On the number of eigenvalues for parameter‐dependent diffusion problem on time scales

In this study, we consider parameter‐dependent diffusion eigenvalue problem on time scales. An upper bound on the number of eigenvalues for this problem on a finite time scale is given.     

Applications of mapping cones over Clements–Lindström rings

We prove that Gotzmann's Persistence Theorem holds over every Clements–Lindström ring. We also construct the infinite minimal free resolution of a square-free Borel ideal over such a ring.     

Socio-Economic Impact of the Covid-19 Pandemic in the U.S.

This paper proposes a dynamic cascade model to investigate the systemic risk posed by sector-level industries within the U.S. inter-industry network. We then use this model to study the effect of the disruptions presented by Covid-19 on the U.S. economy. We construct a weighted digraph G = (V,E,W) using the industry-by-industry total requirements table for 2018, provided by the Bureau of Economic Analysis (BEA). We impose an initial shock that disrupts the production capacity of one or more industries, and we calculate the propagation of production shortages with a modified Cobb–Douglas production function. For the Covid-19 case, we model the initial shock based on the loss of labor between March and April 2020 as reported by the Bureau of Labor Statistics (BLS). The industries within the network are assigned a resilience that determines the ability of an industry to absorb input losses, such that if the rate of input loss exceeds the resilience, the industry fails, and its outputs go to zero. We observed a critical resilience, such that, below this critical value, the network experienced a catastrophic cascade resulting in total network collapse. Lastly, we model the economic recovery from June 2020 through March 2021 using BLS data.     

The Double Face of Ketamine—The Possibility of Its Identification in Blood and Beverages

The purpose of this study was to develop and validate a high-sensitivity methodology for identifying one of the most used drugs—ketamine. Ketamine is used medicinally to treat depression, alcoholism, and heroin addiction. Moreover, ketamine is the main ingredient used in so-called “date-rape” pills (DRP). This study presents a novel methodology for the simultaneous determination of ketamine based on the Dried Blood Spot (DBS) method, in combination with capillary electrophoresis coupled with a mass spectrometer (CE-TOF-MS). Then, 6-mm circles were punched out from DBS collected on Whatman DMPK-C paper and extracted using microwave-assisted extraction (MAE). The assay was linear in the range of 25–300 ng/mL. Values of limits of detection (LOD = 6.0 ng/mL) and quantification (LOQ = 19.8 ng/mL) were determined based on the signal to noise ratio. Intra-day precision at each determined concentration level was in the range of 6.1–11.1%, and inter-day between 7.9–13.1%. The obtained precision was under 15.0% (for medium and high concentrations) and lower than 20.0% (for low concentrations), which are in accordance with acceptance criteria. Therefore, the DBS/MAE/CE-TOF-MS method was successfully checked for analysis of ketamine in matrices other than blood, i.e., rose wine and orange juice. Moreover, it is possible to identify ketamine in the presence of flunitrazepam, which is the other most popular ingredient used in DRP. Based on this information, the selectivity of the proposed methodology for identifying ketamine in the presence of other components of rape pills was checked.     

A family of 2D and 3D coordination polymers involving a trigonal tritopic linker

Five new coordination polymers, namely, [Zn(2)(H(2)O)(2)(BBC)](NO(3))(DEF)(6) (DUT-40), [Zn(3)(H(2)O)(3)(BBC)(2)] (DUT-41), [(C(2)H(5))(2)NH(2)][Zn(2)(BBC)(TDC)](DEF)(6)(H(2)O)(7) (DUT-42), [Zn(10)(BBC)(5)(BPDC)(2)(H(2)O)(10)](NO(3))(DEF)(28)(H(2)O)(8) (DUT-43), and [Co(2)(BBC)(NO(3))(DEF)(2)(H(2)O)](DEF)(6)(H(2)O) (DUT-44), where BBC--4,4',4'-(benzene-1,3,5-triyl-tris(benzene-4,1-diyl))tribenzoate, TDC--2,5-thiophenedicarboxylate, BPDC--4,4'-biphenyldicarboxylate, DEF--,N-diethylformamide, were obtained under solvothermal conditions and structurally characterized. It has been shown that compounds DUT-40, DUT-41 and DUT-44 exhibit 2D layered structures with large hexagonal channels. Utilization of additional angular dicarboxylic TDC linker led to the formation of the DUT-42 compound with the structure consisting of three interpenetrated 3D networks. Using the linear co-linker dicarboxylic BPDC, DUT-43 was obtained which forms a complicated 3D architecture arising from the polycatenation of triple-layered 2D building units and 2D single layer units. The pore accessibility of the synthesized compounds in the liquid phase was proved by the adsorption of dye molecules.     

Synthesis of 3-hexahelicenol and its transformation to 3-hexahelicenylamines,diphenylphosphine, methyl carboxylate,and dimethylthiocarbamate

A nonphotochemical synthetic route to 3-hexahelicenol is reported. It involves a key [2+2+2] cycloisomerization of CH(3)O-substituted triyne that is readily available from 1-methoxy-3-methylbenzene and 1-bromo-2-(bromomethyl)naphthalene. Further functional group transformations led to 3-CO(2)CH(3), 3-NH(2), 3-PPh(2), and 3-SC(O)N(CH(3))(2) substituted hexahelicenes.     

Thin-Layer Chromatography with an Isolated Support and Forced Flow of the Mobile Phase

JPC – Journal of Planar Chromatography – Modern TLC -     

The influence of temperature on photodynamic cell killing in vitro with 5-aminolevulinic acid

Cell survival was investigated after exposing cells in vitro to different temperatures before or after photodynamic therapy with 5-aminolevulinic acid. The photodynamic process was found to be temperature dependent. Cells exposed for 1h to 41 degrees C before light exposure or to 7 degrees C after light exposure showed decreased survival. Furthermore, the photobleaching rate of protoporphyrin IX in the cells was found to increase with increasing temperature during the light exposure. Thus, the photodynamic effect with 5-aminolevulinic acid may be enhanced by heating the tumour area before, and by cooling it immediately after the treatment.     

Synthesis of the novel conjugated ω,ω′-diaryl/heteroaryl hexatriene system with the central double bond in a heteroaromatic ring: photochemical transformations of 2,3-divinylfuran derivatives

New β,β′-aryl/heteroaryl 2,3-divinylfuran derivatives (9a-d) in which a hexatriene system is a part of heteroaromatic ring have been synthesized and their photochemical properties were investigated. The primary process observed was the isomerization to trans,trans-isomers 9a-d followed by photochemical rearrangement of the furan ring giving the phototransposition products (I-IV). Stilbenes (20, 21) and phenanthrenes (22, 25, and 26), formed as secondary products from the competitive intermolecular cycloadditions, were also observed.