Students’ conceptualisations of multiplication as repeated addition or equal groups in relation to multi-digit and decimal numbers

Multiplicative understanding is essential for mathematics learning and is supported by models for multiplication, such as equal groups and rectangular area, different calculations and arithmetical properties, such as distributivity. We investigated two students’ multiplicative understanding through their connections between models for multiplication, calculations and arithmetical properties and how their connections changed during the school years when multiplication is extended to multi-digits and decimal numbers. The case studies were conducted by individual interviews over five semesters. The students did not connect calculations to models for multiplication, but showed a robust conceptualisation of multiplication as repeated addition or equal groups. This supported their utilisation of distributivity to multi-digits, but constrained their utilisation of commutativity and for one student to make sense of decimal multiplication     

Ion mobility spectrometric analysis of vaporous chemical warfare agents by the instrument with corona discharge ionization ammonia dopant ambient temperature operation

The ion mobility behavior of nineteen chemical warfare agents (7 nerve gases, 5 blister agents, 2 lachrymators, 2 blood agents, 3 choking agents) and related compounds including simulants (8 agents) and organic solvents (39) was comparably investigated by the ion mobility spectrometry instrument utilizing weak electric field linear drift tube with corona discharge ionization, ammonia doping, purified inner air drift flow circulation operated at ambient temperature and pressure. Three alkyl methylphosphonofluoridates, tabun, and four organophosphorus simulants gave the intense characteristic positive monomer-derived ion peaks and small dimer-derived ion peaks, and the later ion peaks were increased with the vapor concentrations. VX, RVX and tabun gave both characteristic positive monomer-derived ions and degradation product ions. Nitrogen mustards gave the intense characteristic positive ion peaks, and in addition distinctive negative ion peak appeared from HN3. Mustard gas, lewisite 1, o-chlorobenzylidenemalononitrile and 2-mercaptoethanol gave the characteristic negative ion peaks. Methylphosphonyl difluoride, 2-chloroacetophenone and 1,4-thioxane gave the characteristic ion peaks both in the positive and negative ion mode. 2-Chloroethylethylsulfide and allylisothiocyanate gave weak ion peaks. The marker ion peaks derived from two blood agents and three choking agents were very close to the reactant ion peak in negative ion mode and the respective reduced ion mobility was fluctuated. The reduced ion mobility of the CWA monomer-derived peaks were positively correlated with molecular masses among structurally similar agents such as G-type nerve gases and organophosphorus simulants; V-type nerve gases and nitrogen mustards. The slope values of the calibration plots of the peak heights of the characteristic marker ions versus the vapor concentrations are related to the detection sensitivity, and within chemical warfare agents examined the slope values for sarin, soman, tabun and nitrogen mustards were higher. Some CWA simulants and organic solvents gave the ion peaks eluting at the similar positions of the CWAs, resulting in false positive alarms.     

Nitrogen-15 Fractionation in the Thermal Decomposition of Nitrous Oxide of Natural Isotopic Composition

Abstract

The ¹⁵N fractionation in the thermal decompostion of nitrous oxide (N₂O) of natural isotopic composition has been investigated in quartz reaction vessel in the temperature interval 888–1073K. The formulas relating the observed experimentally ¹⁵N fractionations with the primary ¹⁵N kinetic isotope effect, (k ¹⁴/k ¹⁵)_p for ¹⁴N¹⁵N¹⁶O, and secondary ¹⁵N kinetic isotope effect, (k ¹⁴/k ¹⁵)_s for ¹⁵N¹⁴N¹⁶O, have been derived. The experimentally estimated ¹⁵N kinetic isotope effects have been compared with the primary and secondary ¹⁵N kinetic isotope effects calculated with the absolute rate theory formulations applied to linear three atom molecules. A good agreement was found for the primary ¹⁵N kinetic isotope effect, (k ¹⁴/k ¹⁵)_p, in the temperature interval 888–1007K. But at 1073K the decompositions of N₂O, accompanied by NO (nitric oxide) formation proceed with a twice times smaller primary kinetic isotope effect, (k ¹⁴/k ¹⁵)_p of 1.0251 ± 0.0009, only, suggesting the nonlinear transition state structures with participation of the fourth external atom at high temperature decompositions of nitrous oxide. The nitrogen isotope effects determined in this study correlate well with nitrogen isotope fractionations observed in the natural biological, earth and atmospheric processes.     

