An organ forming the maternal–fetal exchange interface during pregnancy. Exchange occurs across specialized tissue barriers rather than requiring unrestricted mixing of maternal and fetal blood.

Maternal endometrial tissue modified during pregnancy. It contributes to the maternal side of the placental interface, distinguishing it from fetal trophoblast and other fetal placental tissues.

A dating measure conventionally reckoned from the first day of the last menstruation, rather than directly from observed fertilization.

Spontaneous loss of a pregnancy before the locally specified threshold of viability. The definition uses a clinical convention, while the underlying causes and stage of development vary.

A pregnancy implanted outside the normal endometrial cavity; tubal rupture can cause severe internal haemorrhage.

An abnormal gestation with disordered trophoblastic proliferation and characteristic changes in placental villi. Complete and partial forms differ genetically and developmentally, so the term does not imply one uniform fetal or placental outcome.^[ref]

Rebound felt after displacement of a mobile object in fluid. In a suitable obstetric setting it is a probable sign of pregnancy, not by itself proof of a living fetus.

The mother's first perception of fetal movement; a symptom rather than an independent examiner's demonstration.

Movement produced by a fetus, detectable through maternal perception or observation. The first subjective perception is quickening; perception and a direct measurement of movement are different kinds of evidence.

A historical linseed-based poultice. The preparation illustrates use of hydrated plant material as a local dressing; an edition-specific formula is distinct from a general assertion of therapeutic efficacy.^[ref]

A historical charcoal-containing poultice. Its ingredients and preparation belong to a specified pharmacopoeial edition, distinguishing a named historical formulation from a universally standardized modern product.^[ref]

A historical yeast-based poultice. Its official composition depends on the pharmacopoeial edition; the name identifies the preparation rather than evidence that its historical therapeutic rationale was correct.^[ref]

For a fixed impermeable sphere of radius $a$ and incident uniform flow $U{\mathbf{e}}_z$, the velocity potential is the displayed expression and the Stokes streamfunction is $\Psi =(U/2)(r^2-a^3/r){\sin }^2\theta$. Differentiation gives $u_r=U(1-a^3/r^3)\cos \theta$ and $u_{\theta }=-U(1+a^3/(2r^3))\sin \theta$. Thus the no-penetration boundary condition holds, the poles are stagnation points, and the equatorial surface speed is $3U/2$. The disturbance is a potential dipole decaying as $r^{-3}$ in velocity. The sphere theorem for a Stokes streamfunction constructs this solution from ${\Psi }_0=U{r}^2{\sin }^2\theta /2$.

For a planar potential flow outside a bounded body, suppose its single-valued complex velocity $q=u-iv$ is holomorphic near infinity and tends to zero. Its exterior Laurent series begins $q=b_1/z+O(z^{-2})$. The outward volume flux $Q$ and counterclockwise circulation $\Gamma$ satisfy $\Gamma +iQ=2\pi i{b}_1$. Thus both vanish precisely when the leading term is absent. A nonzero $b_1$ gives $|q{|}^2\sim |b_1{|}^2/r^2$ and logarithmically divergent exterior kinetic energy. When $b_1=0$, $q=O(r^{-2})$ and the far-field energy integral converges. Zero circulation alone does not exclude the radial source field $\nabla \log r$.

For a smooth constant-density exterior potential flow satisfying the finite-energy condition for planar exterior potential flow, use $\mathbf{u}=\nabla \varphi$ and the planar streamfunction convention $u={\psi }_y$, $v=-{\psi }_x$. Since ${\nabla }^2\varphi =0$, $\nabla \cdot (\varphi \nabla \varphi )=|\mathbf{u}{|}^2$. Apply the divergence theorem to a truncated exterior region. The outer term vanishes; on a counterclockwise body boundary the body's outward normal satisfies ${\partial }_n\varphi ds=d\psi$, while the fluid's outward normal points the opposite way. This gives the displayed kinetic energy per unit span. The formula yields the added mass of a circular cylinder directly from its surface values of $\varphi$ and $\psi$.

For $0<a<1$, the Joukowski map $z=\zeta +a^2/\zeta$ maps the exterior unit circle to an ellipse of horizontal and vertical semiaxes $1+a^2$ and $1-a^2$. The Milne-Thomson circle theorem gives $W(\zeta )=U(e^{-i\alpha }\zeta +e^{i\alpha }/\zeta )$ for a uniform flow inclined by $\alpha$. The chain rule produces the displayed complex velocity in the physical plane. Since $z\sim \zeta$, the far-field flow retains its speed and direction. Its two stagnation points areobtained from $\zeta =\pm e^{i\alpha }$. The map derivative is nonzero on and outside the unit circle, so these zeros are preserved without introducing a boundary singularity.

The Kutta condition selects the circulation of an idealized potential flow past a body with a sharp trailing edge by requiring finite limiting velocity at that edge. For the Joukowski map $z=\zeta +a^2/\zeta$, the trailing edge $z=2a$ corresponds to a simple zero of $dz/d\zeta$ at $\zeta =a$. If $W$ is the complex potential in the circle plane, then $dw/dz=W^{\prime }(\zeta )/(1-a^2/{\zeta }^2)$ is finite there only if $W^{\prime }(a)=0$. For a uniform flow of speed $U$ at angle $\alpha$ and a point vortex of circulation $\Gamma$, this gives $\Gamma =-4\pi Ua\sin \alpha$, and cancellation of the simple zeros gives the tangential trailing-edge velocity $U\cos \alpha$. The opposite endpoint can retain a leading-edge singularity.

A uniform planar stream combined with an equal source and sink produces a closed dividing streamline enclosing them. Outside it the flow approaches the uniform stream; inside it streamlines connect the source and sink. For positive $U,m$ and separation one, the complex velocity is $U-m/[2\pi z(z-1)]$ and the stagnation points are $[1\pm \sqrt{1+2m/(\pi U)}]/2$. Both lie on the dividing streamline, which has zero streamfunction with consistent logarithm branches.

Postmortem muscular stiffening associated with loss of sufficient ATP to maintain normal detachment of actin–myosin cross-bridges. It is distinct from freezing and heat coagulation.

Here ${\varphi }_u(x)$ counts increasing position embeddings of the word $u$ as a subsequence of $x$. Counting embeddings retains repeated-letter multiplicities. The empty word has one embedding in every string. Prefix dynamic programming computes this positive-semidefinite kernel by $F(i,j)=F(i-1,j)+F(i,j-1)-F(i-1,j-1)+1_{\{x_i=y_j\}}F(i-1,j-1)$ with boundary values one. The time complexity is $O(|x||y|)$ arithmetic operations, and rolling rows require $O(\min (|x|,|y|))$ integer cells. Counting pairs of position subsets bounds output bit length by $O(|x|+|y|)$.