Stereochemistry of cyclobutanone resulted from cycloadditions of t-butylcyanoketene to bicyclo[2.2.1]heptene derivatives, as evidence for a π2s+π2a reaction mode

The stereochemistry of the cyclobutanones 1-7, resulted from the reaction of t-butylcyanoketene with bicyclo[2.2.1]heptene, bicyclo[2.2.1]heptadiene, 1,4 - dihydro - 1,4 - methanonaphthalene, 1,4 - dihydro - 9 - (1 - methylethylidene) - 1,4 - methanonaphthalene, 1,4 - dihydro - 1,4 - epoxynaphthalene, l,4,4a,8b - tetrahydro - 1,4 - methanobiphenylene (l,4,4a,8b) and 1,4,4a,8b - tetrahydro - 1,4 - methanobiphenylene(1,4,4aβ,8bβ) was established as having the cyclobutanone ring exo and the t-Bu group in the configuration. These findings represent a stereochemical argument in favour of a _π2_s + _π2_a reaction mode of t-butylcyanoketene to the above mentioned bicyclo[2.2.1]heptene derivatives. Observations regarding preservation of the original configurations of alkenes as well as the geometrical distorsion of the cyclobutanones are shortly discussed.     

121Sb-Mössbauer-Spektren von Antimon(V)-Verbindungen. II

¹²¹Sb Mössbauer Spectra of Antimony (V) Compounds. II The Mössbauer resonance effect of ¹²¹Sb has been studied at 4.2 K in a series of 11 antimony(V) compounds which are in most cases bridged. Isomer shift and quadrupole splitting variations are considered in the light of results of X-ray and vibrational spectroscopy. Preparation and the vibrational spectra of [NMe₄][SbCl₄(n₃)₂] are described. Within the limitations of available structural data related tin compounds are compared with those of corresponding ¹¹⁹Sn Mössbauer spectra.     

Sukzessive Minima mit und ohne Nebenbedingungen

Given semi-normsf andg on ⁿ and a real number >0. Then the successive minima off under the constraintg are defined by _j : = inf {: there existj linear independent vectors inZ ⁿ withf andg}. The main theorem of this paper (Lagrange multiplier theorem) states that the successive minima of a certainnorm h on ⁿ (without constraints) coincide with the _j 's up to bounded factors. Moreover, this norm is constructed explicitly. Using Minkowski's wellknown theorem on successive minima and our result certain inequalities on simultaneous Diophantine approximations are derived.     

A sufficient condition for a graph to be hamiltonian

Those non-hamiltonian graphsG withn vertices are characterized, which satisfy the Ore-type degree-conditiond(x)+d(y)n–2 for each pairx,yM of different nonadjacent vertices whereM consists of two vertices ofG. As an application a theorem on hamiltonian connectivity of graphs is given. Furthermore, a condition is presented which is sufficient for the existence of a covering of a graph by two disjoint paths with prescribed set of startpoints and prescribed set of endpoints. A class of graphs is described which have no covering of this kind.     

Über Mittelwerte multiplikativer zahlentheoretischer Funktionen mehrerer Variablen

In [8] the author extended the concept of neighbouring functions (cp. [9]) to the case of several variables. Using these results it is shown that under some weak conditions a multiplicative functionf in two variables has a mean-value different from zero if and only if the two multiplicative functionsf ₁(n)=f(n, 1) andf ₂(n)=f(1,n) have mean-values different from zero. Applications to theorems ofDelange [3],Elliott [6] andDaboussi [1] are given.     

Approximations of inventory models

Summary A general procedure is presented for constructing approximations of discrete review single product dynamic inventory models. Bounds are derived for the approximations and compared with the ones ofHinderer [1978],Whitt [1978] for the approximation of a general dynamic program. Good order-policies are constructed. Finally, conditions are given under which the sequence of bounds associated with a sequence of approximating models converges to zero.

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Zusammenfassung Es wird ein allgemeines Verfahren zur Approximation periodisch inspizierter dynamischer Ein-Produkt-Lagerhaltungsmodelle betrachtet. Dazu werden Fehlerschranken gegeben. Diese werden verglichen mit denen vonHinderer [1978],Whitt [1978] für ein allgemeines dynamisches Entscheidungsmodell. Außerdem werden gute Bestellpolitiken konstruiert und hinreichende Bedingungen gegeben, unter denen die Fehlerschranken einer Folge von approximierenden Modellen gegen Null konvergiert.

