A distributed Poisson approximation for preempt-resume clockedschedules

Many telecommunication systems with time-critical requirements use a preempt-resume clocked schedule. An approximation to the ergodic distribution of the time to completion of a low-priority task is obtained by treating the priority service time distribution as the limit of compound Poisson distributions. Explicit formulas for the mean and variance that are highly accurate are given. For random clocked loads, a stochastic bound is provided for the discrepancy between the exact and approximate distributions. For deterministic clocked loads, sample path bounds are found. Simulation results are given to demonstrate the accuracy of the model     

Synthesis of nonactin (author's transl)]

Synthesis of Nonactin. The macrotetrolide antibiotic nonactin (I), containing four units of a C₁₀ hydroxy acid, has been synthesized starting from two adequately protected derivatives (III and IV) of nonactic acid (II). The 32-membered ring of the macrotetrolide is built up by a sequence of condensation and deprotection steps leading first to a product with two, and subsequently to one with four nonactic acid residues (VIII) which is then cyclized in the presence of Ag⁺-ions. Two reactions forming ester bonds have been developed to condense the hydroxy acids and to effect the final cyclization. In one the activation of the carboxyl group is achieved by conversion into the mixed anhydride with 2,4,6-trimethylbenzene sulfonyl chloride in pyridine. In the other the Ag⁺-ion induced reaction of a S-(2-pyridyl) hydroxy carbothioate is used to form the corresponding macrocyclic lactone. In the case of nonactin the ring closure is promoted by the coordinating effect of Ag⁺-ions present in the reaction mixture.     

Analyzing social media data having discontinuous underlying dynamics

This paper develops a real time algorithm which identifies times of emotional discontinuity as reflected in social media. The paper formulates the optimization problem to solve, develops an algorithm to solve it using dynamic programming, and illustrates the new method by analyzing mood shifts reflected in 380,000 Twitter messages related to one of the world’s most popular soccer teams, Manchester United, during their 2011–12 season.     

Influence of Temperatures on the Tautomerism of the N‐(1H‐imidazoline‐2‐yl)‐1H‐benzimidazol‐2‐amine and Investigation of Its Electrochemical Behaviour

Synthesis of N‐(1H‐imidazoline‐2‐yl)‐1H‐benzimidazol‐2‐amine was carried out under microwave irradiation (MWI) conditions. Dynamic ¹H NMR investigation of N‐(1H‐imidazoline‐2‐yl)‐1H‐benzimidazol‐2‐amine compound was reported at temperature range of 223–333 K in DMF‐d₇. Some physical parameters, such as coalescence temperature (T_c), the free energy of activation (ΔG^??) and rate constant (k) values were calculated from its ¹H NMR spectra at various temperatures. Electrochemical feature of this compound was investigated by cyclic (CV) and square wave voltammetry (SWV).     

Questioni di algebra universale in una categoria astratta

Riassunto SiaK una categoria con prodotti finiti e siaA un oggetto diA. Un'operazione n-adica suA è un morfismoA ⁿ→A; unastruttura algebrica suA è una famiglia di operazioni suA edA con una tale struttura si dirà un'algebra in K. Con queste definizioni, è possibile studiare alcuni problemi di algebra universale riferiti alle algebre inK.

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Summary LetK be a category with finite products and a null object and letAεOb K Ann-ary operation on A is any morphismA ⁿ→A and analgebra in K is an object together with a family of operations on it. We study some problems concerning algebras inK.

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Lavoro eseguito nell'ambito dell'attività dei Gruppi di Ricerca Matematici del C.N.R., nell'anno 1969.

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Nota diMario Servi a Parma—V.le La Grola, 29.—43100 Parma.     

Optimizing Bernoulli Routing Policies for Balancing Loads on Call Centers and Minimizing Transmission Costs

We address the problem of assigning probabilities at discrete time instants for routing toll-free calls to a given set of call centers to minimize a weighted sum of transmission costs and load variability at the call centers during the next time interval.We model the problem as a tripartite graph and decompose the finding of an optimal probability assignment in the graph into the following problems: (i) estimating the true arrival rates at the nodes for the last time period; (ii) computing routing probabilities assuming that the estimates are correct. We use a simple approach for arrival rate estimation and solve the routing probability assignment by formulating it as a convex quadratic program and using the affine scaling algorithm to obtain an optimal solution.We further address a practical variant of the problem that involves changing routing probabilities associated with k nodes in the graph, where k is a prespecified number, to minimize the objective function. This involves deciding which k nodes to select for changing probabilities and determining the optimal value of the probabilities. We solve this problem using a heuristic that ranks all subsets of k nodes using gradient information around a given probability assignment.The routing model and the heuristic are evaluated for speed of computation of optimal probabilities and load balancing performance using a Monte Carlo simulation. Empirical results for load balancing are presented for a tripartite graph with 99 nodes and 17 call center gates.     

Microwave‐assisted from synthesis of 2‐arylamino‐2‐imidazolines on a solid support

An efficient synthesis of 2‐arylamino‐2‐imidazolines from dimethyl N‐aryldithioimidocarbonates and ethylenediamine on solid support under microwave irradiation has been developed. The reaction time has been reduced from hours to minutes with improved yields as compared to conventional heating. Their piperidin‐4‐ylmethyl and morpholin‐4‐ylmethyl derivatives were synthesized by treatment with formaldehyde and piperidine or morpholine. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:142–222, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20081     

Stereoselective Preparation of Allylic Alcohol Intermediates in the Synthesis of Deoxysugars

ABSTRACT

4S-cis-2, 2, 5-Trimethyl-l, 3-dioxolane-4-carboxaldehyde (1) undergoes stereoselective nucleophilic addition with different vinyl metals. Allylic alcohols thus obtained are possible intermediates in the synthesis of deoxysugars. By ? reiterative 1 C extension cycle, 6-deoxyhexoses can be obtained.     

One‐Pot Synthesis of Iminoimidazolines under Microwave Irradiation in Solvent‐Free Conditions

Substituted iminoimidazolines were synthesized from a one‐pot reaction of aromatic or hetero‐aromatic amines with imidazolidine‐2‐thione under solvent‐free conditions using microwave irradiation with good to excellent yields.     

Noetherian varieties in definably complete structures

We prove that the zero-set of a C ^∞ function belonging to a noetherian differential ring M can be written as a finite union of C ^∞ manifolds which are definable by functions from the same ring. These manifolds can be taken to be connected under the additional assumption that every zero-dimensional regular zero-set of functions in M consists of finitely many points. These results hold not only for C ^∞ functions over the reals, but more generally for definable C ^∞ functions in a definably complete expansion of an ordered field. The class of definably complete expansions of ordered fields, whose basic properties are discussed in this paper, expands the class of real closed fields and includes o-minimal expansions of ordered fields. Finally, we provide examples of noetherian differential rings of C ^∞ functions over the reals, containing non-analytic functions.