Improved access to 19-nor-7β, 8β-methylene-taxoids and formation of a 7-membered C-ring analog of doxetaxel by electrochemistry

A new route to semisynthetic 19-nor-7β, 8β-methylene taxoids, such as compound 8, from the 7-O-trifluoromethanesulfonyl derivative 6 is reported. Evidence for a dissociation of the triflate to form a carbocation at C-7 under the reaction conditions is presented. Electrochemical reduction of the cyclopropane taxoid 8 gives, besides the expected 10-dehydroxy-cyclopropane analog 10, the 7-membered C-ring derivative 11.     

Novel Sesquiterpenoids from Siegesbeckia orientalis

Five new sesquiterpenoids, namely, 8β‐(angeloyloxy)‐4β,6α,15‐trihydroxy‐14‐oxoguaia‐9,11(13)‐dien‐12‐oic acid 12,6‐lactone ( 1 ), 4β,6α,15‐trihydroxy‐8β‐(isobutyryloxy)‐14‐oxoguaia‐9,11(13)‐dien‐12‐oic acid 12,6‐lactone ( 2 ), 11,12,13‐trinorguai‐6‐ene‐4β,10β‐diol ( 3 ), (1(10)E,4E,8Z)‐8‐(angeloyloxy)‐6α,15‐dihydroxy‐14‐oxogermacra‐(1(10),4,8,11(13)‐tetraen‐12‐oic acid 12,6‐lactone ( 9 ), and (1(10)E,4β)‐8β‐(angeloyloxy)‐6α,14,15‐trihydroxygermacra‐1(10),11(13)‐dien‐12‐oic acid 12,6‐lactone ( 11 ), and three new artifacts, (1(10)E,4Z)‐8β‐(angeloyloxy)‐9α‐ethoxy‐6α,15‐dihydroxy‐14‐oxogermacra‐1(10),4,11(13)‐trien‐12‐oic acid 12,6‐lactone ( 6 ), (1(10)E,4Z)‐8β‐(angeloyloxy)‐9α,13‐diethoxy‐6α,15‐dihydroxy‐14‐oxogermacra‐1(10),4‐dien‐12‐oic acid 12,6‐lactone ( 7 ), and (1(10)E,4Z)‐8β‐(angeloyloxy)‐9α‐ethoxy‐6α,15‐dihydroxy‐13‐methoxy‐14‐oxogermacra‐1(10),4‐dien‐12‐oic acid 12,6‐lactone ( 8 ), together with the three known sesquiterpenoids 4, 5 , and 10 , were isolated from the aerial parts of Siegesbeckia orientalis L. Their structures were established by spectral methods, especially 1D‐ and 2D‐NMR spectral methods.     

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.