Superparamagnetic nanocomposites based on poly(styrene-b-ethylene/butylene-b-styrene)/cobalt ferrite compositions

Magnetic nanoparticles were created in or around the sulfonated (s) polystyrene domains in a phase separated poly[styrene-b-(ethylene-co-butylene)-b-styrene)] block copolymer (BCP) using an in situ inorganic precipitation procedure. The sBCP was neutralized with a mixed iron/cobalt chloride electrolyte and the doped samples were converted to their oxides by reaction with sodium hydroxide and further washing with water. Transmission electron microscopy indicated the presence of nanoparticles in the 5–25 nm size range. The metal oxide particle structures were studied using select area electron diffraction, which revealed that they are of the cobalt iron oxide composition (CoFe₂O₄). These nanocomposites were shown, using a superconducting quantum interference device magnetometer, to be superparamagnetic at 300 K and ferrimagnetic at 5 K. Nanocomposites consisting of smaller particles have a blocking temperature of 70 K, whereas it was 140 K for larger particles.     

A novel block turbo code for high-speed long-haul DWDM optical communication systems

A novel super forward error correction (SFEC) coding scheme, based on the block turbo code (BTC) of Bose–Chaudhuri–Hocguenghem (BCH)(64,57)×BCH(64,57), in high-speed long-haul dense wavelength division multiplexing (DWDM) optical communication systems is proposed. The simulation results and its analyses show that the net coding gain (NCG) of the novel SFEC code at iteration 6 is, respectively, 0.31 and 0.34 dB more than those of the BCH(3860, 3824)+BCH(2040, 1930) code and Reed–Solomon (RS)(255,239)+convolutional–self-orthogonal code (CSOC)(k₀/n₀=6/7, J=8) code in the Recommendation of ITU-T G.975.1 at iteration 3 for the bit error rate (BER) of 10⁻¹². The performance analyses for the novel SFEC code show that it has excellent advantages such as the shorter component code and rapid encoding/decoding speed; thus, both the complexity to implement its software/hardware and the delay time for its encoding/decoding can be greatly reduced. As a result, the novel SFEC coding scheme can better be applicable in high-speed long-haul DWDM optical communication systems. In addition, the design and implementation of the novel BTC are also analyzed and probed.     

Automorphism groups of Cayley graphs generated by block transpositions and regular Cayley maps

This paper deals with the Cayley graph $\mathrm{Cay}({\mathrm{Sym}}_n,T_n)$, where the generating set consists of all block transpositions. A motivation for the study of these particular Cayley graphs comes from current research in Bioinformatics. As the main result, we prove that $\text{Aut}\left(\mathrm{Cay}({\mathrm{Sym}}_n,T_n)\right)$ is the product of the left translation group and a dihedral group ${\mathsf{D}}_{n+1}$ of order $2(n+1)$. The proof uses several properties of the subgraph $\Gamma$ of $\mathrm{Cay}({\mathrm{Sym}}_n,T_n)$ induced by the set $T_n$. In particular, $\Gamma$ is a $2(n?2)$-regular graph whose automorphism group is ${\mathsf{D}}_{n+1},$ $\Gamma$ has as many as $n+1$ maximal cliques of size $2$, and its subgraph $\Gamma \left(V\right)$ whose vertices are those in these cliques is a 3-regular, Hamiltonian, and vertex-transitive graph. A relation of the unique cyclic subgroup of ${\mathsf{D}}_{n+1}$ of order $n+1$ with regular Cayley maps on ${\text{Sym}}_n$ is also discussed. It is shown that the product of the left translation group and the latter group can be obtained as the automorphism group of a non-$t$-balanced regular Cayley map on ${\text{Sym}}_n$.     

Projective aspects of the AES inversion

We consider the nonlinear function used in the Advanced Encryption Standard (AES). This nonlinear function is essentially inversion in the finite field GF(2⁸), which is most naturally considered as a projective transformation. Such a viewpoint allows us to demonstrate certain properties of this AES nonlinear function. In particular, we make some comments about the group generated by such transformations, and we give a characterisation for the values in the AES Difference or XOR Table for the AES nonlinear function and comment on the geometry given by this XOR Table.      

