Heuristische Verfahren zur Tourenplanung bei der Hausmüllentsorgung in ländlichen Regionen

Zusammenfassung Tourenprobleme bei der Hausmüllsammlung lassen sich in die Reihe der Lieferplanprobleme einordnen. Zur Lösung praktischer Größenordnungen werden hier einfache heuristische Verfahren (Prioritätsregeln) vorgestellt, weniger um der Vielzahl heuristischer Verfahren weitere hinzuzufügen als vielmehr dem Praktiker einen vielversprechenden Weg beim Lösen seiner Probleme aufzuzeigen.

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Summary The discussed solid waste collection problem shows the properties of the so called truck dispatching problem. To solve problems for typical problem structure heuristic rules are pointed out in order to show the planner an efficient way of problem solving.

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Zusammenfassung dreier Vorträge im 4. planungstechnischen Seminar Tourenplanung bei der Abfallbeseitigung am Institut für Siedlungswasserwirtschaft der Universität Karlsruhe am 1.10.1976.     

Kriterien in der Theorie der Gleichverteilung

It is the aim of this paper to introduce two new notions of discrepancy. They are defined by the formulas $$\begin{gathered} \Delta _N^r \left( {\omega ;f} \right) = \mathop {\sup }\limits_{\left| z \right| = r} \left| {\left( {{1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-\nulldelimiterspace} N}} \right)\sum\limits_{n = 1}^N {f\left( {z e^2 \pi i\omega \left( n \right)} \right)} - f\left( 0 \right)} \right|, and \hfill \\ \delta _N^r \left( {\omega ;f} \right) = \mathop {\sup }\limits_{\left| z \right| = r} \left| {\left( {{1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-\nulldelimiterspace} N}} \right)\sum\limits_{n = 1}^N {f\left( {z \omega \left( n \right)} \right)} \cdot z - \int\limits_0^z {f\left( \zeta \right)d\zeta } } \right|, \hfill \\ \end{gathered} $$ wheref is a holomorphic function defined in the unit disc withf ^(k) (0)≠0 for allk∈?,r<1 is a positive number, and ω is a sequence in [0, 1]. The first of these discrepancies can be generalized for multidimensional sequences. ω is uniform distributed if and only if lim _N→∞ Δ _N ^r (ω;f)=0 resp. lim _N→∞δ _N ^r (ω;f)=0. These results are proved in a quantitative way by estimating the classical discrepancyD _N (ω) by means ofΔ _N ^r (ω;f) and δ _N ^r (ω;f): $$\begin{gathered} \Delta _N^r \left( {\omega ;f} \right) \ll D_N \left( \omega \right) \ll \Phi \left( {\Delta _N^r \left( {\omega ;f} \right)} \right), \hfill \\ \delta _N^r \left( {\omega ;f} \right) \ll D_N \left( \omega \right) \ll \Psi \left( {\delta _N^r \left( {\omega ;f} \right)} \right). \hfill \\ \end{gathered} $$ The functions Φ and Ψ only depend onf andr. These estimations are based on the inequalities ofKoksma-Hlawka andErdös-Turán.     

Zwitterionic and cationic bis(phosphine) platinum(II) complexes: structural,electronic, and mechanistic comparisons relevant to ligand exchange and benzene C-H activation processes

