Cohen–Macaulayness and Limit Behavior of Depth for Powers of Cover Ideals

Let 𝕂 be a field, and let R = 𝕂[x ₁,…, x _n ] be the polynomial ring over 𝕂 in n indeterminates x ₁,…, x _n . Let G be a graph with vertex-set {x ₁,…, x _n }, and let J be the cover ideal of G in R. For a given positive integer k, we denote the kth symbolic power and the kth bracket power of J by J ^(k) and J ^[k], respectively. In this paper, we give necessary and sufficient conditions for R/J ^k , R/J ^(k), and R/J ^[k] to be Cohen–Macaulay. We also study the limit behavior of the depths of these rings.     

Substituted six-membered ring carbenes: the effects of amino and cyclopropyl groups through DFT calculations

DFT calculations are employed to compare and contrast six-membered ring carbenes including 1,3-dimethyltetrahydropyrimidin-2-ylidene (1a), 1-methyl-3-cyclopropyltetrahydropyridine-2-ylidene (2a), and 1,3-dicyclopropylcyclohexane-2-ylidene (3a) as well as their unsaturated analogues 1b, 2b, 3b, and 2c. The amino groups exert singlet-triplet energy separation (?E_s−t) of 60.9 kcal/mol to 1a while cyclopropyls induce a ?E_s−t of 14.8 kcal/mol to 3a. The simultaneous presence of amino and cyclopropyl in 2a leads to a ?E_s−t of 43.3 kcal/mol. Unsaturation slightly increases the ?E_s−t of 1a and 3a but not that of 2a. Our thermodynamic, kinetic, and reactivity results are compared with those of synthetic five-membered ring N-heterocyclic carbenes.     

An efficient one-pot synthesis of pyrimido[2,1-b][1,3]thiazine derivatives by reaction of activated acetylenes, thiouracils, and isocyanides

The reactive 1:1 zwitterionic intermediate, formed by the addition of isocyanides to dialkyl acetylenedicarboxylates, was trapped by thiouracils to yield a ketenimine intermediate, which cyclized and then rearranged to afford pyrimido[2,1-b][1,3]thiazines in good yields.     

Heat-resistant and soluble fluorinated poly(amide imide)s based on non-coplanar ortho-linked diimide-dicarboxylic acid

A series of novel fluorinated heat-resistant poly(amide imide)s (PAIS) based on non-coplanar diimide-diacid monomer (DIDA) were synthesized and characterized. The poly(amide imide)s were obtained in high yields and possessed inherent viscosities in the range of 0.47-0.91 dL g⁻¹. All of the polymers were amorphous in nature, showed outstanding solubility and could be readily soluble in common organic solvents such as N,N-dimethylacetamide, N-methyl-2-pyrrolidinoned, dimethyl sulfoxide, N,N-dimethylformamide, pyridine and tetrahydrofuran. Glass transition temperatures were in the range of 221-263 °C, as determined by differential scanning calorimetry. Degradation temperatures for 10% weight loss occurred all above 520 °C and char yields was more than 50% at 700 °C in nitrogen atmosphere. Moreover, these PAIs possessed low refractive indexes (n = 1.58-1.59), birefringence (Δn = 0.008-0.013), and dielectric constants (? ≈ 2.5) due to the trifluoromethyl pendent groups and ortho-catenated aromatic rings that interrupt chain packing and increase free volume.     

Fully integrated PDMS/SU-8/quartz microfluidic chip with a novel macroporous poly dimethylsiloxane (PDMS) membrane for isoelectric focusing of proteins using whole-channel imaging detection

A fully integrated polydimethylsiloxane (PDMS)/modified PDMS membrane/SU-8/quartz hybrid chip was developed for protein separation using isoelectric focusing (IEF) mechanism coupled with whole-channel imaging detection (WCID) method. This microfluidic chip integrates three components into one single chip: (i) modified PDMS membranes for separating electrolytes in the reservoirs from the sample in the microchannel and thus reducing pressure disturbance, (ii) SU-8 optical slit to block UV light (below 300?nm) outside the channel aiming to increase detection sensitivity, and (iii) injection and discharge capillaries for continuous operation. Integration of all these components on a single chip is challenging because it requires fabrication techniques for perfect bonding between different materials and is prone to leakage and blockage. This study has addressed all the challenges and presented a fully integrated chip, which is more robust with higher sensitivity than the previously developed IEF chips. This chip was tested by performing protein and pI marker separation. The separation results obtained in this chip were compared with that obtained in commercial cartridges. Side-by-side comparison validated the developed chip and fabrication techniques.     

