A modeling language for describing software structures and behavior. A class diagram records types and relationships; a sequence diagram records ordered interactions; a state diagram records states and event-triggered transitions.

The anterior cranial fossa is the anterior depression of the internal skull base supporting the frontal brain regions. Its bony floor also relates to the orbit and nasal region. Thin partitions here connect intracranial anatomy to nearby sensory passages.

A cavity containing fluid produced by separation within or beneath the epidermis.

Visible reddening of skin, typically associated with increased superficial blood flow.

A small elevated lesion containing pus; it must be distinguished from a blister containing predominantly clear fluid.

A viral skin disease; a current approved topical cantharidin indication, distinct from the remote diseases for which historical counterirritation was advocated.

A hair follicle is an epithelial appendage-producing structure embedded in the skin. It generates a hair shaft through regulated cell proliferation and differentiation, with growth cycles changing its activity. It also interacts with supporting tissues rather than functioning as a detached miniature tube.

The rotator cuff is the group of shoulder muscles and tendons that surround and help stabilize the humeral head. Their coordinated activity supports movement as well as joint centering. Stability is therefore an active control problem in addition to a property of passive joint shape.

The deltoid muscle covers the shoulder with anterior, middle and posterior regions having different pulling directions. It contributes to arm elevation and position-dependent flexion or extension. Regional recruitment therefore matters when interpreting the force of the whole named muscle.

The biceps brachii crosses the shoulder and elbow and inserts toward the radius. It contributes to elbow flexion and forearm supination. Its effective action depends on joint position and load, connecting a familiar muscle name to a multi-joint mechanical problem.

The brachialis spans the anterior humerus to the ulna and flexes the elbow. Because its insertion is on the ulna, its leverage is less directly changed by forearm rotation than that of biceps brachii. This is an example of attachment geometry constraining muscle function.

The triceps brachii is the principal elbow-extensor muscle group of the posterior arm. Its heads join a tendon inserting at the ulna, while the long head also crosses the shoulder. Different joint positions can therefore affect the mechanical contribution of its components.

The admissibility conditions below concern a specified dimensionless shallow water equations model,where $h>0$ is water depth, $u$ is signed downstream velocity and $F$ is the reference Froude number. The square in this source term matters when interpreting a profile that changes the sign of $u$.

For an upstream-travelling wave profile in $\xi =x+ct$, $c>0$, starting from $(h,u)=(1,1)$, volume conservation gives $h(u+c)=1+c$. A second equilibrium at water depth $H>1$ on the negative-velocity branch has $u=-\sqrt{H}$, henceA positive denominator from $h=1$ requires $F<1/(1+c)=(H-1)/(H+H^{3/2})$.

To test whether the numerator stays positive before $H$, put $r=\sqrt{h}$ and $R=\sqrt{H}$. One factor has its only positive root at $r=1$; the other isThe first downstream endpoint is $r=R$ exactly when $1<R\le 2$, giving $1<H\le 4$. At $H=4$ the endpoint root is double. For larger $H$, an intervening equilibrium blocks the smooth connection.

These are algebraic admissibility conditions for the displayed source law. Along every such connection, $u=(1+c)/h-c$ crosses zero before reaching $H$. Physical signed quadratic drag instead involves $u|u|$, and replacing $u^2$ by $u|u|$ removes the negative-velocity equilibrium of this downhill-driven model. The conditions cannot therefore be applied to a complete reversing tidal current without specifying a consistent friction and forcing model.

A flat pool of depth $h_0$ between a wall at $-a$ and a removed dam at zero initially develops the shallow water equations rarefaction $u=2(c_0+x/t)/3$, $c=(2c_0-x/t)/3$, where $c_0=\sqrt{g{h}_0}$. It has $Q_{+}=u+2c=2c_0$ and front $x=2c_{0}t$. Its right-running characteristics satisfy $x_{+}=2c_{0}t+C{t}^{1/3}$, obtained by integrating $x_{+}^{\prime }-x_{+}/(3t)=4c_0/3$.

The first rarefaction signal reaches the wall at $(-a,a/c_0)$. The right-running characteristic through that event is the displayed curve. To its right the original fan remains valid; to its left reflected wall data alter the invariant. Continuing the original fan to the wall after that time would give nonzero wall velocity, contradicting impermeability. This is a concrete domain of dependence calculation for a nonlinear hyperbolic system.

In a quasi-one-dimensional inviscid channel with depth $H$ and width $b(x)=b_0{e}^{\mu x}$, the linear shallow water equations are ${\eta }_t+(H/b)(bu{)}_x=0$ and $u_t+g{\eta }_x=0$. Combining them gives ${\eta }_{tt}=gH({\eta }_{xx}+\mu {\eta }_x)$.

For a time dependence $e^{i\omega t}$, write the elevation amplitude as $N(x)=e^{-\mu x/2}V(x)$. The spatial equation becomesThere is a travelling spatial phase only when the bracket is positive, so the cutoff frequency is ${\omega }_c=\mu \sqrt{gH}/2$. Above it, an outgoing wave has a phase proportional to $\omega t-kx$ and amplitude proportional to $e^{-\mu x/2}$; below it the spatial response is evanescent. Geometric widening introduces the cutoff even though a constant-width channel has the nondispersive speed $\sqrt{gH}$.

The one-dimensional open-channel shallow water equations express conservation of water volume and depth-averaged momentum. Here $h$ is water depth, $u$ the mean velocity, $\eta$ the free-surface elevation and ${\tau }_b$ the resisting bed shear stress. The elevation includes the bed profile, so its gradient already includes gravitational driving by bed slope. A constant volume flux in space and time forces $h_t=0$ through the first equation; an unsteady reduction that imposes that flux while retaining momentum relaxation is consequently an approximation to this full system.

An incoming tide can form a moving surge that propagates upstream against a river's current. A discontinuous idealization is a shock wave of the shallow water equations, while weaker or dispersive bores can have an undular wave train. A boundary overtaking upstream-propagating characteristic curves warns that a smoothly attached quasi-steady description may fail; the appropriate discontinuity must satisfy the conservative jump conditions of the chosen model.

A hermaphrodite is an organism with both male and female reproductive functions. Those functions can occur together or at different times in the life history. The term concerns reproductive capacity, rather than requiring a particular external body shape.

Hermaphrodite individuals can still outcrossing: producing both kinds of gametes does not guarantee self-fertilization. Compatibility mechanisms and the timing or position of reproductive structures determine which combinations can actually form a zygote.

Conveying a session key selected by one participant to its intended users with the required secrecy and authentication. It differs from jointly contributing to a key-agreement calculation.

A fixed-width collection of flip-flops storing a binary representation. A synchronous load-enabled digital register captures all its input bits on the active clock edge when load is asserted and otherwise retains its old value. One multiplexer before each D flip-flop can select new data or feedback from its old output. A processor register is a particular use inside a processor; temporary state in a standalone binary multiplier is another.