Experiments with a symbolic programming system for complex analysis

The paper reports the results of work on the construction of LISP programs for various symbolic operations in complex analysis, including the evaluation of integrals around closed contours by the use of Cauchy's Theorem. It is concluded that the only difficulty in the way of the preparation of programs for all of the important and useful textbook calculations in complex analysis is that large amounts of fast storage in the computer are needed.     

High resolution Ne KLL Auger spectra produced by H+ and He+ bombardment

Ne KLL Auger satellite lines are measured with an energy resolution of 0.02% FWHM. The relative intensities of initial 2p vacancy satellite lines are observed to be four times larger with He⁺ than with H⁺ bombardment. The He⁺ beam also produces new satellite lines which are assigned to double initial 2p vacancies.     

Algorithms for constructing stable manifolds of stationary solutions

Algorithms for computing stable manifolds of hyperbolic stationarysolutions of autonomous systems are of two types: either theaim is to compute a single point on the manifold or the entire(local) manifold. Traditionally only indirect methods have beenconsidered, i.e. first the continuous problem is discretizedby a one-step scheme and then the Liapunov-Perron or Hadamardgraph transform are applied to the resulting discrete dynamicalsystem. We will consider different variants of these indirectmethods but also algorithms of the above two types which areapplied directly to the continuous problem.     

Bumpy metrics and closed parametrized minimal surfaces in Riemannian manifolds

The purpose of this article is to study conformal harmonic maps , where is a closed Riemann surface and is a compact Riemannian manifold of dimension at least four. Such maps define parametrized minimal surfaces, possibly with branch points. We show that when the ambient manifold is given a generic metric, all prime closed parametrized minimal surfaces are free of branch points, and are as Morse nondegenerate as allowed by the group of automorphisms of . They are Morse nondegenerate in the usual sense if has genus at least two, lie on two-dimensional nondegenerate critical submanifolds if has genus one, and on six-dimensional nondegenerate critical submanifolds if has genus zero.

     

Scheduling reconstruction operations with modes of execution

Since the decline of the Cold War, the risk of major conflict between powerful, industrialized nations has decreased. Insecurities in the 21st century are more apt to arise from the debris of imploding states. Such situations may require intervention—military or otherwise—by concerned states. To meet this new operational challenge, nations must adapt their planning procedures to account for Security, Stabilization, Transition, and Reconstruction Operations (SSTRO). This paper develops a project scheduling framework for post-conflict reconstruction that schedules reconstruction activities to maximize the positive impact to the local economy during the initial phase of SSTRO. Specifically, this paper builds on the Multimode Resource Constrained Project Scheduling Problem with Generalized Precedence Relations (MM-RCPSP-GPR) using goal programming to maximize the reconstruction operations’ positive impact to local population's economic welfare. This MM-RCPSP-GPR variant is applied to a notional example to illustrate its potential use in post-conflict SSTRO. The basic framework can be extended to other settings.     

Cohomology over Fiber products of local rings

Let S and T be local rings with common residue field k, let R be the fiber product $S{\times }_{k}T$, and let M be an S-module. The Poincaré series $P_M^R$ of M has been expressed in terms of $P_M^S$, $P_k^S$ and $P_k^T$ by Kostrikin and Shafarevich, and by Dress and Krämer. Here, an explicit minimal resolution, as well as theorems on the structure of ${\mathrm{Ext}}_R(k,k)$ and ${\mathrm{Ext}}_R(M,k)$ are given that illuminate these equalities. Structure theorems for the cohomology modules of fiber products of modules are also given. As an application of these results, we compute the depth of cohomology modules over a fiber product.     

A Heterogeneous‐Catalyst‐Based,Microwave‐Assisted Protocol for the Synthesis of 2,2′‐Bipyridines

A new method of preparing 2,2′‐bipyridines with short reaction times by using microwave assistance and heterogeneous catalysts has been developed. With a Negishi‐like protocol, it was found that Ni/Al₂O₃–SiO₂ afforded 2,2′‐bipyridine products in up to 86 % yield in 1 h. Palladium supported on alumina also provided yields of 2,2′‐bipyridines comparable to those seen for homogeneous PEPPSI^TM (1,3‐diisopropylimidazol‐2‐ylidene)(3‐chloropyridyl)palladium(II)dichloride) and tetrakis(triphenylphosphanyl)palladium complexes.     

Microwave-assisted synthesis of 3,6-di(pyridin-2-yl)pyridazines: unexpected ketone and aldehyde cycloadditions

3,6-Di(pyridin-2-yl)pyridazines are an interesting class of compounds because of their metal-coordinating ability resulting in the self-assembly into [2x2] gridlike metal complexes with copper(I) or silver(I) ions. These and other substituted pyridazines can be prepared by the inverse-electron-demand Diels-Alder reactions between acetylenes and 1,2,4,5-tetrazines. In this contribution, the effect of (superheated) microwave conditions on these generally slow cycloadditions is described. The cycloaddition of acetylenes to 3,6-di(pyridin-2-yl)-1,2,4,5-tetrazine could be accelerated from several days reflux in toluene or N,N-dimethylformamide to several hours in dichloromethane at 150 degrees C. In addition, the unexpected cycloaddition of the enol tautomers of various ketones and aldehydes to 3,6-di(pyridin-2-yl)-1,2,4,5-tetrazine is described in detail providing an alternative route for the synthesis of (substituted) pyridazines.