Experimental validation of an effective carbon number-based approach for the gas chromatography–mass spectrometry quantification of ‘compounds lacking authentic standards or surrogates’

For the quantitative analysis of ‘compounds lacking authentic standards or surrogates’ (CLASS) in environmental media, we previously introduced an effective carbon number (ECN) approach to develop an empirical equation for the prediction of their response factor (RF). In this research, a series of laboratory experiments were carried out to benchmark the reliability of an ECN approach for sorbent tube/thermal desorption/gas chromatography (GC)/mass spectrometry (MS) applications. First, the ECN values were determined using external calibration data from 25 reference volatile organic compounds (VOCs) using two MS dectectors (quadrupole (Q) and time-of-flight (TOF)). Then, a certified standard mixture of 54 VOCs was analyzed by each system as a simulated unknown sample. The analytical bias, assessed in terms of percentage difference (PD) between the certified and ECN-predicted mass values, averaged 19.2 ± 16.1% (TOF-MS) and 28.2 ± 27.6% (Q-MS). The bias using a more simplified carbon number (CN)-based prediction increased considerably, yielding 53.4 ± 53.3% (TOF-MS) and 61.7 ± 81.3% (Q-MS). However, the bias obtained using the ECN-based prediction decreased significantly to yield average PD values of 9.84 ± 7.28% (TOF-MS) and 16.8 ± 8.35% (Q-MS), if the comparison was limited to 26 (out of 54) VOCs with CN ≥ 4 (i.e., 25 aromatics and hexachlorobutadiene).     

Structural diversity of organotin(IV) complexes self-assembled from hydroxamic acid and mono- or dialkyltin salts

Three hydroxamic acid ligands (HL₁ = acetohydroxamic acid; HL₂ = benzohydroxamic acid; HL₃ = N-phenylbenzohydroxamic acid), have been used to synthesize series of mono- or dialkyltin(IV) complexes, which include (i) the carboxyl acid hybrid five-coordinated dialkyltin complexes (C₄H₉)₂SnL₁L₄ (1), [(CH₃)₂SnL₂L₅]·0.5C₆H₆ (2), (HL₄ = acetic acid; HL₅ = benzoic acid); (ii) the six-coordinated mono-n-butyltin complexes (C₄H₉)SnL₁·Cl₂·H₂O (3), (C₄H₉)SnL₂·Cl₂·H₂O (4), [(C₄H₉)SnL₃·Cl₂·H₂O]·H₂O (5), [(C₄H₉Sn)₂(L₃)₂·Cl₂·(OCH₃)₂] (6); and (iii) the alkali metal-mingled seven-coordinated mono-n-butyltin complexes [(C₄H₉Sn)₃L₂Na]⁺·Cl⁻·(CH₃CH₂)₂O (7), [(C₄H₉Sn)₃L₂K]⁺·Cl⁻·CH₂Cl₂ (8). All complexes were characterized by elemental analyses, IR, ¹H, ¹³C, ¹¹⁹Sn NMR and X-ray single crystal diffraction. In these complexes, hydroxamic acids present bidentate coordination modes with the carbonyl O atom and the hydroxyl O atom binding to tin center. In complexes 1-6, each tin atom is coordinated by one hydroxamic acid ligand. However, in complexes 7 and 8, tin atom is surrounded by three hydroxamic acid ligands, and all hydroxyl O atoms of the ligands also bind to the alkali metal center (Na or K). This kind of organotin(IV) framework containing one alkali metal is found for the first time. Furthermore, the supramolecular structures of 1, 3, 4 and 6 have been found to consist of 1D linear molecular chains formed by intermolecular N-H···X or C-H···X (X = O, N or Cl) hydrogen bonds. For complex 2, an interesting macrocyclic tetramer has been built by the intermolecular N-H···O hydrogen bonds. Fascinatingly, two unique symmetric dimeric structures are recognized in complexes 7 and 8, which is individually bridged by intermolecular N-H···Cl and N-H···O hydrogen bonds. In addition, for 8, the dimeric cycles have been further connected into a 1D supramolecular chain.     

A new biosynthetic tracer for the inline measurement of virus retention in membrane processes: part II. Biochemical and physicochemical characterizations of the new tracer

In a previous work, a reproducible procedure to produce a new biosynthetic tracer was developed. This new tracer is an MS2 bacteriophage with enzymatic probes grafted on its surface, which can induce enzymatic activity of the tracer. In this paper, the biochemical and physicochemical characteristics of this new tracer are determined. A protocol was developed to determine the specific enzymatic activity kcat_TRACER of the tracer, which was found to be 2.93 ± 0.78 × 10⁴ min⁻¹ on average. Physicochemical characterizations of this new tracer showed that it is representative of viruses and may thus be used as a virus surrogate to assess the virus retention of membrane systems inline. Notably, the mean diameter and molecular weight of the tracer were found to be respectively 64.1 ± 0.3 nm and 12140 ± 3654 kDa, which are within the size and molecular weight ranges of pathogenic viruses carried by water. The tracer surface was also studied and revealed the considerable porosity of the grafted probe layer, with a mean porosity of 88%, which could explain why the zeta potential of the tracers (−14.34 ± 1.66 mV) was nearly the same as that of the native MS2 phages. Finally, a comparison between filtration of the reference microorganism used for membrane performance assessment (the MS2 phage) and the tracer suspensions showed the same filtration behaviour.     

Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind

Recently, the authors introduced some generalizations of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials (see [Q.-M. Luo, H.M. Srivastava, J. Math. Anal. Appl. 308 (2005) 290-302] and [Q.-M. Luo, Taiwanese J. Math. 10 (2006) 917-925]). The main object of this paper is to investigate an analogous generalization of the Genocchi polynomials of higher order, that is, the so-called Apostol-Genocchi polynomials of higher order. For these generalized Apostol-Genocchi polynomials, we establish several elementary properties, provide some explicit relationships with the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, and derive various explicit series representations in terms of the Gaussian hypergeometric function and the Hurwitz (or generalized) zeta function. We also deduce their special cases and applications which are shown here to lead to the corresponding results for the Genocchi and Euler polynomials of higher order. By introducing an analogue of the Stirling numbers of the second kind, that is, the so-called λ-Stirling numbers of the second kind, we derive some basic properties and formulas and consider some interesting applications to the family of the Apostol type polynomials. Furthermore, we also correct an error in a previous paper [Q.-M. Luo, H.M. Srivastava, Comput. Math. Appl. 51 (2006) 631-642] and pose two open problems on the subject of our investigation.     

Multiple solutions for the laminar flow in a porous pipe with suction at slowly expanding or contracting wall

In this paper, the asymptotic solution for the similarity equation of the laminar flow in a porous pipe with suction at expanding and contracting wall has been obtained using the singular perturbation method. However, this solution neglects exponentially small terms in the matching process. To take into account these exponentially small terms, a method involving the inclusion of exponentially small terms in a perturbation series was used to find the two solutions analytically. The series involving the exponentially small terms and expansion ratio predicts dual solutions. Furthermore, the result indicates that the expansion ratio has much important influence on the solutions. When the expansion ratio is zero, it is a special case that Terrill has discussed.     

A reduced domain strategy for local mesh movement application in unstructured grids

Automatic control of mesh movement is mandatory in many fluid flow and fluid-solid interaction problems. This paper presents a new strategy, called reduced domain strategy (RDS), which enhances the efficiency of node connectivity-based mesh movement methods and moves the unstructured grid locally and effectively. The strategy dramatically reduces the grid computations by dividing the unstructured grid into two active and inactive zones. After any local boundary movement, the grid movement is performed only within the active zone. To enhance the efficiency of our strategy, we also develop an automatic mesh partitioning scheme. This scheme benefits from a new quasi-structured mesh data ordering, which determines the boundary of active zone in the original unstructured grid very easily. Indeed, the new partitioning scheme eliminates the need for sequential reordering of the original unstructured grid data in different mesh movement applications. We choose the spring analogy method and apply our new strategy to perform local mesh movements in two boundary movement problems including a multi-element airfoil with moving slat or deforming main body section. We show that the RDS is robust and cost effective. It can be readily employed in different node connectivity-based mesh movement methods. Indeed, the RDS provides a flexible local grid deformation tool for moving grid applications.     

On a novel expression of the field scattered by an arbitrary constant impedance plane

The electromagnetic field scattered by an impedance plane is generally given by its plane wave expansion (Fourier representation). Here we derive an alternative expression which is more suitable for point source illumination. For this, we consider an original expression of the Hertz potentials for the incident field and express the scattered potentials in a novel form. A special function then involved can be expressed in an integral which is in turn expanded in a convergent series. The expression presented also permits us to express complete asymptotics. Our development considers an arbitrary impedance, passive or active.     

New fifth‐order two‐derivative Runge‐Kutta methods with constant and frequency‐dependent coefficients

Two‐derivative Runge‐Kutta methods are Runge‐Kutta methods for problems of the form y′ = f(y) that include the second derivative y′′ = g(y) = f ′(y)f(y) and were developed in the work of Chan and Tsai. In this work, we consider explicit methods and construct a family of fifth‐order methods with three stages of the general case that use several evaluations of f and g per step. For problems with oscillatory solution and in the case that a good estimate of the dominant frequency is known, methods with frequency‐dependent coefficients are used; there are several procedures for constructing such methods. We give the general framework for the construction of methods with variable coefficients following the approach of Simos. We modify the above family to derive methods with frequency‐dependent coefficients following this approach as well as the approach given by Vanden Berghe. We provide numerical results to demonstrate the efficiency of the new methods using three test problems.     

临界或超临界增长分数阶Schrodinger-Poisson方程正解的存在性

本文研究如下分数阶Schrodinger-Poisson方程{(-△)^su+Vx(u)+K(x)φu=f(u)+λ|u|^q-2ux∈R³,(-△)^tφ=K(x)u²,x∈R³其中S∈(3/4,1),t∈(0,1),f是在原点超线性无穷远次临界的连续非线性项,指数q≥2_s^*=6/3-2x.当λ>0充分小时,我们利用变分方法证明上述问题正解的存在性.本文的主要贡献是处理了超临界情形.     

三点起爆形成尾翼EFP的数值模拟和实验研究

利用LS-DYNA软件对三点起爆形成尾翼EFP的过程进行了数值模拟,深入研究了爆轰波传播过程中的波形结构和强度的变化规律以及药型罩材料在复合爆轰波作用下驱动变形的特性和规律,加深了对三点起爆条件下药型罩形成带尾翼EFP机理的认识。在此基础上,设计了三点同步起爆装置和EFP装药进行实验。研究结果表明：设计的三点起爆装置作用可靠,满足三点起爆EFP装药的设计要求;形成的EFP弹形稳定,与计算结果吻合较好;尾翼EFP飞行过程中的速度降减小,稳定性提高。