Abstract:
3-Aryl-2-chloropropylisothiocyanates (1) are formed by interaction of arenediazonium chlorides with allyl isothiocyanate. Adducts 1 react with monoacylhydrazines to form 1-acyl-4-(3-aryl-2-chloropropyl)thiosemicarbazides (2a–d). Thiosemicarbazides 2a–d in the presence of bases selectively transform into 2-(2-R1-hydrazino)-5-(R2-benzyl)-2-thiazolines (3a–d).

Abstract:
The title compound, C17H18NO+·I , is an adduct resulting from an intramolecular Diels–Alder reaction of methallyl chloride with 3,4-dihydro-1-furylisoquinoline. The cation comprises a fused pentacyclic system containing three five-membered rings (dihydropyrrole, dihydrofuran and tetrahydrofuran) and two six-membered rings (tetrahydropyridine and benzene). The five-membered rings have the usual envelope conformations, and the central six-membered tetrahydropyridine ring adopts the unsymmetrical half-boat conformation. In the crystal, cations and iodide anions are bound by weak intermolecular hydrogen-bonding interactions into a three-dimensional framework.

Abstract:
The title compound, C23H18N2O6, is the product of an intramolecular thermal cycloaddition within 1-malein-2-[(E)-2-(2-furyl)vinyl]-4-oxo-3,4-dihydroquinazoline. The molecule comprises a previously unknown fused pentacyclic system containing two five-membered rings (2-pyrrolidinone and furan) and three six-membered rings (benzene, 2,3-dihydro-4-pyrimidinone and dihydrocyclohexane). The central five-membered pyrrolidinone ring has the usual envelope conformation. The six-membered dihydropyrimidinone and dihydrocyclohexane rings adopt a half-boat and a half-chair conformation, respectively. The dihedral angle between the planes of the terminal benzene and furan rings is 45.99 (7)°. In the crystal, O—H...O hydrogen bonds link the molecules into centrosymmetric dimers. Weak C—H...O hydrogen bonds consolidate further the crystal packing, which exhibits π–π interactions, with a short distance of 3.556 (3) between the centroids of benzene rings of neighbouring molecules.

Abstract:
In the crystal structure of the title compound, C18H12N2OS, centrosymmetric dimers are stabilized both by van der Waals interactions and by two types of intermolecular O—H...N hydrogen bonds. In addition, an intramolecular C—H...S hydrogen bond is observed. The dihedral angles between the central ring and the two pendant phenyl rings are 7.4 (1) and 45.06 (9)°.

Abstract:
The molecule of the title compound, C14H7Cl2NO2, is not planar; the dihedral angle between the mean planes of the chlorophenyl and benzisoxazole rings is 20.32 (7)°. The carbonyl chloride group is twisted with respect to the benzisoxazole ring by 2.5 (1)°. The molecular conformation is stabilized by an intramolecular C—H...Cl hydrogen bond. In the crystal packing, adjacent molecules are linked into dimers by intermolecular C—H...O hydrogen bonds. The dimers are further stacked into columns along the unique axis direction by π–π stacking interactions, with a centroid...centroid distance of 3.828 (5) . Other weak intermolecular C—H...O and C—H...Cl interactions are also present.

Abstract:
We consider a problem without initial conditions for degenerate nonlinear evolution equations with nonlinear dynamical boundary condition in spatial unbounded domains. We obtain sufficient conditions for the well-posedness of this problem without any restrictions at infinity.

Abstract:
A strategic choice between NATO membership and closer cooperation with Russia is at the heart of Ukrainian foreign policy. Locked within this dilemma, Ukraine often misses out other important foreign policy variables. Most importantly, the framework for strategic choice is shifting, with potential risks and benefits changing significantly. Moreover, Ukrainian decision-makers often believe that the right choice between East and West will be enough to settle Ukrainian security. This article puts forward the hypothesis that the context of this choice is more important, namely, that structural factors and additional regional arrangements are crucial to both national and regional security.

Abstract:
A simple and self-contained treatment of the superstring BRST no-ghost theorem at non-zero momentum and arbitrary picture number is presented. We prove by applying the spectral sequence that the absolute BRST cohomology is isomorphic to two copies of the light-cone spectrum at adjacent ghost numbers. We single out a representative in each cohomology class. A non-degenerate pairing between the Fock spaces, an induced pairing on the cohomology and a Hermitian inner product on the cohomology are constructed.

Abstract:
Chiral algebras in the cohomology of the $\bar{Q}_+$ supercharge of two-dimensional $\mathcal{N}=(0,2)$ theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For $\mathcal{N}=(0,2)$ Landau-Ginzburg models, it is also tree-level exact up to subtleties of defining composite operators. We study these theories and then specialize to the $\mathcal{N}=(2,2)$ models and consider some examples.

Abstract:
We consider a topological quantum mechanics described by a phase space path integral and study the 1-dimensional analog for the path integral representation of the Kontsevich formula. We see that the naive bosonic integral possesses divergences, that it is even naively non-invariant and thus is ill-defined. We then consider a super-extension of the theory which eliminates the divergences and makes the theory naively invariant. This super-extension is equivalent to the correct choice of measure and was discussed in the literature. We then investigate the behavior of this extended theory under diffeomorphisms of the extended phase space and despite of its naive invariance find out that the theory possesses anomaly under nonlinear diffeomorphisms. We localize the origin of the anomaly and calculate the lowest nontrivial anomalous contribution.