电激励DF化学激光器光腔流场荧光光谱测量与分析

 观察并记录了增大D₂流量时DF激光光腔流场可见光荧光的变化现象,对光轴处的可见光荧光进行了光谱测量,使用波长为632.8 nm和543.5 nm的He-Ne激光器对光谱仪进行标定。对激光器光腔内介质成分进行了理论分析,并理论计算了DF高次泛频谱线及D原子谱线,通过比对荧光的实验测量光谱与光腔内介质成分谱线,发现荧光是由F,He,D,N,DF及其它激发态介质共同形成的,对光轴处荧光的颜色构成作出了解释。     

大长宽比矩形有源非稳腔模式的数值模拟

 利用快速傅里叶变换算法和薄层增益近似方法,在Matlab计算平台上,对大长宽比正支共焦有源谐振腔进行了数值模拟。得到了长宽比为3.6∶1的大功率化学激光器输出的近场模式强度和相位分布,以及理想聚焦下的远场光斑的强度分布。给出了由非均匀增益引起的强度分布不均对远场光斑的影响。得到的近场图像结果和实验结果基本一致,表明本方法可以对大长宽比矩形腔的输出模式进行仿真,从而为激光器的光束质量改善提供计算参考。     

Performance analysis of PDMA-based hybrid satellite–terrestrial networks with decode-and-forward relaying

As one of the most promising non-orthogonal multiple access (NOMA) technologies in 5G communication, pattern division multiple access (PDMA) has theoretically higher spectrum utilization and a larger communication capacity than conventional orthogonal multiple access (OMA) technologies. In this letter, PDMA is applied to hybrid satellite–terrestrial networks with decode-and-forward (DF) relaying in the downlink, and an in-depth study on the performance of outage probability (OP), ergodic capacity and system throughput is performed. For a more comprehensive analysis, hybrid satellite–terrestrial relay networks (HSTRNs) with conventional OMA technology are used in the comparative analysis. Analysis and simulation results show that PDMA-based hybrid satellite–terrestrial relay networks outperform the other system in terms of OP and ergodic capacity.     

New Stable Complexes of Au(III) with Biuret: X-ray Structure of cis-[Au(Biu)Br2]PPh4 and Ab Initio Investigation of cis-[Au(Biu)X2]−

Two anionic complexes of Au(III) with the bioligand biuret, cis-[Au(Biu)X₂]^? (BiuH₂=biuret, X=Cl, Br), have been synthesized and characterized. The molecular structure of cis-[Au(Biu)Br₂]PPh₄ has been determined by X-ray diffraction analysis. The complex anion has square-planar geometry with one deprotonated biuret dianion coordinated bidentately to the metal center via the terminal amino nitrogen atoms and two bromide ions in cis positions. There are no significant intermolecular Au-Au interactions in the solid state. Ab initio calculations of the geometric structure at different computational levels for biuret and both anionic complexes as well an IR study of the structures obtained are performed.     

Polarized Infrared and Raman Spectra and Ab-Initio Calculations of 2-(Methylthio)Benzothiazole

Abstract

The infrared spectra of 2-(methylthio)benzothiazole have been measured from 4000 to 180 cm^?1 for liquid and polycrystalline samples, polarized spectra of oriented films have also been obtained. the Raman spectra of polycrystalline and liquid samples have been investigated. the structural parameters, energies and vibrational frequencies have been calculated from ab-initio RHF calculations using the 6-31G?? basis set for various conformations. a detailed assignment of most of the observed bands has been proposed on the basis of the infrared dichroism, Raman polarization data and frequency calculations.     

Validation of computations by high pressure measurements: Solutions to problems that experiments cannot solve

Abstract

Calculations of the properties of condensed matter systems can be crucially tested by comparison with their experimental pressure behavior. When validated by such a comparison theoretical models become reliable computer experiments and can be used to explore properties of the system which are intrinsically unobservable by experiment alone.

Three examples are given of such methods:

(i) The behavior of wurtzite indium nitride under pressure which is shown to be due to a second-order isostructural phase transition.

(ii) The instability of tetrahedrally bonded semiconductors (Ge) under pressure which turns out to be related to a second-order process.

(iii) The explanation of the lattice dynamics of a-boron at ambient conditions which can be understood only by comparison of its high pressure behavior with calculations.     

Effect of correlation on energy of solids

In the present paper we make an attempt to model the lattice energy with the lattice constants through the first-principles calculations. This formalism is designed particularly for application with the self-consistent pseudopotential (PP) method within the density functional (DF) framework and includes exchange and correlation effects. Applying the above formalism we have calculated the lattice energy and correlation energy for a number of solids belonging to groups I–VII and II–VI of the periodic table. The convergence of our results is in the favour of used PP. These results will be helpful in determining various structural and elastic properties of these solids and in the generation of equation of state.