Fr.: problème de Riemann
The combination of a → partial differential equation and a → piecewise constant → initial condition. The Riemann problem is a basic tool in a number of numerical methods for wave propagation problems. The canonical form of the Riemann problem is: ∂u/∂t + ∂f(u)/∂x = 0, x ∈ R, t > 0, u(x,0) = ul if x < 0, and u(x,0) = ur if x > 0 .
Fr.: géométrie de Riemann
Same as → Riemannian geometry.
Of or pertaining to Georg Friedrich Bernhard Riemann (1826-1866) or his mathematics findings. → Riemannian geometry, → Riemannian manifold, → Riemannian metric, → Riemann problem, → Riemann curvature tensor.
After the German mathematician Georg Friedrich Bernhard Riemann (1826-1866), the inventor of the elliptic form of → non-Euclidean geometry, who made important contributions to analysis and differential geometry, some of them paving the way for the later development of → general relativity.
Fr.: géométrie riemannienne
A → non-Euclidean geometry in which there are no → parallel lines, and the sum of the → angles of a → triangle is always greater than 180°. Riemannian figures can be thought of as figures constructed on a curved surface. The geometry is called elliptic because the section formed by a plane that cuts the curved surface is an ellipse.
Fr.: variété riemannienne
Fr.: métrique riemannienne
A positive-definite inner product, (.,.)x, on Tx(M), the tangent space to a manifold M at x, for each x ∈ M, which varies continually with x (Douglas N. Clark, Dictionary of Analysis, Calculus, and Differential Equations).
Fr.: rift; fissure, crevasse
1) General: a gap or break made by splitting, cleaving, etc.; fissure; cleft.
M.E., from a Scandinavian source; cf. Dan., Norw. rift "a cleft."
1) Câk "fissure, rupture, cleft, crack," related to caqidan "to drive a nail, strike together, fix a spike;" caxidan "to quarrel, strive;" diatectal Shughni cuγ, Roshani coγ "breaking, tearing, ripping up;" Malâyeri ceqidan "cracking of a cold porcelain bowl when receiving hot water;" Yazghulami cok-, coxt "to pound, to stamp;" Wakhi cuk-, cukt "to strike;" Ossetic cædyn "to shake, strike iron;" Lori cok "a mark fixed to separate two grounds;" Sogd. cax "to battel, fight;" Mid.Pers. (prefixed) pacên "copy" (see also Cheung 2007). Gosal-darré, from gosal, → fault, + darré, → valley.
Fr.: fossé d'effondrement, ~ tectonique
Rigel (β Ori)
The brightest star in the constellation → Orion (visual magnitude 0.18). A → blue supergiant of type B8 Iab with an initial mass of 17 solar masses, Rigel is 773 light-years away, and actually shines with the light of 40,000 Suns. It is accompanied by a fairly bright, seventh magnitude companion nine seconds of arc apart. The companion is itself double, the components much fainter and much less massive → main sequence stars of type B.
Rigel "foot," short for Ar. rijl al-jauza' (
Rejl, from Ar., as above.
Fr.: Rigil Kentaurus
Same as the star → Alpha Centauri.
From Ar. Rijl al-Qanturis "foot of Centaurus," from rijl "foot," + Qanturis Arabicized → Centaurus.
1) râst (#); 2) dorost; 3) râšan
1a) Straight, free from curves, angles, or irregularities.
→ right ascension.
M.E.; O.E. reht, riht; cf. O.H.G. reht, Ger. recht, O.N. rettr, Goth. raihts; P.Gmc. *rekhtaz, cognate with Pers. râst, as below.
1) Râst "right, true; just, upright, straight;"
Mid.Pers. râst "true, straight, direct;" Soghdian rəšt "right;"
O.Pers. rāsta- "straight, true," rās- "to be right, straight,
true;" Av. rāz- "to direct, put in line, set," razan- "order;"
Mid.Pers. rây-, râyênitan "to arrange;" Mod.Pers.
raj "line, row," variants raž, rak, râk, rezg (Lori),
radé, râdé "line, rule, row,"
rasté, râsté "row, a market with regular ranges of shops;"
ris, risé "straight;"
cf. Skt. raj- "to direct, stretch," rjuyant- "walking straight;"
Gk. orektos "stretched out;"
L. regere "to lead straight, guide, rule," p.p. rectus "right, straight;"
PIE base *reg- "move in a straight line," hence, "to direct, rule;"
Fr.: angle droit
An angle of 90°.
râst afrâz (#)
Fr.: ascension droite
A coordinate in the → equatorial system measured from the → vernal equinox eastward to the point where the object → hour circle intersects the → celestial equator. Right ascension (symbol α) is expressed in hours, minutes, and seconds. See also: → declination.
Râst, → right; afrâz present stem of afrâzidan, afrâštan "to raise, exalt, extole," from Mid.Pers. abrâstan, abrâz- "to lift, raise," from ab-, from O.Pers./Av. abiy-/aiwi- "to, upon, against;" cf. Skt. abhi-, Gk. amphi- + râst "straight, direct, true;" from O.Pers. rāsta- "straight, true," rās- "to be right, straight, true;" Av. rāz- "to direct, put in line, set," razan- "order;" cf. Skt. raj- "to direct, stretch," rjuyant- "walking straight;" Gk. orektos "stretched out;" L. regere "to lead straight, guide, rule," p.p. rectus "right, straight;" Ger. recht; E. right; PIE base *reg- "move in a straight line," hence, "to direct, rule."
sebar-e râst (#)
Fr.: triangle droit
A triangle one of whose angles is a → right angle.
razan-e dast-e râst
Fr.: règle de la main droite
See → Fleming's rules.
right-hand screw rule
razan-e pic-e rast-gard
Fr.: règle de la vis droite
A rule that gives the direction of the resultant vector in a → vector product: A x B = C. It is the direction of advance of a right-hand screw whose axis, held perpendicular to the plane of A and B, is rotated in the same sense that rotates the first-named vector (A) into the second-named vector B through the smaller angle.
râstâl, râstdast (#)
Using the right hand with greater skill or ease than the left.
From L. rigidus "hard, stiff, rough," from rigere "to be stiff;" related to L. frigus "cold," Gk. rhigos "frost, cold."
Saxtpây, from saxt, → hard, + pây present stem of pâyidan "to stand firm, to be constant, steady, fixed;" Mid.Pers. pâyitan, pâtan, pây- "to protect; wait, stand," Sogdian p'y "to protect, watch over;" O.Pers./Av. pâ(y)- "to protect, keep" pâtar- "protector, watcher," cf. Skt. pâ- "to protect, keep," pâti "protects;" Gk. poimen "shepherd," poma "lid, cover;" L. pastor "shepherd," panis "bread;" PIE base *pa- "to protect, guard, pasture, feed."
Fr.: corps rigide
Mechanics: A system of many particles whose positions relative to one another remain fixed.