Eigenvalue inequalities and equalities

We consider cases of equality in three basic inequalities for eigenvalues of Hermitian matrices: Cauchy's interlacing inequalities for principal submatrices, Weyl's inequalities for sums, and the residual theorem. Several applications generalize and sharpen known results for eigenvalues of irreducible tridiagonal Hermitian matrices.     

Extensions of zip rings

A ring R is called right zip provided that if the right annihilator r_R(X) of a subset X of R is zero, r_R(Y)=0 for a finite subset Y⊆X. Faith [5] raised the following questions: When does R being a right zip ring imply R[x] being right zip?; Characterize a ring R such that Mat_n(R) is right zip; When does R being a right zip ring imply R[G] being right zip when G is a finite group? In this note, we continue the study of the extensions of noncommutative zip rings based on Faith's questions.     

Fuzzy rule generation methods for high-level computer vision

In many decision making systems involving multiple sources, the decisions made may be considered as the result of a rule-based system in which the decision rules are usually enumerated by experts or generated by a learning process. In this paper, we discuss the various issues involved in the generation of fuzzy rules automatically from training data for high-level computer vision. Features are treated as linguistic variables that appear in the antecedent clauses of the rules. We present methods to generate the corresponding linguistic labels (values) and their membership functions. Rules are generated by constructing a minimal approximate fuzzy aggregation network and then training the network using gradient descent methods. Several examples are given.     

Methionine synthase reductase polymorphisms are associated with serum osteocalcin levels in postmenopausal women

Homocysteine (Hcy) is thought to play an important role in the development of osteoporosis and fracture. Methionine synthase reductase (MTRR) is an enzyme involved in the conversion of Hcy to methionine. We hypothesized that certain genetic polymorphisms of MTRR leading to reduced enzyme activity may cause hyperhomocysteinemia and affect bone metabolism. We therefore examined the associations of the A66G and C524T polymorphisms of the MTRR gene with bone mineral density (BMD) and serum osteocalcin levels in postmenopausal women. Although we did not detect any significant associations between MTRR polymorphisms and BMD or serum osteocalcin levels, we found that the 66G/524C haplotype, which has reduced enzyme activity, was significantly associated with serum osteocalcin levels in a gene-dose dependent manner (P = 0.002). That is, the highest osteocalcin levels (34.5 +/- 16.8 ng/ml) were observed in subjects bearing two copies, intermediate osteocalcin levels (32.6 +/- 14.4 ng/ml) were observed in subjects bearing one copy, and the lowest levels of osteocalcin (28.8 +/- 10.9 ng/ml) were observed in subjects bearing no copies. These results suggest that the 66G/524C haplotype of the MTRR gene affect bone turn over rate.     

Metal filament growth in electrically conductive polymers for nonvolatile memory application

Solution processable polymers that can reproducibly form metal filament by applying voltage are investigated for nonvolatile memory application. Up to present, the understanding of materials enabling to make the metal filament has not been well-documented and the vacuum deposition methods were dominantly used in device fabrication. After screening various polymers, we found that only the polymers having two functionalities, the presence of strongly coordinating heteroatom (S or N) with metal ions and the electrical conductivity, showed the reproducible filament formation behavior. Among the polymers screened, the regiorandom poly(3-hexylthiophene) showed the best switching endurance over 30,000 write-read-erase-read cycles without any switching failure.     

Miscibility of Solution Blends of Unsaturated Polyester Resin with Polystyrene and Polycarbonate

Miscibility studies of unsaturated polyester resin (UPR) blends with two different thermoplastics—polystyrene (PS) and polycarbonate (PC), in a common solvent, chloroform, were carried out by viscosity, ultrasonic velocity, density, and refractive index methods. Two interaction parameters, μ and α were calculated using viscosity data for these blends. The positive interaction parameter values (μ and α > 0) obtained for the UPR/PS blend and the negative interaction parameter values (μ and α < 0) obtained for the UPR/PC blend indicate that the former is a miscible blend and the latter is an immiscible blend. These results were further confirmed by the ultrasonic velocity, density, and refractive index measurements.     

Development of New Atom Transfer Radical Polymerization System by Iron (III)‐Metal Salts Without Using any External Initiator and Reducing Agent

Atom transfer radical polymerization (ATRP) catalyzed by high oxidation state metal salts of FeX₃ is developed for the first time in the absence of both external initiator and reducing agent. Methyl methacrylate (MMA) and styrene are polymerized successfully using FeX₃/Phosphorous ligands with well‐controlled molecular weight distributions (=1.5). The molecular weight of the polymers increases with monomer consumption with the progress of time and the polymerization behaviors show a decent ATRP trend. Activators and initiators are suggested to generate in situ by the addition reaction of MMA and one equivalent of FeX₃. The PMMA synthesized from without‐initiator system is characterized by ¹H, ¹³C and DEPT (distortionless enhancement by polarization transfer nuclear magnetic resonance) nuclear magnetic resonance spectroscopy. Chain extension and copolymerization experiments prove the livingness of the obtained polymer.