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In nature, methoxy groups are found on nucleosides that have been subjected to 2′-O-methylation, for example in variations of the 5′-cap structure known as cap-1 and cap-2. They are also common substituents in O -methylated flavonoids , whose formation is catalyzed by O-methyltransferases that act on phenols , such as catechol- O -methyl ...
In organic chemistry, a functional group is a substituent or moiety in a molecule that causes the molecule's characteristic chemical reactions.The same functional group will undergo the same or similar chemical reactions regardless of the rest of the molecule's composition.
If M is a module over a ring R, then the support of M as a module coincides with the support of the associated quasicoherent sheaf ~ on the affine scheme Spec R. Moreover, if { U α = Spec ( R α ) } {\displaystyle \{U_{\alpha }=\operatorname {Spec} (R_{\alpha })\}} is an affine cover of a scheme X , then the support of a quasicoherent ...
The kernel of a module homomorphism f : M → N is the submodule of M consisting of all elements that are sent to zero by f, and the image of f is the submodule of N consisting of values f(m) for all elements m of M. [4] The isomorphism theorems familiar from groups and vector spaces are also valid for R-modules.
In this type of substitution reaction, one group of the substrate participates initially in the reaction and thereby affects the reaction. A classic example of NGP is the reaction of a sulfur or nitrogen mustard with a nucleophile, the rate of reaction is much higher for the sulfur mustard and a nucleophile than it would be for a primary or secondary alkyl chloride without a heteroatom.
To relate an octahedral fragment, ML n, where M has a d x electron configuration to a square planar analogous fragment, the formula ML n−2 where M has a d x+2 electron configuration should be followed. Further examples of the isolobal analogy in various shapes and forms are shown in figure 8.
For example, sulfuric acid (H 2 SO 4) is a diprotic acid. Since only 0.5 mol of H 2 SO 4 are needed to neutralize 1 mol of OH −, the equivalence factor is: f eq (H 2 SO 4) = 0.5. If the concentration of a sulfuric acid solution is c(H 2 SO 4) = 1 mol/L, then its normality is 2 N. It can also be called a "2 normal" solution.
This definition reflects the close connection between the polynomial hierarchy and the arithmetical hierarchy, where R and RE play roles analogous to P and NP, respectively. The analytic hierarchy is also defined in a similar way to give a hierarchy of subsets of the real numbers .