Structurally similar but charge-differentiated platinum complexes have been prepared using the bidentate phosphine ligands [Ph(2)B(CH(2)PPh(2))(2)], ([Ph(2)BP(2)], [1]), Ph(2)Si(CH(2)PPh(2))(2), (Ph(2)SiP(2), 2), and H(2)C(CH(2)PPh(2))(2), (dppp, 3). The relative electronic impact of each ligand with respect to a coordinated metal center's electron-richness has been examined using comparative molybdenum and platinum model carbonyl and alkyl complexes. Complexes supported by anionic [1] are shown to be more electron-rich than those supported by 2 and 3. A study of the temperature and THF dependence of the rate of THF self-exchange between neutral, formally zwitterionic [Ph(2)BP(2)]Pt(Me)(THF) (13) and its cationic relative [(Ph(2)SiP(2))Pt(Me)(THF)][B(C(6)F(5))(4)] (14) demonstrates that different exchange mechanisms are operative for the two systems. Whereas cationic 14 displays THF-dependent, associative THF exchange in benzene, the mechanism of THF exchange for neutral 13 appears to be a THF independent, ligand-assisted process involving an anchimeric, eta(3)-binding mode of the [Ph(2)BP(2)] ligand. The methyl solvento species 13, 14, and [(dppp)Pt(Me)(THF)][B(C(6)F(5))(4)] (15), each undergo a C-H bond activation reaction with benzene that generates their corresponding phenyl solvento complexes [Ph(2)BP(2)]Pt(Ph)(THF) (16), [(Ph(2)SiP(2))Pt(Ph)(THF)][B(C(6)F(5))(4)] (17), and [(dppp)Pt(Ph)(THF)][B(C(6)F(5))(4)] (18). Examination of the kinetics of each C-H bond activation process shows that neutral 13 reacts faster than both of the cations 14 and 15. The magnitude of the primary kinetic isotope effect measured for the neutral versus the cationic systems also differs markedly (k(C(6)H(6))/k(C(6)D(6)): 13 = 1.26; 14 = 6.52; 15 approximately 6). THF inhibits the rate of the thermolysis reaction in all three cases. Extended thermolysis of 17 and 18 results in an aryl coupling process that produces the dicationic, biphenyl-bridged platinum dimers [[(Ph(2)SiP(2))Pt](2)(mu-eta(3):eta(3)-biphenyl)][B(C(6)F(5))(4)](2) (19) and [[(dppp)Pt](2)(mu-eta(3):eta(3)-biphenyl)][B(C(6)F(5))(4)](2) (20). Extended thermolysis of neutral [Ph(2)BP(2)]Pt(Ph)(THF) (16) results primarily in a disproportionation into the complex molecular salt [[Ph(2)BP(2)]PtPh(2)](-)[[Ph(2)BP(2)]Pt(THF)(2)](+). The bulky phosphine adducts [Ph(2)BP(2)]Pt(Me)[P(C(6)F(5))(3)] (25) and [(Ph(2)SiP(2))Pt(Me)[P(C(6)F(5))(3)]][B(C(6)F(5))(4)] (29) also undergo thermolysis in benzene to produce their respective phenyl complexes, but at a much slower rate than for 13-15. Inspection of the methane byproducts from thermolysis of 13, 14, 15, 25, and 29 in benzene-d(6) shows only CH(4) and CH(3)D. Whereas CH(3)D is the dominant byproduct for 14, 15, 25, and 29, CH(4) is the dominant byproduct for 13. Solution NMR data obtained for 13, its (13)C-labeled derivative [Ph(2)BP(2)]Pt((13)CH(3))(THF) (13-(13)()CH(3)()), and its deuterium-labeled derivative [Ph(2)B(CH(2)P(C(6)D(5))(2))(2)]Pt(Me)(THF) (13-d(20)()), establish that reversible [Ph(2)BP(2)]-metalation processes are operative in benzene solution. Comparison of the rate of first-order decay of 13 versus the decay of d(20)-labeled 13-d(20)() in benzene-d(6) affords k(13)()/k(13-d20)() approximately 3. The NMR data obtained for 13, 13-(13)()CH(3)(), and 13-d(20)() suggest that ligand metalation processes involve both the diphenylborate and the arylphosphine positions of the [Ph(2)BP(2)] auxiliary. The former type leads to a moderately stable and spectroscopically detectable platinum(IV) intermediate. All of these data provide a mechanistic outline of the benzene solution chemistries for the zwitterionic and the cationic systems that highlights their key similarities and differences.     

Efficient nickel-mediated intramolecular amination of aryl chlorides

The use of an in situ generated Ni(0) catalyst associated with 2,2'-bipyridine or N,N'-bis(2,6-diisopropylphenyl)dihydroimidazol-2-ylidene (SIPr) as a ligand and NaO-t-Bu as the base for the intramolecular coupling of aryl chlorides with amines is described. The procedure has been applied to the formation of five-, six-, and seven-membered rings. [reaction: see text]     

High-speed gradient parallel liquid chromatography/tandem mass spectrometry with fully automated sample preparation for bioanalysis: 30 seconds per sample from plasma

In this work, a high-throughput and high-performance bioanalytical system is described that is capable of extracting and analyzing 1152 plasma samples within 10 hours. A Zymark track robot system interfaced with a Tecan Genesis liquid handler was used for simultaneous solid-phase extraction of four 96-well plates in a fully automated fashion. The extracted plasma samples were injected onto four parallel monolithic columns for separation via a four-injector autosampler. The use of monolithic columns allowed for fast and well-resolved separations at a considerably higher flow rate without generating significant column backpressure. This resulted in a total chromatographic run cycle time of 2 min on each 4.6 x 100 mm column using gradient elution. The effluent from the four columns was directed to a triple quadrupole mass spectrometer equipped with an indexed four-probe electrospray ionization source (Micromass MUX interface). Hence, sample extraction, separation, and detection were all performed in a four-channel parallel format that resulted in an overall throughput of about 30 s per sample from plasma. The performance of this system was evaluated by extracting and by analyzing twelve 96-well plates (1152) of human plasma samples spiked with oxazepam at different concentrations. The relative standard deviation (RSD) of analyte sensitivity (slope of calibration curve) across the four channels and across the 12 plates was 5.2 and 6.8%, respectively. An average extraction recovery of 77.6% with a RSD of 7.7% and an average matrix effect of 0.95 with a RSD of 5.2% were achieved using these generic extraction and separation conditions. The good separation efficiency provided by this system allowed for rapid method development of an assay quantifying the drug candidate and its close structural analog metabolite. The method was cross-validated with a conventional liquid chromatography/tandem mass spectrometry (LC/MS/MS) assay.     

