Role of condenser iris in optical tweezer detection system

Optical tweezers have proven to be very useful in various scientific fields, from biology to nanotechnology. In this Letter we show, both by theory and experiment, that the interference intensity pattern at the back focal plane of the condenser consists of two distinguishable areas with anticorrelated intensity changes when the bead is moved in the axial direction. We show that the space angle defining the border of two areas linearly depends on the NA of the objective. We also propose a new octant photodiode, which could significantly improve the axial resolution compared to the commonly used quadrant photodiode technique.     

Assessing the reliability of a nanocomponent using nanocrack growth

In nanoscience and nanotechnology, much attention has been given to the dual problem of designing nanocomponents with novel physical properties and how such nanocomponents can be fabricated. Receiving less attention has been the question of the nanocomponent's reliability; how does a nanocomponent fail and how long does a nanocomponent survive under typical operating conditions? High reliability is necessary to guarantee the advancement and utilization of nanocomponents due to the fact that they account for a high proportion of costs of newly designed nanosystems as well as multiscale systems. A nanocomponent is a component that is made of atoms, and its reliability is determined by these atoms. There are situations where it is hard or impossible to extract information from a nanocomponent about its relationship to its atoms. In this article, we assess the nanocomponent's reliability by using its physical properties. Specifically, it is known that nanocrack growth involves considerable statistical variability and such variability should be accounted for assessing growth. In this paper, we first provide a stochastic nanocrack growth model and then evaluate the reliability of a nanocomponent based on this model. Various properties of this model are obtained. We also evaluate the reliability of a nanocomponent under different assumptions on our proposed growth model. This paper is a modification of the extensive literature on modeling fatigue cracks in materials on a larger scale, applied to nanoscale where growth is not a function of cumulative stress on the component but related to the time to first exceedance of a threshold. Copyright © 2013 John Wiley & Sons, Ltd.     

A Novel Approach for the Synthesis of Furopyrimidine and Oxobenzofuran Derivatives

A novel, efficient one‐pot approach for the synthesis of furopyrimidine and oxobenzofuran derivatives 4 by a multicomponent reaction of an isocyanide, an aldehyde, and a CH‐acid compound in CH₂Cl₂ is reported (Scheme 1 and Table). The reactions were completed after 20 h at room temperature. This method has the advantages of high yields, simple methodology, and easy workup.     

Stereoselective Formation of Triphenylene Ketals

The oxidative trimerization of catechol ketals by MoCl₅ or MoCl₅/TiCl₄ mixtures leads preferentially to the all‐syn stereoisomer of the corresponding triphenylene ketal. The concomitant metal salts of the oxidative coupling most probably form a multinuclear template that directs the diastereoselectivity in a subsequent isomerization step under electrophilic conditions. Several functionalities can serve as coordination sites for the multinuclear metal chloro clusters. Suitable functional groups have to be stable towards the strong electrophilic and oxidizing conditions. Therefore, esters, nitriles, nitro derivatives, triazoles, and pyridines are successfully employed. Based on the flexibility and size of the substrate, different reagent mixtures lead to the stereoselective formation of the all‐syn derivatives.     

Linear Response in Finite Elasticity

This paper presents objective finite elastic equations that reproduce the linear stress-strain behaviour observed in uniaxial tension tests with some materials. More generally, the new equations reduce to linear elastic equations when the deformation is a pure stretch. Further, the response of the proposed equations for the case of isotropic materials in uniaxial tension-compression and simple shear is examined. It is also shown how the new equations can be considered as linear approximations of general equations of finite elasticity.     

Multivariate dynamic information

This paper develops measures of information for multivariate distributions when their supports are truncated progressively. The focus is on the joint, marginal, and conditional entropies, and the mutual information for residual life distributions where the support is truncated at the current ages of the components of a system. The current ages of the components induce a joint dynamic into the residual life information measures. Our study of dynamic information measures includes several important bivariate and multivariate lifetime models. We derive entropy expressions for a few models, including Marshall-Olkin bivariate exponential. However, in general, study of the dynamics of residual information measures requires computational techniques or analytical results. A bivariate gamma example illustrates study of dynamic information via numerical integration. The analytical results facilitate studying other distributions. The results are on monotonicity of the residual entropy of a system and on transformations that preserve the monotonicity and the order of entropies between two systems. The results also include a new entropy characterization of the joint distribution of independent exponential random variables.     

Regioselective One‐pot Synthesis of New Unsymmetric Spiro Dihydrofurans in the Reaction of Mixed Two Different Cyclic β‐Dicarbonyl Compounds with BrCN and Aldehydes in the Presence of Et3N

Crossed one‐pot reaction of mixed cyclic β‐dicarbonyl with various aldehydes in the presence of cyano gen bromide and triethylamine leads to the selective and efficient formation of crossed new unsymmetri cal spiro dihydrofurans at room temperature. The products were obtained in good to excellent yields. Structure elucidation was carried out by ¹H NMR, ¹³C NMR, FT‐IR spectroscopy, Mass analyses and X‐ray crystallography technique. A proposed mechanism was discussed for the formation of products.     

DBU-catalyzed transprotection of N-Fmoc-cysteine di- and tripeptides into S-Fm-cysteine di- and tripeptides

The transprotection of N-Fmoc-cysteine containing di- and tripeptides possessing a free SH group to produce the corresponding S-Fm-cysteine di- and tripeptides bearing a free amino group is accomplished efficiently with DBU in dry THF. The N-Fmoc to S-Fm transformation mechanism is discussed. S-Fm-Cysteine di- and tripeptides readily form amide bonds on coupling with N-(Pg-α-aminoacyl)benzotriazoles and N-(Pg-α-dipeptidoyl)benzotriazoles to give larger peptides.     

On the Roman Bondage Number of Planar Graphs

A Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The weight of a Roman dominating function is the value f (V(G)) = ?_{u ? V(G)} f (u){f (V(G)) = \sum_{u\in V(G)} f (u)}. The Roman domination number, γ _R (G), of G is the minimum weight of a Roman dominating function on G. The Roman bondage number b _R (G) of a graph G with maximum degree at least two is the minimum cardinality of all sets E^￠ í E(G){E^{\prime} \subseteq E(G)} for which γ _R (G − E′) > γ _R (G). In this paper we present different bounds on the Roman bondage number of planar graphs.