Cauchy Problem for the Fermion Field Equation Coupled With the Chern–Simons Gauge

We study initial value problems of the Chern–Simons–Dirac equations. With the Lorentz gauge condition they are formulated in the second-order hyperbolic equations. Under the Coulomb gauge condition Dirac equation is coupled with the elliptic equations which show some smoothing properties of the gauge field. With the temporal gauge condition divergence-curl decomposition and elliptic estimates will be used. JSPS Research Follow supported by JSPS Grant-in-Aid     

Multicomponent syntheses of 5- and 6-membered aromatic heterocycles using group 4–8 transition metal catalysts

In this Perspective, we discuss recent syntheses of 5- and 6-membered aromatic heterocycles via multicomponent reactions (MCRs) that are catalyzed by group 4–8 transition metals. These MCRs can be categorized based on the substrate components used to generate the cyclized product, as well as on common mechanistic features between the catalyst systems. These particular groupings are intended to highlight mechanistic and strategic similarities between otherwise disparate transition metals and to encourage future work exploring related systems with otherwise-overlooked elements. Importantly, in many cases these early- to mid-transition metal catalysts have been shown to be as effective for heterocycle syntheses as the later (and more commonly implemented) group 9–11 metals.

In this Perspective, we discuss recent syntheses of 5- and 6-membered aromatic heterocycles via multicomponent reactions (MCRs) catalyzed by group 4–8 transition metals, with a focus on common mechanisms and synthetic strategies across the series.     

On a Hereditary Radical Property Relating to the Reducedness

In this note, a hereditary radical property, called homomorphically reduced rings, is introduced, observed, and applied. The dual concept of this property is also studied with the help of Courter, proving that any ring R (possibly without identity) has an ideal S such that S/K is not homomorphically reduced for each proper ideal K of S; and if L is an ideal of R with L ? S, then L/H is homomorphically reduced for some ideal H of R with H ? L. The concept of the homomorphical reducedness is shown to be equivalent to the left (right) weak regularity and the (strong) regularity for one-sided duo rings. It is proved that homomorphically reduced rings have several useful properties similar to those of (weakly) regular rings. It is proved that the homomorphical reducedness can go up to classical quotient rings. It is shown that if R is a reduced right Ore ring with the ascending chain condition (ACC) for annihilator ideals, then the maximal right quotient ring of R is strongly regular (hence homomorphically reduced).     

Dinuclear palladium-azido complexes containing thiophene derivatives: reactivity toward organic isocyanides and isothiocyanates

Cyclopalladated tetranuclear Pd(II) complexes, [Pd2(micro-Cl)2(Y)]2 (Y = L1 or L2; H2L1 = di(2-pyridyl)-2,2'-bithiophene; H2L2 = 5,5'-di(2-pyridyl)-2,2':5',2'-terthiophene), containing two pyridyl-alpha, alpha'-disubstituted derivatives of thiophene were prepared. Treating these products with PR3 and subsequently with NaN3 produced the dinuclear Pd-azido complexes [(PR3)2(N3)Pd-Y-Pd(N3)(PR3)2] (Y = L1 or L2) or a cyclometallated complex [(PR3)(N3)Pd-Y'-Pd(N3)(PR3)] (Y' = C,N-L2). Reactions of these Pd-azido complexes with CN-Ar (Ar = 2,6-Me(2)C(6)H(3), 2,6-i-Pr(2)C(6)H(3)) or R-NCS (R = i-Pr, Et, allyl) led to the complexes containing end-on carbodiimido groups [(PMe3)2(N[double bond]C[double bond]N-Ar)Pd-Y-Pd(N[double bond]C[double bond]N-Ar)(PMe3)2] or S-coordinated tetrazole-thiolato groups {(PMe3)2[CN4(R)]S-Pd-Y-Pd-S[CN4)(R)](PMe3)2}. Interestingly, when treated with elemental sulfur, the carbodiimido complexes transformed into the cyclometallated derivatives, [(PMe3)(N[double bond]C[double bond]N-Ar)Pd-Y'-Pd(N[double bond]C[double bond]N-Ar)(PMe3)] (Y' = C,N-L1, C,N-L2). We also report the preparation of linear, thienylene-bridged dinuclear Pd complexes [L2(N3)Pd-X(or X')-Pd(N3)L2] (L = PMe3 or PMe2Ph; H2X = 2,2'-bithiophene or H2X' = 2,2':5',2'-terthiophene) and their reactivity toward organic isocyanide and isothiocyanates.     

