Mean curvature flows and isotopy of maps between spheres

Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area‐decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map. © 2004 Wiley Periodicals, Inc.     

Nowhere zero 4‐flow in regular matroids

Jensen and Toft 8 conjectured that every 2‐edge‐connected graph without a K₅‐minor has a nowhere zero 4‐flow. Walton and Welsh 19 proved that if a coloopless regular matroid M does not have a minor in {M(K_3,3), M*(K₅)}, then M admits a nowhere zero 4‐flow. In this note, we prove that if a coloopless regular matroid M does not have a minor in {M(K₅), M*(K₅)}, then M admits a nowhere zero 4‐flow. Our result implies the Jensen and Toft conjecture. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Synthesis of 2,7‐Carbazolenevinylene‐Based Copolymers and Characterization of Their Photovoltaic Properties

New electroactive and photoactive conjugated copolymers consisting of alternating 2,7‐carbazole and oligothiophene moieties linked by vinylene groups have been developed. Different oligothiophene units have been introduced to study the relationship between the polymer structure and the electronic properties. The resulting copolymers are characterized by UV‐vis spectroscopy, size‐exclusion chromatography, and thermal and electrochemical analyses. Bulk heterojunction photovoltaic cells from different copolymers and a soluble fullerene derivative, [6,6]‐phenyl‐C₆₁ butyric acid methyl ester, have been fabricated, and promising preliminary results are obtained. For instance, non‐optimized devices using poly(N‐(4‐octyloxyphenyl)‐2,7‐carbazolenevinylene‐alt‐3″,4″‐dihexyl‐2,2′;5′,2″;5″,2″′;5″′,2″″‐quinquethiophenevinylene 1″,1″‐dioxide) as an absorbing and hole‐carrier semiconductor exhibit power conversion efficiency up to 0.8 % under air mass (AM) 1.5 illumination. These features make 2,7‐carbazolenevinylene‐based and related polymers attractive candidates for solar‐cell applications.     

Reversible energy recovery logic circuit without non-adiabaticenergy loss

The authors propose a reversible energy recovery logic (RERL) circuit for ultra-low-energy consumption, which consumes only adiabatic energy loss and leakage current loss by completely eliminating non-adiabatic energy loss. It is a dual-rail adiabatic circuit using the concept of reversible logic with a new eight-phase clocking scheme. Simulation results show that at low-speed operation, the RERL consumes much less energy than the complementary static CMOS circuit and other adiabatic logic circuits     

Laser writing techniques for photomask fabrication using a femtosecond laser

Photomasks are the backbone of microfabrication industries. Currently they are fabricated by a lithographic process, which is very expensive and time consuming since it is a multi-step process. These issues can be addressed by fabricating photomasks by direct femtosecond laser writing, which is a single-step process and comparatively cheaper and faster than lithography. In this paper we discuss our investigations on the effect of two types of laser writing techniques, namely front- and rear-side laser writing, with regard to the feature size and the edge quality of a feature. It is proved conclusively that for the patterning of masks, front-side laser writing is a better technique than rear-side laser writing with regard to smaller feature size and better edge quality. Moreover the energy required for front-side laser writing is considerably lower than that for rear-side laser writing. Received: 22 May 2001 / Accepted: 14 September 2001 / Published online: 17 October 2001     

Efficient synthesis of an aldehyde‐capped polythiophene containing fluorinated electron‐withdrawing groups

To incorporate an acceptor type polythiophene segment onto a supramolecular block copolymer for potential light harvesting applications, effective synthetic routes for the end‐functionalized and acceptor‐substituted polythiophenes are critical. The Ullmann coupling reaction can be utilized to obtain electron‐deficient polythiophenes and to attach terminal thiophene units that carry functional groups. In this article, the reactions involving a 2,5‐dibromothiophene monomer containing an electron‐withdrawing fluorinated ester and 5‐bromo‐2‐thiophenecarboxaldehyde (the end‐capper) were studied in detail. It was found that the Ullmann coupling reaction of the dibromide is very fast (completed in a few minutes) and the terminal bromine group does not survive long under the reaction condition. These findings lead to the development of an effective procedure for aldehyde end‐capping of electron‐deficient polythiophenes. Polymers with molecular weights around 4000 Da are routinely obtained. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 41–47, 2007     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007