Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero-sum case we have proved the existence of a Nash equilibrium.

Evolutionary games with two timescales

We consider a two timescale model of learning by economic agents wherein active or 'ontogenetic' learning by individuals takes place on a fast scale and passive or 'phylogenetic' learning by society as a whole on a slow scale, each affecting the evolution of the other. The former is modelled by the Monte Carlo dynamics of physics, while the latter is modelled by the replicator dynamics of evolutionary biology. Various qualitative aspects of the dynamics are studied in some simple cases, both analytically and numerically, and its role as a useful modelling device is emphasized.

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

Reversible Water Intercalation Accompanied by Coordination and Color Changes in a Layered Metal-Organic Framework

A new two-dimensional 3d-4f mixed-metal mixed dicarboxylate (homocyclic and heterocyclic) of the formula [Gd2(H2O)2Ni(H2O)2(1,2-bdc)2(2,5-pydc)2] 3 8H2O (1; 1,2-H2bdc = 1,2-benzenedicarboxylic acid and 2,5-H2pydc = 2,5- pyridinedicarboxylic acid) has been prepared by employing the hydrothermal method. The structure has infinite onedimensional-Gd-O-Gd- chains formed by the edge-shared GdO9 polyhedral units, resulting exclusively from the connectivity between the Gd3+ ions and the 1,2-bdc units. The chains are connected by the [Ni(H2O)2(2,5-pydc)2]2- metalloligand, forming the two-dimensional layer arrangements. The stacking of the layers creates hydrophilic and hydrophobic spaces in the interlamellar region. A one-dimensional water ladder structure, formed by the extraframework water molecules, occupies the hydrophilic region while the benzene ring of 1,2-bdc occupies the hydrophobic region. To the best of our knowledge, the present compound represents the first example of a 3d-4f mixed-metal carboxylate in which two different aromatic dicarboxylate anions act as the linkers. The stabilization energies of the water clusters have been evaluated using density functional theory calculations. The water molecules in 1 are fully reversible accompanied by a change in color (greenish blue to brown) and coordination around Ni2+ ions (octahedral to distorted tetrahedral).

Mode of Coordination and Chemical Reactivity of Alpha-Imine Hydrasone Ligands

Interaction of nickel(I1) and copper(I1) complexes of 4,9-dimethy1-5,8-diazadodeca-4,8diene-2,1 ldione, Ni(baen) and 4,6,9-trimethyl-5, 8diazadodeca-4,8-diene-2,ll-dione, Ni(bapn), with arene diazonium chlorides in buffered solutions of methanol yielded metal derivatives of glyoxaliminearylhydrazones. This typical electrophilic addition at the 3-carbon of the complex occurs owing to the pseudo aromatic behaviour of the chelate ring. A mechanism which predicts the attack of the diazonium cation through the coordination shell of the metal is well documented from the available experimental evidences. The chemical reactivity of a few complexes with a single residual non-substituted y-carbon is reasonably manifested by their reaction with phenyl isocyanate.

Self-assembly of three new coordination complexes: Formation of 2-D square grid, 1-D chain and tape structures

Three distinct coordination complexes, viz., [Co(imi)(2)(tmb)(2)] (1) [where imi = imidazole], {[Ni(tmb)(2)(H2O)(3)]center dot 2H(2)O}(n) (2) and [Cu-2(mu-tmb)(4)(CH3OH)(2)] (3), have been synthesized hydrothermally by the reactions of metal acetates,2,4,6-trimethylbenzoic acid (Htmb) and with or without appropriate amine. The Ni analogue of 1 and the Co analogue of 2 have also been synthesized. X-ray single-crystal diffraction suggests that complex 1 represents discrete mononuclear species and complex 2 represents a 1D chain coordination polymer in which the Ni(H) ions are connected by the bridging water molecules. Complex 3 represents a neutral dinuclear complex. In 1, the central metal ions are associated by the carboxylate moiety and imidazole ligands, whereas the central metal atom is coordinated to the carboxylate moiety and the respective solvent molecules in 2 and 3. In 3, the four 2,4,6-trimethylbenzoate moieties act as a bridge connecting two copper (11) ions and the 0 atoms of methanol coord geometry, with the methanol molecule at the apical position. In all the three structures the central metal atom sits on a crystallographic inversion centre. In all the cases, the coordination entities are further organized via hydrogen bonding interactions to generate multifarious supramolecular networks. Complexes 1, 2 and 3 have also been characterized by spectroscopic (UV/Vis and IR) and thermal analysis (TGA). In addition, the complexes were found to exhibit antimicrobial activity. The magnetic susceptibility measurements, measured from 8 to 300 K, revealed antiferromagnetic interactions between the Co(II) ions in compound 1 and the Ni(II) ions in la, respectively.

Coordination Behaviour of Imino Hydrazone Ligands towards Nickel (II) and Copper (II) Ions

The complexing ability of a new series of ligands, β-N-arylimine hydrazones, toward Ni (II) and Cu (II) ions has been studied. The isolated complexes are characterised on the basis of elemental analysis, spectroscopic methods and magnetic susceptibility measurements. The ligands are notentially bidentate in character coordinating to divalent metal ions through the N1 and N5 nitrogens. Square planar geometry of the metal ions is suggested on the basis of experimental evidence.

