Uniform asymptotics of some q-orthogonal polynomials

Uniform asymptotic formulas are obtained for the Stieltjes-Wigert polynomial, the q⁻¹-Hermite polynomial and the q-Laguerre polynomial as the degree of the polynomial tends to infinity. In these formulas, the q-Airy polynomial, defined by truncating the q-Airy function, plays a significant role. While the standard Airy function, used frequently in the uniform asymptotic formulas for classical orthogonal polynomials, behaves like the exponential function on one side and the trigonometric functions on the other side of an extreme zero, the q-Airy polynomial behaves like the q-Airy function on one side and the q-Theta function on the other side. The last two special functions are involved in the local asymptotic formulas of the q-orthogonal polynomials. It seems therefore reasonable to expect that the q-Airy polynomial will play an important role in the asymptotic theory of the q-orthogonal polynomials.     

Properties of certain semigroups and their potential as platforms for cryptosystems

In this paper, we study some properties of semigroups with presentation 〈a,b ; a ^p =b ^r ,a ^q =b ^s 〉. We will also study their potential as platforms for the Diffie-Hellman key exchange protocol.     

On the oscillation of third order nonlinear difference equations

Some new criteria for the oscillation of third order nonlinear difference equations $$\begin{array}{l}\Delta^{2}\bigl(\frac{1}{a(k)}(\Delta x(k))^{\alpha}\bigr)+q(k)f(x[g(k)])=0\quad\mbox{and}\\[6pt]\Delta^{2}\bigl(\frac{1}{a(k)}(\Delta x(k))^{\alpha}\bigr)=q(k)f(x[g(k)])+p(k)h(x[\sigma(k)])\end{array}$$ are established.     

The existence of multiple positive solutions to boundary value problems of nonlinear delay differential equations with countably many singularities on infinite interval

In this paper, we consider the existence of countably many positive solutions to a boundary value problem of a nonlinear delay differential equation with countably many singularities on infinite interval

     

Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR

Is it possible to obtain an objective and quantifiable measure of risk backed up by choices made by some specific groups of rational investors? To answer this question, in this paper we establish some behavior foundations for various types of VaR models, including VaR and conditional-VaR, as measures of downside risk. In this paper, we will establish some logical connections among VaRs, conditional-VaR, stochastic dominance, and utility maximization. Though supported to some extents with unanimous choices by some specific groups of expected or non-expected-utility investors, VaRs as profiles of risk measures at various levels of risk tolerance are not quantifiable – they can only provide partial and incomplete risk assessments for risky prospects.     

Integrated bank performance assessment and management planning using hybrid minimax reference point – DEA approach

The purpose of assessing past performances and setting future targets for an organisation such as a bank branch is to find where the branch stands in comparison to its peers within the bank branch network and how to improve the efficiency of its operations relatively when compared to the best practice branches. However, future performance targets may be set arbitrarily by the head-office and thus could be unrealistic and not achievable by a branch. A hybrid minimax reference point-data envelopment analysis (HMRP-DEA) approach is investigated to incorporate the value judgements of both branch managers and head-office directors and to search for the most preferred solution (MPS) along the efficient frontier for each bank branch. The HMRP-DEA approach is composed of three minimax models, including the super-ideal point model, the ideal point model and the shortest distance model, which share the same decision and objective spaces, are different from each other only in their reference points and weighting schema, and are proven to be equivalent to the output-oriented DEA dual models. These models are examined both analytically and graphically in this paper using a case study, which provides the unprecedented insight into integrated efficiency and trade-off analyses. The HMRP-DEA approach uses DEA as an ex-post-facto evaluation tool for past performance assessment and the minimax reference point approach as an ex-ante planning tool for future performance forecasting and target setting. Thus, the HMRP-DEA approach provides an alternative means for realistic target setting and better resource allocation. It is examined by a detailed investigation into the performance analysis for the fourteen branches of an international bank in the Greater Manchester area.     

Enantioselective Brønsted base catalyzed [4+2] cycloaddition using novel amino-substituted tetraphenylene derivatives

This paper is concerned with the syntheses of 1,8,9,16-tetrahydroxytetraphenylene derivatives and their applications as Brønsted base organocatalysts for [4+2] cycloaddition between anthrone and maleimides. The structural modifications of the catalysts and their related catalytic properties are described and discussed in details.     

