Sequential decision problems on isolated time domains

In this paper, we shall study the deterministic dynamic sequence problem on isolated time domains. After introducing the Euler equations and the transversality condition, we shall prove that the Euler equations and transversality condition are sufficient for the existence of the optimal solution. We shall also introduce the Bellman equation on isolated time scales. This equation will generalize the well-known Bellman equation in the theory of dynamic programming. As an application in financial economics, we shall optimize a sequence problem of growth model on isolated time domains.     

Synthesis,Crystal Structure and Characterization of Hexakis[2‐methoxy‐4‐formylphenoxy]cyclotriphosphazene

The new cyclotriphosphazene derivative N₃P₃(OC₆H₃OCH₃COH)₆ ( 1 ) was synthesized from hexachlorocyclotriphosphazene, N₃P₃Cl₆, and 4‐hydroxy‐3‐methoxybenzaldehyde in acetonitrile in the presence of K₂CO₃. The structure of 1 was verified by means of elemental analysis, IR, ¹H NMR, ¹³C NMR, ³¹P NMR spectra, thermal analysis and X‐ray diffraction.     

N1‐(2,6‐Di­methyl­phenyl)‐N2‐hydroxy‐α‐oxo‐α‐phenyl­acet­amidine

The structure of the title compound, C₁₆H₁₆N₂O₂, consists of a dimeric arrangement around an inversion centre of acet­amidine mol­ecules linked via O—H⋯N hydrogen bonds. There are also H⋯π‐ring interactions. All these interactions result in the formation of infinite chains parallel to the (101) axis. The oxime group has an E conformation.     

Synthesis,Crystal Structure Properties of {μ-Nitrato-[<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>′-ethylene-bis(3-methoxysalicylideneimin) diaqua nitrato Cu(II)La(III)]nitrat}

Abstract  

The [μ-NO₃-LCuLa(NO₃)·(H₂O)₂]NO₃ (I) complex has been prepared and characterized by single crystal X-ray diffraction properties. The title compound crystallizes in the monoclinic system, space group P 2₁/c, with a = 9.1699(4), b = 21.6796(8), c = 13.7068(6) ?, α = γ = 90o, β = 111.308(3)°, V = 2538.63 (18) ?³ and Z = 4. The unit cell contains four discrete the title compounds. The central region is occupied by Cu^II and La^III ions which are brigged by two phenolato oxygen atoms of ligand. The intramolecular La–Cu distance is 3.5016 (3) Ǻ. The copper (II) ion is in a distorted square pyramidal geometry with the imino nitrogen atoms N1 and N2, and the phenolic oxygen atoms O2 and O3 forming the square base. The La^III ion is deca coordinated.     

2‐[Benzoyl­(hydroxy­imino)­methyl­amino]­benzoic acid

The structure of the title compound, C₁₅H₁₂N₂O₄, consists of a polymeric arrangement, around inversion centres, of mol­ecules linked through O—H⋯N and O—H⋯O hydrogen bonds; there are also intramolecular hydrogen bonds. All these hydrogen‐bond interactions result in the formation of infinite chains parallel to the [010] direction. The oxime group has an E conformation.     

4‐Bromo‐2‐{[4‐(3‐mesityl‐3‐methyl­cyclo­butyl)thia­zol‐2‐yl]hydrazono­meth­yl}phenol,with N—H⋯N,C—H⋯π and π–π inter­actions

The title compound, C₂₄H₂₆BrN₃OS, crystallizes in the triclinic space group P, with two independent mol­ecules in the asymmetric unit. The mol­ecules adopt an E geometry about the azomethine C=N double bond. The structure is stabilized as dimers by N—H⋯N hydrogen bonding. C—H⋯π and π–π inter­actions are also effective in the crystal packing.     

N1‐(4‐Bromo­phen­yl)‐N2‐hydr­oxy‐2‐oxo‐2‐phenyl­acetamidine

In the title compound, C₁₄H₁₁BrN₂O₂, which has the oxime group in an E conformation, molecules are linked by strong O—H⋯O and N—H⋯O hydrogen bonds into chains of edge‐fused rings, unlike closely related compounds.     

Synthesis,crystal structure,HF and DFT calculations of 1-(2-chlorobenzyl)-N-(1-(2-chlorobenzyl)-4,5-dihydro-1H-imidazol-2-yl)-1H-benzimidazol-2-amine

The titled compound (1), has been synthesized and characterized by IR and ¹H-NMR spectroscopy, and single crystal X-ray diffraction. The compound crystallizes in the triclinic space group P-1. The crystal structure is stabilized by C-H…π and aromatic π-π interactions. There are also intramolecular N-H…N and C-H…N hydrogen bonds in the molecule. The use of quantum chemical calculations to characterise and optimise the choice of material is illustrated by ab initio treatments. Vibrational frequencies and LUMO-HOMO energy difference of 1 have also been investigated by Density functional theory (DFT) and Hartree-Fock (HF) calculations. Calculated frequencies are in good agreement with the corresponding experimental data.     

Experimental (X-ray,FT-IR,and UV-Vis Spectroscopy) and Theoretical Methods (DFT Study) of N'-(Dipyridin-2-ylmethylene)-4-methylbenzenesulfonohydrazide

Crystallography Reports - A new hydrazone derivative was synthesized and characterized by IR, UV-Vis spectroscopy, elemental analysis and single-crystal X-ray diffraction. The compound was...