On computing of block ILU preconditioner for block tridiagonal systems

We present the recurrence formulas for computing the approximate inverse factors of tridiagonal and pentadiagonal matrices using bordering technique. Resulting algorithms are used to approximate the inverse of pivot blocks needed for constructing block ILU preconditioners for solving the block tridiagonal linear systems, arising from discretization of partial differential equations. Resulting preconditioners are suitable for parallel implementation. Comparison with other methods are also included.     

Asymptotic existence theorems for frames and group divisible designs

In this paper, we establish an asymptotic existence theorem for group divisible designs of type mn with block sizes in any given set K of integers greater than 1. As consequences, we will prove an asymptotic existence theorem for frames and derive a partial asymptotic existence theorem for resolvable group divisible designs.     

Global relaxed modulus-based synchronous block multisplitting multi-parameters methods for linear complementarity problems

Recently, Bai and Zhang [Numerical Linear Algebra with Applications, 20(2013):425439] constructed modulus-based synchronous multisplitting methods by an equivalent reformulation of the linear complementarity problem into a system of ?xed-point equations and studied the convergence of them; Li et al. [Journal of Nanchang University (Natural Science), 37(2013):307-312] studied synchronous block multisplitting iteration methods; Zhang and Li [Computers and Mathematics with Application, 67(2014):1954-1959] analyzed and obtained the weaker convergence results for linear complementarity problems. In this paper, we generalize their algorithms and further study global relaxed modulus-based synchronous block multisplitting multi-parameters methods for linear complementarity problems. Furthermore, we give the weaker convergence results of our new method in this paper when the system matrix is a block H+?matrix. Therefore, new results provide a guarantee for the optimal relaxation parameters, please refer to [A. Hadjidimos, M. Lapidakis and M. Tzoumas, SIAM Journal on Matrix Analysis and Applications, 33(2012):97-110, (dx.doi.org/10.1137/100811222)], where optimal parameters are determined.     

Clustering of magnetic nanoparticles using a double hydrophilic block copolymer, poly(ethylene oxide)-b-poly(acrylic acid)

The use of a double hydrophilic block copolymer (DHBC), poly(ethylene oxide)-block-poly(acrylic acid) (PEO-b-PAA) to prepare magnetic nanoparticle (MNP) clusters was investigated. In this one-pot synthesis method, the DHBC controlled the particle growth and served as both stabilizer and clustering agent. Depending on the iron-to-polymer ratio, the synthesized particles can be in the form of colonies of small iron oxide particles or clusters of these particles with size larger than 100 nm. Compared to the previous reported result using random copolymers, the clusters prepared with DHBC were more compact and homogeneous. The yield of clusters increased when the amount of polymer added was limiting. Insufficient amounts of polymer resulted in the formation of bare patches on the magnetite surface, and the strong van der Waals attraction induced cluster formation.     

Stimuli-responsive poly(ethylene oxide)-b-poly(2-vinylpyridine)-b-poly(ethylene oxide) triblock copolymers and complexation with poly(acrylic acid) at low pH

The self-organization of the double hydrophilic triblock copolymer poly(ethylene oxide)-b-poly(2-vinylpyridine)-b-poly(ethylene oxide), PEO-b-P2VP-b-PEO, was investigated in dilute aqueous solution under several experimental conditions using turbidimetry, as well as static and dynamic light scattering. As a result of the temperature-sensitive properties of the end PEO blocks and the p H-responsive properties of the middle P2VP block, the formation of large star-like micellar nanostructures is observed at high p H, while at low p H, but in the presence of salt and at high temperature, flower-like micelles are formed. Moreover, the viscosimetric and dynamic light scattering studies at low p H revealed that micelle-like nanostructures are formed upon mixing the triblock copolymer with poly(acrylic acid), PAA, due to hydrogen bonding interpolymer complexation.     

The High Order Block RIP Condition for Signal Recovery

In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurements. A high order sufficient condition based on block RIP is obtained to guarantee the stable recovery of all block sparse signals in the presence of noise, and robust recovery when signals are not exactly block sparse via mixed $l_2/l_1$ minimization. Moreover, a concrete example is established to ensure the condition is sharp. The significance of the results presented in this paper lies in the fact that recovery may be possible under more general conditions by exploiting the block structure of the sparsity pattern instead of the conventional sparsity pattern.