Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.     

Laser photolysis studies of spiropyran-merocyanine aggregate formation in solution

The photoinduced processes leading to formation of J-aggregate stacks of 1-(β-methacryloxyethyl)-3,3-dimethyl-6′- nitrospiro-(indoline-2,2′-[2H-[2H-1] benzopyran) d its associated ring opened merocyanine form B have been determined by N₂-laser transient spectroscopy. Detailed mechanisms for formation of complexes AB, A₂B, and J-aggregate stacks (A₂B) _n in aliphatic and aromatic solvents are presented.     

Electrical-thermal switching in carbon-black-polymer composites as a local effect

Following the lack of microscopic information about the intriguing well-known electrical-thermal switching mechanism in carbon-black-polymer composites, we applied atomic force microscopy in order to reveal the local nature of the process and correlated it with the characteristics of the widely used commercial switches. We conclude that the switching events take place in critical interparticle tunneling junctions that carry most of the current. The macroscopic switched state is then a result of a dynamic-stationary state of fast switching and slow reconnection of the corresponding junctions.     

Novel core-corona hybrid nanomaterials based on the conjugation of amphiphilic polymeric diblocks to the surface of multifunctional nanodiamond anchors

The poor aqueous solubility and the physicochemical instability of many marketed drugs and new chemical entities is one of the most challenging issues in pharmaceutical research and development. Polymeric micelles (PMs) are produced by the self-assembly of polymeric amphiphiles and they represent one of the most extensively investigated nanotechnology platforms for encapsulation, delivery and targeting of hydrophobic drugs. However, a main challenge is preventing their disassembly under extreme dilution in the body fluids, which leads to uncontrolled release of the encapsulated cargo. In this work, we developed an amphiphilic nanomaterial that resembles the core-corona architecture of a PM with superior stability in the body fluids. Specifically, we utilized carboxylated nanodiamonds (cNDs) as particulate anchors to covalently link amphiphilic diblock copolymers consisting of poly(epsilon-caprolactone) (PCL) and poly(ethylene glycol) monomethyl ether (PEG) as hydrophobic and hydrophilic components, respectively. We confirmed a successful core-corona nanostructure using various characterization techniques. In addition, TEM revealed the presence of a thin polymeric layer. Then, the cell compatibility was evaluated in Caco2 cell monolayers, an in vitro model of the intestinal epithelium. Finally, the encapsulation of the hydrophobic anti-helmintic drug nitazoxanide was studied. Cargoes as high as 17.5% w/w were achieved and the sustained release of the cargo according to the Korsmeyer-Peppas model demonstrated in vitro. Overall, preliminary results highlight the potential of this novel approach to extend the applicability of PMs in drug delivery.     

The complexity of identifying redundant and essential elements

In many optimization problems a solution is a subset of optimum number of elements satisfying some desired property. An element is redundant if it does not belong to any solution of the problem. An element is essential if it belongs to every solution of the problem. We consider the complexity of indentifying redundant and essential elements in a sample of NP-Hard optimization problems. It is shown that these identification problems are also NP-Hard. The proofs are based on an analysis of the original reductions of Cook [The complexity of theorem proving procedures, in “Proceedings, Third Annual Assoc. Comput. Mach. Symposium on Theory of Computing”, pp. 151–158, Assoc. Comput. Mach., New York 1971] and Karp [Reducibility among combinational problems, in “Complexity of Computer Computations” (R. E. Miller and J. W. Thatcher, Eds.), pp. 85–104, Plenum, New York 1972].     

Using AFM to explore food nanostructure

The major recent advances in the past year are all in the use of atomic force microscopy as an analytical tool to answer questions related to real food systems. These samples are bio materials and interfaces, all fall in one of the most challenging environments for AFM imaging. The include food dispersions, gels, and raw materials of plant and marine origin.     

Efficient implementation of a shifting algorithm

An efficient implementation of the shifting algorithm [2] for min-max tree partitioning is given. The complexity is reduced from ORk³ + kn) to O(Rk(k + log d) + n) where a tree of n vertices, radius, of R edges, and maximum degree d is partitioned into k + 1 subtrees. The improvement is mainly due to the new junction tree data structure which suggests a succinct representation for subsets of edges, of a given tree, that preserves the interrelation betqween the edges on the tree.     

Image Projection and Representation on S<Superscript>n</Superscript>

In signal processing, communications, and other branches of information technologies, it is often desirable to map the higher-dimensional signals on Sⁿ. In this article we introduce a novel method of representing signals on Sⁿ. This approach is based on geometric function theory, in particular on the theory of quasiregular mappings. The importance of sampling is underlined, and new geometric sampling theorems for general manifolds are presented.