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Riemann problem parâse-ye Riemann 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) = u_{l} if x < 0, and u(x,0) = u_{r} if x > 0 . → Riemann's geometry; → problem. |
Riemann's geometry hendese-ye Riemann Fr.: géométrie de Riemann Same as → Riemannian geometry. → Riemannian; → geometry. |
Riemannian Riemanni (#) Fr.: riemannien 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. |
Riemannian geometry hendese-ye Riemanni 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. → Riemannian; → geometry. |
Riemannian manifold baslâ-ye Riemanni Fr.: variété riemannienne A → manifold on which there is a defined → Riemannian metric (Douglas N. Clark, 2000, Dictionary of Analysis, Calculus, and Differential Equations). → Riemannian; → metric. |
Riemannian metric metrik-e Riemanni Fr.: métrique riemannienne A positive-definite inner product, (.,.)_{x}, on T_{x}(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). → Riemannian; → metric. |
rift câk, gosal-darré 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. |
rift valley gosal-darré Fr.: fossé d'effondrement, ~ tectonique A long, narrow valley formed by the lowering of land between two → faults. Also called → graben. |
Rigel (β Ori) Rejl (#) Fr.: Rigel 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. |
Rigel Kentaurus Pâ-ye Kentawros Fr.: Rigil Kentaurus Same as the star → Alpha Centauri. From Ar. Rijl al-Qanturis "foot of Centaurus," from rijl "foot," + Qanturis Arabicized → Centaurus. Pâ-ye Kantawros, "foot of Centaurus," from pâ, → foot, + Kentawros, → Centaurus. |
right 1) râst (#); 2) dorost; 3) râšan Fr.: droit 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;"
related to
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;" |
right angle zâviye-ye râst Fr.: angle droit An angle of 90°. |
right ascension 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. → right; ascension, M.E. ascencioun, from O.Fr., from L. ascendere "to climb up," from → ad- "to" + scandere "to climb." 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." |
right triangle sebar-e râst (#) Fr.: triangle droit A triangle one of whose angles is a → right angle. |
right-hand rule 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. |
right-handed râstâl, râstdast (#) Fr.: droitier Using the right hand with greater skill or ease than the left. Râstâl, from râst, → right, + -al→ -al. Râstdast, with dast, → hand. |
rigid saxtpây (#) Fr.: rigide 1) General: Stiff or unyielding; inflexible, strict, severe. 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." |
rigid body jesm-e saxtpây Fr.: corps rigide Mechanics: A system of many particles whose positions relative to one another remain fixed. |
rigidity saxtpâyi Fr.: rigidité 1) The quality or state of being → rigid.
See also → modulus of rigidity. |
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