‘One-flask’ transformation of isocyanates and isothiocyanates to guanidines hydrochloride by using sodium bis(trimethylsilyl)amide

A ‘one-flask’ synthesis of guanidines was developed by reacting isocyanates and isothiocyanates with sodium bis(trimethylsilyl)amide followed by addition of primary or secondary amines with a catalytic amount of AlCl₃. The desired guanidines were obtained in good yields and the reaction was applicable to aliphatic and aromatic substrates. A plausible mechanism was proposed through the generation of cyanamide anion from isocyanates or isothiocyanates with sodium bis(trimethylsilyl)amide. Addition of amines and catalytic amount of AlCl₃ smoothly converted the cyanamides to the desired guanidines.     

Evaluation of the state-of-the-art measurement capabilities for selected PBDEs and decaBB in plastic by the international intercomparison CCQM-P114

An international intercomparison involving eight national metrology institutes (NMIs) was conducted to establish their current measurement capabilities for determining five selected congeners from the brominated flame retardant classes polybrominated diphenyl ethers and polybrominated biphenyls. A candidate reference material consisting of polypropylene fortified with technical mixtures of penta-, octa- and decabromo diphenyl ether and decabromo biphenyl, which was thoroughly assessed for material homogeneity and stability, was used as study material. The analytical procedures applied by the participants differed with regard to sample pre-treatment, extraction, clean-up, employed calibrants and type of calibration procedure as well as regarding analytical methods used for separation, identification and quantification of the flame retardant congeners (gas chromatography coupled to an electron capture detector (GC-ECD), gas chromatography-mass spectrometry in the electron ionisation mode (GC-EI-MS), gas chromatography-mass spectrometry in the electron capture negative ionisation mode (GC-ECNI-MS), and liquid chromatography-inductive coupled plasma-mass spectrometry (LC-ICP-MS)). The laboratory means agreed well with relative standard deviations of the mean of means of 1.9%, 4.8%, 5.5% and 5.4% for brominated diphenyl ether (BDE) 47, 183 and 209 and for the brominated biphenyl (BB) congener 209, respectively. For BDE 206, a relative standard deviation of 28.5% was obtained. For all five congeners, within-laboratory relative standard deviations of six measurements obtained under intermediate precision conditions were between 1% and 10%, and reported expanded measurements uncertainties typically ranged from 4% to 10% (8% to 14% for BDE 206). Furthermore, the results are in good agreement with those obtained in the characterization exercise for determining certified values for the flame retardant congeners in the same material. The results demonstrate the state-of-the-art measurement capabilities of NMIs for quantifying representative BDE congeners and BB 209 in a polymer. The outcome of this intercomparison (pilot study) in conjunction with possible improvements for employing exclusively calibrants with thoroughly assessed purity suggests that a key comparison aiming at underpinning calibration and measurement capability (CMC) claims of NMIs can be conducted.

The Effects of Microenvironment Polarity and Dendritic Branching of Aliphatic Hydrocarbon Dendrons on the Self‐Assembly of 2‐Ureido‐4‐pyrimidinones

Two series of aliphatic hydrocarbon‐based G1–G3 dendritic 2‐ureido‐4‐pyrimidinones (UPy) ( S‐Gn )₂ and ( L‐Gn )₂, differing from one another by the distance between the branching juncture to the urea end, were prepared and characterized. These hydrocarbon dendrons were also appended to a p‐aminonitrobenzene solvatochromic chromophore in order to probe their microenvironment polarity. While positive solvatochromism was observed which indicated the chromophore was solvent accessible, there was no significant difference between the microenvironment polarities on going from the G1 to the G3 dendrons. The self‐assembling behavior and tautomeric preference of the dendritic UPy derviatives were examined by ¹H NMR spectroscopy. The dimerization constants (K_dim*) of the DDAA tautomers were unchanged at 10⁷ M ^?1 in CDCl₃ at both 25 and 50 °C, which were comparable to those of UPy compounds bearing other nonpolar substitutents. Furthermore, the lower limits on the K′_dim* of the DADA tautomeric forms of the ( S‐Gn )₂ and ( L‐Gn )₂ series were determined to be 10⁶ and 10⁵ M ^?1 in CDCl₃, respectively. It was found that a closer proximity of the dendron branching juncture to the UPy unit could lead to a destabilization effect on the dimeric states. Hence, the ( L‐Gn )₂ dimers are more stable than those of ( S‐Gn )₂ in the DDAA form, but the latter are more stable than the former in the tautomeric DADA state. This study showed that both the highly nonpolar microenvironment and the proximity of the dendritic branching juncture to the UPy motif could alter the strength and profile of the hydrogen bond‐mediated self‐assembling process.