Correction to: Aziridine-2-Carboxylic Acid Derivatives and Its Open-Ring Isomers as a Novel PDIA1 Inhibitors

Chemistry of Heterocyclic Compounds -     

Design of pincer complexes based on (methylsulfanyl)acetic/propionic acid amides with ancillary S‐ and N‐donors as potential catalysts and cytotoxic agents

Pincer complexes featuring readily tunable tridentate ligand frameworks comprise one of the most actively studied classes of organometallic and metal–organic compounds and find extensive use in catalysis, organic synthesis, materials science, and other fields of chemistry and allied disciplines. Currently growing attention is devoted to non‐classical ligand scaffolds, such as functionalized carboxamides, which offer multiple options for directed structural modifications. In this study, the reactions of (methylsulfanyl)acetyl and propanoyl chlorides with 2‐(aminomethyl)pyridine, 2‐(2‐aminoethyl)pyridine, 8‐aminoquinoline and 2‐(diphenylthiophosphoryl)aniline afford a series of new pincer‐type ligands based on functionalized carboxamides. The ligands obtained readily undergo direct cyclopalladation under the action of PdCl₂(NCPh)₂ in dichloromethane at room temperature, resulting in Pd(II) pincer complexes with N,N,S‐ and S,N,S‐donor sets. Importantly, some of the cyclopalladated derivatives can also be produced efficiently under solvent‐free conditions according to the approach recently developed by our group. The complexes obtained have been tested for cytotoxicity against several human cancer cell lines and catalytic activity in the model Suzuki reaction. The results have been compared to those for the related Pd(II) pincer complexes to define the main structure–activity relationships and to outline the most promising structures for further investigations.     

Application of the Spherical Harmonic Model to the ν(CO) Vibrational Spectra of Some Fe(CO)4 and M(CO)5 (M=Cr, W) Transition Metal Cluster Carbonyl Species

When the Fe(CO)₄ and M(CO)₅ (M=Cr, W) groups are co-ordinated in C_3v and C_4v fashion, respectively, in transition metal carbonyl cluster species they contain two sets of non-symmetry related carbonyl groups. In the application of the spherical harmonic model (SHM) to the interpretation of the infrared spectra of these compounds it proves necessary first to treat these as for a normal, isolated, M(CO)₄ or M(CO)₅ group and then apply the SHM. This recognition gives insights into the general application of the SHM.     

Determination of low-level tritium concentrations in surface water and precipitation in the Czech Republic

Past tests of nuclear weapons in the atmosphere, nuclear energy facilities and tritium of natural origin are main sources of tritium in the environment. Thanks to its presence in environment and its favourable properties, tritium is used as a radiotracer. Since stopping of atmospheric nuclear tests, tritium in precipitation has been decreasing towards natural levels below 1 Bq l^?1 and precise analyses of low level tritium activities are necessary. This paper focuses on tritium development at sites not influenced by any technogenic release of tritium in Elbe River basin (Bohemia) in the Czech Republic using liquid scintillation measurement with electrolytic enrichment.     

Variational Solution of Stochastic Schrödinger Equations With Power-Type Nonlinearity

We investigate a Schrödinger problem with multiplicative Gaussian noise term and power-type nonlinearity on a bounded one-dimensional domain. In order to prove the existence and uniqueness of the variational solution, a further process will be introduced which allows to transform the stochastic nonlinear Schrödinger problem into a pathwise one. Galerkin approximations and compact embedding results are used.     

Credit contagion in a network of firms with spatial interaction

This contribution studies the effects of credit contagion on the credit risk of a portfolio of bank loans. To this aim we introduce a model that takes into account the counterparty risk in a network of interdependent firms that describes the presence of business relations among different firms. The location of the firms is simulated with probabilities computed using an entropy spatial interaction model. By means of a wide simulation analysis we investigate the behavior of the model proposed and study the effects of default contagion on the loss distribution of a portfolio of bank loans.     

Equilibrium Diffusion on the Cone of Discrete Radon Measures

Let \({\mathbb {K}(\mathbb {R}^{d})}\) denote the cone of discrete Radon measures on \(\mathbb {R}^{d}\). There is a natural differentiation on \(\mathbb {K}(\mathbb {R}^{d})\): for a differentiable function \(F:\mathbb {K}(\mathbb {R}^{d})\to \mathbb {R}\), one defines its gradient \(\nabla ^{\mathbb {K}}F\) as a vector field which assigns to each \(\eta \in \mathbb {K}(\mathbb {R}^{d})\) an element of a tangent space \(T_{\eta }(\mathbb {K}(\mathbb {R}^{d}))\) to \(\mathbb {K}(\mathbb {R}^{d})\) at point η. Let \(\phi :\mathbb {R}^{d}\times \mathbb {R}^{d}\to \mathbb {R}\) be a potential of pair interaction, and let μ be a corresponding Gibbs perturbation of (the distribution of) a completely random measure on \(\mathbb {R}^{d}\). In particular, μ is a probability measure on \(\mathbb {K}(\mathbb {R}^{d})\) such that the set of atoms of a discrete measure \(\eta \in \mathbb {K}(\mathbb {R}^{d})\) is μ-a.s. dense in \(\mathbb {R}^{d}\). We consider the corresponding Dirichlet form

$$\mathcal{E}^{\mathbb{K}}(F,G)={\int}_{\mathbb K(\mathbb{R}^{d})}\langle\nabla^{\mathbb{K}} F(\eta), \nabla^{\mathbb{K}} G(\eta)\rangle_{T_{\eta}(\mathbb{K})}\,d\mu(\eta). $$

Integrating by parts with respect to the measure μ, we explicitly find the generator of this Dirichlet form. By using the theory of Dirichlet forms, we prove the main result of the paper: If d ≥ 2, there exists a conservative diffusion process on \(\mathbb {K}(\mathbb {R}^{d})\) which is properly associated with the Dirichlet form \(\mathcal {E}^{\mathbb {K}}\).