A scanning electron microscope permitting a controlled gaseous specimen environment while maintaining the electron column at lower pressure by differential pumping. Ionization of the gas supplies positive ions that can neutralize negative specimen charging, and a suitable gaseous detector collects electron signals. This enables examination of some nonconducting uncoated specimens, with gas scattering and detector response included in interpretation.

Image contrast from changes in secondary-electron escape and collection as surface slope, edges and detector-facing geometry vary. Secondary electrons originate near the surface, but brightness also depends on material, charging and the beam conditions.

Composition-sensitive contrast associated with the generally larger electron backscattering yield of higher-atomic-number regions. Detector geometry, crystal orientation, surface topography and beam energy can also affect intensity, so a bright region is not a unique elemental identification.

An Early Triassic stem frog from Madagascar with an anteriorly elongated ilium, a retained short tail and incompletely transformed limbs. CT redescription identified 15 presacral vertebrae rather than the traditional count of 14.

An Early Jurassic frog relative with a derived caudopelvic apparatus interpreted as consistent with jumping.

For the affinely parametrized geodesic Lagrangian $\mathcal{L}=({\dot{r}}^2+f(r{)}^2{\dot{\varphi }}^2)/2$, the conserved cyclic momentum is $J=f(r{)}^2\dot{\varphi }$. Its Euler-Lagrange equations are $\ddot{r}-f{f}^{\prime }{\dot{\varphi }}^2=0$ and $\ddot{\varphi }+2f^{\prime }\dot{r}\dot{\varphi }/f=0$.

The entropy contribution from populated molecular rotational states. A nonlinear rigid rotor has $q_{\mathrm{rot}}\propto T^{3/2}$ at high temperature, giving $S_{\mathrm{rot},\mathrm{m}}=R(\ln q_{\mathrm{rot}}+3/2)$. Its rotational symmetry number removes redundant orientations.

If each initially stationary ball is released at height $h$ and the subsequent isolated dilute assembly reaches effective classical equilibrium, energy conservation gives $4k_{B}T=mgh$. The height-tail probability above the release height is then $e^{-4}$. The effective temperature refers to mechanical motion, not the material's internal temperature.

A polynomial root that is an integer. For a polynomial with integer coefficients and nonzero constant term, any integer root divides that constant term, by the rational root theorem.

For a circular synchronized binary star, this approximates the volume-equivalent Roche lobe radius, where $q$ is the enclosed star's mass divided by its companion's mass. It describes critical equipotential geometry; it does not give the star's radius response to mass loss. The primary calculation reports radius errors below about one percent across the mass-ratio range.^[ref]

The eukaryotic polymerase responsible for transcription of protein-coding genes and several noncoding transcripts. Its C-terminal-domain phosphorylation state helps regulate elongation.

An RNA polymerase that uses RNA as its template. In some RNA interference pathways it helps generate substrates for small-RNA production.

A protein that confers promoter-recognition specificity on a bacterial-type RNA polymerase. Plastid sigma factors can be nuclear encoded and imported.

RNA polymerase IV is a specialized plant nuclear RNA polymerase required for major small-RNA-dependent silencing pathways. Its transcripts are used with an RNA-dependent polymerase to generate precursors of small interfering RNAs. These help guide RNA-directed DNA methylation, while RNA polymerase V contributes a distinct scaffold-transcript function. Mutating conserved catalytic motifs disrupts silencing, supporting a requirement for polymerase activity rather than only structural presence. ^[ref]

RNA polymerase V is a plant nuclear RNA polymerase involved in RNA-directed DNA methylation. It produces noncoding transcripts that help recruit silencing machinery to selected genomic regions. Its role differs from RNA polymerase IV, which contributes to the small-RNA-generating arm of the pathway. These specialized polymerases connect transcription to repression, illustrating that making RNA need not imply productive expression of a protein-coding gene. ^[ref]

For the standard right-wedge hyperbola and a stationary source at $x=L$ emitting rightmoving photons, the retarded null coordinate is $p=t-x=-e^{-a\tau }/a$. Equating it to the emission value $t_e-L$ gives the displayed reception relation. Differentiating yields the Doppler frequency ratio $\nu /{\nu }_0=d{t}_e/d\tau =e^{-a\tau }$. The limiting emission time $L$ is a supremum: emission exactly at that time is never received at finite proper time. These expressions use $c=1$ and acceleration continued indefinitely.

A leg of a right triangle is either of the two sides meeting at the right angle. The opposite side is the hypotenuse. For leg lengths $a,b$ and hypotenuse $c$, the Pythagorean theorem gives $a^2+b^2=c^2$, while the area is $ab/2$. In the $3$-$4$-$5$ right triangle, the legs have lengths three and four. Relative to an acute angle, one leg is adjacent and the other opposite; these names depend on the chosen angle.

Controlled radical polymerization based on reversible trapping of growing radicals by a nitroxide, forming dormant alkoxyamines. Initiation and end-group retention must be controlled to obtain predictable chain length.

For $g(t)=\alpha e^{-\alpha |t|}/2$ with $\alpha >0$, convolution givesThe coordinate and velocity are continuous at zero. At late times the undamped oscillation has amplitude ${\alpha }^2/(1+{\alpha }^2)$; causality fixes the homogeneous solution only after the no-incoming-oscillation condition is specified.