Proof of claim

Since the projection n Q Q may be thought of as smooth, it follows that the symplectic structure w, the Hamiltonian field sgradff, and the integral /, 

8 Proof of Theorem 2.1,1, Lower Estimates on Number of Stable Periodic Solutions of a System 

By virtue of Theorem 2.1.2, we have for the following decomposition Q = m I II - -q III + rK, The corepresentation of a finitely generated group G with generators ai. and relations W i. Wm will be written as follows  

It is easy to calculate the fundamental groups of these five elementary bricks. We have  

Now we proceed to the proof of those assertions of Theorem 2.1.1 which contain the homology group Hi Q, Z). 

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In this example, Emily is only giving flat assertions with no proof of claim. Shira, on the other hand, describes her strengths. She readily admits her faults, hut also shows how she tries to overcome them. 

For the detailed proof of Claim 2.1.4, see [289] and [298]. For brevity we will prove only a simpler form of the inequality in Claim 2.1.4, namely. 

From Theorem 2.2.3 we immediately obtain an important corollary, namely, the proof of Claim 2.1.2 concerning the possibility to realise any three-dimensional manifold of class (Q) (that is, gluing an arbitrary number of elementary manifolds of types I, II, III) in the form of an isoenergy surface of some integrable Hamiltonian system on an appropriate symplectic manifold M. In other words, from Theorem 2.2.3 there immediately follows the equality (Q) = (H). 

However, the very existence of l,3-4H-oxazines was questioned by Smith and Adkins. They claimed that no sufficient proof of the structure (50) exists. It appears that the problem requires further investigation. 

There is essentially no other question which more vigorously splits the micro reactor and even the chemical community into groups of complete stances. There are even commentators who consider the proof of production feasibility of micro reactors as the central issue to be solved, like a conditio sine qua non . As an extreme view, they claim to see no other raison d etre for micro reactors or at least none of similar importance. 

Jaacks and his colleagues [17] have claimed that when they terminated dioxolan polymerisations with sodium ethylate, they could detect ethyl ethers. It seems to us that these results may very well be due to the same kind of impurity and/or side-reaction that gave us the involatile phenylether, and therefore this evidence alone cannot at present be taken as proof of their mechanism. 

The core first method has been applied to prepare four-arm star PMMA. In this case selective degradation of the core allowed unambiguous proof of the star structure. However, the MWD is a little too large to claim that only four-arm star polymers are present [81], Comb PMMAs with randomly placed branches have been prepared by anionic copolymerization of MMA and monodisperse PMMA macromonomers [82], A thorough dilute solution characterization revealed monodisperse samples with 2 to 13 branches. A certain polydispersity of the number of branches has to be expected. This was not detected because the branch length was very short relative to the length of the backbone [83]. Recently, PMMA stars (with 6 and 12 arms) have been prepared from dendritic... 

Pure 100% ethyl alcohol is a colorless, volatile hquid with a pungent taste. One hundred-proof alcoholic drinks are about 50% ethanol. When consumed, ethanol is a depressant and may be habit-forming. It rapidly oxidizes in the body, but even small amounts cause dizziness, nausea, headaches, and loss of motor control. Proof was how whiskey salesmen of the Old West demonstrated that their product was potent. They would place some gunpowder in a tin dish and then pour on some of their whiskey. If a match would ignite the mixture, this was claimed to serve as 100% proof of the whiskeys quality. It just happens that 100-proof whiskey is about 50% ethanol. 

In spite of the overwhelming importance of the channel mechanism for the transport of alkali and alkaline earth metal ions in biological systems, only carrier transport has been studied extensively by chemists. Studies on ion channel mimics of simple structures have long been limited to antibiotic families of gramicidin, amphotericin B, and others. Several pioneers have reported successful preparation of non-peptide artificial channels. However, their claims have been based on kinetic characteristics observed for the release of metal ions through liposomal membrane and lacked the very critical proofs of channel formation. Such a situation was... 

There was an early report of another benzo[c]furan, namely 1,3-diben-zoylbenzo[c]furan (197). Whereas all benzo[c]furans are known to be susceptible to oxidative cleavage, this compound has been reported to resist further oxidation. A structure proof of the substance claimed to be 197 seems desirable. 

Exercise 7.7 (For students of measure theory) Prove rigorously that all the claims of the last paragraph of the proof of Proposition 7.5 are true. For example, show that if q e well-defined element of... 

Direct bromination of a A -pyrazoline in dichloromethane has been claimed to give a 3//-pyrazole in high yield, but no spectroscopic proof of structure was given.110... 

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