Project Management Duration/Resource Tradeoff Analysis: an Application of the Cut Search Approach

The paper presents an application oriented procedure for solving the project management duration/resource tradeoff problem. A procedure is presented for reducing a project from a normal to a crash duration state at a minimum amount of additional resource expenditure assuming a linear utilization functions. The procedure is network based using a graphical Cut Search Approach to locate the minimal resource level at each reduction in total project duration. Activity-on-arc networks and flow networks are utilized. The paper is presented for practical application and for conceptual development as compared to a theoretical treatment.     

Electroweak tests with τ leptons at LEP

We report on two sensitive tests of lepton universality carried out by the 4 LEP experiments at the Z⁰ pole. From measurements of the τ polarization in e⁺ e^?→τ ⁺ τ ^?, the ratios of the vector and axial vector coupling constants of the electron and the tau lepton to the weak neutral current are obtained to beg _{v e} /g _{a e} =0.066±0.015 andg _{V τ} /g _{A τ} =0.070±0.009 respectively. From measurement of the τ lifetime and the τ leptonic branching ratios, the ratio of the coupling constants describing weak leptonic decays of the τ and the μ is measured to beG _τ /G _μ =0.996±0.008.     

Standard<Emphasis Type="Italic">SU</Emphasis>(5) supergravity grand unification model and predictions

A review is given of the StandardSU(5) supergravity model. This model has passed an important check regarding unification of the electro-weak and the strong couplings using high precision LEP data. It is shown that for a significant domain of the parameter space the model also satisfies constraints on the SUSY spectrum from CDF and LEP, as well as proton stability and cosmological relic density constraints.     

A high-power X-band pulsed microwave induced catalytic decomposition of methane with integral acoustic measurements

A high-power microsecond pulsed microwave system operating in the X-band region was used for the catalytic conversion of methane. Microwave microsecond pulses at repetition rates of 50 and 80 Hz were used to initiate chemical reactions. The Microwave-Induced Acoustic technique was employed in combination with gas chromatography for on-line detection of chemical products. Methane was converted to C₂ and C₃ hydrocarbons. The selectivity of ethane in hydrocarbon products can be >90 %. The contribution of hydrogen evolution and carbon deposition has been shown to be important. A comparison between previous experiments performed with millisecond pulse durations is given.     

Visible light induced photocatalytic reaction of rhodamine B dye via 12-tungstosilicic acid in water

Using 12-tungstosilicic acid (SiW124-) as the catalyst, rhodamine B (RhB) dye in an aerated aqueous solution can undergo an effective photocatalytic stepwise N-deethylation process under visible light irradiation, and dioxygen is reduced to hydrogen peroxide by the reducedSiW12 4-. This provides the potential for moving polyoxometalate-based photocatalytic processes from the near-UV into the visible region of the spectrum.     

Sol-gel polycondensation of methyltrimethoxysilane in ethanol studied by <Superscript>29</Superscript>Si NMR spectroscopy using a two-step acid/base procedure

Sol-gel polymerization of methyltrimethoxysilane (MTMS) in ethanol using a two-step acid/base catalyzed procedure (B2) is followed by ²⁹Si NMR spectroscopy. Analysis of the structural evolution of the B2 system shows that esterification of monomeric and end silicon species is rate-limited while that of linear and cyclic species is able to reach pseudoequilibrium in the second basic step. Condensation reactivity is reduced with increasing network connectivity, however, to a much less degree under B2 conditions than MTMS polymerization under acidic conditions. Steric effects as well as many other factors are attributed to this trend. The concentration of cyclic and polycyclic species of the B2 system is nearly 3 times lower compared to the acid-catalyzed system. The empirical degree of condensation at the gel point is determined to be 0.88. The effects of cyclization and phase separation on MTMS gelation are discussed for both B2 and acid-catalyzed systems. Based on these results it is believed that MTMS-based gels form for B2 and not acid-catalyzed conditions due to reduced cyclization, rapid hydrolysis and condensation, effective use of functional groups, and effective contribution of branched and polycyclic species as crosslinking points to connect polymeric chains in the B2 system.     

Computing the Fukui function from ab initio quantum chemistry: approaches based on the extended Koopmans’ theorem

The extended Koopmans’ theorem is related to Fukui function, which measures the change in electron density that accompanies electron attachment and removal. Two approaches are used, one based on the extended Koopmans’ theorem differential equation and the other based directly on the expression of the ionized wave function from the extended Koopmans’ theorem. It is observed that the Fukui function for electron removal can be modeled as the square of the first Dyson orbital, plus corrections. The possibility of useful generalizations to the extended Koopmans’ theorem is considered; some of these extensions give approximations, or even exact expressions, for the Fukui function for electron attachment.     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.