Shapiro step

Figure 24 Schematic view of the sample with the constriction (a) and the Shapiro steps induced on the I-V characteristics by a microwave field at f - 9.169 GHz and T - 77 K. Ref. 88.

In 4-5 45° ACWJ s, Jc(45°) was nearly sample independent and nonvanishing. [12] For these ACWJ s, they obtained Fraunhofer-like patterns and performed Shapiro step analyses, indicating that their junctions were weak and first order. They also found to be independent of... 

If a Josephson junction is irradiated with microwaves of frequency /, the I-V behavior shows a series of steps, called Shapiro steps, as shown in Figure 30.32. These steps correspond to supercurrents across the junction when the condition for the absorption of microwave photons is satisfied (this is called the ac Josephson effect). Similar behavior is seen when we expose the junction to a magnetic field. How Josephson junctions can be used to detect very small magnetic fields is described in Chapter 33. 

Scheme 13.17 depicts a synthesis based on enantioselective reduction of bicyclo[2.2.2]octane-2,6-dione by Baker s yeast.21 This is an example of desym-metrization (see Part A, Topic 2.2). The unreduced carbonyl group was converted to an alkene by the Shapiro reaction. The alcohol was then reoxidized to a ketone. The enantiomerically pure intermediate was converted to the lactone by Baeyer-Villiger oxidation and an allylic rearrangement. The methyl group was introduced stereoselec-tively from the exo face of the bicyclic lactone by an enolate alkylation in Step C-l. 

In a very recent paper (47), Amer and Shapiro concluded that the thermal degradation oY PVC powder in the temperature range 170-210°C proceeded in such a way that HC1 catalysis was an integral part of the overall process. They proposed a unified mechanism consisting of three steps namely random generation of a single double bond in the cis configuration,... 

The Shapiro reaction occurs when a tosylhydrazone 86, easily prepared from a ketone and tosylhydrazine, is treated with 2 equivalents of an ethereal solution of n-butyllithium 87, resulting first in the removal of the N—H proton to give the anion 88 and then of a one proton from the less-substituted a position to give the dianion 89. Elimination of lithium p-toluenesulfinate in the rate-limiting step gives the lithium aUtenyldiazenide 90, which suffers loss of nitrogen to afford the alkenyllithium 91 (equation 31) ° . ... 

The Shapiro reaction provides a convenient, easy and straightforward method to convert ketones into a plethora of olefinic substances in high yields. Many of these vinyllithium derivatives are useful for further synthetic manipulations. No attempt is made in this chapter to cover all the applications of the Shapiro reaction and only few representative examples will be described. A variety of polyolefins such as 119, used for cation olefin cyclization, can be stereospecifically formed in a concise and modular approach in a single step from the components shown in equation 42 via the Shapiro reaction . 

Wood (1999), Linderoth, Shapiro and Wright (2002) for stochastic linear problems, Kleywegt, Shapiro and Homem-De-Mello (2001), Verweij et al. (2003) for stochastic integer problems, and Wei and Realff (2004), Goyal and Ierapetritou (2007) for MINLP problems. Problem (7.15) can be solved iteratively in order to provide statistical bounds on the optimality gap of the obj ective function value. For details and proofs see N orkin, Pflug and Ruszczysk (1998) and Mark, Morton and Wood (1999). The procedure consists of a number of steps as described in the following section. 

In particular, Shapiro and others calculated state-to-state photodissociation cross sections from vibrationally excited states of HCN and DCN [58], N2O [59], and O3 [60]. Eor instance, the detailed product-vibrational state distributions and absorption spectra of HCN(DCN) were compared [58]. These results were obtained employing a half-collision approximation, where the photodissociation could be depicted as consisting of two steps, that is, absorption of the photon and the dissociation, as well as an exact numerical integration of the coupled equations. In particular, it was predicted that large isotope effects can be obtained in certain regions of the spectrum by photodissociation of vibrationally excited molecules. 

