Dinuclear and Mononuclear Platinum(II) and Palladium(II) Complexes with Modified 2,2′‐Dipyridylamine Ligands Featuring a Cisplatin Analogous Structure Motif

In modern cancer therapy the clinical application of platinum‐based drugs is more and more limited by the occurrence of intrinsic or acquired resistances. In this context the potential use of dinuclear platinum complexes in chemotherapy is increasingly relevant. The novel complexes Pd(Bzdpa)Cl₂, Pd₂(C₄H₈(dpa)₂)Cl₄, and Pt₂(C₄H₈(dpa)₂)Cl₄ allow a direct comparison of mono‐ and dinuclear palladium and platinum complexes respectively deriving from a 2,2′‐dipyridylamine (Hdpa) ligand system. They were characterized by single crystal X‐ray analysis as well as infrared spectroscopy and elemental analysis. The cisplatin analogous mononuclear palladium complex Pd(Bzdpa)Cl₂ ( 1 ) (Bzdpa: (2,2′‐dipyridylbenzyl)amine) belongs to a range of 2,2′‐dipyridylamine‐based compounds which were extensively studied in our laboratories. 1 crystallizes in the orthorhombic space group Pna2₁ with a = 13.722(3), b = 13.457(3), c = 9.483(2), V = 1751.1(6) ų, and Z = 4. The metal binding motif of 1 was expanded by a flexible butyl‐linker to form the tetradentate C₄H₈(dpa)₂ ligand. The resulting isotypic dinuclear complexes Pd₂(C₄H₈(dpa)₂)Cl₄·2CH₃CN ( 2 ) and Pt₂(C₄H₈(dpa)₂)Cl₄·2CH₃CN ( 3 ) crystallize in the triclinic space group with a = 7.8427(2), b = 8.7940(2), c = 11.7645 (3), α = 79.219(2)°, β = 84.033(2)°, γ = 87.744(2)°, V = 792.58(3) ų ( 2 ) and a = 7.831(5), b = 8.814(5), c = 11.817(5), α = 79.271(5)°, β = 83.571(5)°, γ = 88.063(5)°, V = 796.3(8) ų ( 3 ), both with one centrosymmetrical molecule in the unit cell.     

Coordinative Behaviour of Tridentate NS2‐Donor Ligands with Cadmium: Synthesis and Crystal Structures of New Complexes

The reaction of cadmium salts with various amounts of the tridentate NS₂‐chelating ligands 1‐(2‐mercapto‐acetophenone)‐4‐triphenylmethylthiosemicarbazone (H₂L¹) and 1‐(5‐mercapto‐3‐methyl‐1‐phenylpyrazole‐4‐carboxaldehyde)‐4‐triphenyl‐methylthiosemicarbazone (H₂L²) in the presence of bases like N‐methylimidazole (N–MeIm), pyridine (py) or triethylamine (Et₃N) provided a series of novel mono‐, di‐, tri‐ and heptanuclear cadmium complexes. They are of the general formulas [CdL¹(N–MeIm)]₂ ( 1 ), [CdL¹(py)]₂ ( 2 ), [CdL²(N–MeIm)]₂ ( 3 ), [CdL²(py)₃] · 0.25 C₆H₁₄ · 0.5 py ( 4 ), [Et₃NH]₂[Cd₃L ] · 7 MeOH ( 5 ), [Et₃NH]₂[Cd₃L ] ( 6 ) and [Et₃NH]₂[Cd₇L ] · 14 MeOH ( 7 ). The compounds were characterized by elemental analysis, IR‐ and ¹H‐NMR‐spectroscopy. Single‐crystal X‐ray structure analyses are reported for the complexes 2 , 4 , 5 and 7 . While 2 has a dimeric structure where each cadmium ion is pentacoordinated in a N₂S₃‐environment, 4 consists of a monomeric cadmium center with distorted octahedral N₄S₂‐coordination. The complexes 5 and 7 exhibit new structural types for tri‐ and heptanuclear cadmium compounds. It is shown that sulfur bridging might proceed via arylthiolates, iminothiolates or even both functions of the ligand. Aggregation is influenced by various factors like solvents, counterions and ligand properties.     

A General Stochastic Calculus Approach to Insider Trading

The purpose of this paper is to present a general stochastic calculus approach to insider trading. We consider a market driven by a standard Brownian motion $B(t)$ on a filtered probability space $\displaystyle (\Omega,\F,\left\{\F\right\}_{t\geq 0},P)$ where the coefficients are adapted to a filtration ${\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$, with $\F_t\subset\G_t$ for all $t\in [0,T]$, $T>0$ being a fixed terminal time. By an {\it insider} in this market we mean a person who has access to a filtration (information) $\displaystyle{\Bbb H}=\left\{\H_t\right\}_{0\leq t\leq T}$ which is strictly bigger than the filtration $\displaystyle{\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$. In this context an insider strategy is represented by an $\H_t$-adapted process $\phi(t)$ and we interpret all anticipating integrals as the forward integral defined in [23] and [25]. We consider an optimal portfolio problem with general utility for an insider with access to a general information $\H_t \supset\G_t$ and show that if an optimal insider portfolio $\pi^*(t)$ of this problem exists, then $B(t)$ is an $\H_t$-semimartingale, i.e. the enlargement of filtration property holds. This is a converse of previously known results in this field. Moreover, if $\pi^*$ exists we obtain an explicit expression in terms of $\pi^*$ for the semimartingale decomposition of $B(t)$ with respect to $\H_t$. This is a generalization of results in [16], [20] and [2].