     

Facile Synthesis and Palladium‐Catalyzed Cross‐Coupling Reactions of 2,3‐Bis(pinacolatoboryl)‐1,3‐butadiene

Treatment of 1,1‐bis(pinacolatoboryl)ethene with an excess of 1‐bromo‐1‐lithioethene gave 2,3‐bis(pinacolatoboryl)‐1,3‐butadiene in high yield. Palladium‐catalyzed cross‐coupling of the resulting diborylbutadiene with aryl iodides took place smoothly in the presence of a catalytic amount of Pd(OAc)₂/PPh₃ and aqueous KOH to give 2,3‐diaryl‐1,3‐butadienes in good yields. The coupling reaction with commercially available 4‐acetoxyphenylmethyl chloride under the same conditions followed by hydrolysis of the acetyl groups gave anolignan B in a one‐pot manner. A variety of [3]‐ to [6]dendralenes were synthesized by palladium‐catalyzed coupling of the diene or 1,1‐bis(pinacolato)borylethene with alkenyl or dienyl halides, respectively, in good yields.     

(Me2NH2)[(Ph3Sn)3(MoO4)2], ein Triorganozinnmolybdat mit Schichtstruktur

(Me₂NH₂)[(Ph₃Sn)₃(MoO₄)₂], a Triorganotin Molybdate with Layer Structure The reaction of [(Ph₃Sn)₂MoO₄] with (Me₂NH₂)Cl in an acetonitrile/water mixture leads to the formation of (Me₂NH₂)[(Ph₃Sn)₃(MoO₄)₂] ( 1 ). ( 1 ) crystallizes in the space group Pca2₁ with a = 1967.0(4), b = 1353.1(2) and c = 2176.6(5) pm. In the crystal structure of 1 Ph₃SnO₂ bipyramides and MoO₄ tetrahedra are linked by corner sharing to give a layer structure. Additionally the layers are connected by O···H···N hydrogen bridges between MoO₄ groups and [Me₂NH₂]⁺ ions to give a 3D network structure.     

Novel Pb(II), Zn(II), and Cd(II) coordination polymers constructed from ferrocenyl-substituted carboxylate and bipyridine-based ligands

Treatment of two kinds of ferrocenyl-substituted carboxylate ligands (3-ferrocenyl-2-crotonic acid, HOOC-CH=(CH(3))CFc (Fc=(eta(5)-C(5)H(5))Fe(eta(5)-C(5)H(4))) or O-ferrocecarbonyl benzoic acid, o-HOOCC(6)H(4)COFc with Pb(OAc)(2).3H(2)O, Zn(OAc)(2).2H(2)O, or Cd(OAc)(2).2H(2)O) resulted in four novel ferrocene-containing coordination polymers [[Pb(mu(2)-eta(2)-OOCCH=(CH(3))CFc)(2)].MeOH](n) (1), [[Zn(o-OOCC(6)H(4)COFc)(2)(4,4'-bipy)(H(2)O)(2)].2MeOH.2H(2)O](n) (4,4'-bipy = 4,4'-bipyridine) (2), [[Cd(o-OOCC(6)H(4)COFc)(2)(bpe)(MeOH)(2)].2H(2)O](n) (bpe = 1,2-bis(4-pyridyl)ethene) (3), and [Pb(o-OOCC(6)H(4)COFc)(eta(2)-o-OOCC(6)H(4)COFc)(bpe)](n)() (4). Their crystal structures have been characterized by single X-ray determinations. In polymer 1, Pb(II) ions are bridged by tridentate FcC(CH(3))=CHCOO(-) anions, forming an infinite chain [Pb(mu(2)-eta(2)-OOC=CH(CH(3))CFc)(2)](n). In polymers 2-4, there are three kinds of components, metal ions, o-FcCOC(6)H(4)COO(-) units, and organic bridging ligands. The bipyridine-based ligands connect metal ions leading to a one-dimensional chain with o-FcCOC(6)H(4)COO(-) units acting as monodentate or chelate ligands in the side chain. Such coordination polymers containing ferrocenyl-substituted carboxylate and bipyridine-based ligands are very rare. The solution-state differential pulse voltammetries of polymers 1-4 were determined. The results indicate that the half-wave potential of the ferrocenyl moieties is influenced by the Pb(II) ions in polymer 1 and strongly influenced by Zn(II), Cd(II), or Pb(II) ions in polymers 2-4. The thermal properties of the four polymers were also investigated.