Branched And Spiral Organic Nanotubes Based On The Self-assembly Of Bile Acids

The self-assembly of chiral amphiphilic molecules in aqueous solutions is of particular interest because the chirality of individual molecules is often expressed in their supermolecular structures. Self-assembled tubes made of chiral amphiphilic molecules represent useful supramolecular architectures which hold promise as controlled release vehicles for drug delivery, encapsulates for functional molecules, and nanoreactors for chemical reactions. Lithocholic acid (LCA) is a secondary bile acid with the concentration being identical to that of cholesterol in the hepatic bile and gallbladder. It has a rigid, nearly planar hydrophobic steroid nucleus, with four hydrogen atoms and one hydroxyl group directed toward the concave side, and the convex side with three methyl groups. The ionic head with a carboxyl group is linked to the steroid nucleus through a short alkyl chain. In this thesis work, I study the self-assembly behavior of LCA at the liquid-solid interface, in confined spaces, and bulk solution. We find that the initially formed LCA vesicles further assemble into fractal tubes on glass slides by diffusion-limited aggregation and pronglike tubes by the capillary flow generated in an evaporating vesicle solution confined by two parallel glass slides. While in bulk solution, the LCA vesicles linearly aggregate and fuse into spiral tubes at pH 12.0. The spiral tubes can transition into a straight shape as the pH of solution is reduced to 7.4. The shape transition of the tubes is reversible as the pH of solution is adjusted back to 12.0. The pH-switchable shape transition suggests that the self-assembled LCA tubes can act as a supramolecular chemical spring. Finally, the LCA tubes are endowed with optical functionality by embedding cadmium sulfide nanopaticles (CdS) in the tube walls by the co-assembling synthesis of cadmium sulfide iv (CdS) nanoparticles with lithocholic acid (LCA) molecules. The fluorescent composite tubes can undergo pH switchable spiral/straight, which are a promising system for a variety of materials and biological applications

Composition type operator from Bergman space to μ-Bloch type space in Cn

AbstractLet φ be a holomorphic self-map of B and ψ∈H(B). A composition type operator Tψ,φ is defined by Tψ,φ(f)=ψf○φ. We can regard this operator as a generalization of a multiplication operator and a composition operator. For normal functions μ, some necessary and sufficient conditions are given for which Tψ,φ is a bounded or compact operator from Bergman space to μ-Bloch type space βμ on the unit ball of Cn. As a Corollary, we obtain the pointwise multiplier from Bergman space to μ-Bloch type space on B

A new algorithm for finding the k shortest transport paths in dynamic stochastic networks

The static K shortest paths (KSP) problem has been resolved. In reality, however, most of the networks are actually dynamic stochastic networks. The state of the arcs and nodes are not only uncertain in dynamic stochastic networks but also interrelated. Furthermore, the cost of the arcs and nodes are subject to a certain probability distribution. The KSP problem is generally regarded as a dynamic stochastic optimization problem. The dynamic stochastic characteristics of the network and the relationships between the arcs and nodes of the network are analyzed in this paper, and the probabilistic shortest path concept is defined. The mathematical optimization model of the dynamic stochastic KSP and a genetic algorithm for solving the dynamic stochastic KSP problem are proposed. A heuristic population initialization algorithm is designed to avoid loops and dead points due to the topological characteristics of the network. The reasonable crossover and mutation operators are designed to avoid the illegal individuals according to the sparsity characteristic of the network. Results show that the proposed model and algorithm can effectively solve the dynamic stochastic KSP problem. The proposed model can also solve the network flow stochastic optimization problems in transportation, communication networks, and other networks

A family of stabilizer-free virtual elements on triangular meshes

A family of stabilizer-free $P_k$ virtual elements are constructed on triangular meshes. When choosing an accurate and proper interpolation, the stabilizer of the virtual elements can be dropped while the quasi-optimality is kept. The interpolating space here is the space of continuous $P_k$ polynomials on the Hsieh-Clough-Tocher macro-triangle, where the macro-triangle is defined by connecting three vertices of a triangle with its barycenter. We show that such an interpolation preserves $P_k$ polynomials locally and enforces the coerciveness of the resulting bilinear form. Consequently the stabilizer-free virtual element solutions converge at the optimal order. Numerical tests are provided to confirm the theory and to be compared with existing virtual elements