Optical diffraction in twisted liquid-crystalline media-phase grating mode

We have calculated the diffraction of light perpendicular to the twist axis in a chiral smectic C liquid crystal. In contrast to a cholesteric liquid crystal, in a chiral smectic C liquid crystal we find extra orders which form the odd orders in the diffraction pattern. For an incident linearly polarized light, at a general azimuth, these odd orders are linearly polarized and the even orders are elliptically polarized. The intensities of the odd orders are always independent of the azimuth of the incident light, while this is possible for even orders only at a particular tilt angle of the chiral smectic C liquid crystal. Also, for the incident vibration parallel or perpendicular to the twist axis the odd orders are polarized in the orthogonal linear state with respect to incident vibration, while the even orders are in the same linear state.     

Wild African elephants (Loxodonta africana) discriminate between familiar and unfamiliar conspecific seismic alarm calls

The ability to discriminate between call types and callers as well as more subtle information about the importance of a call has been documented in a range of species. This type of discrimination is also important in the vibrotactile environment for species that communicate via vibrations. It has recently been shown that African elephants (Loxodonta africana) can detect seismic cues, but it is not known whether they discriminate seismic information from noise. In a series of experiments, familiar and unfamiliar alarm calls were transmitted seismically to wild African elephant family groups. Elephants respond significantly to the alarm calls of familiar herds (p=0.004) but not to the unfamiliar calls and two different controls, thus demonstrating the ability of elephants to discriminate subtle differences between seismic calls given in the same context. If elephants use the seismic environment to detect and discriminate between conspecific calls, based on the familiarity of the caller or some other physical property, they may be using the ground as a very sophisticated sounding board.     

FeCl3 catalysed two consecutive aminomethylation at the α-position of the β-dicarbonyl compounds: an easy access to hexahydropyrimidines and its spiro analogues

Multicomponent synthesis of 1,3-diaryl-hexahydropyrimidines by a one-pot reaction of 1,3-dicarbonyl compounds, amines and formaldehyde catalysed by FeCl₃ in dichloromethane at room temperature (25-30 °C) has been reported. Double amino methylation occurs at the α-position of the 1,3-dicabonyl compounds/β-keto esters. The same methodology leads to spiro compounds with indane-1,3-dione. In this reaction, six molecules condense in one pot to form six new covalent bonds, thus, creating high atom economy. This is the first report of the synthesis of the substituted hexahydropyrimidines involving β-keto esters and its spiro analogues with indane-1,3-dione.     

胶束催化体系中的对映选择性环醚化反应

The enantioselective cycloetherification of substituted keto phenols into their corresponding dihydrobenzofuran derivatives was carried out using hydrogen peroxide and chiral quaternary ammonium iodide in micellar media. This approach increased the conversion rate of cycloetherification and also widened the scope of this particular reaction for various substituted keto phenols with electron withdrawing as well as electron donating functionalities. The use of a surfactant in the cycloetherification reaction ...     

Comparison of Planar and 3‐D Interdigitated Electrodes as Electrochemical Impedance Biosensors

It has been reported that the introduction of a dielectric barrier between adjacent digits of an interdigitated electrode array can improve the sensitivity of the array as an electrochemical impedance biosensor. Here we present an in‐depth analysis of the impedance in planar interdigitated electrodes and 3‐D interdigitated electrodes (with dielectric barriers). The analysis indicates that the planar geometry not only provides lower impedance but also a higher change impedance as a result of molecular immobilization on the electrode array surface.     

Boxicity of Leaf Powers

The boxicity of a graph G, denoted as boxi(G), is defined as the minimum integer t such that G is an intersection graph of axis-parallel t-dimensional boxes. A graph G is a k-leaf power if there exists a tree T such that the leaves of the tree correspond to the vertices of G and two vertices in G are adjacent if and only if their corresponding leaves in T are at a distance of at most k. Leaf powers are used in the construction of phylogenetic trees in evolutionary biology and have been studied in many recent papers. We show that for a k-leaf power G, boxi(G)??? k?1. We also show the tightness of this bound by constructing a k-leaf power with boxicity equal to k?1. This result implies that there exist strongly chordal graphs with arbitrarily high boxicity which is somewhat counterintuitive.     

Do commercially available metal salts mediate calixarene formation via hydrogen-bonded dimers?

In this article we report the first example of a Lewis acid promoted, one-pot, Br?nsted acid free, high-yielding synthesis of the calixarene macrocycle from the "monomer" p-tert-butylphenol. We report that when a commercially available metal salt (Lewis acid) is incorporated within the calixarene-forming reaction, a certain amount of control over the size of the calixarenes produced can be gained. Although a detailed mechanistic rationale on how the macrocycle is assembled is unclear, what is evident from this work is that the metal cation, the counteranion, and the oxidation state of the salt employed are all important contributors to the outcome of the reaction process. Indeed, evidence to date suggests that a subtle "symbiotic" relationship exists between the metal cation, its oxidation state, and the anion that allows the efficient transformation of the "monomeric" p-tert-butylphenol into linear oligomers and, ultimately, into macrocyclic calixarenes. Athough the metal salt mediated process described herein is efficient and high-yielding, what is also fundamentally important is that a comprehensive mechanistic understanding of how the calixarenes are assembled be accrued. Searching for possible indicators or clues, we propose that oligomeric methylene-linked phenolic entities are initially formed and that these, we tentatively suggest, generate metal and/or anion hydrogen-bonded supramolecular intermediates. It is possible that the preorganization of the linear polyphenolic oligomers allows the formation of hydrogen-bonded structures which, critically, result in the formation of supramolecular assemblies that are subsequently "stitched" together, generating the p-tert-butylcalix[n]arenes (n = 4-9) in excellent yields. Substantiating the possibility that hydrogen-bonded entities are generated (and that these subsequently afford metal-templated assemblies), we make reference to a seldom cited 1962 Nature publication that reported the propensity of polyphenolic linear oligomers to form "well-defined intramolecularly hydrogen-bonded conformations".     

Reduced-order models for control of fluids using the eigensystem realization algorithm

As sensors and flow control actuators become smaller, cheaper, and more pervasive, the use of feedback control to manipulate the details of fluid flows becomes increasingly attractive. One of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this article, we show that using the Eigensystem Realization Algorithm (ERA) (Juang and Pappa, J Guid Control Dyn 8(5):620?C627, 1985) one can theoretically obtain exactly the same reduced-order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.     

A mathematical fractional model with nonsingular kernel for thrombin receptor activation in calcium signalling

In calcium signalling, activation of receptor is a very significant aspect. To understand the mechanism of calcium signalling, receptors are the important components. The mobilization of intracellular calcium from intracellular stores depends upon binding of agonist to cell surface receptor. Thrombin is chosen as model ligand. In order to understand thrombin receptor activation, we analyze fractional model incorporating derivative of arbitrary order and nonsingular kernel which can precisely describe the effect of memory and can explain the model in better and more efficient manner as compared with fractional operators with singular kernels. The problem has been solved by perturbation iterative method. Using fixed‐point theorem, it is proved that solution of the system will exist and also it will be unique.