N(2) of salbn and the copper atom is displaced from the plane in spite of the lack of any apical ligand. The gadolinium(III) ion is nine-coordinated by the two oxygen atoms of the salbn moiety, three bidentate nitrate ions and one water molecule. The geometry of Gd^III can be described as a square antiprism, in which compound Cu^II and Gd^III are bridged by the two phenolic oxygens of salbn. The Cu^II–Gd^III distance is 3.269(1) Å. The bridging core CuO2Gd is a butterfly shape. Significant distortion was observed for the complex having the larger diamino string. The title compound exhibits seven e.s.r. transitions with |D| = 0.0467 cm^–1, which demonstrates the existence of zero field splitting. This outcome indicates that compound (2) consists of a perfectly isolated dinuclear Cu–Gd core and steric bulk alters the dihedral angle in the Cu–O–Gd bridge.     

Synthesis of flexible ligands for assembling two metals in close proximity. Magnetic,electrochemical and spectral properties of binuclear copper (II) complexes with different exogenous bridging motifs

Binuclear Cu^II complexes having new flexible heptadentate ligands 2,6-bis{[bis(3,3-N,N-dimethylaminopropyl)amino]methyl}-4-bromophenol [HL¹], 2,6-bis(3,3-N,N-dimethylaminopropyl)amino]methyl}-4-methylphenol [HL²], and 2,6-bis{[bis(3,3-N,N-dimethylaminopropyl)amino]methyl}-4-methoxyphenol [HL³], capable of assembling two copper ions in close proximity have been synthesized. Comparisons of the charge-transfer (CT) features, observed in electronic spectra of these complexes, are correlated with the electronic effect on the aromatic ring of the ligand systems. Cyclic voltammetry has revealed the existence of two reduction couples,

Synthesis,electrochemical and e.p.r. spectral studies of binuclear copper(II) complexes with new pentadentate L-proline-based binucleating ligands

The synthesis, reduction, optical and e.p.r. spectral properties of a series of new binuclear copper(II) complexes, containing bridging moieties (OH^–, MeCO₂ ^–, NO₂ ^–, and N₃ ^–), with new proline-based binuclear pentadentate Mannich base ligands is described. The ligands are: 2,6-bis[(prolin-1-yl)methyl]4-bromophenol [H₃L¹], 2,6-bis[(prolin-1-yl)methyl]4-t-butylphenol [H₃L²] and 2,6-bis[(prolin-1-yl)methyl]4-methoxyphenol [H₃L³]. The exogenous bridging complexes thus prepared were hydroxo: [Cu₂L¹(OH)(H₂O)₂] · H₂O (1a), [Cu₂L²(OH)(H₂O)₂] · H₂O (1b), [Cu₂L³(OH)(H₂O)₂] · H₂O (1c), acetato [Cu₂L¹(OAc)] · H₂O (2a), [Cu₂L²(OAc)] · H₂O (2b), [Cu₂L³(OAc)] · H₂O (2c), nitrito [Cu₂L¹(NO₂)(H₂O)₂] · H₂O (3a), [Cu₂L²(NO₂)(H₂O)₂] · H₂O (3b), [Cu₂L³(NO₂)(H₂O)₂] · H₂O (3c) and azido [Cu₂L¹(N₃)(H₂O)₂] · H₂O (4a), [Cu₂L²(N₃)(H₂O)₂] · H₂O (4b) and [Cu₂L³(N₃)(H₂O)₂] · H₂O (4c). The complexes were characterized by elemental analysis and by spectroscopy. They exhibit resolved copper hyperfine e.p.r. spectra at room temperature, indicating the presence of weak antiferromagnetic coupling between the copper atoms. The strength of the antiferromagnetic coupling lies in the order: NO₂ N₃ OH OAc. Cyclic voltammetry revealed the presence of two redox couples Cu^IICu^II Cu^IICu^I Cu^ICu^I. The conproportionality constant K _con for the mixed valent Cu^IICu^I species for all the complexes have been determined electrochemically.     

Interstitial Substitution of VO(II) in Hexaaquazinc(diaquabismalonato)zincate: A Rare Observation

Single-crystal electron paramagnetic resonance (EPR) studies of VO(II) doped in hexaaquazinc(diaquabismalonto)zincate have been performed at room temperature. Single-crystal rotations along the three orthogonal axes show the presence of a single site in an interstitial position and the location has been identified from crystal data of the host lattice. The spin-Hamiltonian parameters calculated from EPR spectra are g _xx  = 1.973, g _yy  = 1.972, g _zz  = 1.930, A _xx  = 7.05 mT, A _yy  = 6.85 mT, A _zz  = 18.93 mT. Molecular orbital coefficients β ² = 0.71 and ε ² = 0.62 have been calculated and reveal a moderately covalent metal–ligand bond. Optical and EPR data have been used to obtain crystal field parameters, admixture and molecular orbital coefficients.     

Observation of a Substitutional Location for VO(II) in Hexaaquazinc(diaquabismalonato)zincate in Different Crystals,in Addition to Interstitial: An Unusual Observation

Single-crystal electron paramagnetic resonance (EPR) studies of VO(II) doped in hexaaquazinc(diaquabismalonto)zincate have indicated interstitial location for vanadyl, which was a rare observation, considering the structure of the host lattice (K. Arun Prasath Lingam, S. Mithira and P. Sambasiva Rao, Appl. Magn. Reson. 38:295, 2010). However, substitutional location is noticed in a different crystal, in which interstitial resonances are almost absent. Generally, both types of resonances will be noticed in the same crystal. The spin Hamiltonian parameters calculated from the EPR spectra for substitutional location are: g _xx  = 1.981, g _yy  = 1.976, g _zz  = 1.941, A _xx  = 7.96 mT, A _yy  = 6.09 mT, and A _zz  = 17.83 mT. Crystal-field parameters, admixture and molecular orbital coefficients have been calculated from optical data, which reveal a moderately covalent metal–ligand bonding.