Vapor phase polymerization of EDOT from submicrometer scale oxidant patterned by dip-pen nanolithography

Some of the most exciting recent advances in conducting polymer synthesis have centered around the method of vapor phase polymerization (VPP) of thin films. However, it is not known whether the VPP process can proceed using significantly reduced volumes of oxidant and therefore be implemented as part of nanolithography approach. Here, we present a strategy for submicrometer scale patterning of the conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT) via in situ VPP. Attolitre (10(-18) L) volumes of oxidant "ink" are controllably deposited using dip-pen nanolithography (DPN). DPN patterning of the oxidant ink is facilitated by the incorporation of an amphiphilic block copolymer thickener, an additive that also assists with stabilization of the oxidant. When exposed to EDOT monomer in a VPP chamber, each deposited feature localizes the synthesis of conducting PEDOT structures of several micrometers down to 250 nm in width. PEDOT patterns are characterized by atomic force microscopy (AFM), conductive AFM, two probe electrical measurement, and micro-Raman spectroscopy, evidencing in situ vapor phase synthesis of conducting polymer at a scale (picogram) which is much smaller than that previously reported. Although the process of VPP on this scale was achieved, we highlight some of the challenges that need to be overcome to make this approach feasible in an applied setting.     

On L-spaces and left-orderable fundamental groups

Examples suggest that there is a correspondence between L-spaces and three-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of manifolds. In particular, we prove that they are equivalent for any closed, connected, orientable, geometric three-manifold that is non-hyperbolic, a family which includes all closed, connected, orientable Seifert fibred spaces. We also show that they are equivalent for the twofold branched covers of non-split alternating links. To do this we prove that the fundamental group of the twofold branched cover of an alternating link is left-orderable if and only if it is a trivial link with two or more components. We also show that this places strong restrictions on the representations of the fundamental group of an alternating knot complement with values in $\text{ Homeo}_+(S^1)$ .     

Divisibility of Certain Partition Functions by Powers of Primes

Let be the prime factorization of a positive integer k and let b _k (n) denote the number of partitions of a non-negative integer n into parts none of which are multiples of k. If M is a positive integer, let S _k (N; M) be the number of positive integers N for which b _k(n ) 0(mod M). If we prove that, for every positive integer j In other words for every positive integer j, b _k(n) is a multiple of for almost every non-negative integer n. In the special case when k=p is prime, then in representation-theoretic terms this means that the number ofp -modular irreducible representations of almost every symmetric groupS _n is a multiple of p ^j. We also examine the behavior of b _k(n) (mod ) where the non-negative integers n belong to an arithmetic progression. Although almost every non-negative integer n (mod t) satisfies b _k(n) 0 (mod ), we show that there are infinitely many non-negative integers n r (mod t) for which b _k(n) 0 (mod ) provided that there is at least one such n. Moreover the smallest such n (if there are any) is less than 2 .     

Prior decisions and experiences about mathematics of students in bridging courses

We report on the survey responses of 51 students attending mathematics bridging courses at a major Australian university, investigating what mathematics, if any, these students had studied in the senior years of schooling and what factors affected their decisions about the level of mathematics chosen. Quantitative findings are augmented by qualitative responses to open-ended questions in the survey as well as excerpts from follow-up emails. The findings show that the major reasons for students taking lower levels of mathematics in senior year(s), or dropping mathematics, include finding enough time for non-mathematics subjects, confidence in mathematical capability, advice and maximizing potential ranking for university admission.     