Spectroscopic and Coordination Behavior of α-Cyanothioacetamide

α-Cyanothioacetamide (CTAM) complexes of cuprous chloride CuCl–2CTAM and cuprous bromide CuBr–2CTAM have been prepared. The infrared spectra of CTAM and its complexes, and the laser Raman spectrum of CTAM have been recorded. Assignment of the frequencies of the ligand has been made on the basis of a normal coordinate analysis using the Urey-Bradley force field. The copper (I) complexes are inferred to have thiocarbonyl sulfur and amide nitrogen bonded CTAM as evidenced from infrared and electronic spectra.

Ambidentate coordination of isonitrosoacetylacetone imines in their nickel(II) and palladium(II) complexes

Nickel(I1) and palladium(I1) complexes of the types Ni(R-IAI)(IAI'), Pd(IAI)(IAI'), and Pd(R-IAI), , where IAI and IAI' represent isonitrosoacetylacetone imine and R-IAI represents its Aralkyl derivative, have been prepared. The molar conductance, molecular weight, magnetic moment, and ir, pmr, and electronic spectra of these com- plexes have been studied. It is suggested that the isonitroso group of R-IAI coordinates through the nitrogen and that of IAI' thiough the oxygen in Ni(R-IAI)(IAI'). In Pd(R-IAI), the isonitroso groups of both ligands coordinate through nitrogen while Pd(IAI)(IAI') has a structure similar to that of Ni(R-IAI)(IAI'). The amine- exchange reactions of nickel(I1) and palladium(I1) complexes are discussed and compared on the basis of their structures.

Coordination properties of vic-isonitrosoimines in their copper (II) and palladium (II) complexes

Preparation and structural characterization of palladium (II) complexes of ligands III-V and copper (II) complexes of III are reported. The elemental analyses of the complexes show that the metal: ligand ratio is 1 : 2. The electrical conductance in acetone shows the non-electrolytic nature of the complexes. The diamagnetic character suggests a gross square-planar geometry for the palladium (II) complexes. Copper (II) complexes are paramagnetic with/~eff.~l'90 B.M. Spectral data suggest that in all the complexes the ligand coordinates to the metal (II) symmetrically through isonitroso-nitrogen and imine-nitrogen, forming a ¡ membered chelate ring. Amine-exchange reactions of the complexes are discussed and compared on the basis of their structures.

Lanthanide coordination in dimethyl sulphoxide and antipyrine complexes of rare earth nitrates

Abstract is not available.

Synthesis of a one-dimensional coordination polymer containing pendant hydrosulfide groups

In view of the recent interest in compounds containing M-SH units, an organotin hydrosulfide compound, Me2Sn(SH)(O2CMe) (1) was prepared by controlled hydrolysis of the diorganotin thioacetate. Under similar mild hydrolytic conditions the corresponding benzoate could not be isolated. Instead, the thiobenzoate complex, Me2Sn(SOCPh)(2) (3) was obtained in excellent yields indicating that there was no hydrolysis. Both 1 and 3 were characterized by X-ray crystallography. Some properties of the polymeric compound 1, such as spectral, electrical conductivity and NLO response were also studied. The reactivity and properties were explained using density functional calculations.

Nuclear quadrupole resonance in coordination compounds

Abstract is not available.

X-ray crystal structure of a ternary copper(II) vitamin B6 complex, hydroxo(2,2'-bipyridyl)(pyridoxinato) copper(II) monohydrate. A rare example of monodentate coordination of copper(II) by the hydroxyl ion

A ternary metal complex involving Vitamin B6 with the formula [Cu(bipy)(pn) (OH)]H2O (bipy = 2,2'²-bipyridine, PN = anionic pyridoxine) has been synthesized and studied in the solid state by means of spectroscopy and X-ray crystallography. The geometry around copper(II) is distorted square pyramidal, two oxygens from phenolic and 4-(hydroxymethyl) groups of pn, two nitrogens from bipy and an axial OH- ion forming the coordination sphere. In this structure pn exists in a new anionic form with deprotonation of the phenolic group. The structure also provides a rare example of monodentate hydroxyl coordination to copper.

A study of the nature of coordination in metal monothiocarbamates based on infrared spectroscopy and the HSAB concept

The nature of coordination in metal monothiocarbamates is shown to depend on the hardness or softness of the metal ton. Thus, the monothiocarbamate ion acts as a monodentate ligand with metal-sulphur bending when the metal ion is a soft acid while it acts as a bidentate ligand when the metal ion is a hard acid; it can exhibit either behaviour when the metal ion is a borderline acid. In dialkyltin and dialkylmonocholorotin complexes, the monothiocarbamate ion acts as a bidentate ligand with strong Sn-S bonding while in trialkyl-or triaryl-tin complexes it acts essentially as a monodentate ligand. Thus, R3Sn(I) seems to be a soft or borderline acid while R2Sn(II) is a hard acid.