Torsions of 3-Dimensional Small Covers

In this paper,it is shown that for a 3-dimensional small cover M over a polytope P,there are only 2-torsions in H1(M;Z).Moreover,the mod 2 Betti number growth of finite covers of M is studied.     

Triple Systems are Eulerian

An Euler tour of a hypergraph (also called a rank‐2 universal cycle or 1‐overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, using a graph‐theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour. Horan and Hurlbert have previously shown that for every admissible order >3, there exists a Steiner triple system with an Euler tour, while Dewar and Stevens have proved that every cyclic Steiner triple system of order >3 and every cyclic twofold triple system admits an Euler tour.     

The Hamilton–Waterloo Problem for ‐Factors and ‐Factors

The Hamilton–Waterloo problem asks for a 2‐factorization of (for v odd) or minus a 1‐factor (for v even) into ‐factors and ‐factors. We completely solve the Hamilton–Waterloo problem in the case of C₃‐factors and ‐factors for .     

The fourth power mean of the general 2-dimensional Kloostermann sums mod <Emphasis Type="Italic">p</Emphasis>

The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it.     

Phase II monitoring of changes in mean from high‐dimensional data

The generalized T² chart (GT‐chart), which is composed of the T² statistic based on a small number of principal components and the remaining components, is a popular alternative to the traditional Hotelling's T² control chart. However, the application of the GT‐chart to high‐dimensional data, which are now ubiquitous, encounters difficulties from high dimensionality similar to other multivariate procedures. The sample principal components and their eigenvalues do not consistently estimate the population values, and the GT‐chart relying on them is also inconsistent in estimating the control limits. In this paper, we investigate the effects of high dimensionality on the GT‐chart and then propose a corrected GT‐chart using the recent results of random matrix theory for the spiked covariance model. We numerically show that the corrected GT‐chart exhibits superior performance compared to the existing methods, including the GT‐chart and Hotelling's T² control chart, under various high‐dimensional cases. Finally, we apply the proposed corrected GT‐chart to monitor chemical processes introduced in the literature.     

Adsorptive Removal of Cd,Cu, Ni and Mn from Environmental Samples Using Fe3O4-Zro2@APS Nanocomposite: Kinetic and Equilibrium Isotherm Studies

In this study, Fe₃O₄-ZrO₂ functionalized with 3-aminopropyltriethoxysilane (Fe₃O₄-ZrO₂@APS) nanocomposite was investigated as a nanoadsorbent for the removal of Cd(II), Cu(II), Mn (II) and Ni(II) ions from aqueous solution and real samples in batch mode systems. The prepared magnetic nanomaterials were characterized using X-ray powder diffraction (XRD), scanning electron microscopy/energy dispersion x-ray (SEM/EDX) Fourier transform infrared spectroscopy (FTIR) and transmission electron microscopy (TEM). Factors (such as adsorbent dose and sample pH) affecting the adsorption behavior of the removal process were studied using the response surface methodology. Under optimized condition, equilibrium data obtained were fitted into the Langmuir and Freundlich isotherms and the data fitted well with Langmuir isotherms. Langmuir adsorption capacities (mg/g) were found to be 113, 111, 128, and 123 mg/g for Cd, Cu, Ni and Mn, respectively. In addition, the adsorption kinetics was analyzed using five kinetic models, pseudo-first order, pseudo-second order, intraparticle diffusion and Boyd models. The adsorbent was successfully applied for removal of Cd(II), Cu(II), Mn (II) and Ni(II) ions in wastewater samples.     

The Physico-Chemical Properties of Glipizide: New Findings

The present work is a concrete example of how physico-chemical studies, if performed in depth, are crucial to understand the behavior of pharmaceutical solids and constitute a solid basis for the control of the reproducibility of the industrial batches. In particular, a deep study of the thermal behavior of glipizide, a hypoglycemic drug, was carried out with the aim of clarifying whether the recognition of its polymorphic forms can really be done on the basis of the endothermic peak that the literature studies attribute to the melting of the compound. A number of analytical techniques were used: thermal techniques (DSC, TGA), X-ray powder diffraction (XRPD), FT-IR spectroscopy and scanning electron microscopy (SEM). Great attention was paid to the experimental design and to the interpretation of the combined results obtained by all these techniques. We proved that the attribution of the endothermic peak shown by glipizide to its melting was actually wrong. The DSC peak is no doubt triggered by a decomposition process that involves gas evolution (cyclohexanamine and carbon dioxide) and formation of 5-methyl-N-[2-(4-sulphamoylphenyl) ethyl] pyrazine-2-carboxamide, which remains as decomposition residue. Thermal treatments properly designed and the combined use of DSC with FT-IR and XRPD led to identifying a new polymorphic form of 5-methyl-N-[2-(4-sulphamoylphenyl) ethyl] pyrazine-2-carboxamide, which is obtained by crystallization from the melt. Hence, our results put into evidence that the check of the polymorphic form of glipizide cannot be based on the temperature values of the DSC peak, since such a peak is due to a decomposition process whose Tonset value is strongly affected by the particle size. Kinetic studies of the decomposition process show the high stability of solid glipizide at room temperature.     

Inclined Substrate Deposition of Nanostructured TiO2 Thin Films for DSSC Application

Nanostructured TiO₂ films were deposited onto Indium Tin Oxide (ITO) and glass substrates by dc reactive magnetron sputtering at different substrate inclination angles. The structural and optical properties of the deposited films were studied by X-ray diffraction, scanning electron microscopy and UV–Vis spectrophotometer, respectively. Dye-sensitized solar cells (DSSC) were assembled using these TiO₂ films as photoelectrodes and the effect of the substrate inclination angle in the preparing process of TiO₂ films on the DSSC conversion efficiency was studied.     

Design,Synthesis, and Evaluation of Dihydropyranopyrazole Derivatives as Novel PDE2 Inhibitors for the Treatment of Alzheimer’s Disease

Phosphodiesterase 2 (PDE2) has been regarded as a novel target for the treatment of Alzheimer’s disease (AD). In this study, we obtained (R)-LZ77 as a hit compound with moderate PDE2 inhibitory activity (IC₅₀ = 261.3 nM) using a high-throughput virtual screening method based on molecular dynamics. Then, we designed and synthesized 28 dihydropyranopyrazole derivatives as PDE2 inhibitors. Among them, compound (+)-11h was the most potent PDE2 inhibitor, with an IC₅₀ value of 41.5 nM. The molecular docking of PDE2-(+)-11h reveals that the 4-(trifluoromethyl)benzyl)oxyl side chain of the compound enters the H-pocket and forms strong hydrophobic interactions with L770/L809/F862, which improves inhibitory activity. The above results may provide insight for further structural optimization of highly potent PDE2 inhibitors and may lay the foundation for their use in the treatment of AD.