Nanopatterning of functional materials by gas phase pattern deposition of self-assembled molecular thin films in combination with electrodeposition

We present a general methodology to pattern functional materials on the nanometer scale using self-assembled molecular templates on conducting substrates. A soft lithographic gas phase edge patterning process using poly(dimethylsiloxane) molds was employed to form electrically isolating organosilane patterns of a few nanometer thickness and a line width that could be tuned by varying the time of deposition. Electrodeposition was employed to deposit patterns of Ni and ZnO on these prepatterned substrates. Deposition occurred only on patches of the substrate where no organosilane monolayer was present. The process is simple, inexpensive, and scalable to large areas. We achieved formation of metallic and oxide material patterns with a lateral resolution of 80 nm.     

Comparison between 2-hydroxypropyl-��-cyclodextrin and 2-hydroxypropyl-��-cyclodextrin for inclusion complex formation with danazol

Complexation in solution between danazol and two different cyclodextrins [2-hydroxypropyl-??-cyclodextrin (HP-??-CD) and 2-hydroxypropyl-??-cyclodextrin (HP-??-CD)] was studied using phase solubility analysis, and one- and two-dimensional ¹H-NMR. The increase of danazol solubility in the aqueous cyclodextrin solutions showed a linear relationship (A_L profile). The apparent stability constant, K _1:1, of each complex was calculated and found to be 51.7 × 10³ and 7.3 × 10³ M^?1 for danazol?CHP-??-CD and danazol?CHP-??-CD, respectively. ¹H-NMR spectroscopic analysis of varying ratios of danazol and the different cyclodextrins in a mixture of EtOD?CD₂O confirmed the 1:1 stoichiometry. Cross-peaks, from 2D ROESY ¹H-NMR spectra, between protons of danazol and H3?? and H5??of cyclodextrins, which stay inside the cyclodextrin cavity, proved the formation of an inclusion complex between danazol and the cyclodextrins. For HP-??-CD, the inclusion complex is formed by entrance of the isooxazole and the A rings of danazol in the cyclodextrin cavity. For HP-??-CD, two different inclusion structures may exist simultaneously in solution: one with the isooxazole and A ring in the cavity and the other with the C and D ring inside the cavity. DLS showed that self-aggregation of the CD??s was absent in the danazol HP-??-CD system up to a CD concentration of 10% and in the danazol HP-??-CD system up to a CD concentration of 5%.     

Nanoparticulate Pd supported catalysts: size-dependent formation of Pd(I)/Pd(0) and their role in CO elimination

A combination of time-resolved X-ray absorption spectroscopy (XAS), hard X-ray diffraction (HXRD), diffuse reflectance infrared spectroscopy (DRIFTS), and mass spectrometry (MS) reveals a series of size-dependent phenomena at Pd nanoparticles upon CO/(NO+O(2)) cycling conditions. The multitechnique approach and analysis show that such size-dependent phenomena are critical for understanding Pd CO elimination behavior and, particularly, that different Pd(I) and Pd(0) centers act as active species for a size estimated by XAS to be, respectively, below and above ca. 3 nm. The relative catalytic performance of these two noble metal species indicates the intrinsic higher activity of the Pd(I) species.     

Continuous Blooming of Convex Polyhedra

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.     

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].     

Fractional Tikhonov regularization for linear discrete ill-posed problems

Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of the Moore-Penrose pseudoinverse of AA ^T as weighting matrix. Properties of this regularization method are discussed. Numerical examples illustrate that the proposed scheme for a suitable fractional power may give approximate solutions of higher quality than standard Tikhonov regularization.     

Subspace methods for three‐parameter eigenvalue problems

We propose subspace methods for three‐parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular example is the Helmholtz equation in ellipsoidal and paraboloidal coordinates. While several subspace methods for two‐parameter eigenvalue problems exist, their extensions to a three‐parameter setting seem challenging. An inherent difficulty is that, while for two‐parameter eigenvalue problems, we can exploit a relation to Sylvester equations to obtain a fast Arnoldi‐type method, such a relation does not seem to exist when there are three or more parameters. Instead, we introduce a subspace iteration method with projections onto generalized Krylov subspaces that are constructed from scratch at every iteration using certain Ritz vectors as the initial vectors. Another possibility is a Jacobi–Davidson‐type method for three or more parameters, which we generalize from its two‐parameter counterpart. For both approaches, we introduce a selection criterion for deflation that is based on the angles between left and right eigenvectors. The Jacobi–Davidson approach is devised to locate eigenvalues close to a prescribed target; yet, it often also performs well when eigenvalues are sought based on the proximity of one of the components to a prescribed target. The subspace iteration method is devised specifically for the latter task. The proposed approaches are suitable especially for problems where the computation of several eigenvalues is required with high accuracy. MATLAB implementations of both methods have been made available in the package MultiParEig (see http://www.mathworks.com/matlabcentral/fileexchange/47844-multipareig ).     

Sparse geometric graphs with small dilation

Given a set S of n points in , and an integer k such that 0k<n, we show that a geometric graph with vertex set S, at most n−1+k edges, maximum degree five, and dilation O(n/(k+1)) can be computed in time O(nlogn). For any k, we also construct planar n-point sets for which any geometric graph with n−1+k edges has dilation Ω(n/(k+1)); a slightly weaker statement holds if the points of S are required to be in convex position.