Groups with many subgroups having polycyclic-by-finite layers or derived subgroup

A group is called (PF)L if the subgroups generated by its elements having same order (finite or infinite) are polycyclic-by-finite. In the present paper we prove that a group is locally graded minimal non-((PF)L∪(𝔓𝔉)𝔄) if, and only if, it is non-perfect minimal non-FC, where (𝔓𝔉)𝔄 denotes the class of (polycyclic-by-finite)-by-abelian groups. We prove also that a group of infinite rank whose proper subgroups of infinite rank are in ((PF)L∪(𝔓𝔉)𝔄) is itself in ((PF)L∪(𝔓𝔉)𝔄) provided that it is locally (soluble-by-finite) without simple homomorphic images of infinite rank. Our last result concerns groups that satisfy the minimal condition on non-((PF)L∪(𝔓𝔉)𝔄)-subgroups.     

A door to model reduction in high-dimensional parameter space

Model reduction techniques such as Proper Generalized Decomposition (PGD) are decision-making tools that are about to revolutionize many domains. Unfortunately, their computation is still problematic for problems involving many parameters, for which one has to face the “curse of dimensionality”. An answer to this challenge is given in solid mechanics by the so-called “parameter-multiscale PGD”, which is based on Saint-Venant's principle. In this article, a model problem composed of up to a thousand parameters is presented, showing that the method is able to overcome the “curse of dimensionality”.     

Influence of counter-anion on the coordination geometry of manganese(II) complexes with methyl-2-pyrazinecarboximidate ligand

Two new complexes of [Mn(2-MPyzCI)₂Cl₂].H²O (1) and [Mn(2-MPyzCI)₂(H₂O)₂](NO₃)₂ (2) were synthesized from the reaction of MnX₂.4H₂O (X=Cl^? and NO₃^?) with 2-cyanopyrazine in methanolic solution. The chelating methyl pyrazine-2-carboximidate (2-MPyzCI) ligand is formed via the methanolysis of 2-cyanopyrazine. Although coordination environment around manganes(II) ions is similar, but these complexes are different in geometrical position of 2-MPyzCI ligands. As both compounds are synthesized under the same reaction conditions, the only difference between these two complexes are counter ions and changing of geometrical position of ligands can be considered as a result of influence of the counter-anions on the molecular structures.     

A new ternary Cu (II) complex with 4,7-dimethyl-1,10-phenanthroline and NOO-type tridentate Schiff base ligand: Synthesis,crystal structure,biomacromolecular interactions,and radical scavenging activities

NOO-type tridentate Schiff base, N-salicylidene-2-aminobenzoic acid, (H₂L), and its ternary Cu (II) complex containing H₂L Schiff base and 4,7-dimethyl-1,10-phenanthroline (4,7-dmphen), [Cu(4,7-dmphen)(H₂L)]₂7H₂O, have been synthesized and characterized by CHN analysis, ESI-MS, FTIR, and single-crystal X-ray diffraction techniques. The interaction of alone H₂L Schiff base ligand and ternary Cu (II) complex with biomacramolecules {calf thymus DNA (CT-DNA) and bovine serum albumin (BSA)} has been investigated by electronic absorption and fluorescence spectroscopy. The experimental results indicate that H₂L Schiff base ligand and ternary Cu (II) complex bind to CT-DNA by means of a moderate intercalation mode. Furthermore, the fluorescence quenching mechanism between H₂L Schiff base ligand and ternary Cu (II) complex with BSA possesses a static quenching process. Radical scavenging activity of H₂L Schiff base ligand and ternary Cu (II) complex was measured in terms of EC₅₀, using the DPPH and H₂O₂ methods. Biomacromolecule interactions and scavenging activity studies revealed that ternary Cu (II) complex yielded better results than H₂L Schiff base ligand alone.     

The self-assemblies of a newly designed star-shaped molecule end-capped with bromine atoms studied by scanning tunneling microscopy

A new star-shaped molecule StOF-Br_3 containing oligofluorenes and halogen atoms(Bromine) has been synthesized and studied by Scanning Tunneling Microscopy(STM) at the highly oriented pyrolytic graphite(HOPG) surface.We have obtained the high-resolution self-assembled STM images,from which the highly ordered and closely packed non-porous arrangements of the StOF-Br_3 molecular selfassemblies at the heptanoic acid/HOPG surface could be observed.The molecular models and selfassembled StOF-Br_3 architectures have been given in the following text.Besides,we have also figured out the surface free energy by the density functional theory(DFT) calculation,which proved that the halogen...halogen interaction was strong enough to stabilize the ordered molecular self-assemblies.This work verifies the existence of bromine...bromine interactions,and meanwhile provides a kind of effective approach for quickly building ordered molecular nanoarchitectures with large areas and different geometries.     

