Novel Redox-Active Cyclophanes Based on 3,3'-Biindolizines: Synthesis and Chirality

The first compounds of a new series of redox-active cyclophanes were prepared by dehydrocyclization of bridged indolizines of type 1. The bridged dipyridino-compounds 2a and 2b obtained by reaction of 2 mol of lithiated alpha-picolines with dihalides were used as starting materials. Subsequent treatment of 2a,b with 2 mol of alpha-bromo ketones gave quaternary pyridinium halides. Ring closure in an alkaline medium (Chichibabin reaction) yielded the starting material for the synthesis of the macrocycles. Oxidative C-C coupling gave the diastereomeric cyclophanes of type 3. In all cases one pair of the enantiomers was obtained in excess. CV-investigations have shown that the main products are reversible redox systems. To clarify their conformations, compounds 3c, 3d/1, and3d/2 were subjected to X-ray analysis.     

A Heuristic Decomposition Algorithm for Scheduling Problems on Mixed Graphs

We consider a scheduling problem where a set of n jobs has to be processed on a set of m machines and arbitrary precedence constraints between operations are given. Moreover, for any two operations i and j values a _ij >0 and a _ji >0 may be given where a _ij is the minimal difference between the starting times of operations i and j when operation i is processed first. Often, the objective is to minimize the makespan but we consider also arbitrary regular criteria. Even the special cases of the classical job shop problem J//C_max belong to the set of NP-hard problems. Therefore, approximation or heuristic algorithms are necessary to handle large-dimension problems. Based on the mixed graph model we give a heuristic decomposition algorithm for such a problem, i.e. the initial problem is partitioned into subproblems that can be solved exactly or approximately with a small error bound. These subproblems are obtained by a relaxation of a subset of the set of undirected edges of the mixed graph. The subproblems are successively solved and a proportion of the results obtained for one subproblem is kept for further subproblem definitions. Numerical results of the algorithm presented here are given.     

Classification of bicovariant differential calculi on quantum groups of type A,B, C and D

Under the assumptions thatq is not a root of unity and that the differentialsdu _j ⁱ of the matrix entries span the left module of first order forms, we classify bicovariant differential calculi on quantum groupsA _n–1 ,B _n ,C _n andD _n . We prove that apart one dimensional differential calculi and from finitely many values ofq, there are precisely2n such calculi on the quantum groupA _n–1 =SL _q (n) forn3. All these calculi have the dimensionn ². For the quantum groupsB _n ,C _n andD _n we show that except for finitely manyq there exist precisely twoN ²-dimensional bicovariant calculi forN3, whereN=2n+1 forB _n andN=2n forC _n ,D _n . The structure of these calculi is explicitly described and the corresponding ad-invariant right ideals of ker are determined. In the limitq1 two of the 2n calculi forA _n–1 and one of the two calculi forB _n ,C _n andD _n contain the ordinary classical differential calculus on the corresponding Lie group as a quotient.     

Yrast excitations in129Te

Using an 11.4MeV/u¹³⁶Xe beam of the UNILAC accelerator of GSI and a^natW target, A=184 isobars were produced and separated by using an on-line mass separator. A new isomeric state was found in¹⁸⁴Hf. This state decays with a half-life of 48(10) s and emits three -rays of 73, 482, and 555 keV as well as lower-lying cascade transitions. The hindrance of the 73 keV-E1 transition with K=8 is compared with those of other even-even hafnium isotopes. The half-life of¹⁸⁴Lu was estimated to be between 15 and 25s.     

Quantitative determination of chloride by means of flow injection analysis with spectrophotometric detection in the UV/VIS range

Chloride is determined indirectly by Spectrophotometric flow injection analysis. Two systems are compared, both based on the principle of ion exchange of easily detectable anions versus chloride from suitable mercury salts. The first method is based on the exchange of chloride with chloranilate which is detected at 332 nm or at 306 nm in neutral or in acidic medium respectively. In the second case, chloride reacts with Hg(SCN)₂. The liberated thiocyanate forms a strongly coloured complex with Fe(III) in acidic solution with an absorption maximum at 460 nm. Both methods have a detection limit of about 5 mol Cl^–/l (175 ng/ml). In the case of the thiocyanate method, the relative standard deviation is about 2% (7 measurements) in the range of 5 to 150 mol/l and decreases significantly to a value of approximately 0.2% at higher concentrations; for the chloranilate method it is 10% for lower and about 1% for higher concentrations respectively.     

The job-shop problem and immediate selection

The job-shop problem is one of the most difficult NP-hard scheduling problems. A 10×10-problem published in 1963 has been solved only recently by Carlier and Pinson using a branch and bound method. Other branch and bound algorithms have been developed recently. The efficiency of all these branch and bound methods relies on the concept of immediate selection which allows to introduce order relations on the setI of all operations to be processed on the same machine before branching. We present new algorithms for immediate selection. Among them are

1. anO(max {n logn,f})-algorithm for fixing all disjunctions induced by cliques;
2. anO(n ²)-algorithm based on concepts which are different from those used by Carlier and Pinson.

Here,n is the number of operations inI andf is the number of induced order relations.