VC Dimensions of Principal Component Analysis

Motivated by statistical learning theoretic treatment of principal component analysis, we are concerned with the set of points in ℝ ^d that are within a certain distance from a k-dimensional affine subspace. We prove that the VC dimension of the class of such sets is within a constant factor of (k+1)(d−k+1), and then discuss the distribution of eigenvalues of a data covariance matrix by using our bounds of the VC dimensions and Vapnik’s statistical learning theory. In the course of the upper bound proof, we provide a simple proof of Warren’s bound of the number of sign sequences of real polynomials.     

Thermo-responsive extraction of cadmium(II) ion with TPEN-NIPA gel. Effect of the number of polymerizable double bond toward gel formation and the extracting behavior

N,N,N′,N′-(Tetrakis-2-pyridylmethyl)ethylenediamine (TPEN) derivatives bearing the different number (1-4) of a double bond moiety on the pyridine ring are synthesized and subjected to copolymerization with N-isopropylacrylamide in the presence of AIBN. The obtained poly(TPEN-NIPA) gels show thermo-responsive swelling/shrinking behaviors and are employed for the extraction of cadmium(II) ion from the aqueous solution to examine the relationship of the gel characteristics and the extraction performance. The polymer gels composed of the TPEN derivative bearing three or four double bonds exhibit temperature-dependent change of swelling and shrinking in water. These gels extract Cd^II ion efficiently from the aqueous solution in the swelling state at 5 °C, while little extraction was observed at 45 °C with shrinking.     

Multireference character of 1,3-dipolar cycloaddition of ozone with ethylene and acrylonitrile

In the present study, the concerted and stepwise reaction mechanisms for 1,3-dipole cycloaddition of ozone with ethylene (1) and acrylonitrile (2) are investigated. The stationary points are optimized by using four hybrid R(U)DFT methods. A geometry optimization method based on an approximate spin projection (AP-opt method) is applied to eliminate a spin contamination from the broken-symmetry (BS) solution. The AP-opt method reveals that a diradical intermediate for the stepwise pathway is spurious due to the spin contamination. The revised reaction profile with no diradical intermediate supports the stereospecificity. On the basis of the experimental data, the RCCSD(T) method outperforms AP-UCCSD(T), AP-UBD(T), and MkMRCCSD(4e,4o) for the systems, indicating that the RCCSD(T) method can describe the diradical character of ozone within a framework of single reference wave function. The subsequent single point energy calculations show that the highly synchronous transition state is much more favorable than the asynchronous one for 1. In the case of 2, there is not much difference between two transition states because of its asymmetric structure and charge separations in the transition states.     

Modification of flexible part in Cu(2+) interdigitated framework for CH(4)/CO(2) separation

The structural flexibility of Cu(2+) interdigitated layer type framework was controlled and the compound represented clear separation property of CH(4)/CO(2) at range of 0-1.0 MPa and recovery of adsorbed CO(2) above 0.1 MPa.     

Separation of a Slater Determinant Wave Function with a Neck Structure into Spatially Localized Subsystems

A method of separating a Slater determinant wave function with a two-center neck structure into spatially localized subsystems is proposed, and it is applied to α + α Margenau–Brink cluster wave functions and antisymmetrized molecular dynamics wave functions of the ground state in ¹⁰Be and a negative-parity largely deformed state in ³⁵S.     

Reaction of Titanium Isopropoxide with Alkanolamines and Association of the Resultant Ti Species

