Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma

In this paper, we propose a computational method for nonlinear partial differential equations modeling ion-acoustic waves as well as dusty plasmas in laboratory and space sciences. Many types of solitary waves including soliton solutions, N-soliton solutions and singular N-soliton solutions are derived. The characteristic line method and graphical analysis are applied to discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Furthermore, the effects of inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed.     

Spontaneous Stepwise Self‐Assembly of a Polyoxometalate–Organic Hybrid into Catalytically Active One‐Dimensional Anisotropic Structures

An inorganic–organic hybrid surfactant with a hexavanadate cluster as the polar head group was designed and observed to assemble into micelle structures, which further spontaneously coagulate into a 1D anisotropic structure in aqueous solutions. Such a hierarchical self‐assembly process is driven by the cooperation of varied noncovalent interactions, including hydrophobic, electrostatic, and hydrogen‐bonding interactions. The hydrophobic interaction drives the quick formation of the micelle structure; electrostatic interactions involving counterions leads to the further coagulation of the micelles into larger assemblies. This process is similar to the crystallization process, but the specific counterions and the directional hydrogen bonding lead to the 1D growth of the final assemblies. Since most of the hexavanadates are exposed to the surface, the 1D assembly with nanoscale thickness is a highly efficient heterogeneous catalyst for the oxidation of organic sulfides with appreciable recyclability.     

Exploring the Symmetry,Structure, and Self‐Assembly Mechanism of a Gigantic Seven‐Fold Symmetric {Pd84} Wheel

The symmetry, structure and formation mechanism of the structurally self‐complementary { Pd₈₄ } = [Pd₈₄O₄₂(PO₄)₄₂(CH₃CO₂)₂₈]^70? wheel is explored. Not only does the symmetry give rise to a non‐closest packed structure, the mechanism of the wheel formation is proposed to depend on the delicate balance between reaction conditions. We achieve the resolution of gigantic polyoxopalladate species through electrophoresis and size‐exclusion chromatography, the latter has been used in conjunction with electrospray mass spectrometry to probe the formation of the ring, which was found to proceed by the stepwise aggregation of {Pd₆}^? = [Pd₆O₄(CH₃CO₂)₂(PO₄)₃Na_6?nH_n]^? building blocks. Furthermore, the higher‐order assembly of these clusters into hollow blackberry structures of around 50 nm has been observed using dynamic and static light scattering.     

A new procedure for consistency testing of binary vapour—liquid equilibrium data

A procedure has been proposed for testing the thermodynamic consistency of low-pressure binary vapour—liquid equilibrium data. The method, employing the idea of local defects due to Mc Dermott and Ellis, is based on the statistical nature of consistency and is systematically formulated using the methods of mathematical statistics. It provides well-defined limits for the test quantities and consequently is superior to all empirically evaluated tests. In addition, the proposed procedure provides an estimate of experimental error and enables any systematic characteristic to be identified. The efficiency of the method developed here has been investigated through Monte Carlo simulations and its applicability to actual vapour—liquid equilibrium data has been demonstrated using a number of examples. A comparison with the methods of Ulrichson and Stevenson and Samuels et al., which also utilize a statistical treatment of the local defects, reveals a serious error involved in both. For the case when credit is placed in the vapour—liquid equilibrium data, the consistency may be used to draw some conclusions on the vapour phase non-ideality. In this respect, minimization of the consistency criterion proposed is shown to lead to the maximum likelihood estimate of the second-cross virial coefficient.     

Exploration of the relationship between topology and designability of conformations

Protein structures are evolutionarily more conserved than sequences, and sequences with very low sequence identity frequently share the same fold. This leads to the concept of protein designability. Some folds are more designable and lots of sequences can assume that fold. Elucidating the relationship between protein sequence and the three-dimensional (3D) structure that the sequence folds into is an important problem in computational structural biology. Lattice models have been utilized in numerous studies to model protein folds and predict the designability of certain folds. In this study, all possible compact conformations within a set of two-dimensional and 3D lattice spaces are explored. Complementary interaction graphs are then generated for each conformation and are described using a set of graph features. The full HP sequence space for each lattice model is generated and contact energies are calculated by threading each sequence onto all the possible conformations. Unique conformation giving minimum energy is identified for each sequence and the number of sequences folding to each conformation (designability) is obtained. Machine learning algorithms are used to predict the designability of each conformation. We find that the highly designable structures can be distinguished from other non-designable conformations based on certain graphical geometric features of the interactions. This finding confirms the fact that the topology of a conformation is an important determinant of the extent of its designability and suggests that the interactions themselves are important for determining the designability.     

Toward whole-body optical imaging of rats using single-photon counting fluorescence tomography

We used single-photon counting (SPC) detection for diffuse fluorescence tomography to image nanomolar (nM) concentrations of reporter dyes through a rat. Detailed phantom data are presented to show that every centimeter increase in tissue thickness leads to 1 order of magnitude decrease in the minimum fluorophore concentration detectable for a given detector sensitivity. Specifically, here, detection of Alexa Fluor 647 dyes is shown to be achievable for concentrations as low as 1 nM (<200 fM) through more than 5 cm in tissue phantoms, which indicates that this is feasible in larger rodent models. Because it is possible to detect sub-nM fluorescent inclusions with SPC technology in rats, it follows that it is possible to localize subpicomolar fluorophore concentrations in mice, putting the concentration sensitivity limits on the same order as nuclear medicine methods.     

Antifungal Activity of Alpha-Mangostin against Colletotrichum gloeosporioides In Vitro and In Vivo

We investigated alpha-mangostin (α-mangostin, α-MG), a xanthone natural product extracted from the pericarp of mangosteen (Garcinia mangostana), for its antifungal activities and possible mechanism against Colletotrichum gloeosporioides, which causes mango anthracnose. The results demonstrated that α-MG had a relatively high in vitro inhibitory activity against C. gloeosporioides among 20 plant pathogenic fungi. The median effective concentration (EC₅₀) values of α-MG against mycelial growth were nearly 10 times higher than those of spore germination inhibition for both strains of C. gloeosporioides, the carbendazim-sensitive (CBD-s) and carbendazim-resistant (CBD-r). The results suggested that α-MG exhibited a better inhibitory effect on spore germination than on the mycelial growth of C. gloeosporioides. Further investigation indicated that the protective effect could be superior to the therapeutic effect for mango leaves for scab development. The morphological observations of mycelium showed that α-MG caused the accumulation of dense bodies. Ultrastructural observation further revealed that α-MG caused a decrease in the quantity and shape of the swelling of mitochondria in the mycelium cells of C. gloeosporioides. In addition, bioassays disclosed that the inhibitory activity of α-MG on spore germination was reduced by adding exogenous adenosine triphosphate (ATP). These results suggested that the mode of action of α-MG could be involved in the destruction of mitochondrial energy metabolism. The current study supports α-MG as a natural antifungal agent in crop protection.     

Toward a New Algorithm for Nonlinear Fractional Differential Equations

This paper is concerned with the development of an efficient algorithm for the analytic solutions of nonlinear fractional differential equations. The proposed algorithm Laplace homotopy analysis method (LHAM) is a combined form of the Laplace transform method with the homotopy analysis method. The biggest advantage the LHAM has over the existing standard analytical techniques is that it overcomes the difficulty arising in calculating complicated terms. Moreover, the solution procedure is easier, more effective and straightforward. Numerical examples are examined to demonstrate the accuracy and efficiency of the proposed algorithm.