sigma

(noun)

The symbol $\Sigma$, used to indicate summation of a set or series.

Related Terms

Examples of sigma in the following topics:

  • Regulation of Sigma Factor Activity

    • Sigma factors are proteins that function in transcription initiation .
    • The activity of sigma factors within a cell is controlled in numerous ways.
    • However, if transcription of genes is not required, sigma factors will not be active.
    • The anti-sigma factors will bind to the RNA polymerase and prevent its binding to sigma factors present at the promoter site.
    • The anti-sigma factors are responsible for regulating inhibition of transcriptional activity in organisms that require sigma factor for proper transcription initiation.

  • Regulation of Sigma Factor Translation

    • Sigma factor expression is often associated with environmental changes that cause changes in gene expression .
    • Sigma factors include numerous types of factors.
    • The most commonly studied sigma factors are often referred to as a RpoS proteins as the rpoS genes encode for sigma proteins of various sizes.
    • Specifically, the translational control of the sigma factor is a major level of control.
    • The translational control of sigma factors involves the presence and function of small noncoding RNAs.

  • Variance Sum Law II

  • Rosseland Approximation

    • $\displaystyle I_\nu (z,\mu ) = S_\nu - \frac{\mu}{\alpha_\nu +\sigma_\nu} \frac{\partial I_\nu}{\partial z}.$
    • $\displaystyle F_\nu(z) = \int I_\nu^{(1)} \cos\theta d \Omega = -2\pi \frac{\partial B_\nu}{\partial z} \frac{1}{\alpha_\nu +\sigma_\nu} \int_{-1}^{+1} \mu^2 d \mu \\ \displaystyle = -\frac{4\pi}{3} \frac{1}{\alpha_\nu +\sigma_\nu} \frac{\partial B_\nu}{\partial z} = -\frac{4\pi}{3} \frac{1}{\alpha_\nu +\sigma_\nu} \frac{\partial B_\nu}{\partial T} \frac{\partial T}{\partial z}$
    • $\displaystyle \frac{1}{\alpha_R} \equiv \frac{\int_0^\infty \left (\alpha_\nu +\sigma_\nu\right)^{-1} \frac{\partial B_\nu}{\partial T} d\nu}{\int_0^\infty \frac{\partial B_\nu}{\partial T} d\nu} = \frac{\pi}{4\sigma T^3} \int_0^\infty \left (\alpha_\nu +\sigma_\nu\right)^{-1} \frac{\partial B_\nu}{\partial T} d\nu$
    • where $\alpha_R$ is the Rosseland mean absorption coefficient.In stellar astrophysics one often uses the column density $\Sigma$ as the independent variable rather than $z$, $d\Sigma = \rho dz$.Making the substitution yields
    • $\displaystyle F(z) = -\frac{16 \sigma T^3}{3\alpha_R} \rho \frac{\partial T}{\partial \Sigma}.= -\frac{16 \sigma T^3}{3\kappa_R} \frac{\partial T}{\partial \Sigma}

  • Probability

    • This probability distribution has the mean and variance, denoted by $\mu$ and $\sigma ^2$, respectively.
    • As shown below, the probability to have $x$ in the range $[\mu - \sigma, \mu + \sigma]$ can be calculated from the integral
    • Probability distribution function of a normal (or Gaussian) distribution, where mean $\mu=0 $  and variance $\sigma^2=1$.

  • Examining the standard error formula

    • If X and Y are two random variables with variances $\sigma^2_{x_1}$ and $\sigma^2_y$, then the variance of X−Y is $\sigma^2_x+\sigma^2_y$.
    • Likewise, the variance corresponding to $\bar{x}_1-\bar{x}_2$ is $\sigma^2_{x_1}+\sigma^2_{x_2}$.
    • Because $\sigma^2_{x_1}$ and $\sigma^2_{x_2}$are just another way of writing $SE^2_{x_1}$and $SE^2_{x_2}$, the variance associated with $\bar{x_1}-\bar{x_2}$ may be written as $SE^2_{x_1}+SE^2_{x_2}$.

  • Operations-Management Tools

    • Six Sigma and Lean are two popular operations-management theories that help managers improve the efficiency of their production processes.
    • In order to accomplish this task, managers utilize various tools, two of the most influential being Six Sigma and Lean.
    • Six Sigma is a strategy designed to improve the quality of process outputs.
    • In many ways, Lean manufacturing and Six Sigma is reminiscent of Henry Ford and systematic process improvements.
    • Lean and Six Sigma are the two main tools for managers in operations management.

  • Series and Sigma Notation

    • Sigma notation, denoted by the uppercase Greek letter sigma $\left ( \Sigma \right ),$ is used to represent summations—a series of numbers to be added together.
    • One way to compactly represent a series is with sigma notation, or summation notation, which looks like this:
    • The main symbol seen is the uppercase Greek letter sigma.

  • Single Covalent Bonds

    • Single covalent bonds are sigma bonds, which occur when one pair of electrons is shared between atoms.
    • The strongest type of covalent bonds are sigma bonds, which are formed by the direct overlap of orbitals from each of the two bonded atoms.
    • Regardless of the atomic orbital type, sigma bonds can occur as long as the orbitals directly overlap between the nuclei of the atoms.
    • These are all possible overlaps between different types of atomic orbitals that result in the formation of a sigma bond between two atoms.

  • Driven Harmonic Oscillator

    • $\omega \ll\ \omega_0: \sigma(\omega) \rightarrow \sigma_T \left (\frac{\omega}{\omega_0} \right )^4 $