Blood plasma is the fluid component of blood in which cells are suspended. It contains water, proteins and dissolved substances, including components of coagulation. Serum is obtained after clotting and therefore is not compositionally identical to plasma.

Formation of the cellular constituents of blood; normal adult production is chiefly associated with bone marrow.

A small cellular fragment produced by a megakaryocyte.

A linear time scan can retain the earliest start of the current monotone suffix, the earliest start of the current bitonic suffix, the most recent nonzero direction and the endpoint of its most recent strict step. At a strict direction reversal, the new bitonic suffix begins at the old monotone start; the new monotone suffix begins at the old strict-step endpoint. Zero differences leave these boundaries unchanged. The suffix invariants show that no longer valid suffix is discarded, and recording the largest length gives a global optimum using constant auxiliary storage.

The +3 oxidation state of bismuth. The actual aqueous species can depend on pH, hydrolysis and ligands; a bare ionic formula is an analytical shorthand.

For fixed nonnegative integer $n$, the row $\left(\genfrac{}{}{0ex}{}{n}{0}\right),\dots ,\left(\genfrac{}{}{0ex}{}{n}{n}\right)$ increases to its middle and then decreases. Indeed, for $0\le k<n$, the ratio of consecutive binomial coefficients is $(n-k)/(k+1)$, which is greater than, equal to, or less than $1$ according as $k$ is less than, equal to, or greater than $(n-1)/2$. Thus even $n$ has one maximum at $k=n/2$, while odd $n$ has two equal maxima at $k=(n-1)/2,(n+1)/2$.

A splay tree is a binary search tree whose access operations use splaying to move a selected key to the root through tree rotations. It stores no explicit balance or height information. A single access can take linear time, while the standard operations have logarithmic amortized time complexity. The distinction matters: amortized analysis bounds the total cost of an operation sequence, not the worst cost of every individual operation.^[ref]

Two stored keys $a<b$ are consecutive when no stored key lies strictly between them. Their numerical difference need not be one. After splaying on $a$ followed by splaying on $b$, the node $a$ is the left child of $b$ with an empty right subtree. To prove this, after the first call $b$ is the minimum of the right subtree of $a$. The last step crossing $a$ is either a zig step or a right-left zig-zag step; both make $a$ the left child of $b$. A nonempty right subtree of $a$ would require a stored key strictly between them.

A red-black tree colours each stored node red or black, treats absent-child sentinels as black, permits no red node to have a red child, and gives every path from a node to an absent-child sentinel the same number of black nodes. We also require a black root. These invariants bound its height of a binary tree by $2{\log }_2(n+1)$ for $n$ stored keys: a path has at most twice as many real nodes as black nodes, and a subtree of black height $b$ has at least $2^b-1$ real nodes by mathematical induction. The structure therefore supports logarithmic-time directed binary search tree lookup.

Turn a binary search tree into a sorted doubly linked list by reusing each linked list node's left and right child fields as predecessor and successor fields. An inorder traversal determines the required order. A recursive implementation first saves both child references, flattens the disjoint child subtrees, and splices their endpoints around the root. Structural induction proves that it preserves every original entry exactly once and produces reciprocal links with null outside endpoints. An explicit stack implements the same traversal without recursive calls; each original right child must be saved before its field is overwritten. Both versions take linear time complexity and $O(h+1)$ auxiliary space for original height $h$. The old binary search tree representation is consumed, so outside aliases must not continue to interpret the changed links as child pointers.

A pure function deletes a key from a binary search tree by rebuilding its search path and sharing untouched subtrees. At a matching node with two children, replace its key by the least key in its right subtree, removing that occurrence from the right subtree. The ordering invariant is preserved, with time complexity and fresh-node allocation proportional to the height of a binary tree.

In the implementation that exchanges the root with the final leaf and then applies heapify down, a max-heap of size at least four with distinct keys requires at least one downward exchange: the old final leaf's parent remains and has a larger key. One downward exchange can suffice, even for large heaps, by promoting the opposite root child and letting the moved key dominate that child's descendants. Thus the best case is two pairwise exchanges when the initial root/final-leaf exchange is counted. This is a convention about that implementation: a hole-moving implementation uses assignments rather than pairwise exchanges, and the worst case still has logarithmic time complexity.

A digital counter cycling through six stored values. With ordinary binary representation, the valid three-bit states are $000,001,010,011,100,101$. The unused encodings require either an initialization assumption or specified recovery transitions.

Irregular plural of bile canaliculus.

A bile salt is an amphipathic derivative of a bile acid. Its interactions with lipids and water help solubilize otherwise poorly water-soluble material in the intestine. Recovery and reuse through enterohepatic circulation differ from the initial hepatic synthesis.

Bilirubin is a pigment arising from heme breakdown, including turnover of red-cell hemoglobin. Transport, hepatic processing and biliary elimination contribute to its handling. An increased concentration can therefore result from different changes in production, processing or outflow.

An opening through which bile drains by an abnormal or experimentally created route. Historical external collection was used to investigate bile secretion and digestive function.

Pigmented products associated with haem breakdown and bile, including bilirubin.

The Bell-LaPadula model restriction that a readable object's classification must not exceed the subject's maximum clearance.