Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

数学建模对高中生构建数学底层思维的作用及其教学实施建议

数学底层思维即用数学的眼光观察世界、用数学的思维分析世界以及用数学的语言表达世界,是人们面对自然和社会中纷繁多样的现象和问题时,所展现的自发的、不依赖监督的、融汇数学学科核心素养的思维方式.作为国家高中新课程标准中数学六大核心素养之一的数学建模,是培养学生数学底层思维的良好载体,对人才培养和社会发展均起到良好的促进作用.本文主要阐述了数学建模对高中生构建数学底层思维的作用,并结合教学实例给出教学实施建议.     

Negative thermal expansion in NbF_3 and NbOF_2:A comparative theoretical study

Thermal expansion control is always an obstructive factor and challenging in high precision engineering field. Here,the negative thermal expansion of Nb F_3 and Nb OF_2 was predicted by first-principles calculation with density functional theory and the quasi-harmonic approximation(QHA). We studied the total charge density, thermal vibration, and lattice dynamic to investigate the thermal expansion mechanism. We found that the presence of O induced the relatively strong covalent bond in Nb OF_2, thus weakening the transverse vibration of F and O in Nb OF_2, compared with the case of Nb F_3.In this study, we proposed a way to tailor negative thermal expansion of metal fluorides by introducing the oxygen atoms.The present work not only predicts two NTE compounds, but also provides an insight on thermal expansion control by designing chemical bond type.     

Dynamic Modeling of the Feed Drive System of a CNC Metal Cutting Machine

Studying the vibrational behavior of feed drive systems is important for enhancing the structural performance of computer numerical control (CNC) machines. The preload on the screw and nut position have a great influence on the vibration characteristics of the feed drive as two very important operational conditions. Rotational acceleration of the screw also affects the performance of the CNC feed drive when machining small parts. This paper investigates the influence of preload and nut position on the vibration characteristics of the feed drive system of a CNC metal cutting machine in order to be able to eliminate an observed resonance occurred at high rotational speeds of the screw, corresponding to high feed rates. Additionally, rational structural parameters of the feed drive system are selected in order to increase the rotational acceleration for improving the performance of the CNC machine. Experiments and analyses showed that by selecting specific parameters of feed drive system and simultaneously applying a certain value of preload, a 97% increase in rotational acceleration and 30% time reduction considering the vibration resistance at high rotational speeds can be achieved.     

Stability of Multiplier Ideal Sheaves

Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.     

Dinuclear gold (I)-di-N-heterocyclic carbene complexes: syntheses,structure, density functional theory calculation and photoluminescence study

The synthesis and characterizations for a series of dinuclear gold (I)-di-NHC complexes, 1–8 through the trans-metalation method of their respective silver (I)-di-NHC complexes, i–viii are reported (where NHC = N-heterocyclic carbene). The successful complexation of a series of unusual non-symmetrical and symmetrical di-NHC ligands, 3,3'-(ethane-1,2-diyl)-1-alkylbenzimidazolium-1'-butylbenzimidazolium (with alkyl = methyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, benzyl) with the gold (I) ions are suggested by elemental analysis, Fourier transform-infrared, ¹H- and ¹³C-NMR data. The ¹³C-NMR spectra of 1–8 show a singlet sharp peak in the range of 190.00–192.00 ppm, indicating the presence of a carbene carbon that bonded to the gold (I) ion. From single crystal X-ray diffraction data, the structure of complex 6 with the formula of [di-NHC-Au (I)]₂·2PF₆ is obtained [where NHC = 3,3'-(ethane-1,2-diyl)-1-hexylbenzimidazolium-1'-butylbenzimidazolium]. The photophysical study in solid state of 6 displays an intense photoluminescence with a strong emission maxima, λ_em = 480 nm, upon excitation at 340 nm at room temperature. Interestingly, the emission maximum at 77 K shows a structural character with a strong peak at 410 nm, a medium at 433 nm and a weak at 387 nm, accompanied by a tail band to about 500 nm.     

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

Kinetics Study of the Thermal Decomposition of Post-consumer Poly(Ethylene Terephthalate) in an Argon Atmosphere

The thermal decomposition of post-consumer samples of a carbonated water bottle made of poly(ethylene terephthalate), PC-PET, was examined by linear temperature programing under an argon atmosphere to determine its mass loss kinetics. A simple kinetic model, called the first order pseudo single-component model, was used. The total weight-loss of each sample assumed to be in two periods, with each period corresponding to a one step decomposition of the PC-PET to volatiles. Three methods for determining the kinetic parameters by thermal gravimetric analysis were examined: differential analysis at a constant heating rate (differential), temperatures of a given conversion at a number of heating rates (isoconversional), and the maximum rate at multiple heating rates (peak temperature). The latter two multiple heating rates methods results were comparable to each other but they were not in agreement with the results from the differential method. The results of the differential method were insensitive to the heating rate and consistent with kinetics data reported in the literature for PET.     

Development and validation of an ultra‐high‐performance liquid chromatography–tandem mass spectrometry method to determine the bioavailability of warfarin and its major metabolite 7‐hydroxy warfarin in rats dosed with oral formulations containing different polymorphic forms

A simple, sensitive and rapid ultra‐high‐performance liquid chromatography–electrospray ionization–tandem mass spectrometry method was developed and validated for the quantification of warfarin and 7‐hydroxy warfarin in Sprague Dawley (SD) rats. Animals were administered a single dose of warfarin sodium formulations (crystalline and amorphous) at 12 mg/kg via oral gavage and blood was drawn over a 96‐h time course. Sample process recoveries, matrix effect and analyte stability were determined. The linearity for warfarin and 7‐hydroxy warfarin was from 5 to 2000 ng/mL in blank SD rat plasma. Correlation coefficients (r²) for standard calibration curves were >.98 and analytes quantified within ±15% of target at all calibrator concentrations. The average percent accuracy and precision for intra‐ and inter‐day were 93.7%–113.8% and ≤12.1%, respectively, for warfarin and 7‐hydroxy warfarin, across the quality control standards (5, 10, 500, 1800 and 2000 ng/mL). Acceptable analytical recovery (>55%) was achieved with process efficiencies >41.5% and matrix effects <139.9% over the analytical range. Both analytes were stable in stock solution, autosampler, benchtop and three cycles of freeze–thaw with percent accuracy ≥90.2% and precision (percent relative standard deviation) ≤14%. The validated method was successfully applied to a pre‐clinical bioavailability study of crystalline and amorphous warfarin sodium formulations in SD rats.