Controlling potential traps for filtering solitons in Bose-Einstein condensates

We present a controlling potential method for solving the three-dimensional Gross-Pitaevskii equation (GPE), which governs the nonlinear dynamics of the Bose-Einstein condensates (BECs) in an inhomogeneous potential trap. Our method allows one to construct ground and excited matter wave states whose longitudinal profiles can have bright solitons. This method provides the confining potential that filters and controls localized BECs. Moreover, it is predicted that, while the BEC longitudinal soliton profile is controlled and kept unchanged, the transverse profile may exhibit oscillatory breathers (the unmatched case) or move as a rigid body in the form of either coherent states (performing the Lissajous figures) or a Schrödinger cat state (matched case).     

Inequalities for Taylor series involving the divisor function

Czechoslovak Mathematical Journal - Let $$T(q) = sumlimits_{k = 1}^infty {d(k){q^k},,,,,left| q right| < 1,} $$ where d(k) denotes the number of positive divisors of the natural...     

A Menon-type identity with Dirichlet characters in residually finite Dedekind domains

This paper studies Menon–Sury’s identity in a general case, i.e., the Menon–Sury’s identity involving Dirichlet characters in residually finite Dedekind domains. By using the filtration of the ring \({\mathfrak {D}}/{\mathfrak {n}}\) and its unit group \(U({\mathfrak {D}}/{\mathfrak {n}})\), we explicitly compute the following two summations:

$$\begin{aligned} \sum _{\begin{array}{c} a\in U({\mathfrak {D}}/{\mathfrak {n}}) \\ b_1, \ldots , b_r\in {\mathfrak {D}}/{\mathfrak {n}} \end{array}} N(\langle a-1,b_1, b_2, \ldots , b_r \rangle +{\mathfrak {n}})\chi (a) \end{aligned}$$

and

$$\begin{aligned} \sum _{\begin{array}{c} a_{1},\ldots , a_{s}\in U({\mathfrak {D}}/{\mathfrak {n}}) \\ b_1, \ldots , b_r\in {\mathfrak {D}}/{\mathfrak {n}} \end{array}} N(\langle a_{1}-1,\ldots , a_{s}-1,b_1, b_2, \ldots , b_r \rangle +{\mathfrak {n}})\chi _{1}(a_1) \cdots \chi _{s}(a_s), \end{aligned}$$

where \({\mathfrak {D}}\) is a residually finite Dedekind domain and \({\mathfrak {n}}\) is a nonzero ideal of \({\mathfrak {D}}\), \(N({\mathfrak {n}})\) is the cardinality of quotient ring \({\mathfrak {D}}/{\mathfrak {n}}\), \(\chi _{i}~(1\le i\le s)\) are Dirichlet characters mod \({\mathfrak {n}}\) with conductor \({\mathfrak {d}}_i\).

     

单轴拉伸过程中双相不锈钢局部微观变形行为的细观力学有限元分析

针对双相不锈钢中奥氏体相和铁素体相分别展开了纳米压痕实验,并通过有限元反演得到两相各自的拉伸应力-应变关系,利用Voronoi Tessellation法生成代表性的微结构体积单元,对双相不锈钢的单轴拉伸行为进行了有限元仿真和模拟,研究了双相不锈钢在拉伸过程中的局部应力、应变分布和演化规律．结果表明,利用Voronoi Tessellation法建立单元模型,结合本文通过纳米压痕实验获取的两相力学性能参数,可以很好地模拟双相不锈钢的整体单拉行为,奥氏体比铁素体软,拉伸载荷下双相不锈钢的应变集中在奥氏体中,应力集中在铁素体中;局部应力应变的分布特征与两相分布特征和晶粒形状有关,最大应变值主要集中在奥氏体晶粒狭长且尖锐的区域,而最大应力则主要发生在铁素体晶粒狭长和尖锐的区域;对于奥氏体和铁素体晶粒占比相当的双相不锈钢,其虽然可以具有较为综合的宏观力学性能,但是其微观应力集中的区域和应力最大值相对较大．研究成果为进一步揭示双相不锈钢局部失效机理奠定了基础．     

