Λ-Shaped Policies to Schedule Deteriorating Jobs

We study a problem of scheduling deteriorating jobs, i.e. jobs whose processing times are an increasing function of their starting times. We consider the case of a single machine and linear job-independent deterioration. The objective is to minimize the sum of weighted completion times, with weights proportional to the basic processing times. The optimal schedule is shown to be Λ-shaped, i.e. the sequence of the basic processing times has a single local maximum. Moreover, we show that the problem is solved in O(N log N) time. In the last section we test heuristics for the case of general weights.     

Analysis of Open Discrete Time Queueing Networks: A Refined Decomposition Approach

This paper deals with approximate analysis methods for open queueing networks. External and internal flows from and to the nodes are characterized by renewal processes with discrete time distributions of their interarrival times. Stationary distributions of the waiting time, the queue size and the interdeparture times are obtained using efficient discrete time algorithms for single server (GI/G/1) and multi-server (GI/D/c) nodes with deterministic service. The network analysis is extended to semi-Markovian representations of each flow among the nodes, which include parameters of the autocorrelation function.     

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.     

Knoevenagel condensation of 2-carbethoxycyclohexanone and malononitrile: Synthesis of 4-cyano-3-ethoxy-1-hydroxy-5,6,7,8-tetrahydroisoquinoline,an isomer of the abnormal product

The structure of the abnormal product 1a formed in the Knoevenagel condensation of 2-carbethoxycyclohexanone and malononitrile has been further confirmed. Oxidation of the tetrahydroisoquinoline 3b using Na₂Cr₂O-AcOH-H₂SO₄ gave the keto isoquinoline 3d and the isoquinoline-1-carboxylic acid 5a. The acid chloride of 5a was condensed with diethyl ethoxymagnesiomalonate to afford after decarbethoxylation the methyl ketone 5d which on Baeyer-Villiger oxidation gave a mixture of the acetate 1g and the title compound 1b. The unambiguous synthesis of 1b confirms the structure assigned earlier to the title compound also formed during the partial hydrolysis of the diethoxy compound 1c. Condensation of 2-acetylcyclohexane-1,3-dione with malononitrile gave the quinoline derivative 4c which on ethylation yielded the ketoquinoline 4d. The present studies have confirmed that the quinoline compound 4a is also formed in the condensation of 2-acetylcyclohexanone and cyanoacetamide.     

Pressure dependence of the compressibility of alkali halides

The parameterC ₁=[(1/K _T )/P] _T , which describes the pressure variation of the compressibility, has been examined correlating the thermodynamical and interatomic potential approaches employing fewer approximations than has been usual heretofore. General expressions have been derived forC ₁ by including the thermal correction terms, which have generally been ignored in previous studies concerning thermal properties of ionic crystals. The parameterC ₁ has also been related to the Grüneisen parameter, , using a relation given earlier. The applicability of the derived equations is investigated and discussed for alkali halides employing few realistic potential forms. A good general accord is found with the available experimental data, which exhibits an essential improvement over other theoretical determinations.     

Cerate oxidimetry : Oxidation of formic,glycolic, malic,malonic and tartaric acids

1. Contrary to the observations of earlier workers, it has been shown that formic acid can be quantitatively oxidixed by ceric sulphate in the presence of concentrated sulphuric acid. 2. Tartaric, malonic, malic and glycolic acids can also be oxidized completely to carbon dioxide and water by the following general procedure : to a known amount of the organic acid is added ceric sulphate (excess) solution in dilute sulphuric acid and the mixed solution refluxed for ten to fifteen minutes. Concentrated sulphuric acid (double the volume of the reaction mixture) is then added taking care that formic acid is not lost during the addition, and the mixture again refluxed for 45 to 50 minutes. The excess ceric sulphate is determined by titrating against ferrous ammonium sulphate. 3. The complete oxidation of the above acids provides satisfactory methods for their quantitative estimation.     

Tast polarography of europium(III)-l-histidine complex

Study of europium(III)-l-histidine complex has been made in sodium perchlorate at μ=0.1 by tast polarography. The reduction process appears to be quasi irreversible. The apparent rate constants have been determined byGellings method¹. With the knowledge ofE ₁ ^2/r and use ofLingane's method, one complex Eu(Histd)²⁺ with the instability constant 6.77×10^?5 is reported.