**JACKKNIFE** in Statistics. David (1995) gives Rupert G. Miller’s "A Trustworthy Jackknife,"
*Annals of Mathematical Statistics,* **35** (1964), 1594-1605 as the first
published use of the term. Miller explains that John W. Tukey had adopted the term
because "a boy-scout’s jackknife is symbolic of a rough-and-ready instrument capable of
being utilized in all contingencies and emergencies." M. H. Quenouille, in "Notes on
Bias in Estimation" *Biometrika,* **43**, (1956), 353-360, had written colourlessly
of a procedure for supplying "an approximate correction for bias" [John Aldrich].

The term **JACOBIAN** was coined by James J. Sylvester
(1814-1897), who used the term in 1852 in *The Cambridge & Dublin Mathematical
Journal.*

Sylvester also used the word in 1853 "On a Theory of the Syzygetic Relations of Two Rational Integral Functions,
Comprising an Application to the Theory of Sturm’s Functions, and That of the
Greatest Algebraical Common Measure," *Philosophical Transactions of the Royal Society of London,*
CXLIII, Part III, pp. 407-548: "In Arts. 65, 66, I consider the relation
of the Bezoutiant to the differential determinant, so called by Jacobi, but
which for greater brevity I call the Jacobian."
C. G. J. Jacobi’s
(1804-1851) paper was
*De determinantibus functionalibus* (1841).

**JEFFREYS PRIOR.** In 1946 Harold Jeffreys published "An Invariant
Form for the Prior Probability in Estimation Problems," *Proceedings of the
Royal Society, A*, **186**, 453-461. He incorporated the material in the
second edition of his *Theory of Probability* (1948). The expression "Jeffreys
prior" (or variants of it) became established in the 1960s; see e.g. Bruce
M. Hill "The Three-Parameter Lognormal Distribution
and Bayesian Analysis of a Point-Source Epidemic," *Journal
of the American Statistical Association*, **58**,
(1963), 72-84 or J. Hartigan "Invariant Prior Distributions, *Annals of Mathematical
Statistics*, **35**, (1964), 836-845.

See NONINFORMATIVE PRIOR

**JENSEN’S INEQUALITY** was given in
J. L. W. V. Jensen’s
"Sur les fonctions convexes et les inégalités entre les valeurs moyennes,"
*Acta Math*., **30**, (1906), 175-193. This paper is
based on his earlier ‘Om konvexe funktioner og uligheder mellem midelvaerdier,’
*Nyt Tidsskr. Math. B* **16** (1905), pp. 49-69. The inequality is
discussed in *Inequalities* by G. H. Hardy, J. E. Littlewood and G. Polya (1934).

See CONVEX FUNCTION.

**JERK** was used by J. S. Beggs in 1955 in *Mechanism* iv.
122: "Since the forces to produce accelerations must arise from
strains in the materials of the system, the rate of change of
acceleration, or jerk, is important" (OED2).

The word has found its way into at least one calculus textbook.

**JORDAN CANONICAL FORM** refers to a result given by
Camille
Jordan in the section "Réduction d'une substitution linéaire à sa forme canonique" (p. 114)
of his *Traité des substitutions et des
équations algébriques* (1870). H. W. Turnbull and A. C. Aitken *An
Introduction to the Theory of Canonical Matrices* (1932, p. 81) give
this reference and comment "the matrices given there of positive integers
modulo *p*, the determinants involved being "non-singular",
that is, prime to *p*."

**JORDAN CURVE** appears in W. F. Osgood, "On the Existence of the
Green’s Function for the Most General Simply Connected Plane Region,"
*Transactions of the American Mathematical Society,* Vol. 1, No.
3. (July 1900): "By a *Jordan curve* is meant a curve of the
general class of continuous curves without multiple points,
considered by Jordan, *Cours d'Analyse,* vol. I, 2d edition,
1893..." (OED2).

**JORDAN CURVE THEOREM** is dated 1915-20 in RHUD2.

*Jordan curve-theorem* is found in D. W. Woodard, "On
two-dimensional analysis situs with special reference to the Jordan
curve-theorem," *Fundamenta* (1929).

*Jordan curve theorem* is also found in L. Zippin, "Continuous
curves and the Jordan curve theorem," *Bulletin A. M. S.*
(1929).

**JULIA SET** is named for Gaston Julia
and a construction in his “Mémoire sur l'iteration des fonctions rationnelles,”
*Journal
de mathématiques pures et appliquées,* **8** (1918) pp. 47–245. MathWorld