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.     

Existence of optimal solutions for general stochastic linear complementarity problems

In this paper we show the solvability of the expected residual minimization (ERM) formulation for the general stochastic linear complementarity problem (SLCP) under mild assumptions. The properties of the ERM formulation are dependent on the choice of NCP functions. We focus on the ERM formulations defined by the “min” NCP function and the penalized FB function, both of which are nonconvex programs on the nonnegative orthant.     

Representing a Functional Curve by Curves with Fewer Peaks

In this paper, we study the problems of (approximately) representing a functional curve in 2-D by a set of curves with fewer peaks. Representing a function (or its curve) by certain classes of structurally simpler functions (or their curves) is a basic mathematical problem. Problems of this kind also find applications in applied areas such as intensity-modulated radiation therapy (IMRT). Let f\bf f be an input piecewise linear functional curve of size n. We consider several variations of the problems. (1) Uphill–downhill pair representation (UDPR): Find two nonnegative piecewise linear curves, one nondecreasing (uphill) and one nonincreasing (downhill), such that their sum exactly or approximately represents f\bf f. (2) Unimodal representation (UR): Find a set of unimodal (single-peak) curves such that their sum exactly or approximately represents f\bf f. (3) Fewer-peak representation (FPR): Find a piecewise linear curve with at most k peaks that exactly or approximately represents f\bf f. Furthermore, for each problem, we consider two versions. For the UDPR problem, we study its feasibility version: Given ε>0, determine whether there is a feasible UDPR solution for f\bf f with an approximation error ε; its min-ε version: Compute the minimum approximation error ε ^∗ such that there is a feasible UDPR solution for f\bf f with error ε ^∗. For the UR problem, we study its min-k version: Given ε>0, find a feasible solution with the minimum number k ^∗ of unimodal curves for f\bf f with an error ε; its min-ε version: given k>0, compute the minimum error ε ^∗ such that there is a feasible solution with at most k unimodal curves for f\bf f with error ε ^∗. For the FPR problem, we study its min-k version: Given ε>0, find one feasible curve with the minimum number k ^∗ of peaks for f\bf f with an error ε; its min-ε version: given k≥0, compute the minimum error ε ^∗ such that there is a feasible curve with at most k peaks for f\bf f with error ε ^∗. Little work has been done previously on solving these functional curve representation problems. We solve all the problems (except the UR min-ε version) in optimal O(n) time, and the UR min-ε version in O(n+mlog m) time, where m<n is the number of peaks of f\bf f. Our algorithms are based on new geometric observations and interesting techniques.     

An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context

In an evidential reasoning context, a group consensus (GC) based approach can model multiple attributive group decision analysis problems with GC requirements. The predefined GC is reached through several rounds of group analysis and discussion (GAD) in the approach. However, the GAD with no guidance may not be the most appropriate way to reach the predefined GC because several rounds of GAD will spend a lot of time of all experts and yet cannot help them to effectively emphasize on the assessments which primarily damage the GC. In this paper, an attribute weight based feedback model is constructed to effectively identify the assessments primarily damaging the GC and accelerate the GC convergence. Considering important attributes with the weights more than or at least equal to the mean of the weights of all attributes, the feedback model constructs identification rules to identify the assessments damaging the GC for the experts to renew. In addition, a suggestion rule is introduced to generate appropriate recommendations for the experts to renew their identified assessments. The identification rules are constructed at three levels including the attribute, alternative and global levels. The feedback model is used to solve an engineering project management software selection problem to demonstrate its detailed implementation process, its validity and applicability, and its advantages compared with the GC based approach.     

Comments on “Competitive analysis of a better on-line algorithm to minimize total completion time on a single-machine”

For the single machine scheduling problem of minimizing the total completion time, Montoya Torres (J Glob Opt 27:97–103, 2003) presented a semi-online algorithm under the assumption that release dates are known in advance, and showed that it was \({\sqrt{3}}\)-competitive. However, there are flaws in the proof, and the conclusion about the competitive ratio is not correct. In this note, we show that the semi-online algorithm cannot perform better than the best non-clairvoyant online algorithm with a competitive ratio of 2.     