Octahedral (cis-cyclam)iron(III) complexes with O,N-coordinated o-iminosemiquinonate(1-) pi radicals and o-imidophenolate(2-) anions

Three octahedral complexes containing a (cis-cyclam)iron(III) moiety and an O,N-coordinated o-iminobenzosemiquinonate pi radical anion have been synthesized and characterized by X-ray crystallography at 100 K: [Fe(cis-cyclam)(L(1-3)(ISQ))](PF(6))(2) (1-3), where (L(1-3)(ISQ)) represents the monoanionic pi radicals derived from one-electron oxidations of the respective dianion of o-imidophenolate(2-), L(1), 2-imido-4,6-di-tert-butylphenolate(2-), L(2), and N-phenyl-2-imido-4,6-di-tert-butylphenolate(2-), L(3). Compounds 1-3 possess an S(t) = 0 ground state, which is attained via strong intramolecular antiferromagnetic exchange coupling between a low-spin central ferric ion (S(Fe) = 1/2) and an o-imino-benzosemiquinonate(1-) pi radical (S(rad) = 1/2). Zero-field M?ssbauer spectra of 1-3 at 80 K confirm the low-spin ferric electron configuration: isomer shift delta = 0.26 mm s(-1) and quadrupole splitting DeltaE(Q) = 1.96 mm s(-1) for 1, 0.28 and 1.93 for 2, and 0.33 and 1.88 for 3. All three complexes undergo a reversible, one-electron reduction of the coordinated o-imino-benzosemiquinonate ligand, yielding an [Fe(III)(cis-cyclam)(L(1-3)(IP))](+) monocation. The monocations of 1 and 2 display very similar rhombic signals in the X-band EPR spectra (g = 2.15, 2.12, and 1.97), indicative of low-spin ferric species. In contast, the monocation of 3 contains a high-spin ferric center (S(Fe) = 5/2) as is deduced from its M?ssbauer and EPR spectra.     

Purine analog inhibitors of xanthine oxidase - structure activity relationships and proposed binding of the molybdenum cofactor

A number of new hypoxanthine analogs have been prepared as substrate inhibitors of xanthine oxidase. Most noteworthy inhibitory new hypoxanthine analogs are 3-(m-tolyl)pyrazolo[1,5-a]pyrimidin-7-one ( 47 ), ID₅₀ 0.06 μM and 3-phenylpyrazolo[1,5-a]pyrimidin-7-one ( 46 ), ID₅₀ 0.40 μM. 5-(p-Chlorophenyl)pyrazolo[1,5-a]pyrimidin-7-one ( 63 ) and the corresponding 5-nitrophenyl derivative 64 exhibited an ID₅₀ of 0.21 and 0.23 μM, respectively. 7-Phenylpyrazolo[1,5-a]-s-triazin-4-one ( 40 ) is shown to exhibit an ID₅₀ of 0.047 μM. The structure-activity relationships of these new phenyl substituted hypoxanthine analogs are discussed and compared with the xanthine analogs 3-m-tolyl- and 3-phenyl-7-hydroxypyrazolo[1,5-a]pyrimidin-5-ones ( 90 ) and ( 91 ), previously reported from our laboratory to have ID₅₀ of 0.025 and 0.038 μM, respectively. The presence of the phenyl and substitutedphenyl groups contribute directly to the substrate binding of these potent inhibitors. This work presents an updated study of structure-activity relationships and binding to xanthine oxidase. In view of the recent elucidation of the pterin cofactor and the proposed binding of this factor to the molybdenum ion in xanthine oxidase, a detailed mechanism of xanthine oxidase oxidation of hypoxanthine and xanthine is proposed. Three types of substrate binding are viewed for xanthine oxidase. The binding of xanthine to xanthine oxidase is termed Type I binding. The binding of hypoxanthine is termed Type II binding and the specific binding of alloxanthine is assigned as Type III binding. These three types of substrate binding are analyzed relative to the most potent compounds known to inhibit xanthine oxidase and these inhibitors have been classified as to the type of inhibitor binding most likely to be associated with specific enzyme inhibition. The structural requirements for each type of binding can be clearly seen to correlate with the inhibitory activity observed. The chemical syntheses of the new 3-phenyl- and 3-substituted phenylpyrazolo[1,5-a]pyrimidines with various substituents are reported. The syntheses of various 8-phenyl-2-substituted pyrazolo-[1,5-a]-s-triazines, certain s-triazolo[1,5-a]-s-triazines and s-triazolo[1,5-a]pyrimidine derivatives prepared in connection with the present study are also described.     

