Stereoselective synthesis of highly oxygenated cyclohexanes through a [3+3] annulation approach

The synthesis of highly oxygenated cyclohexanes has been achieved through a Michael–Wittig protocol via a [3+3] annulation of the enal that is derived from 2,3-O-isopropylidene-(R)-glyceraldehyde. The γ-alkoxy enal system is responsible for the stereoselectivity.     

Potential fields induced by point sources in assemblies of shells weakened with apertures

Well‐posed boundary‐value problems in multiply‐connected regions are targeted for some sets of two‐dimensional Laplace equations written in geographical coordinates on joint surfaces of revolution. Those are problems that simulate potential fields induced by point sources in joint perforated thin shell structures consist of fragments of different geometry. A semi‐analytical approach is proposed to accurately compute solutions of such problems. The approach is based on the matrix of Green's type formalism. The elements of required matrices of Green's type are obtained analytically and expressed in closed computer‐friendly form. This makes it possible to efficiently deal with the targeted class of problems. Copyright © 2014 John Wiley & Sons, Ltd.     

Tricyclic Steiner Triple Systems

A Steiner triple system of order ν, denoted STS(ν), is said to be tricyclic if it admits an automorphism whose disjoint cyclic decomposition consists of three cycles. In this paper we give necessary and sufficient conditions for the existence of a tricyclic STS(ν) for several cases. We also pose conjectures concerning their existence in two remaining cases.     

Edge Partition of Graphs Embeddable in the Projective Plane and the Klein Bottle

In a previous paper by the author joint with Baogang XU published in Discrete Math in 2018, we show that every non-planar toroidal graph can be edge partitioned into a planar graph and an outerplanar graph. This edge partition then implies some results in thickness and outerthickness of toroidal graphs. In particular, if each planar graph has outerthickness at most $2$ (conjectured by Chartrand, Geller and Hedetniemi in 1971 and the confirmation of the conjecture was announced by Gon\c{c}alves in 2005), then the outerthickness of toroidal graphs is at most 3 which is the best possible due to $K_7$. In this paper we continue to study the edge partition for projective planar graphs and Klein bottle embeddable graphs. We show that (1) every non-planar but projective planar graph can be edge partitioned into a planar graph and a union of caterpillar trees; and (2) every non-planar Klein bottle embeddable graph can be edge partitioned into a planar graph and a subgraph of two vertex amalgamation of a caterpillar tree with a cycle with pendant edges. As consequences, the thinkness of projective planar graphs and Klein bottle embeddabe graphs are at most $2$, which are the best possible, and the outerthickness of these graphs are at most $3$.     

Sparse PCA by iterative elimination algorithm

In this paper we proposed an iterative elimination algorithm for sparse principal component analysis. It recursively eliminates variables according to certain criterion that aims to minimize the loss of explained variance, and reconsiders the sparse principal component analysis problem until the desired sparsity is achieved. Two criteria, the approximated minimal variance loss (AMVL) criterion and the minimal absolute value criterion, are proposed to select the variables eliminated in each iteration. Deflation techniques are discussed for multiple principal components computation. The effectiveness is illustrated by both simulations on synthetic data and applications on real data.     

An ETD Crank‐Nicolson method for reaction‐diffusion systems

A novel Exponential Time Differencing Crank‐Nicolson method is developed which is stable, second‐order convergent, and highly efficient. We prove stability and convergence for semilinear parabolic problems with smooth data. In the nonsmooth data case, we employ a positivity‐preserving initial damping scheme to recover the full rate of convergence. Numerical experiments are presented for a wide variety of examples, including chemotaxis and exotic options with transaction cost. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012     

Identification of molecular reactive sites with an interactive volume rendering tool

A new molecular visualization tool is presented, EVolVis (an abbreviation of electronic volume visualizer). This software enables the user to interactively explore a molecule's electronic charge density for topological features. Using novel volume rendering techniques, the entire molecule can be probed without obstruction by opaque surfaces or preselection of specific orbitals or contours. Menus with sliding scales permit various ranges of the function of interest to be examined interactively. We have investigated the Laplacian of the electronic charge density calculated for several biomolecules that contain a variety of reactive sites: cisplatin, penamecillin and isomers of nitrogen bases from DNA. EVolVis is useful in identifying inner-shell features (cisplatin), polar, nonpolar and aromatic regions (penamecillin), hydrogen-bonding sites of varying strength (nitrogen bases and penamecillin) and other reactive sites (strained heterocycle in penamecillin). Received: 1 June 2000 / Accepted: 4 October 2000 / Published online: 28 February 2001     

Nonlinear Regression Using the “Big Three” Spreadsheets

Nonlinear regression using the spreadsheet Excel has appeared in the literature in several places. This paper extends the use of this technique to two other popular spreadsheets, Lotus 123 and Quattro Pro. Associated files, which can be downloaded, are included. These are the spreadsheet templates and ScreenCam movies that illustrate the use of equation solvers for minimization in these spreadsheets.     

A multivariate Powell–Sabin interpolant

We consider the problem of constructing a C ¹ piecewise quadratic interpolant, Q, to positional and gradient data defined at the vertices of a tessellation of n-simplices in \mathbbRⁿ \mathbb{R}^{n} . The key to the interpolation scheme is to appropriately subdivide each simplex to ensure that certain necessary geometric constraints are satisfied by the subdivision points. We establish these constraints using the Bernstein–Bézier form for polynomials defined over simplices, and show how they can be satisfied. When constructed, the interpolant Q has full approximation power.