Statistical structure of the velocity field in cavitating flow around a 2D hydrofoil

Transformation of flow turbulence structure with cavitation occurrence, determination of the flow conditions favorable for nucleation of cavitation bubbles, influence of the statistical structure of turbulence on this process and the inverse effect of cavitation on the flow dynamics are challenging problems in modern fluid mechanics. The paper reports on the results of statistical processing of the velocity fields measured by a PIV technique in cavitating flow over a 2D symmetric hydrofoil for four flow conditions, starting from a cavitation-free regime and finishing by unsteady cloud cavitation. We analyze basic information on the statistical structure of velocity fluctuations in the form of histograms and Q-Q diagrams along with profiles of the mean velocity and turbulent kinetic energy. The research reveals that the flow turbulence pattern and distributions of turbulent fluctuations change significantly with the cavitation development. Under unsteady cloud cavitation conditions, the probability density function of the fluctuating velocity has a two-mode distribution, which indicates switching of two alternating flow conditions in a region above the hydrofoil aft part due to periodic passing of cavitation clouds. Behaviors of the mean and most probable velocities unexpectedly appear to be different with a monotonous increase of the incoming flow velocity. This finding must be caused by modification of the skewness coefficient of the fluctuating velocity.     

Lump and interaction solutions to the (3+1)-dimensional Burgers equation

The(3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics,is considered. Two types of semi-rational solutions, namely, the lump–kink solution and the lump–two kinks solution, are constructed from the quadratic function ansatz. Some interesting features of interactions between lumps and other solitons are revealed analytically and shown graphically, such as fusion and fission processes.     

Effect of nitrogen plasma treatment on the crystallinity and self‐bonding of polyetheretherketone (PEEK) for biomedical applications

Polyetheretherketone (PEEK) is a thermoplastic material with outstanding properties and high potential for biomedical applications, including hermetic encapsulation of active implantable devices. Different biomedical grade PEEK films with initial degree of crystallinity ranging from 8% to 32% (with or without mineral filling) were inspected. PEEK surfaces were treated with nitrogen RF plasma and the effects on materials crystallinity and self‐bonding were evaluated. In particular, the relationship between auto‐adhesive properties and crystalline content of PEEK before and after plasma treatment was examined. PEEK samples showed different bonding strength depending on their degree of crystallinity, with higher self‐bonding performance of mineral‐filled semi‐crystalline films. XRD did not show any modification of the PEEK microstructure as a result of plasma treatment, excluding a significant influence of crystallinity on the self‐bonding mechanisms. Nevertheless, plasma surface treatment successfully improved the self‐bonding strength of all the PEEK films tested, with larger increase in the case of semi‐crystalline unfilled materials. This could be interpreted to the increase in chain mobility that led to interfacial interpenetration of the amorphous phase.     

An investigation of paddle wheel Cu2(μ2-O2CCH3)4 for gas molecule adsorptions

Metal organic frameworks (MOFs) have been well-known and extensively researched due to the high storage /good selectivity for gas molecules. Herein, the structures and electron paramagnetic resonance (EPR) spectra for dicopper paddle wheel MOF compound (Cu₂(µ₂-O₂CCH₃)₄ with various gas molecule are theoretically investigated by density functional theory (DFT) calculations. The adsorption energies and isotherms (including pure gas molecules and the mixed ones) are calculated for the gas molecules interacting with the unsaturated Cu₂(µ₂-O₂CCH₃)₄. Both quantities exhibit the roughly consistent orders (e.g. H₂S?>?NH₃?>?CO₂?>?CO?>?H₂O?>?N₂?>?NO?>?H₂ for isotherms and H₂S?>?NH₃?>?N₂?>?CO₂?>?NO?>?H₂O?>?H₂?>?CO for adsorption energies), possibly suggesting that this material may act as a potential adsorbent of these gas molecules. The catalytic property of Cu₂(µ₂-O₂CCH₃)₄ for oxidation of CO and NO into non-toxic molecules and splitting of H₂O into H₂ and O₂ in the solvent condition are uniformly discussed. Simulation of Grand Canonical Monte Carlo (GCMC) in MS 8.0 and calculations in Langmuir model reveal that Cu₂(µ₂-O₂CCH₃)₄ has good selectivity for CH₄ in natural gas (CH₄/CO₂/N₂) and SO₂ in fog (SO₂/NO/NO₂/H₂O/O₂), which would exhibit potential environmentally friendly applications.     

Interaction of 1-acylamino-2,2-dichloroethenyl(triphenyl)phosphonium chlorides with alkanolamines

Abstract

It is shown that the interaction of 1-acylamino-2,2-dichloroethenyl(triphenyl)-phosphonium chlorides with alkanolamines having a primary amino group results in the formation of 4-oxazolylphosphonium salts containing hydroxyalkylamine substituents at position 5 of the oxazole cycle. Under similar conditions the reaction of N-substituted alkanolamines with 1-acylamino-2,2-dichloroethenyl-(triphenyl)phosphonium chlorides leads to the formation of 1,3-oxazolidin-2-ylidene derivatives, in which the triphenylphosphonium group is located in the side chain. The structure of the new synthesized compounds has been reliably proven by elemental analysis, IR, ¹Н, ¹³С, ³¹Р NMR spectroscopy, mass spectrometry and single crystal X-ray diffraction.