Stability and convergence of the two parameter cubic spline collocation method for delay differential equations

AbstractIn this paper, we propose the cubic spline collocation method with two parameters for solving delay differential equations (DDEs). Some results of the local truncation error and the convergence of the spline collocation method are given. We also obtain some results of the linear stability and the nonlinear stability of the method for DDEs. In particular, we design an algorithm to obtain the ranges of the two parameters α,β which are necessary for the P-stability of the collocation method. Some illustrative examples successfully verify our theoretical results

Achieving Strong Chemical Interface and Superior Energy-Saving Capability at the Crosslinks of Rubber Composites Containing Graphene Oxide Using Thiol-Vinyl Click Chemistry

Rapidly developments in international transportation inevitably lead to an increase in the consumption of energy and resources. Minimizing the rolling resistance of tires in this scenario is a pressing challenge. To lower the rolling resistance of tires, enhancing the interaction between fillers and rubber molecules while improving the dispersion of fillers are required to reduce the internal mutual friction and viscous loss of rubber composites. In this study, graphene oxide (GO) was modified using γ-mercaptopropyltrimethoxysilane (MPTMS) with thiol groups. A modified GO/natural rubber (MGO/NR) masterbatch with a fine dispersion of MGO was then introduced into solution-polymerized styrene butadiene rubber (SSBR) to create an MGO/SiO2/SSBR composite. During the crosslinking process at high temperatures, a strong chemical interface interaction between the MGO and rubber molecules was formed by the thiol-vinyl click reaction. The MGO sheets also act as crosslinks to enhance the crosslinking network. The results showed that the rolling resistance of the MGO SiO2/SSBR composite was superior by 19.4% and the energy loss was reduced by 15.7% compared with that of the base SiO2/SSBR composite. Strikingly, the wear performance and wet skid resistance improved by 19% and 17.3%, respectively. These results showed a strong interface that not only improved rolling resistance performance but also contributed to balancing the “magic triangle” (the combination of wear resistance, fuel efficiency, and traction) properties of tires

Intra-Storm Temporal Patterns of Rainfall in China Using Huff Curves

Intra-storm temporal distributions of precipitation are important for infiltration, runoff, and erosion process understanding and models. A convenient and established method for characterizing precipitation hyetographs is the use of non-dimensional Huff curves. In this study, 11,801 erosive rainfall events with 1 min resolution data collected over 30 to 40 years from 18 weather stations located across the central and eastern parts of China were analyzed to produce Huff curves. Each event was classified according to the quartile period within the event that contained the greatest fraction of rainfall. The results showed that 38.3% of events had the maximum rainfall amounts in the first quartile, followed by the second (26.8%), third (22.4%), and fourth (12.5%) quartiles. Quartile I and II events were generally characteristic of shorter duration and heavier intensity events. Quartile I events averaged 23% shorter durations than quartile IV events, whereas the mean intensity (Iavg), mean maximum 30 min intensity (I30), and mean rainfall erosivity index (EI30) were 1.71, 1.22, and 1.23 times greater, respectively, than those for quartile IV and were significant at a 5% level based on two-sample t-tests. The proportion of quartile I events was less for events of longer duration, whereas the proportions of quartile III and IV events were greater. Two-sample Kolmogorov-Smirnov tests suggested that regional Huff curves can be derived for the central and eastern parts of China. Regional Huff curves developed in this study exhibited dissimilarities in terms of the percentages of storms for different quartiles and the shapes of the curves compared to those reported for Illinois, peninsular Malaysia, and Santa Catarina in Brazil

Diaqua­(2,2′-bipyridine-6,6′-dicarboxyl­ato)nickel(II)

In the title compound, [Ni(C12H6N2O4)(H2O)2], the NiII atom (site symmetry 2) displays a distorted cis-NiN2O4 octa­hedral coordination geometry with two N atoms and two O atoms of the tetra­dentate 2,2′-bipyridine-6,6′-dicarboxyl­ate ligand in the equatorial plane and two water mol­ecules in axial positions. The complete dianionic ligand is generated by crystallographic twofold symmetry. In the crystal, a two-dimensional supra­molecular structure parallel to (001) is formed through O—H⋯O hydrogen-bond inter­actions between the coordinated water mol­ecules and the O atoms of nearby carboxyl­ate groups

N-Ethyl-N-phenyl-N′-tosyl­formamidine

The title compound, C16H18N2O2S, was obtained as an unexpected product while attempting to form carbon–nitro­gen bonds by catalytic amidation. The mol­ecule displays an E conformation about the C=N double bond. The planes of the two aromatic rings in the mol­ecule form a dihedral angle of 47.06 (9)°

Sialolipoma of the Floor of the Mouth: A Case Report

Intra-oral lipoma is a well-known entity, but lipomatous tumors including salivary gland tissue containing clustered or peripherally located ducts and acinar cells are uncommon. They are a newly recognized entity of salivary gland lipoma, designated sialolipoma. We describe a case of sialolipoma arising in the floor of the mouth presenting with apparently normal salivary gland tissue, as demonstrated by both histologic and immunohistochemical findings, in a 67-year-old female. Complete surgical removal of the tumor with preservation of the sublingual gland was implemented after a careful examination confirming that the lesion did not originate from the sublingual gland

Central obesity and atherogenic dyslipidemia in metabolic syndrome are associated with increased risk for colorectal adenoma in a Chinese population

<p>Abstract</p> <p>Background</p> <p>Metabolic syndrome (MetS) is composed of cardiovascular risk factors including insulin resistance, obesity, dyslipidemia, and hypertension. Most of the components of MetS have been linked to the development of neoplasm. The purpose of this study was to evaluate the relationship between individual components of MetS and colorectal adenoma.</p> <p>Methods</p> <p>The study subjects were recruited from a pool of 4872 individuals who underwent a health check-up examination during the period January 2006 to May 2008. Each participant fulfilled a structured questionnaire. MetS was defined based on the America Heart Association and National Heart Lung Blood Institute criteria. Subjects with history of colon cancer, colon polyps, colitis, or prior colonic surgery were excluded.</p> <p>Results</p> <p>A total of 4122 subjects were included for final analysis (2367 men and 1755 women; mean age, 49.6 ± 11.7 years). Of them, MetS was diagnosed in 708 men (29.9%) and in 367 women (20.9%). Among the patients with MetS, 34.6% had adenoma, 31.7% had hyperplastic polyps and 23.3% were polyp-free (p < 0.0001, Chi-square test). The adjusted OR for colorectal adenoma was significantly higher in the subjects with MetS (OR, 1.31, CI: 1.09-1.57). A stronger association between MetS and colorectal adenoma was found in men (OR:1.44, CI:1.16-1.80) than in women (OR:1.04, CI:0.74-1.46). The adjusted OR for adenoma increased as the number of MetS components increased (p for trend = 0.0001 ). When the individual components of MetS were analyzed separately, only central obesity (OR:1.36, CI:1.14-1.63), low HDL cholesterol levels (OR:1.30, CI:1.10-1.54) and high triglyceride levels (OR:1.26, CI:1.04-1.53) were independently associated with colorectal adenoma.</p> <p>Conclusions</p> <p>Of the components of MetS analyzed in this study, central obesity and dyslipidemia are independent risk factors for colorectal adenoma. With regard to the prevention of colorectal neoplasm, life-style modification such as weight reduction is worthwhile.</p