⊕-Cofinitely Supplemented Modules

Let R be a ring and M a right R-module. M is called -cofinitely supplemented if every submodule N of M with M/N finitely generated has a supplement that is a direct summand of M. In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R-module is -cofinitely supplemented. In addition, if M has the summand sum property, then M is -cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of M.     

Neural Network Models for Finline Discontinuities

The radial basis network is used as the finline discontinuities electromagnetic artifical neural network(EMANN) models. EM software analysis is employed to characterize finline discontinuities. EMANN models are then trained using physical parameters and frequency as inputs and equivalent electric circuit element parameters of finline discontinuities as outputs. Once trained , the EMANN models can simulate equivalent electric circuit element parameters of finline step, notch and strip very fast and efficiently.     

High-efficiency clean EUV plasma source at 10–30 nm, driven by a long-pulse-width excimer laser

A long-pulse-width high-output energy (120 ns FWHM, 7 J) XeCl laser has been focused on thin tape targets (Cu and Ta) to generate more than 100-ns-long (FWHM) EUV pulses in the 10–30 nm spectral region, suitable for projection microlithography. The conversion efficiency was more than 20% over a 2π solid angle. We observed debris emission using a gated CCD camera, and measured the debris speed for different irradiation conditions. We found irradiation conditions such that the measured velocities were low enough that simple mechanical devices combined with krypton at low-pressure could efficiently stop both ionic debris and cluster debris. Our results show that a suitable combination of driving-laser characteristics, target material and thickness, environment gas and mechanical choppers can make clean and increase the power of EUV solid-target laser-plasma sources. Received: 21 October 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +39-06/9400-5334, E-mail: bollanti@frascati.enea.it     

Orders on Braid Groups

It is shown that the braid group defies lattice ordering.     

Shapley value for constant-sum games

It is proved that Youngs [4] axiomatization for the Shapley value by marginalism, efficiency, and symmetry is still valid for the Shapley value defined on the class of nonnegative constant-sum games with nonzero worth of grand coalition and on the entire class of constant-sum games as well.The research was supported by NWO (The Netherlands Organization for Scientific Research) grant NL-RF 047-008-010.I am thankful to Theo Driessen, Natalia Naumova and Elena Yanovskaya for interesting discussions and comments. The useful remarks of two anonymous referees are also appreciated.     

Approximation and Prediction of the Numerical Solution of Some Burgers Problems

The Aitken's ²-prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's ²-process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of ²-prediction, the so-called -prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method.     

Influence of the Structure of an Inhomogeneously Broadened NMR Line on the Shape of the Free Precession Signal

We have obtained theoretically an expression for the nuclear free precession signal in an inhomogeneously broadened spin system with a complex structure of the NMR spectrum. It is shown that in this case in the nuclear precession signal there appear maxima the moments of whose formation depend on the detuning of the pulse carrier frequency from the central frequencies of the NMR lines, their widths, and the Rabi frequency. The theoretical results are in good agreement with the experimental data on the observation of proton free precession in toluene. We have constructed a physical model explaining the appearance of maxima in the free precession signal of the spin system.     

Optimal Ternary Linear Rate 1/2 Codes

In this paper, we classify all optimal linear[n, n/2] codes up to length 12. We show that thereis a unique optimal [10, 5, 5] code up to equivalence.     

Complex Forming Ability of a Family of Isolated Cyclosophoraoses with Ergosterol and Its Monte Carlo Docking Computational Analysis

Neutral cyclosophoraoses (unbranched cyclic -1,2-d-glucans) produced by the Rhizo-bium meliloti 2011 were prepared by size exclusion and anion-exchange chromatographic techniques. The degree of polymerization (DP) of isolated cyclosophoraoses was determined by matrix associated laser desorption/ionization mass spectrometry (MALDI/MS) techniques. A family of purified neutral cyclosophoraoses (DP 17–27) was used as a host for the inclusion complexation with hardly soluble ergosterol. High performance liquid chromatographic (HPLC) analysis showed that it induced much enhanced solubility of ergosterol compared to -cyclodextrin. In order to understand the molecular basis of the complex forming ability of cyclosophoraoses, a Monte Carlo (MC) docking-minimization method was used for host-guest complex formation of cyclosophoraoses or -cyclodextrin with ergosterol. From the MC simulation we propose the `hand-shake' mechanism for complexation of cyclosophoraoses with ergosterol.     

Crystal structures of 4,7-phenanthrolino-5,6:5′,6′-pyrazine tetrahydrate and 1,4,5,8,9,12-hexaazatriphenylene dihydrate

The crystal structures of 4,7-phenanthrolino-5,6:5,6-pyrazine tetrahydrate (I) and 1,4,5,8,9,12-hexaazatriphenylene dihydrate (II) have been determined from low temperature (173 K) x-ray single crystal diffraction data. I crystallizes in the triclinic system, space group P with a = 11.2687(6), b = 12.4766(6), c = 12.7068(7) Å, = 113.4740(10), = 91.605(2), = 114.587(2)°, V = 1449.33(13) ų, and Z = 4. II crystallizes in the orthorhombic system, space group Pca2₁ with a = 18.187(2), b = 9.2576(11), c = 6.9672(8) Å, V = 1173.0(2) ų, and Z = 4. In both structures the planar heterocyclic molecules stack with interplanar distances down to 3.3 Å, which is consistent with self--complexation. The crystal water molecules provide links between the columns of stacked molecules through hydrogen bonds. In each compound the N-C bond lengths fall into two distinct groups (mean values 1.330(3) vs 1.361(1) Å in I and 1.320(3) vs 1.357(5) Å in II), as do the C-C bonds of the central phenyl rings (1.411(4) vs 1.467(1) Å in I and 1.405(5) vs 1.458(4) Å in II).