Multiring system

From Multiring Systems Containing Pyrazoles. The pyrazolopyrimidine (65) on treatment with diazomethane forms the cyclopropane (66), which undergoes a ring-opening reaction with potassium hydroxide to yield the pyrazole (67) (eq. 16) (44). 

Hanusch-Kompa C, Ugi I (1998) Multi-component reactions 13 synthesis of [gamma]-lactams as part of a multiring system via Ugi-4-centre-3-component reaction. Tetrahedron Lett 39(18) 2725-2728... 

Vaidyanathan, 1993] Vaidyanathan, P. (1993). Multirate Systems and Filter Banks. PrenticeHall, Englewood Cliffs, NJ. 

The compact multiring systems have a number of very interesting properties which will be discussed below, and although some progress has been made toward synthesis of these heterocycles, none has yet been completed. 

Aryne cycloadditions have been coupled with radical cyclizations to rapidly assemble multiring systems For example, benzyne addition to furan 278 followed by radical cyclization onto the newly formed double bond gave 280 in two steps and fair yield. 

As will be apparent, the problems involved in deciding how to name a multiring heterocyclic skeleton are considerably greater than those for monocycles. However, with regard to the systems recommended above, it is possible to give some general advice as to when and how these systems should be used. 

Zoelzer et al., 1990] Zoelzer, U., Fleige, N., Schonle, M., and Schusdziara, M. (1990). Multirate Digital Reverberation System . In Proc. Audio Eng. Soc. Conv. Preprint 2968. 

Another possibility would be to use a multirate code which integrates each differential equation individually using different step sizes. Orailoglu (16) and Gear (17) discuss this approach but their procedure uses multistep Jacobian methods which are not efficient for our system of equations. What we need is a fixed order single step multirate method. 

The pulse height window cuts off a large fraction of the scattered radiations, which is limited by the width of the window. In 2D acquisition, the use of septa in multiring PET systems removes additional scattered events, whereas in 3D acquisition, they become problematic because of the absence of septa. Typically, the scatter fraction ranges from 15% in 2D mode to more than 40% in 3D mode for modern PET scanners. 

Amino-3-morpholino-1H-1,2,4-triazol-1 -yl)-A-methylcarbothiohydrazides 55 are the starting compounds for the synthesis of the novel 7,5-bicyclic systems 56 and 57. Further reactions and rearrangements can lead to other multiring products <97JHC1575>. 

Topological isomers of linear [njcatenanes are the so-called multiring interlocked systems that bear a number of smaller rings all threaded on the saine larger macro-... 

Bitsch, F. Dietrich-Buchecker, C.O. Khemiss. A.-K. Sauvage. J.-P. Van Dorsselaer, A. Multiring interlocked systems Structure elucidation by electrospray mass spectrometry. J. Am. Chem. Soc. 1991. 113. 4023-4025. 

Kern. J.-M. Sauvage, J.-P. Weidemann. J.-L. Multiring interlocked systems via transition metal-templated strategy The single-cyclization synthesis of [3]-catenates. 1. Tetrahedron 8996, 52. 10921-10934. 

Multiring interlocking systems will be considered in the second section. Remarkable X-ray structures will be included, especially those of a free [3]catenane and of a dicopper(I) complex. 

Figure 14 Template synthesis of multiring catenanes. The coordination fragments are drawn in thick lines and the triangles represent the terminal acetylenic functions. The systems obtained are made of w +1 peripheral rings interlocked to a large central ring resulting from a cyclooligomerization process.

Daws, C. Yovine, S. (1995). Two examples of verification of multirate timed automata with kronos. Proceedings of the 16th IEEE Real-Time Systems Symposium (RTSS 95), IEEE Computer Society, Washington, DC, USA, p. 66. 

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