Hamiltonian Formulation of Singular Lagrangians on Time Scales

The Hamiltonian formulation of Lagrangian on time scale is investigated and the equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed.     

Multiple Categories: The Equivalence of a Globular and a Cubical Approach

We show the equivalence of two kinds of strict multiple category, namely the well-known globular ω-categories, and the cubical ω-categories with connections.     

Interweaving Markov Chain Monte Carlo Strategies for Efficient Estimation of Dynamic Linear Models

In dynamic linear models (DLMs) with unknown fixed parameters, a standard Markov chain Monte Carlo (MCMC) sampling strategy is to alternate sampling of latent states conditional on fixed parameters and sampling of fixed parameters conditional on latent states. In some regions of the parameter space, this standard data augmentation (DA) algorithm can be inefficient. To improve efficiency, we apply the interweaving strategies of Yu and Meng to DLMs. For this, we introduce three novel alternative DAs for DLMs: the scaled errors, wrongly scaled errors, and wrongly scaled disturbances. With the latent states and the less well known scaled disturbances, this yields five unique DAs to employ in MCMC algorithms. Each DA implies a unique MCMC sampling strategy and they can be combined into interweaving and alternating strategies that improve MCMC efficiency. We assess these strategies using the local level model and demonstrate that several strategies improve efficiency relative to the standard approach and the most efficient strategy interweaves the scaled errors and scaled disturbances. Supplementary materials are available online for this article.     

The Antiproliferative and Apoptotic Effects of a Novel Quinazoline Carrying Substituted-Sulfonamides: In Vitro and Molecular Docking Study

In order to investigate for a new effective and safe anticancer drug, we synthesized a novel series of quinazoline containing biologically active substituted-sulfonamide moiety at 3- position 4a–n. The structure of the newly prepared compounds was proved by microanalysis, IR, ¹H-NMR, ¹³C-NMR and mass spectral data. All the synthesized compounds were evaluated for their in vitro cytotoxic activity in numerous cancer cell lines including A549, HepG-2, LoVo and MCF-7 and normal HUVEC cell line. The two most active compounds 4d and 4f were then tested for their apoptosis induction using DNA content and Annexin V-FITC/PI staining. Moreover, apoptosis initiation was also confirmed using RT-PCR and Western blot. To further understand the binding preferences of quinazoline sulfonamides, docking simulations were used. Among the fourteen new synthesized compounds, we found that compounds 4d and 4f exerted the strongest cytotoxicity against MCF-7 cells with an IC₅₀ value of 2.5 and 5 μM, respectively. Flow cytometry data revealed the ability of compounds 4d and 4f to mediate apoptosis and arrest cell cycle growth at G1 phase. Furthermore, RT-PCR and Western blot results suggested that both 4d and 4f activates apoptotic cell death pathway in MCF-7 cells. Molecular docking assessments indicated that compounds 4d and 4f fit perfectly into Bcl2’s active site. Based on the biological properties, we conclude that both compounds 4d and 4f could be used as a new type of anticancer agent, which provides a scientific basis for further research into the treatment of cancer.     

Capture of carbon dioxide from air and flue gas in the alkylamine-appended metal-organic framework mmen-Mg2(dobpdc)

Two new metal-organic frameworks, M(2)(dobpdc) (M = Zn (1), Mg (2); dobpdc(4-) = 4,4'-dioxido-3,3'-biphenyldicarboxylate), adopting an expanded MOF-74 structure type, were synthesized via solvothermal and microwave methods. Coordinatively unsaturated Mg(2+) cations lining the 18.4-?-diameter channels of 2 were functionalized with N,N'-dimethylethylenediamine (mmen) to afford Mg(2)(dobpdc)(mmen)(1.6)(H(2)O)(0.4) (mmen-Mg(2)(dobpdc)). This compound displays an exceptional capacity for CO(2) adsorption at low pressures, taking up 2.0 mmol/g (8.1 wt %) at 0.39 mbar and 25 °C, conditions relevant to removal of CO(2) from air, and 3.14 mmol/g (12.1 wt %) at 0.15 bar and 40 °C, conditions relevant to CO(2) capture from flue gas. Dynamic gas adsorption/desorption cycling experiments demonstrate that mmen-Mg(2)(dobpdc) can be regenerated upon repeated exposures to simulated air and flue gas mixtures, with cycling capacities of 1.05 mmol/g (4.4 wt %) after 1 h of exposure to flowing 390 ppm CO(2) in simulated air at 25 °C and 2.52 mmol/g (9.9 wt %) after 15 min of exposure to flowing 15% CO(2) in N(2) at 40 °C. The purity of the CO(2) removed from dry air and flue gas in these processes was estimated to be 96% and 98%, respectively. As a flue gas adsorbent, the regeneration energy was estimated through differential scanning calorimetry experiments to be 2.34 MJ/kg CO(2) adsorbed. Overall, the performance characteristics of mmen-Mg(2)(dobpdc) indicate it to be an exceptional new adsorbent for CO(2) capture, comparing favorably with both amine-grafted silicas and aqueous amine solutions.     

Fractional variational optimal control problems with delayed arguments

The paper deals with optimal control problems in the presence of delay in the state variables as well as the presence of the Riemann–Liouville fractional derivatives of the state variables. One example is analyzed in detail.     

Hydrogen Storage and Selective,Reversible O2 Adsorption in a Metal–Organic Framework with Open Chromium(II) Sites

A chromium(II)‐based metal–organic framework Cr₃[(Cr₄Cl)₃(BTT)₈]₂ (Cr‐BTT; BTT^3?=1,3,5‐benzenetristetrazolate), featuring coordinatively unsaturated, redox‐active Cr²⁺ cation sites, was synthesized and investigated for potential applications in H₂ storage and O₂ production. Low‐pressure H₂ adsorption and neutron powder diffraction experiments reveal moderately strong Cr–H₂ interactions, in line with results from previously reported M‐BTT frameworks. Notably, gas adsorption measurements also reveal excellent O₂/N₂ selectivity with substantial O₂ reversibility at room temperature, based on selective electron transfer to form Cr^III superoxide moieties. Infrared spectroscopy and powder neutron diffraction experiments were used to confirm this mechanism of selective O₂ binding.     

Highly Efficient Methylene Blue Dye Removal by Nickel Molybdate Nanosorbent

Removing methylene blue (MB) dye from aqueous solutions was examined by the use of nickel molybdate (α-NiMoO₄) as an adsorbent produced by an uncomplicated, rapid, and cost-effective method. Different results were produced by varying different parameters such as the pH, the adsorbent dose, the temperature, the contact time, and the initial dye concentration. Adsorbent dose and pH had a major removal effect on MB. Interestingly, a lower amount of adsorbent dose caused greater MB removal. The amount of removal gained was efficient and reached a 99% level with an initial methylene blue solution concentration of ≤160 ppm at pH 11. The kinetic studies indicated that the pseudo-second-order kinetic model relates very well with that of the obtained experimental results. The thermodynamic studies showed that removing the MB dye was favorable, spontaneous, and endothermic. Impressively, the highest quantity of removal amount of MB dye was 16,863 mg/g, as shown by the Langmuir model. The thermal regeneration tests revealed that the efficiency of removing MB (11,608 mg/g) was retained following three continuous rounds of recycled adsorbents. Adsorption of MB onto α-NiMoO₄ nanoparticles and its regeneration were confirmed by Fourier transform infrared spectroscopy (FTIR) analysis and scanning electron microscopy (SEM) analysis. The results indicated that α-NiMoO₄ nanosorbent is an outstanding and strong candidate that can be used for removing the maximum capacity of MB dye in wastewater.