随机支付红利的跳-扩散模型的期权定价

假设股票随机支付红利,且红利的大小与支付红利时刻及股票价格有关,并假设股票价格过程服从跳—扩散模型(其中跳跃过程为Poisson过程)的条件下,建立了股票价格行为模型,应用保险精算法给出了欧式看涨和看跌期权的定价公式,推广了Merton关于期权定价的结果。     

Determination of nitrite in tap waters based on fluorosurfactant-capped gold nanoparticles-enhanced chemiluminescence from carbonate and peroxynitrous acid

Fluorosurfactant (FSN)-capped gold nanoparticles (GNPs), which exhibit higher stability at a wider pH range and high ionic strength, were utilized for investigating the chemiluminescence (CL) effect on the reaction between high concentration carbonate (~0.3 M) and peroxynitrous acid. When the pH of the colloidal solution was 10.2 by dropwise addition of 0.05 M NaOH, FSN-capped GNPs offer an enhanced CL intensity. Based on the CL spectra, XPS spectra and the quenching effect of reactive oxygen species, a possible CL mechanism is proposed. The tolerance of FSN-capped GNPs towards salt concentrations (salt proofing effect) within a large pH range is an interesting feature, compared to the other previously reported work on nanoparticles CL systems. The CL intensity is proportional to the concentration of nitrite in the range from 0.1 to 100 μM. The detection limit (S/N = 3) is 0.036 μM and the relative standard deviation (RSD) for seven repeated measurements of 0.5 μM nitrite was 2.4%. This method has been successfully applied to determine nitrite in tap waters with recoveries of 97-106%.     

Using an on-line microdialysis/HPLC system for the simultaneous determination of melamine and cyanuric acid in non-dairy creamer

The recent revelation of melamine (MEL) contamination in foodstuffs in China has rocked the international public health community. Many food categories have been involved in this scandal, including non-dairy creamer (NDC). In this study, we investigated the use of hollow-fiber microdialysis (MD) sampling coupled on-line with high-performance liquid chromatography (HPLC) as an alternative to sample pretreatment for the direct determination of MEL and its analogue cyanuric acid (CYA) in NDC. After MD sampling, the dialysate was injected on-line into the chromatographic system for analysis of MEL and CYA with UV detection at 203 nm. We monitored the effects of various parameters affecting the MD efficiency, namely the characteristics of the MD probe membrane, the flow-rate and the nature of the polarity modifier in the perfusion stream, and the addition of salt in the sample solution. The optimal enrichment efficiency for collecting MEL and CYA from aqueous NDC samples occurred with MD sampling using a hollow polysulfone MD fiber and MeOH as the perfusate at a flow rate of 10 μL min⁻¹. The optimized chromatographic conditions involved using a reversed-phase phenyl column and a mobile phase of 5 mM phosphate buffer in 10% (v/v) MeOH, buffered at pH 6.5. Detection was linear in the concentration range from 0.02 to 5 ppm for MEL and from 2 to 100 ppm for CYA, with detection limits of 1 ppb for MEL and 30 ppb for CYA. The volume of perfusate required to extract MEL and CYA from the NDC solution was only 21 μL. The total MD sampling time was 2.1 min. This method allows the sensitive, eco-friendly, and rapid determination of MEL and CYA in NDC—a risk food for economically motivated adulteration.     

Ocular Pharmacokinetic Study of l-Carnosine and N-Acetyl-l-carnosine in Rabbit by Microdialysis Coupled with UPLC-MS-MS

In order to provide useful information for rational drug design, the ocular pharmacokinetics of l-carnosine (CAR) and its acetylized prodrug N-acetyl-l-carnosine (NAC) were investigated. The in vivo microdialysis sampling coupled with ultra-performance liquid chromatography-tandem mass spectrometry (UPLC-MS-MS) was developed for continuously simultaneous monitoring of CAR and NAC in rabbit aqueous humor. The measured in vitro recoveries of the probe were 61.3% for CAR and 65.8% for NAC, while in vivo recoveries decreased to 43.1% for CAR and 43.0% for NAC, respectively. The method was sensitive with LLOQ 20.5 ng mL^?1 for CAR and 20.4 ng mL^?1 for NAC. The initial data indicated that the value of C _max and AUC_(0?C??) of NAC were higher than these of CAR (C _max 2305 vs. 1,802 ng mL^?1), (AUC_(0?C??) 1,337 vs. 1,891 ng h mL^?1), which indicated that the NAC exhibited better ocular bioavailability and duration. The method was rapid, specific and sensitive for continuously monitoring of aqueous humor and it was successfully applied to pharmacokinetic studies of CAR and NAC.