富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

White and some colored marbles as alternative radiation shielding materials for applications

ABSTRACT

In this paper, the radiation shielding parameters such as linear attenuation coefficients (LAC, µ), mass attenuation coefficients (MAC, µ/ρ), effective atomic numbers (Z_eff), effective electron densities (N_eff), half value of layers (HVL), mean free paths (MFP) and buildup factors (exposure (EBF) and energy absorption (EABF)) were investigated for cream (M1), pink (M2), white (M3), maroon (M4) and green (M5) marbles. Attenuation coefficients were measured in the energy region 31.18–661.66 keV photon energies. The values of Z_eff and N_eff were then calculated using these coefficients with logarithmic interpolation method, and HVLs and MFPs were calculated using the values of LAC of marble samples at the same photon energies. The experimental results were compared with the theoretical values obtained from WinXCom program, and good agreements were observed between the experimental and theoretical results. HVLs and MFPs of all marble samples were compared with those of some concretes, glasses and commercial radiation shielding glasses (SCHOTT Co.). The studied marbles were better radiation shielding materials than standard shielding concretes due to lower HVL and MFP values lower than the ordinary concrete. Finally, EBFs and EABFs of the marbles were calculated in the energy region 0.015–1?MeV up to penetration depths of 40 mfps by Geometric Progression method (G-P), and the results were discussed in terms of photon energies and chemical compositions of the marbles.     

任意阶光子先增后减和先减后增相干态的非经典性

研究了任意阶的光子先增后减(CA)和光子先减后增(AC)相干态的非经典特性,并给出了相应的解析表达式.AC操作和CA操作由于湮灭算符和产生算符的不对易性,导致产生的两种态具有不同的非经典特性.文中首先给出了两种态的归一化因子的解析表达式,随后在此基础上研究了MandelQ参数、光子数分布和Wigner函数等表征非经典特性的统计量,研究表明两种态都具有非常明显的非经典特性,并且AC操作比CA操作能产生更强的非经典性.     

Free convection of a dusty‐gas flow along a semi‐infinite vertical cylinder

An analysis is performed to study the free convection of a dusty‐gas flow along a semi‐infinite isothermal vertical cylinder. The governing equations of the flow problem are transformed into non‐dimensional form and the resulting nonlinear, coupled parabolic partial differential equations have been solved numerically using an implicit finite difference scheme of Crank–Nicholson type. The flow variables such as gas–velocity, dust‐particle velocity and temperature, shearing stress and heat transfer coefficients are calculated numerically for various parameters occurring in the problem. It is observed that due to the presence of dust particles, the gas velocity is found to decrease. Copyright © 2009 John Wiley & Sons, Ltd.     

乘积图的Fractional控制

Let G =(V,E) be a simple graph.For any real function g :V-→ R and a subset S V,we write g(S) =∑v∈Sg(v).A function f :V-→ [0,1] is said to be a fractional dominating function(F DF) of G if f(N [v]) ≥ 1 holds for every vertex v ∈ V(G).The fractional domination number γf(G) of G is defined as γf(G) = min{f(V)|f is an F DF of G }.The fractional total dominating function f is defined just as the fractional dominating function,the difference being that f(N(v)) ≥ 1 instead of f(N [v]) ≥ 1.The fractional total domination number γ0f(G) of G is analogous.In this note we give the exact values ofγf(Cm × Pn) and γ0f(Cm × Pn) for all integers m ≥ 3 and n ≥ 2.     

SUBSTITUTED 4,5-DIOXO-1,3-DIAZA-2λ3,4λ4-DIPHOSPHOLANE AND RELATED COMPOUNDS

Abstract

Cyclization of 1 with 2 yielded the title compound 3, which was transformed into the corresponding 1,3,2,4-diazadiphospholanes 4 and 5 by using DMSO or sulfur respectively. The addition reaction of 3 with butanedione gave 3,4-di-oxo-1-phenyl-2,5-diaza-6,9-dioxa-1λ⁵,3λ⁴-diphosphaspiro[4,4]nonane 6. The structures of 3, 4 and 5 were confirmed by elemental analysis, IR, NMR and GC-MS. Although 6 could not be isolated in pure form because of its rapid decomposition, the ₃₁P NMR data indicated its existence. It was found that there were cis- and trans-isomers in 3, 4, 5 and 6.     

An in silico expert system for the identification of eye irritants

This report describes development of an in silico, expert rule-based method for the classification of chemicals into irritants or non-irritants to eye, as defined by the Draize test. This method was developed to screen data-poor cosmetic ingredient chemicals for eye irritancy potential, which is based upon exclusion rules of five physicochemical properties – molecular weight (MW), hydrophobicity (log P), number of hydrogen bond donors (HBD), number of hydrogen bond acceptors (HBA) and polarizability (Pol). These rules were developed using the ADMET Predictor software and a dataset of 917 eye irritant chemicals. The dataset was divided into 826 (90%) chemicals used for training set and 91 (10%) chemicals used for external validation set (every 10th chemical sorted by molecular weight). The sensitivity of these rules for the training and validation sets was 72.3% and 71.4%, respectively. These rules were also validated for their specificity using an external validation set of 2011 non-irritant chemicals to the eye. The specificity for this validation set was revealed as 77.3%. This method facilitates rapid screening and prioritization of data poor chemicals that are unlikely to be tested for eye irritancy in the Draize test.     

Nonstationarity and related measures for time‐dependent hartree–fock and multiconfigurational models

Based on an earlier article (Eberly and Singh, Phys. Rev. D 1973 , 7, 359) and related works on short‐time evolution, this article proposes a many‐electron formulation for the nonstationarity degree which can be assigned to quantum system at each time point. The key measure introduced, , is a nonstationarity index that can be thought of as an inverse nominal lifetime at each instance of time. The index is directly computed from the time derivative of one‐electron density matrix and is a size‐consistent quantity. In this article, the approach is developed for the time‐dependent Hartree–Fock (TDHF), single‐excitation (TDCIS), and time‐dependent full configuration interaction (TDFCI) models. As a rule, nonstationarity effects are more pronounced in correlated electron systems, and a joint analysis of and the multiconfigurational character of wave functions apparently provide a deeper insight into dynamical molecular processes. The performed calculations on small molecules in laser fields show a preference for the TDCIS model when comparing TDCIS and TDHF with the “exact” TDFCI model. © 2013 Wiley Periodicals, Inc.     

Effects of Spacer Chain Length and Additives on Solution Properties of Cationic Gemini Surfactant

The critical micelle concentration (CMC) has been determined for the gemini surfactant trimethylene-1,3-bis(dodecyldimethyl ammonium bromide)12-s-12,2Br^?1 by means of electricity conductivity measurements. For the same number of carbon atoms in the hydrophobic chain per hydrophilic head group, geminis have CMC values well below those of conventional single-chain cationic surfactants. The CMC of 12-3-12 reduces with the addition of n-alcohol except ethanol and with the increase of n-alcohol chain length as well as increase of concentration of n-butanol and sodium chloride. Steady-state fluorescence quenching technology has been employed to study the aggregation number of micelle, which increases with increase in the length of n-alcohol. The Kraft temperature measurements also indicate that the stability of solid surfactant hydrate decreases along with the improvement of concentration of n-butanol and sodium chloride.