Solutions to a gradient-dependent integro-differential parabolic problem arising in the pricing of financial options in a Lévy market

We study an integro-differential parabolic problem modeling a process with jumps arising in financial mathematics. Under suitable conditions, we prove the existence of solutions in a general domain by proving a uniform bound on an iterative sequence of solutions and then applying the Arzelà–Ascoli theorem.     

Highly Stable Double‐Stranded DNA Containing Sequential Silver(I)‐Mediated 7‐Deazaadenine/Thymine Watson–Crick Base Pairs

The oligonucleotide d(TX)₉, which consists of an octadecamer sequence with alternating non‐canonical 7‐deazaadenine (X) and canonical thymine (T) as the nucleobases, was synthesized and shown to hybridize into double‐stranded DNA through the formation of hydrogen‐bonded Watson–Crick base pairs. dsDNA with metal‐mediated base pairs was then obtained by selectively replacing W‐C hydrogen bonds by coordination bonds to central silver(I) ions. The oligonucleotide I adopts a duplex structure in the absence of Ag⁺ ions, and its stability is significantly enhanced in the presence of Ag⁺ ions while its double‐helix structure is retained. Temperature‐dependent UV spectroscopy, circular dichroism spectroscopy, and ESI mass spectrometry were used to confirm the selective formation of the silver(I)‐mediated base pairs. This strategy could become useful for preparing stable metallo‐DNA‐based nanostructures.     

Structure, spectroscopic properties, and reversible solid-to-solid reactions of metal complexes of 5-nitro-pyrimidin-2-olate

In searching for coordination polymers containing the highly polarized 5-nitro-pyrimidin-2-olate ligand (NP), a number of species containing 3d transition metals have been prepared and characterized, namely Co(NP)2(H2O)4, [Co(NP)2]n, Ni(NP)2(H2O)4, [Ni(NP)2]x, and [Zn(NP)2]n. Their structures have been determined by X-ray powder diffraction methods. The hydrated compounds contain mononuclear M(NP)2(H2O)4 units interconnected by means of a three-dimensional (3D) network of hydrogen bonds. The homoleptic species, at variance from the already known metal(II) pyrimidin-2-olate ones, crystallize as two-dimensional (2D) slabs, where the metal coordination is of the MN3O kind. The electron-withdrawing nitro group, never bound to the metal ion, is likely to influence the observed stereochemistry through steric and dipolar effects within the crystal lattice. The thermal, spectroscopic, and magnetic properties of these species are presented. The M(NP)2(H2O)4/[M(NP)2]x,n systems interconvert reversibly upon dehydration/rehydration processes.     

Synthesis of 1,2,3,4-tetrahydroquinazoline derivatives as potential alpha-adrenergic blocking agents

The synthesis of N,N′-bis[6-(1,2,3,4-tetrahydro-3-quinazolidyl)hexyl]cystamine (I) and 3-(6-aminohexyl)-1,2,3,4-tetrahydroquinazoline (II) are described. Compound I is obtained by condensation of o-nitrobenzoyl chloride with 3-(6-aminohexyl)-1,3-thiazolidine (III) followed by dimerization, reduction and formation of tetrahydroquinazoline ring. A similar method was used for preparation of compound II. These compounds and some synthesis intermediates are potential alpha-adrenergic blockers.     

Dynamics of a single ion in a perturbed Penning trap: octupolar perturbation

Imperfections in the design or implementation of Penning traps may give rise to electrostatic perturbations that introduce nonlinearities in the dynamics. In this paper we investigate, from the point of view of classical mechanics, the dynamics of a single ion trapped in a Penning trap perturbed by an octupolar perturbation. Because of the axial symmetry of the problem, the system has two degrees of freedom. Hence, this model is ideal to be managed by numerical techniques like continuation of families of periodic orbits and Poincaré surfaces of section. We find that, through the variation of the two parameters controlling the dynamics, several periodic orbits emanate from two fundamental periodic orbits. This process produces important changes (bifurcations) in the phase space structure leading to chaotic behavior.     

Brillouin light scattering characterization of the surface acoustic wave velocity in sp<Superscript>2</Superscript> allotropes thin films

Carbon thin films have been deposited by DC magnetron sputtering at different substrate temperatures ranging from 200 K to 400 K. The influence of the preparation substrate temperature on the elastic properties has been evidenced by means of the High Resolution Brillouin Spectroscopy. Thus, the surface acoustic wave (SAW) velocity evolution could be assessed for the different samples. The observed variation is analysed in terms of the relative population of sp² allotropes phases forming the film.     

Complete homogeneous varieties: Structure and classification

Homogeneous varieties are those whose group of automorphisms acts transitively on them. In this paper we prove that any complete homogeneous variety splits in a unique way as a product of an abelian variety and a parabolic variety. This is obtained by proving a rigidity theorem for the parabolic subgroups of a linear group. Finally, using the results of Wenzel on the classification of parabolic subgroups of a linear group and the results of Demazure on the automorphisms of a flag variety, we obtain the classification of the parabolic varieties (in characteristic different from ). This, together with the moduli of abelian varieties, concludes the classification of the complete homogeneous varieties.

     

Chiral pyrimidine metallacalixarenes: synthesis, structure and host-guest chemistry

A set of enantiomerically pure cyclic multinuclear complexes with the formula cis-[a(2)PdL](n) (n+) [a(2)=(R,R)-1,2-diaminocyclohexane (R,R-dach), (S,S)-1,2-diaminocyclohexane (S,S-dach); n=4, 6; LH=2-hydroxypyrimidine (2-Hpymo), 4,6-dimethyl-2-hydroxypyrimidine (2-Hdmpymo) and 4-hydroxypyrimidine (4-Hpymo)] were obtained by reaction of cis-[a(2)Pd(H(2)O)(2)](2+) and LH in aqueous media. The polynuclear complexes were studied by (1)H NMR spectroscopy and X-ray crystallography. These studies revealed that the N1,N3-bridging mode exhibited by the pyrimidine moieties is ideally suited for formation of inorganic analogues of calixarenes (metallacalixarenes) in a self-assembly process. The most stable species are the tetranuclear metallacalix[4]arenes, which are obtained in all cases. Hexanuclear species, namely, [a(2)Pd(2-dmpymo)](6) (6+), were also isolated and fully characterised. (1)H NMR experiments show conversion of [a(2)Pd(2-dmpymo)](6) (6+) to [a(2)Pd(2-dmpymo)](4) (4+) on heating. Analogously to organic calixarenes, these systems are also capable of incorporating hard metal ions at the oxo surface. Additionally, investigations on the receptor properties of these metallacalixarenes towards mononucleotides showed that enantioselective recognition processes occur in aqueous media.     

Novel mechanism for priming aromatic polyketide synthases

In this issue of Chemistry & Biology, a novel priming mechanism is proposed for aromatic polyketide biosynthesis, with an iterative type I polyketide synthase generating a starter unit primed for a type II polyketide synthase. This novel priming system participates in hedamycin biosynthesis, a DNA alkylating agent.