Examples of R group in the following topics:
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- An amino acid contains an amino group, a carboxyl group, and an R group, and it combines with other amino acids to form polypeptide chains.
- Every amino acid also has another atom or group of atoms bonded to the central atom known as the R group.
- There are 21 amino acids present in proteins, each with a specific R group or side chain.
- The 21st amino acid, not shown here, is selenocysteine, with an R group of -CH2-SeH.
- Amino acids have a central asymmetric carbon to which an amino group, a carboxyl group, a hydrogen atom, and a side chain (R group) are attached.
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- Note that the nucleophile (Nuc) uses a lone pair of electrons to form a bond with the carbon at R (which represents a carbon-containing structure), and the electrons from the R-LG bond end up attached to the leaving group (LG).
- The LG: species can have a neutral or negative charge, but the R group must be positive after it detaches.
- Leaving groups are almost always negative.
- In SN2, the nucleophile "pushes" the leaving group off the carbon in the R group.
- SN2 is known as a "backside" reaction: it always occurs opposite the R-LG bond.
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- Functional groups are groups of molecules attached to organic molecules and give them specific identities or functions.
- Functional groups are groups of atoms that occur within organic molecules and confer specific chemical properties to those molecules.
- When functional groups are shown, the organic molecule is sometimes denoted as "R."
- This carboxyl group ionizes to release hydrogen ions (H+) from the COOH group resulting in the negatively charged COO- group; this contributes to the hydrophilic nature of whatever molecule it is found on.
- The functional groups shown here are found in many different biological molecules, where "R" is the organic molecule.
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- X = the number of items from the group of interest that are in the chosen sample.
- X may take on the values x= 0, 1, ..., up to the size of the group of interest.
- r = the size of the group of interest (first group)
- The standard deviation is: .$ \sigma = \sqrt{\frac{rbn ( r + b + n )}{( r + b )^2 ( r + b 1)}}$
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- Suppose, in a fictitious experiment, 4 subjects in an Experimental Group and 4 subjects in a Control Group are asked to solve an anagram problem.
- Three of the 4 subjects in the Experimental Group and none of the subjects in the Control Group solved the problem.
- where N is the total sample size (8), n is the sample size for the first group (4), r is the number of successes in the first group (3), and R is the total number of successes (3).
- This is a one-tailed probability since it only considers outcomes as extreme or more extreme favoring the Experimental Group.
- An equally extreme outcome favoring the Control Group is shown in Table 2, which also has a probability of 0.0714.
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- Read this as "X is a random variable with a hypergeometric distribution. " The parameters are r, b, and n. r = the size of the group of interest (first group), b = the size of the second group, n = the size of the chosen sample
- The men are the group of interest (first group).
- X takes on the values 0, 1, 2, 3, 4, where r = 6, b = 5 , and n = 4.
- The formula for the mean is µ = (n.r)/(r + b) = (4 .6)/(6 + 5) = 2.18
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- It is an extension of the Mann–Whitney $U$ test to 3 or more groups.
- Rank all data from all groups together; i.e., rank the data from $1$ to $N$ ignoring group membership.
- and where $\bar{r} = \frac{1}{2} (N+1)$ and is the average of all values of $r_{ij}$, $n_i$ is the number of observations in group $i$, $r_{ij}$ is the rank (among all observations) of observation $j$ from group $i$, and $N$ is the total number of observations across all groups.
- $\begin{aligned}
K &= \frac{12}{N(N+1)} \cdot \sum_{i=1}^g n_i \left( \bar{r}_{i \cdot} - \dfrac{N+1}{2}\right)^2 \\
&= \frac{12}{N(N+1)} \cdot \sum_{i=1}^g n_i \bar{r}_{i\cdot}^2 - 3 (N+1)
\end{aligned}$
- where $G$ is the number of groupings of different tied ranks, and $t_i$ is the number of tied values within group $i$ that are tied at a particular value.
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- An ether group is an oxygen atom connected to two alkyl or aryl groups.
- They follow the general formula R-O-R'.
- The general formula is R-O-O-R'.
- Ethers can be formed in the laboratory through the dehydration of alcohols (2R-OH → R-O-R + H2O at high temperature), nucleophilic displacement of alkyl halides by alkoxides (R-ONa + R'-X → R-O-R' + NaX), or electrophilic addition of alcohols to alkenes (R2C=CR2 + R-OH → R2CH-C(-O-R)-R2).
- An ether is characterized by an oxygen bonded to two alkyl or aryl groups, represented here by R and R'.
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- $\displaystyle \left [ -\frac{\hbar^2}{2 \mu_{AB}} \left ( \frac{d^2}{dR^2} - \frac{L(L+1)}{R^2} \right ) + E_j({\bf R}) - E \right ] F_j({\bf R}) = 0 $
- $\displaystyle E_j(R) = E_j(R_0) + (R-R_0) \left [ {E_j(R)}{R} \right ]_{R=R_0} + \frac{1}{2} (R-R_0)^2 \left [ \frac{d^2 E_j(R)}{d R^2} \right ]_{R=R_0} + \cdots$
- $\displaystyle \left [ -\frac{\hbar^2}{2 \mu_{AB}} \frac{d^2}{dR^2} - \frac{\hbar^2}{2\mu_{AB}} \frac{L(L+1)}{R^2} + E_j(R_0) + \frac{1}{2} k (R-R_0)^2 - E \right ] F_j({\bf R}) = 0 $
- $\displaystyle |d| = Z_1 e r_1 + Z_2 e r_2 + |d_e| \neq 0 $
- In general each vibration transition includes a rotational transition as well so one gets group of transitions.
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- In quantum mechanics we characterize the state of a particles (or group of particles) by the wavefunction ($\Psi$).
- $\displaystyle \left( -\frac{\hbar^2}{2m} \sum_j \nabla_j^2 - E - Ze^2 \sum_j \frac{1}{r_j} + \sum_{i>j} \frac{e^2}{r_{ij}} \right ) \psi ({\bf r}_1,{\bf r}_2,\ldots,{\bf r}_j) = 0$
- $\displaystyle \left( \frac{1}{2} \sum_j \nabla_j^2 + E - Z \sum_j \frac{1}{r_j} + \sum_{i>j} \frac{1}{r_{ij}} \right ) \psi ({\bf r}_1,{\bf r}_2,\ldots,{\bf r}_j) = 0$