Role of Zr4+ cations in NO2 adsorption on Ce(1-x)Zr(x)O2 mixed oxides at ambient conditions

Mixed oxides Ce(1-x)Zr(x)O(2) prepared by slow coprecipitation in NaOH were tested for NO(2) adsorption in dynamic conditions at room temperature. The samples were characterized before and after exposure to NO(2) by XRD, N(2)-adsorption, thermal analysis, potentiometric titration, and FT-IR. Mixed oxides show a better NO(2) adsorption capacity than the parent materials (CeO(2) and Zr(OH)(4)). This effect is linked to the presence of reduced cerium and oxygen vacancies induced by the addition of Zr(4+) cations to the structure. The results indicate that NO(2) reacts with Ce(3+) to form nitrite and nitrate species on the surface. The NO retention increases with an increase in the Zr(OH)(4) content. A decrease in the density of -OH groups on the surface after the exposure to NO(2), suggests their involvement in reactive adsorption of NO and/or NO(2). From the structural point of view, no real difference was observed on the Ce(1-x)Zr(x)O(2) materials before and after exposure to NO(2).     

Novel method for in-situ surfactant-based solid-phase extraction: application to the determination of Co(II) and Ni(II) in aqueous samples

We report on a completely new kind of solid phase extraction which we term in-situ surfactant-based solid-phase extraction (ISS-SPE). It represents a simple and rapid method for extraction from aqueous samples and preconcentration of compounds containing hydrophobic (alkyl) groups. A cationic surfactant containing alkyl chain is dissolved in the aqueous sample. Following the addition of hexafluorophosphate (HFP; an ion-pairing anion), solutions turn cloudy due to the interaction between the surfactant and the HFP ion. This is due to the formation of fine solid particles composed of the HFP salt of the cationic surfactant. The alkyl groups of the surfactant in the solid particles strongly interact with hydrophobic groups of analytes and become bound. The solid particles are centrifuged, and the sedimented particles can be either dissolved in an appropriate organic solvent, or leached with a solvent to recover the absorbed analyte(s). The method presented here has distinct advantages in that the extraction times are short and recoveries are high, probably a result of the formation of very fine particles of large specific surface, and of their good dispersion in the sample solution. The performance of ISS-SPE was demonstrated by extracting chelates of Co(II) and Ni(II) from water samples. Under the optimized conditions, the preconcentration factors are 51 and 45, respectively, and the detection limits are 0.9 and 0.6???g?L^?1. The method was validated by the analysis of a certified reference material and by comparing results with those obtained by electrothermal AAS.

Silica-bonded N-propylsulfamic acid as a recyclable catalyst for the synthesis of 2,3-dihydroquinazolin-4(1H)-ones

2,3-Dihydroquinazolin-4(1H)-one derivatives are synthesized via a one-pot,three component reaction of isatoic anhydride and an aromatic aldehyde with ammonium acetate or primary amine catalyzed by silica-bonded N-propylsulfamic acid(SBNPSA) in refluxing ethanol.     

SBA-15-functionalized TEMPO confined ionic liquid: an efficient catalyst system for transition-metal-free aerobic oxidation of alcohols with improved selectivity

A novel SBA-15-functionalized TEMPO confined ionic liquid [BMIm]Br was found to be a highly efficient and recyclable catalyst system for the transition-metal-free aerobic oxidation of a wide range of structurally diverse alcohols. Thanks to the strong physical confinement of the ionic liquid inside the mesochannels of SBA-15-supported TEMPO, the resulting solid catalyst showed improved selectivity in the aerobic oxidation of allylic alcohols. The catalyst can be recovered and re-used for at least 11 reaction runs without significant loss of either activity or confined IL.     

Magnetic properties of isostructural M(H2O)4[Au(CN)4]2-based coordination polymers (M = Mn, Co, Ni, Cu, Zn) by SQUID and μSR studies

A series of isomorphous M(H(2)O)(4)[Au(CN)(4)](2)·4H(2)O (M = Mn, Co, Ni, Zn; Cu is similar) coordination polymers was synthesized from the reaction of M(II) with KAu(CN)(4); they consist of octahedrally coordinated metal centres with four equatorial water molecules and trans-axial N-cyano ligands from [Au(CN)(4)](-) moieties, generating a linear 1-D chain of M(H(2)O)(4)[Au(CN)(4)]-units. An additional interstitial [Au(CN)(4)](-) unit forms AuN and hydrogen bonds with adjacent chains. The Cu(II) system readily loses water to yield Cu[Au(CN)(4)](2)(H(2)O)(4), which was not structurally characterized. The magnetic properties of these polymers were investigated by a combination of SQUID magnetometry and zero-field muon spin relaxation (ZF-μSR). Only weak antiferromagnetic interactions along the chains are mediated by the [Au(CN)(4)]-units, but the ZF-μSR data indicates that interchain interactions yield a phase transition to a magnetically ordered state for Cu[Au(CN)(4)](2)(H(2)O)(4) below 0.6 K, while for M(H(2)O)(4)[Au(CN)(4)](2)·4H(2)O (M = Co), depopulation of zero-field split Kramer's doublets to an effective "S = 1/2" ground state yields a transition to a spin-frozen magnetic state below 0.26 K. On the other hand, only a simple slowing-down of spins above 0.02 K is observed for the more weakly zero-field split M(H(2)O)(4)[Au(CN)(4)](2)·4H(2)O (M = Mn, Ni) complexes.