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.     

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.     

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.     

Collinear broadband optical parametric generation in periodically poled lithium niobate crystals by group velocity matching

Collinear broadband optical parametric generation (OPG) using periodically poled lithium niobate (PPLN) crystals were designed and experimentally demonstrated with the quasi-phase matching (QPM) periods of 21.5, 24.0, and 27.0 μm. The broad gain bandwidth was accomplished by choosing a specific set of the period and the pump wavelength that allows the group velocities of the signal and the idler to match close to the degeneracy point. OPG gain bandwidth and also the spectral region could be controlled by proper design of QPM period and pump wavelength. The total OPG gain bandwidth of 600, 900, and 1200 nm was observed for the PPLN devices with QPM periods of 21.5, 24.0, and 27.0 μm, respectively. We have also observed multiple color visible generation whenever the OPG spectrum was significantly broad. From the visible peaks of the three PPLN samples, it is found that broad gain bandwidth is crucial in the temperature-insensitive collinear simultaneous RGB generation from a single crystal.     

Microfluidic assembly blocks

An assembly approach for microdevice construction using prefabricated microfluidic components is presented. Although microfluidic systems are convenient platforms for biological assays, their use in the life sciences is still limited mainly due to the high-level fabrication expertise required for construction. This approach involves prefabrication of individual microfluidic assembly blocks (MABs) in PDMS that can be readily assembled to form microfluidic systems. Non-expert users can assemble the blocks on glass slides to build their devices in minutes without any fabrication steps. In this paper, we describe the construction and assembly of the devices using the MAB methodology, and demonstrate common microfluidic applications including laminar flow development, valve control, and cell culture.     

Encapsulation of tris(4,7-diphenyl-1,10-phenanthroline)ruthenium(II) complex linked with dendrons in sol-gels: Stable optical sensing membranes for dissolved oxygen

To circumvent the leaching problem of optical sensing membranes used for dissolved oxygen (DO) measurements, the encapsulation of Ru(II) complexes linked with bulky dendron(s) in a sol-gel matrix was investigated. A dendron, readily formed via chemical transformations such as amidation and catalytic reduction, was covalently incorporated into tris(4,7-diphenyl-1,10-phenanthroline)ruthenium(II) complex, leading to an increase in the size and lipophilicity of dye molecules. Sol-gel-based sensing membranes encapsulating these Ru(II) complexes displayed a strong luminescence emission at 590 nm induced by radiation at 480 nm, and showed excellent DO sensing properties and stability for repeated measurements in aqueous solution. The encapsulation of the dendron-incorporated Ru(II) complexes in sol-gels prevented the dyes from leaching out of the membranes.     

A delicate electronic balance between metal and ligand in [Cu-P-Cu-P] diamondoids: oxidation state dependent plasticity and the formation of a singlet diradicaloid

Transition metal atoms often participate in redox reactions as catalytic sites, where ligand groups play an important role in orchestrating catalytic activity, especially in metalloenzymes. A major issue is to understand connections between oxidation state and geometry at the metal center, because geometric reorganization is directly related to reaction rate. In this article, we analyze an intriguing oxidation-induced geometrical change in [Cu-P-Cu-P] ring structures ( approximately 0.6 A change in metal-metal distance) using quantum chemical approaches. We find that the Cu-P interactions in the ring of the neutral species consist of four localized P --> Cu dative bonds. Successive oxidations extract electrons predominantly from P atoms on the ring rather than Cu sites. It emerges that as a result, the Cu-P interactions change and also exhibit partial Cu(3d) --> P donation, which causes the large distortion in geometry. We also find that the dication possesses a large degree of diradical character, forming a rare example of an observed species that is a singlet diradicaloid. This hypothesis is supported by our computational results as well as previously reported experimental features.     

De Novo Synthesis of Furanose Sugars: Catalytic Asymmetric Synthesis of Apiose and Apiose‐Containing Oligosaccharides

A de novo synthetic method towards apiose, a structurally unusual furanose, is reported. The key feature is sequential metal catalysis consisting of the palladium‐catalyzed asymmetric intermolecular hydroalkoxylation of an alkoxyallene and subsequent ring‐closing metathesis (RCM). This strategy enabled the efficient synthesis of various apiose‐containing disaccharides and a unique convergent synthesis of trisaccharides.