On the number of Fourier coefficients that determine a Hilbert modular form

We estimate the number of Fourier coefficients that determine a Hilbert modular cusp form of arbitrary weight and level. The method is spectral (Rayleigh quotient) and avoids the use of the maximum principle.

     

Geometric Phase Observation with Dispersed Fringes

Geometric and dynamic phases are separately observed using dispersed fringes, and the difference between them is clearly demonstrated. Independence of geometric phase of wavelength is straightforwardly shown in the dispersed fringe.     

Synthesis of RE Y zeolite for formulation of FCC catalyst and the catalytic performance in cracking of n-hexadecane

Research on Chemical Intermediates - This study presents the synthesis of rare earth-doped Y (RE Y) zeolite, its application in formulation of a fluid catalytic cracking (FCC) catalyst and the...     

A heuristic approach for dividing graphs into bi-connected components with a size constraint

In this paper we propose a new problem of finding the maximal bi-connected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on the open ear decomposition of graphs. Its essential part is an adaptation of the breadth first search which makes it possible to grow bi-connected subgraphs. The proposed randomized algorithm consists of growing several subgraphs in parallel. The quality of solutions generated in this way is further improved using a local search which exploits neighboring relations between the subgraphs. In order to evaluate the performance of the method, an algorithm for generating pseudo-random unit disc graphs with known optimal solutions is created. Computational experiments have also been conducted on graphs representing electrical distribution systems for the real-world problem of dividing them into a system of fault tolerant interconnected microgrids. The experiments show that the proposed method frequently manages to find optimal solutions and has an average error of only a few percent to known optimal solutions. Further, it manages to find high quality approximate solutions for graphs having up to 10,000 nodes in reasonable time.     

Solvent-induced selectivity switching: intermolecular allylsilylation, arylsilylation, and silylation of alkynes over montmorillonite catalyst

Proton-exchanged montmorillonite showed catalytic activity for intermolecular allylsilylation, arylsilylation, and terminal silylation of alkynes with allylsilanes. The reaction selectivity greatly depended on the solvent used. Reactions proceeded with various terminal alkynes and allylsilanes in good to moderate yields. The reaction pathways involving cationic Si species on the montmorillonite surface were also investigated.     

Cage-shaped borate esters with tris(2-oxyphenyl)methane or -silane system frameworks bearing multiple tuning factors: geometric and substituent effects on their Lewis acid properties

Boron complexes that contain new tridentate ligands, tris(o‐oxyaryl)methanes and ‐silanes, were prepared. These complexes had a cage‐shaped structure around a boron center and showed higher Lewis acidity and catalytic activity than open‐shaped boron compounds. The cage‐shaped ligands determined the properties of the borates by altering the geometry and were consistently bound to the metal center by chelation. The synthesized compounds were L?B(OC₆H₄)₃CH, L?B(OC₆H₄)₃SiMe, and its derivatives (L=THF or pyridine as an external ligand). Theoretical calculations suggested that the cage‐shaped borates had a large dihedral angle (C_ipso‐O‐B‐O) compared with open‐shaped borates. The geometric effect due to the dihedral angle means that compared with open‐shaped, the cage‐shaped borates have a greater Lewis acidity. The introduction of electron‐withdrawing groups on the aryl moieties in the cage‐shaped framework increased the Lewis acidity. Substitution of a bridgehead Si for a bridgehead C decreased the Lewis acidity of the boron complexes because the large silicon atom reduces the dihedral angle of C_ipso‐O‐B‐O. The ligand‐exchange rates of the para‐fluoro‐substituted compound B(OC₆H₃F)₃CH and the ortho‐phenyl‐substituted compound B(OC₆H₃Ph)₃CH were less than that of the unsubstituted borate B(OC₆H₄)₃CH. The ligand‐exchange rate of B(OC₆H₄)₃SiMe was much faster than that of B(OC₆H₄)₃CH. A hetero Diels–Alder reaction and Mukaiyama‐type aldol reactions were more effectively catalyzed by cage‐shaped borates than by the open‐shaped borate B(OPh)₃ or by the strong Lewis acid BF₃?OEt₂. The cage‐shaped borates with the bulky substituents at the ortho‐positions selectively catalyzed the reaction with less sterically hindered substrates, while the unsubstituted borate showed no selectivity.     

Nb2O5·nH2O as a heterogeneous catalyst with water-tolerant Lewis acid sites

Niobic acid, Nb(2)O(5)·nH(2)O, has been studied as a heterogeneous Lewis acid catalyst. NbO(4) tetrahedra, Lewis acid sites, on Nb(2)O(5)·nH(2)O surface immediately form NbO(4)-H(2)O adducts in the presence of water. However, a part of the adducts can still function as effective Lewis acid sites, catalyzing the allylation of benzaldehyde with tetraallyl tin and the conversion of glucose into 5-(hydroxymethyl)furfural in water.     

A clinical trial for therapeutic drug monitoring using microchip-based fluorescence polarization immunoassay

Microchip analysis is a promising method for therapeutic drug monitoring. This led us to evaluate a microchip-based fluorescence polarization immunoassay (FPIA) system for point-of-care testing on patients being treated with theophylline. The sera were collected from 20 patients being treated with theophylline. Fluorescence polarization was measured on the microchip and theophylline concentrations in serum were obtained. Regression analysis of the correlations was done between the results given by the microchip-based FPIA and the conventional cloned enzyme donor immunoassay (CEDIA), and between the results given by the microchip-based FPIA and the conventional particle-enhanced turbidimetric inhibition immunoassay (PETINIA). We successfully carried out a quantitative analysis of theophylline in serum at values near its therapeutic range in 65 s. The results obtained by the microchip-based FPIA correlated well with CEDIA and PETINIA results; the correlation coefficients (R ²) were 0.986 and 0.989, respectively. The FPIA system is a simple and rapid method for point-of-care testing of drugs in serum, and its accuracy is the same as the conventional CEDIA and PETINIA. It is essential to use real samples from patients and to confirm good correlations with conventional methods for a study on the realization of microchip.     

Theoretical study on reaction scheme of silver(I) containing 5-substituted uracils bridge formation

We present a reaction scheme of silver containing 5-substituted uracils (N) bridge formation with two silver ions to a silver-mediated base pair [N-Ag(2)-N] by using the conductor-like polarizable continuum model (CPCM)-B3LYP/aug-cc-pVDZ level of theory. The whole reaction scheme is divided into the following three steps: (1) silver ion binding and deprotonation, (2) silver ion transfer, and (3) dimer formation and structural fluctuation. With a new pK(a) computing scheme proposed in our previous studies, it is found that a silver coordination decreases the pK(a) of N by 2.5-3.0 pK(a) units, which is an important clue for silver-ion selectivity by N. Judging from the calculation, we revealed that the silver ion transfer reaction and the dimerization reaction occur spontaneously. Moreover, both reactions are independent of the C5 ligand in N so that the deprotonation reaction, which is the first step of this scheme, plays a key role in forming the [N-Ag(2)-N] pairing.