C24N24负载Sc单原子催化剂催化甲烷氧化为甲醇的理论计算

甲醇是一种很有前途的清洁能源,有望替代不可再生的石油能源.因此,将储量巨大,但不易运输的甲烷氧化为甲醇具有十分重要的意义.首先通过密度泛函理论(density functional theory, DFT)计算研究了Sc原子与C₂₄N₂₄之间的稳定性.结果表明,Sc原子与C₂₄N₂₄的结合能(-9.064 eV)小于Sc原子的内聚能(-4.518 eV),即Sc@C₂₄N₂₄具有良好的稳定性.在此基础上,进一步研究了甲烷在Sc@C₂₄N₂₄表面催化氧化制备甲醇的工艺过程,以N₂O为氧化剂在Sc@C₂₄N₂₄单原子上进行甲醇的催化氧化反应.结果表明：N₂O首先吸附在Sc@C₂₄N₂₄上,然后直接分解为N₂和O_ads.N₂...     

N-(4,6-二取代嘧啶-2-基)-N'-[1-(杂芳基)甲基-5-甲基-1H-1,2,3-三唑基-4- 甲酰基]硫脲的合成与除草活性研究

采用2-氯-5-(氯甲基)吡啶和2-氯-5-(氯甲基)噻唑为原料, 经过叠氮化, 与乙酰乙酸乙酯环化, 水解, 酰氯化, 然后与异硫氰酸钾反应生成相应的异硫氰酸酯5, 最后与2-氨基-4,6-二取代嘧啶加成, 合成了10种未见文献报道的目标化合物, 其结构经IR, ¹H NMR, MS和元素分析确证, 初步的生物活性测定结果表明, 部分目标化合物在100 mg/L浓度下显示出良好的除草活性.     

基于机器视觉的农田作物行检测

为了快速有效地提取作物行,提出了基于机器视觉的农田作物行检测方法.图像预处理过程中,用中心线检测算法代替垂直投影法获得作物行信息;直线检测中提出了一种基于随机方法的新算法.该算法首先在由图像定位点构成的数据空间中随机选取两个不同点,这两点决定一条直线;然后在一定的距离容忍度下,得到一个沿直线方向的条形区域,并在此区域内搜索定位点的个数;最后根据阈值规则,判断该直线的真实性.针对大量不同生长时期、不同光照条件下麦田图像的处理,结果表明,一幅图像的处理时间约为120 ms,能够快速准确地提取作物行.对比该算法与霍夫变换和随机霍夫变换,证实了它具有节省内存、速度快、抗干扰等优点.     

Determination of urinary androgen glucuronides by capillary electrophoresis with electrospray tandem mass spectrometry

Capillary electrophoresis–electrospray tandem mass spectrometry (CE‐ESI/MS/MS) is a simple and highly sensitive method for quantifying seven urinary androgen glucuronides. The urine samples were diluted and filtered through a membrane filter, and the filtrate was injected into a CE‐MS/MS system without further sample preparation steps such as extraction and derivatization. The calibration ranges were 0.01–5 µg/mL for glucuronides of androsterone and 11β‐OHAn‐3G, and 5–500 ng/mL for glucuronides of 11‐ketoAn, DHEA, testosterone, epitestosterone and DHT. The linearity of the method was 0.992–0.998, and the limits‐of‐detection at a signal‐to‐noise ratio of 3 were 5–10 ng/mL. The coefficients of variation were in the range of 4.0–9.0% for intra‐day assay and 4.1–9.8% for inter‐day assay. The proposed method may be applicable to metabolic profiling in both quantitative and qualitative analysis. Copyright © 2008 John Wiley & Sons, Ltd.     

Lattice, magnetic and transport properties in antiperovskite compounds

The temperature-dependent magnetization, lattice, and transport properties of Mn₃Sn_1−xGe_xC (0≤x≤0.5) compounds are systematically investigated. The Mn–Mn atomic distance decreases as Ge content is increased, and the transition temperature from ferromagnetic (or ferrimagnetic) to paramagnetic state decreases too. Mn₃SnC has a large magnetovolume effect (MVE). However, Ge-doping in Mn₃SnC gradually reduces the MVE, till the MVE disappears. Whether there is an abnormal lattice change or not, there always exists an anomalous increase in resistivity near the magnetic phase transition point with decreasing temperature.     

Fatigue testing of condoms

Tests currently used for condoms are surrogates for the challenges they face in use. The tests involve looking for holes and slow stretching to break. This article describes a test that adds cyclic strain to a level well below breakage, and examines the differences among brands and types of condom. It is shown that there are very significant differences in resistance to cyclic straining. Such a test could be developed into a standard test for condom acceptability.