Studies on the chemistry of 1,4-oxazines. 18. Synthesis of tricyclic 1,4-benzoxazines via nucleophilic substitution of activated precursors

Starting from activated benzoxazines 1 and 2 new synthetic pathways to the tricyclic compounds 4, 9, 12 and 16 are described. Reaction of the hydrazides 17a,b with thionylchloride leads to the novel thiatriazolo-benzoxazines 18a,b .     

Ruthenium Complexes Containing "Noninnocent" o-Benzoquinone Diimine/o-Phenylenediamide(2-) Ligands. Synthesis and Crystal Structure of the Nitrido-Bridged Complex [{LRu(o-C(6)H(4)(NH)(2))}(2)(&mgr;-N)](PF(6))(2).3CH(3)CN.C(6)H(5)CH(3)

Reaction of LRu(III)Cl(3) (L = 1,4,7-trimethyl-1,4,7-triazacyclononane) with 1,2-phenylenediamine (opdaH(2)) in H(2)O in the presence of air affords [LRu(II)(bqdi)(OH(2))](PF(6)) (1), where (bqdi) represents the neutral ligand o-benzoquinone diimine. From an alkaline methanol/water mixture of 1 was obtained the dinuclear species [{LRu(II)(bqdi)}(2)(&mgr;-H(3)O(2))](PF(6))(3) (1a). The coordinated water molecule in 1 is labile and can be readily substituted under appropriate reaction conditions by acetonitrile, yielding [LRu(II)(bqdi)(CH(3)CN)](PF(6))(2) (2), and by iodide and azide anions, affording [LRu(II)(bqdi)I](PF(6)).0.5H(2)O (3) and [LRu(bqdi)(N(3))](PF(6)).H(2)O (4), respectively. Heating of solid 4 in vacuum at 160 degrees C generates N(2) and the dinuclear, nitrido-bridged complex [{LRu(o-C(6)H(4)(NH)(2))}(2)(&mgr;-N)](PF(6))(2) (5). Complex 5 is a mixed-valent, paramagnetic species containing one unpaired electron per dinuclear unit whereas complexes 1-4 are diamagnetic. The crystal structures of 1, 1a.3CH(3)CN, 3, 4.H(2)O, and 5.3CH(3)CN.0.5(toluene) have been determined by X-ray crystallography: 1 crystallizes in the monoclinic space group P2(1)/m, Z = 2, with a = 8.412(2) ?, b = 15.562(3) ?, c = 10.025 ?, and beta = 109.89(2) degrees; 1a.3CH(3)CN, in the monoclinic space group C2/c, Z = 4, with a = 19.858(3) ?, b = 15.483(2) ?, c = 18.192(3) ?, and beta = 95.95(2) degrees; 3, in the orthorhombic space group Pnma, Z = 4, with a = 18.399(4) ?, b = 9.287(2) ?, and c = 12.052(2) ?, 4.H(2)O, in the monoclinic space group P2(1)/c, Z = 4, with a = 8.586(1) ?, b = 15.617(3) ?, c = 16.388(5) ?, and beta = 90.84(2) degrees; and 5.3CH(3)CN.0.5(toluene), in the monoclinic space group P2(1)/c, Z = 4, with a = 15.003(3) ?, b = 16.253(3) ?, c = 21.196(4) ?, and beta = 96.78(3) degrees. The structural data indicate that in complexes 1-4 the neutral o-benzoquinone diimine ligand prevails. In contrast, in 5 this ligand has predominantly o-phenylenediamide character, which would render 5 formally a mixed-valent Ru(IV)Ru(V) species. On the other hand, the Ru-N bond lengths of the Ru-N-Ru moiety at 1.805(5) and 1.767(5) ? are significantly longer than those in other crystallographically characterized Ru(IV)=N=Ru(IV) units (1.72-1.74 ?). It appears that the C(6)H(4)(NH)(2) ligand in 5 is noninnocent and that formal oxidation state assignments to the ligands or metal centers are not possible.