Highly Selective Addition of a Broad Spectrum of Trimethylsilane Pro‐nucleophiles to N‐tert‐Butanesulfinyl Imines

Addition of organotrimethylsilane reagents to chiral N‐tert‐butanesulfinyl imines can be achieved in good yields and with excellent diastereoselectivities by employing TMSO^?/Bu₄N⁺ as a Lewis base activator in THF. A variety of aliphatic, aromatic, heteroaromatic and organometallic chiral imines were utilised as electrophiles for the synthesis of enantioenriched N‐tert‐butanesulfinyl amides. Remarkably, the same sets of reaction conditions could be used with a highly diverse range of bench‐stable organotrimethylsilane reagents, which highlights the generality and robustness of this methodology.     

Stability of some set-valued functional equations

In this paper, we prove the Hyers–Ulam stability of some set-valued functional equations.     

Highly sensitive fluorescence detection system for microfluidic lab-on-a-chip

We demonstrate a compact, low cost and practical fluorescence detection system for lab-on-a-chip applications. The system comprises a commercially available InGaN light emitting diode (501 nm) as light source, an organic or silicon photodiode detector, absorptive dye coated colour filters and linear and reflective polarisers. An injection moulded polystyrene microfluidic chip is used as the platform for fluorescence immunoassays for cardiac markers myoglobin and CK-MB. The optical limit of detection (LOD) is measured using a TransFluoSphere? suspension at 5.6 × 10(4) beads μl(-1) which can be equated to ～3 nM fluorescein equivalent concentration. The LOD for the human plasma immunoassays is measured as 1.5 ng ml(-1) for both myoglobin and CK-MB.     

Mechanistic insight into stereoselective carbolithiation

This article addresses the mechanistic features of asymmetric carbolithiation of β‐methylstyrenes. While often the presence of functional groups is required to obtain high enantioselectivities in carbolithiation reactions, simple β‐methylstyrene also gives high selectivities in (?)‐sparteine‐mediated addition of alkyl lithium compounds. Computational studies on the carbolithiation of β‐methylstyrene with (?)‐sparteine show that the observed selectivities are the result of repulsion effects in the diastereomeric transition states between the (?)‐sparteine ? alkyl lithium adduct and the β‐methylstyrene, upon approximation of the two reactants. In contrast, for the ortho‐amino β‐methylstyrene (E)‐benzyl(2‐propenylphenyl)amine ( 4 ) X‐ray structure analyses of intermediate lithium amides indicate a carbolithiation mechanism in which one side of the double bond is shielded by the amide moiety, leaving only one side free for approach of the chiral alkyl lithium adduct.     

Projective Character Degree Patterns of p-Groups for p Odd

In this article, we classify up to isomorphism the character tables of 2-generator p-groups of class two.     

Boundary Value Problems with Sign Changing Nonlinearities for Second Order Singular Ordinary Differential Equations

General existence criteria, based on upper and lower solution type arguments, are presented for the Dirichlet boundary value problem y " + f ( t , y , y ') = 0, 0 < t < 1 with y (0) = y (1) = 0. Our nonlinearity may be singular in its dependent variable and is allowed to change sign.     

Common fixed point theorems and minimax inequalities in locally convex Hausdorff topological vector spaces

In this article, we introduce the concept of a family of set-valued mappings generalized Knaster–Kuratowski–Mazurkiewicz (KKM) w.r.t. other family of set-valued mappings. We then prove that if X is a nonempty compact convex subset of a locally convex Hausdorff topological vector space and 𝒯 and 𝒮 are two families of self set-valued mappings of X such that 𝒮 is generalized KKM w.r.t. 𝒯, under some natural conditions, the set-valued mappings S ∈ 𝒮 have a fixed point. Other common fixed point theorems and minimax inequalities of Ky Fan type are obtained as applications.     

Constant sign solutions for parameter-dependent superlinear second-order difference equations

This paper studies the existence of constant sign solutions for a second-order parameter-dependent super linear difference equation. The approach is based on variational methods on finite dimensional Banach spaces.     

Competition between the charge transfer state and the singlet states of donor or acceptor limiting the efficiency in polymer:fullerene solar cells

We study the appearance and energy of the charge transfer (CT) state using measurements of electroluminescence (EL) and photoluminescence (PL) in blend films of high-performance polymers with fullerene acceptors. EL spectroscopy provides a direct probe of the energy of the interfacial states without the need to rely on the LUMO and HOMO energies as estimated in pristine materials. For each polymer, we use different fullerenes with varying LUMO levels as electron acceptors, in order to vary the energy of the CT state relative to the blend with [6,6]-phenyl C61-butyric acid methyl ester (PCBM). As the energy of the CT state emission approaches the absorption onset of the blend component with the smaller optical bandgap, E(opt,min) ≡ min{E(opt,donor); E(opt,acceptor)}, we observe a transition in the EL spectrum from CT emission to singlet emission from the component with the smaller bandgap. The appearance of component singlet emission coincides with reduced photocurrent and fill factor. We conclude that the open circuit voltage V(OC) is limited by the smaller bandgap of the two blend components. From the losses of the studied materials, we derive an empirical limit for the open circuit voltage: V(OC) ? E(opt,min)/e - (0.66 ± 0.08)eV.     

Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.