However, the question as to whether the first methylation step, the conversion from noradrenaline to adrenaline, is an active process over-all in the body should be susceptible of fairly easy study by repeating the experiments of Richter and Macintosh (12) and of Beyer and Shapiro (4) but administering noradrenaline instead of adrenaline. The urine-excreted compounds could be bioassayed after suitable hydrolysis and the relative amounts of noradrenaline and adrenaline in the hydrolyzate determined by using the differential activities of the two compounds on rabbit intestine and rat uterus as first reported by West (16). The differences between normal persons and those in successive stages of essential hypertension with regard to their abilities to conjugate noradrenaline and adrenaline and with regard to their abilities to transform the former into the latter surely should be a subject of precise chemical study in the near future. 

Gerbasi D, Brumer P, Thanopulos I, Krai P, Shapiro M. Theory of the Two Step Enantiomeric Purification of Dimethylallene . J. Chem. Phys.. submitted. 

What is the mechanism of the cyclopropanation step g How does this step differ in the number of equivalents of base required with respect to a Shapiro reaction ... 

Finally, hindered arenesulfonylhydrazones can undergo addition of the alkyllithium rather than deprotonation, and, in fact, the normal Shapiro conditions generally do not give any alkene if an a-methine proton must be removed in the initial deprotonation step. Shapiro reported that the use of LDA overcomes the problem,but there are later examples in which this modification is ineffective. In one such case, lithium t-butylamide proved to be superior (Scheme 72) and in another it proved necessary to re-son to the aforementioned N-aminoaziridine derivative in an aprotic Bamford-Stevens reaction, when the normal Shapiro and Bamford-Stevens conditions failed (Scheme 73). ... 

The conversion of ketone 38 to alkene 40 in the context of Winterfeldt s synthesis of (-)-myltaylenol was accomplished in two steps using classical conditions for the Shapiro reaction.22 The tosylhydrazone 39 was generated cleanly from 38 in near quantitative (98%) yield. Treatment of 39 with excess n-BuLi provided 40 in 90% yield. 

A synthetic route that provides rapid access to the tetracyclic core of ingenol was recently described by Cha in which a Shapiro reaction is used for the construction of a key C-C bond.23 As shown below, treatment of trisylhydrazone 41 with two equivalents of r-BuLi followed by addition of hindered ketone 42 provided allylic alcohol 43 in 75-88% yield. The carbonyl addition occurred with high diastereoselectivity for approach of the nucleophile from the less hindered face. Alcohol 43 was converted to the tetracyclic core of the natural product (44) via a 7-step sequence. 

The Shapiro reaction has also been employed as a key step in Sorensen s synthesis of (-)-hispidospermidin.24 As shown below, Shapiro reaction of 45 followed by transmetalation to Mg and trapping with pyruvate derivative 46 provided 47 in 55% yield as a single diastereomer. 

Manipulation of the carbonyl function to epoxide 3 was accomplished by conversion to the tosylhydrazone, Shapiro olefination, and epoxidation.The latter step occurred with high ster-eocontrol, as did the epoxide ring opening with acidic methanol. Oxidation to ketone 4 was then performed, and from this product the desired derivative 5 was obtained by known procedures. 

In the saussurea lactone synthesis by Grieco (Scheme 31) [18], cleavage of the C(2)-C(3) link was carried out by ozonolysis of the C(2)-C(3) double bond in compound 247, obtained regioselectively from tetrahydrosantonin 3b by a Shapiro reaction, to give diol 51. Subsequent elimination of both hycftoxyl groups in several steps yielded saussurea lactone (56). An improvement of tWs procedure, described by our group [17], was based on the transformation of diol 51 into diselenide 52, which could then be transformed directly into saussurea lactone (56) (see Scheme 8). 

A vinylogous Shapiro reaction was used in a four-step synthesis of bicyclic diene (7) from n-pincne (4). In place of the usual base (methyllithium), 4 equiv. 

If the function g(x) is twice differentiable, then the above sample path method produces estimators that converge to an optimal solution of the true problem at the same asymptotic rate as the stochastic approximation method, provided that the stochastic approximation method is applied with the asymptotically optimal step sizes (Shapiro 1996). On the other hand, if the underlying probability distribution is discrete and g(x) is piecewise linear and convex, then w.p.l the sample path method provides an exact optimal solution of the true problem for N large enough, and moreover the probability of that event approaches one exponentially fast as A — (Shapiro and Homem-de-MeUo 1999). 

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