The management of high seas fisheries

The intergovernmental United Nations Conference on Highly Migratory and Straddling Stocks, initiated in 1993 and finished in 1995, addressed the conservation and management of fishery resources located both within the coastal state 200 mile Exclusive Economic Zone (EEZ) and the adjacent high seas. These types of marine resources continue to be a source for international conflicts and debates. The original United Nations Law of the Sea of 1982 failed to address transboundary fisheries in a proper way. In particular, the agreement did not recognize the emergence of the complicated straddling stock issue. In the new United Nations Law of the Sea agreement of 1995, a consensus was reached that the management of the straddling and highly migratory fish stocks should be carried out through regional fisheries management organizations. We present a review of the straddling stock issues in the international agreement emerging from the negotiations within the United Nations. The review is contrasted with and clarified by game theoretic analyses. We also discuss one international fishery exemplifying the case, the Norwegian springspawning herring. The main conclusion is that the local problems, faced during the stage of setting up regional fisheries organizations for the management of straddling and highly migratory fish stocks, are expected to be much more complicated and difficult to solve as compared to the cases of shared fish stocks. In the current paper, we present two reasons for this increased complexity. The first is the larger number of players as compared to the case of shared fish stocks and the second is the possibility of new members entering the regional fisheries organizations.     

Randomized large distortion dimension reduction

Consider a random matrix \(H:{\mathbb {R}}^{n}\longrightarrow {\mathbb {R}}^{m}\) . Let \(D\ge 2\) and let \(\{W_l\}_{l=1}^{p}\) be a set of \(k\) -dimensional affine subspaces of \({\mathbb {R}}^{n}\) . We ask what is the probability that for all \(1\le l\le p\) and \(x,y\in W_l\) , $$\begin{aligned} \Vert x-y\Vert _2\le \Vert Hx-Hy\Vert _2\le D\Vert x-y\Vert _2. \end{aligned}$$ We show that for \(m=O\big (k+\frac{\ln {p}}{\ln {D}}\big )\) and a variety of different classes of random matrices \(H\) , which include the class of Gaussian matrices, existence is assured and the probability is very high. The estimate on \(m\) is tight in terms of \(k,p,D\) .     

On the minimum of several random variables

For a given sequence of real numbers , we denote the th smallest one by . Let be a class of random variables satisfying certain distribution conditions (the class contains Gaussian random variables). We show that there exist two absolute positive constants and such that for every sequence of real numbers and every , one has

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where are independent random variables from the class . Moreover, if , then the left-hand side estimate does not require independence of the 's. We provide similar estimates for the moments of as well.

     

Minimal covers of the prisms and antiprisms

This paper contains a classification of the regular minimal abstract polytopes that act as covers for the convex polyhedral prisms and antiprisms. It includes a detailed discussion of their topological structure, and completes the enumeration of such covers for convex uniform polyhedra. Additionally, this paper addresses related structural questions in the theory of string C-groups.     

Enhanced-interval linear programming

An enhanced-interval linear programming (EILP) model and its solution algorithm have been developed that incorporate enhanced-interval uncertainty (e.g., A^±, B^± and C^±) in a linear optimization framework. As a new extension of linear programming, the EILP model has the following advantages. Its solution space is absolutely feasible compared to that of interval linear programming (ILP), which helps to achieve insight into the expected-value-oriented trade-off between system benefits and risks of constraint violations. The degree of uncertainty of its enhanced-interval objective function (EIOF) would be lower than that of ILP model when the solution space is absolutely feasible, and the EIOF’s expected value could be used as a criterion for generating the appropriate alternatives, which help decision-makers obtain non-extreme decisions. Moreover, because it can be decomposed into two submodels, EILP’s computational requirement is lower than that of stochastic and fuzzy LP models. The results of a numeric example further indicated the feasibility and effectiveness of EILP model. In addition, EI nonlinear programming models, hybrid stochastic or fuzzy EILP models as well as risk-based trade-off analysis for EI uncertainty within decision process can be further developed to improve its applicability.     

Formulation and Application of the Initially Rigid Cohesive Finite Element Method

The presented procedure for cohesive crack propagation is based on an adaptive finite element (FE) implementation, which enables the introduction of cohesive surfaces in dependence on the current crack state. In contrast to already existing formulations, the focus of the present model lies on failure processes that can be described at quasi-static conditions within an implicit framework. Furthermore, an extension for mesh independent crack propagation in terms of an additional mesh adaptive formulation is presented. By the evaluation of the failure criterion considering the preferred crack direction, a new crack tip coordinate is computed and the discretization is accordingly adjusted. The remaining mesh is modified for the new boundary representation. The application of the proposed method is shown by the numerical investigation of a concrete fracture specimen from an experimental research project. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)