A clear alcoholic solution of titanium alkoxide with an addition of various alkanolamines is suitable for a sol-gel coating of titania films. The reaction of titanium isopropoxide, Ti(OPr ⁱ )₄ (TIP), with alkanolamines, such as triethanolamine (TEAH₃), diethanolamine (DEAH₂), and N-ethyldiethanolamine (EDEAH₂), and an association of the Ti species in the resultant mixtures were examined via liquid-state nuclear magnetic resonance (NMR), infrared spectroscopy (IR), and cryoscopy measurements. Regardless of the kinds of the alkanolamines used, the IR and NMR spectra showed that alcohol exchange reactions occurred between the alcoholic moieties in alkanolamines and the isopropoxy groups in TIP, and that the N atom in the alkanolamines might be datively bonded to Ti. In the DEAH₂ and EDEAH₂ systems with the molar ratio of amine/TIP = 1, the results of the NMR and cryoscopy measurements showed that an association degree of the formed Ti species increased with an increase in the concentration of TIP, according to the thermodynamical equilibriums of associations between various oligomers. The increase was larger in the DEAH₂ system than in the EDEAH₂ one, because of the larger equilibrium constants due to the smaller size of the DEA group. In the system of EDEAH₂/TIP = 2, the NMR spectra showed that only one kind of oligomer was formed as a Ti species, independent of the concentration of TIP. The oligomer may be a much more stable species than other species. The cryoscopy results showed that the oligomer had a tetrameric structure.     

Head-to-tail dimerization of acrylates catalyzed by iridium complexes

Head-to-tail dimerizations of acrylates and vinyl ketone were successfully performed by the use of iridium complexes in good yields. An iridium hydride complex generated in situ from [IrCl(cod)]2 and alcohols in the presence of Na2CO3 and (MeO)3P was found to be an active species promoting the head-to-tail dimerization of acrylates. Thus, butyl acrylate afforded the corresponding head-to-tail dimer in 86% yield.     

Enantio- and diastereoselective Michael reaction of 1,3-dicarbonyl compounds to nitroolefins catalyzed by a bifunctional thiourea

We synthesized a new class of bifunctional catalysts bearing a thiourea moiety and an amino group on a chiral scaffold. Among them, thiourea 1e bearing 3,5-bis(trifluoromethyl)benzene and dimethylamino groups was revealed to be highly efficient for the asymmetric Michael reaction of 1,3-dicarbonyl compounds to nitroolefins. Furthermore, we have developed a new synthetic route for (R)-(-)-baclofen and a chiral quaternary carbon center with high enantioselectivity by Michael reaction. In these reactions, we assumed that a thiourea moiety and an amino group of the catalyst activates a nitroolefin and a 1,3-dicarbonyl compound, respectively, to afford the Michael adduct with high enantio- and diastereoselectivity.     

Ruthenium complexes of easily accessible tridentate ligands based on the 2-aryl-4,6-bis(2-pyridyl)-s-triazine motif: absorption spectra, luminescence properties, and redox behavior

A family of tridendate ligands 1 a-e, based on the 2-aryl-4,6-di(2-pyridyl)-s-triazine motif, was prepared along with their hetero- and homoleptic Ru(II) complexes 2 a-e ([Ru(tpy)(1 a-e)](2+); tpy=2,2':6',2"-terpyridine) and 3 a-e ([(Ru(1 a-e)(2)](2+)), respectively. The ligands and their complexes were characterized by (1)H NMR spectroscopy, ES-MS, and elemental analysis. Single-crystal X-ray analysis of 2 a and 2 e demonstrated that the triazine core is nearly coplanar with the non-coordinating ring, with dihedral angles of 1.2 and 18.6 degrees, respectively. The redox behavior and electronic absorption and luminescence properties (both at room temperature in liquid acetonitrile and at 77 K in butyronitrile rigid matrix) were investigated. Each species undergoes one oxidation process centered on the metal ion, and several (three for 2 a-e and four for 3 a-e) reduction processes centered on the ligand orbitals. All compounds exhibit intense absorption bands in the UV region, assigned to spin-allowed ligand-centered (LC) transitions, and moderately intense spin-allowed metal-to-ligand charge-transfer (MLCT) absorption bands in the visible region. The compounds exhibit relatively intense emissions, originating from triplet MLCT levels, both at 77 K and at room temperature. The incorporation of triazine rings and the near planarity of the noncoordinating ring increase the luminescence lifetimes of the complexes by lowering the energy of the (3)MLCT state and creating a large energy gap to the dd state.