Online text: www.feynmanlectures.caltech.edu/I_20.html

Cited passages: Richard P. Feynman, Robert B. Leighton and Matthew Sands, The Feynman Lectures on Physics, volume I, section 20-4: nonparallel angular momentum and angular velocity, principal axes, and rotational energy.

Online text: www.feynmanlectures.caltech.edu/I_19.html

Cited passages: Feynman, Leighton and Sands, The Feynman Lectures on Physics, volume I, sections 19-3 and 19-4: perpendicular distance to an axis and its relation to rotational energy.

Online text: www.ncbi.nlm.nih.gov/books/NBK9870/

Cited passages: Cooper, The Cell: A Molecular Approach, 2nd edition (2000), Pathways of Intracellular Signal Transduction: repeated receptor/relay activation and second-messenger production as amplification mechanisms.

Cited passages: Cooper, The Cell, 2nd edition: amplification in the cAMP pathway; Cooper, The Cell, 2nd edition: cAMP formation and degradation.

By Ming Gu.

Online text: www.netlib.org/utk/people/JackDongarra/etemplates/node95.html

Online text: www.netlib.org/utk/people/JackDongarra/etemplates/node211.html

Cited passages: Hermitian Eigenvalue Problems → Single- and Multiple-Vector Iterations → Power Method, introductory paragraph: largest absolute eigenvalue and corresponding eigenvector; Hermitian Eigenvalue Problems → Single- and Multiple-Vector Iterations → Power Method, paragraph after the angle definition: perpendicular starting vector fails to select the dominant eigenvector in exact arithmetic.

Cited passages: Non-Hermitian Eigenvalue Problems → Single- and Multiple-Vector Iterations → Power Method, convergence paragraph: largest magnitude eigenvalue and spectral-ratio rate.

Type II superstring theory is a ten-dimensional closed oriented superstring theory with spacetime supersymmetry and no tachyon. Its massive closed-string levels have squared masses separated by $4/{\alpha }^{\prime }$.

An unoriented theory containing open and closed superstrings. Consistent gauge and gravitational anomaly cancellation yields the familiar $\mathfrak{so}(32)$ gauge algebra. Open-string Chan-Paton factors supply the gauge degrees of freedom, while closed strings contain gravity. It is related by strong/weak duality to the corresponding heterotic theory.

If a density of states has high-energy growth proportional to a power of energy times $e^{{\beta }_{H}E}$, its canonical Boltzmann sum fails for $\beta <{\beta }_H$. The Hagedorn temperature is the corresponding threshold. The open bosonic string mass spectrum and large-level degeneracy of an open bosonic string give ${\beta }_H=4\pi \sqrt{{\alpha }^{\prime }}$ in units with Boltzmann's constant, the speed of light and Planck's constant set to one. Polynomial prefactors affect behavior at the threshold itself; the growth alone does not distinguish a limiting temperature from a phase transition.

A fundamental string is the perturbative string of a string-theory description. Its string tension is the displayed expression in the string metric. It couples to the Neveu–Schwarz two-form.

An NS5-brane has five spatial dimensions and is magnetically charged under the Neveu–Schwarz two-form. Its string-frame brane tension scales as $g_s^{-2}$.

A string duality identifies apparently different string theory descriptions as descriptions of the same physical system, with a map between their states, parameters and observables. It can exchange quantities interpreted very differently in the two descriptions, such as momentum and winding around a compact dimension.

T-duality relates a circle of radius $R$ to one of radius ${\alpha }^{\prime }/R$ by interchanging momentum and winding quantum numbers. A small geometrical circle in one description can therefore correspond to a large one in another; comparing only the classical geometry would miss the matching spectrum. S-duality instead relates coupling regimes and can turn a difficult strong-coupling question into a weak-coupling one. A proposed duality needs a concrete dictionary and consistency checks; a coincidental equality of one calculation is insufficient to establish equivalence of full theories.