$$\mathcal {F}_\pi $$Fπ-residuality of generalized Baumslag–Solitar groups

Archiv der Mathematik - A generalized Baumslag–Solitar group is a finitely generated group that acts on a tree with infinite cyclic edge and vertex stabilizers. A group G is residually a...     

Characterization of new Pt(IV)–thiazole complexes: Analytical,spectral, molecular modeling and molecular docking studies and applications in two opposing pathways

New thiazole derivatives were synthesized and fully characterized, then coordinated with PtCl₄ salt. Also, the newly synthesized Pt(IV) complexes were investigated analytically (elemental and thermogravimetric analyses), spectrally (infrared, UV–visible, mass, ¹H NMR, ¹³C NMR, X‐ray diffraction) as well as theoretically (kinetics, modeling and docking). The data extracted led to the establishment of the best chemical and structural forms. Octahedral geometry was the only formula proposed for all complexes, which is favorable for d⁶ systems. The molecular ion peaks from mass spectral analysis coincide with all analytical data, confirming the molecular formula proposed. X‐ray diffraction (XRD) and scanning electron microscopy (SEM) allowed discrimination of features between crystalline particles and other amorphous morphology. By applying Gaussian09 as well as HyperChem 8.2 programs, the best structural forms were obtained, as well as computed significant parameters. Computed parameters such as softness, hardness, surface area and reactivity led us towards application in two opposing pathways: tumor inhibition and oxidation activation. The catalytic oxidation for CO was conducted over PtO₂, which was yielded from calcination of the most reactive complex. The success of catalytic role for synthesized PtO₂ was due to its particulate size and surface morphology, which were estimated from XRD patterns and SEM images, respectively. The antitumor activity was tested versus HCT‐116 and HepG‐2 cell lines. Mild toxicity was recorded for two of the derivatives and their corresponding complexes. This degree of toxicity is more favorable in most cases, due to exclusion of serious side effects, which is coherently attached with known antitumor drugs.     

Comparison of fast field-cycling magnetic resonance imaging methods and future perspectives

ABSTRACT

Fast field-cycling (FFC) nuclear magnetic resonance relaxometry is a well-established method to determine the relaxation rates as a function of magnetic field strength. This so-called nuclear magnetic relaxation dispersion gives insight into the underlying molecular dynamics of a wide range of complex systems and has gained interest especially in the characterisation of biological tissues and diseases. The combination of FFC techniques with magnetic resonance imaging (MRI) offers a high potential for new types of image contrast more specific to pathological molecular dynamics. This article reviews the progress in FFC-MRI over the last decade and gives an overview of the hardware systems currently in operation. We discuss limitations and error correction strategies specific to FFC-MRI such as field stability and homogeneity, signal-to-noise ratio, eddy currents and acquisition time. We also report potential applications with impact in biology and medicine. Finally, we discuss the challenges and future applications in transferring the underlying molecular dynamics into novel types of image contrast by exploiting the dispersive properties of biological tissue or MRI contrast agents.     

Intramolecular Hydroamination of Selenoalkynes to 2-Selenylindoles in the Absence of Catalyst

In this work, a series of 2-chalcogenylindoles was synthesized by an efficient methodology, starting from chalcogenoalkynes, including a previously unreported tellurium indole derivative. For the first time, these 2-substituted chalcogenylindoles were obtained in the absence of metal catalyst or base, under thermal conditions only. In addition, the results described herein represent a methodology with inverse regioselectivity for the chalcogen functionalization of indoles.     

Binary functions,degeneracy, and alternating dimaps

This paper continues the study of combinatorial properties of binary functions — that is, functions $f:2^E\to ?$ such that $f(0?)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.