Self-assembled peptide architecture with a tooth shape: folding into shape

Molecular self-assembly is the spontaneous association of molecules into structured aggregates by which nature builds complex functional systems. While numerous examples have focused on 2D self-assembly to understand the underlying mechanism and mimic this process to create artificial nano- and microstructures, limited progress has been made toward 3D self-assembly on the molecular level. Here we show that a helical β-peptide foldamer, an artificial protein fragment, with well-defined secondary structure self-assembles to form an unprecedented 3D molecular architecture with a molar tooth shape in a controlled manner in aqueous solution. Powder X-ray diffraction analysis, combined with global optimization and Rietveld refinement, allowed us to propose its molecular arrangement. We found that four individual left-handed helical monomers constitute a right-handed superhelix in a unit cell of the assembly, similar to that found in the supercoiled structure of collagen.     

Functional integration of DNA purification and concentration into a real time micro-PCR chip

Microfluidic devices for on-chip amplification of DNA from various biological and environmental samples have gained extensive attention over the past decades with many applications including molecular diagnostics of disease, food safety and biological warfare testing. But the integration of sample preparation functions into the chip remains a major hurdle for practical application of the chip-based diagnostic system. We present a PCR-based molecular diagnostic device comprised of a microfabricated chip and a centrifugal force assisted liquid handling tube (CLHT) that is designed to carry out concentration and purification of DNA and subsequent amplification of the target gene in a single chip. The reaction chamber of the chip contains an array of pillar structures to increase the surface area for capturing DNA from a raw sample of macro volume in the presence of kosmotropic agents. The CLHT was designed to provide an effective interface between sample preparation and the microfluidic PCR chip. We have characterized the effect of various fluidic parameters including DNA capture, amplification efficiency and centrifugal pressure generated upon varying sample volume. We also evaluated the performance of this system for quantitative detection of E. coli O157:H7. From the samples containing 10(1) to 10(4) cells per mL, the C(T) value linearly increased from 25.1 to 34.8 with an R(2) value greater than 0.98. With the effectiveness and simplicity of operation, this system will provide an effective interface between macro and micro systems and bridge chip-based molecular diagnosis with practical applications.     

A highly Lewis acidic triarylborane bearing peripheral o-carborane cages

A triarylborane (2) bearing three o-carborane cages at peripheral positions on the aryl groups was prepared and its crystal structure was determined from X-ray diffraction study. Treatment of 2 with KF in the presence of 18-crown-6 led to the potassium salt, [2F](-). A UV-vis titration experiment carried out in THF/H(2)O (9/1 v/v) showed that 2 binds fluoride ions with a binding constant (K) of 4.8 × 10(4) M(-1), which is an order-of-magnitude greater than K for the mono-carborane substituted triarylborane. The enhanced fluoride ion affinity of 2 indicates an apparent additive effect of multiple carborane substitutions on the Lewis acidity enhancement of the triarylborane. The highly Lewis acidic nature of 2 was further utilized in evaluating the fluoride ion affinity of tris(pentafluorophenyl)borane (B(C(6)F(5))(3)). A fluoride exchange reaction between [2F](-) and B(C(6)F(5))(3) resulted in 15 times higher fluorophilicity for B(C(6)F(5))(3) than for 2. The lower Lewis acidity of 2 compared with B(C(6)F(5))(3) was confirmed from its greater cathodic reduction potential.     

Scaled memoryless symmetric rank one method for large-scale optimization

This paper concerns the memoryless quasi-Newton method, that is precisely the quasi-Newton method for which the approximation to the inverse of Hessian, at each step, is updated from the identity matrix. Hence its search direction can be computed without the storage of matrices. In this paper, a scaled memoryless symmetric rank one (SR1) method for solving large-scale unconstrained optimization problems is developed. The basic idea is to incorporate the SR1 update within the framework of the memoryless quasi-Newton method. However, it is well-known that the SR1 update may not preserve positive definiteness even when updated from a positive definite matrix. Therefore we propose the memoryless SR1 method, which is updated from a positive scaled of the identity, where the scaling factor is derived in such a way that positive definiteness of the updating matrices are preserved and at the same time improves the condition of the scaled memoryless SR1 update. Under very mild conditions it is shown that, for strictly convex objective functions, the method is globally convergent with a linear rate of convergence. Numerical results show that the optimally scaled memoryless SR1 method is very encouraging.