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Richardson cascade peyšâr-e Richardson Fr.: cascade de Richarson Same as → energy cascade Named after L. F. Richardson (1922), Weather Prediction by Numerical Process (Cambridge Univ. Press); → cascade. |
Richardson criterion sanjidâr-e Richardson Fr.: critère de Richardson A condition for the onset of → instability in multilayer fluids which compares the balance between the restoring force of → buoyancy and the destabilizing effect of the → shear. Named after the British meteorologist Lewis Fry Richardson (1881-1953), who first arrived in 1920 to the dimensionless ratio now called → Richardson number. The first formal proof of the criterion, however, came four decades later for → incompressible flows (Miles, J. W. 1961, J. Fluid Mech., 10, 496; Howard, L. N., 1961, J. Fluid Mech., 10, 509). Its extension to → compressible flows was demonstrated subsequently (Chimonas 1970, J. Fluid Mech., 43, 833); → criterion. |
Richardson number adad-e Richardson Fr.: nombre de Richardson A dimensionless number which is used according to the → Richardson criterion to describe the condition for the → stability of a flow in the presence of vertical density stratification. If the → shear flow is characterized by linear variation of velocity and density, with velocities and densities ranging from U_{1} to U_{2} and ρ_{1} to ρ_{2} (ρ_{2}>ρ_{1}), respectively, over a depth H, then the Richardson number is expressed as: Ri = (ρ_{2} - ρ_{1}) gH / ρ_{0} (U_{1} - U_{2})^{2}. If Ri < 0.25, somewhere in the flow turbulence is likely to occur. For Ri > 0.25 the flow is stable. → Richardson criterion; → number. |
richness pordâri Fr.: richesse The property of being very abundant. |
richness class rade-ye pordâri Fr.: classe de richesse A classification of → galaxy clusters into six groups (0 to 5), as in the → Abell catalog. It depends on the number of galaxies in a given cluster that lie within a → magnitude range m_{3} to m_{3+2}, where m_{3} is the magnitude of the 3rd brightest member of the cluster. The first group contains 30-49 galaxies and the last group more than 299 galaxies. |
riddle kervas (#) Fr.: énigme, devinette 1) A question or statement so framed as to exercise one's ingenuity in answering it
or discovering its meaning; conundrum. M.E. redel, redels, from O.E. rædels "riddle; counsel; conjecture; imagination;" cf. O.Fr. riedsal "riddle," O.Sax. radisli, M.Du. raetsel, Du. raadsel, O.H.G. radisle, Ger. Rätsel "riddle." Kervas "riddle, puzzle" [Dehxodâ], Kurd. karvâs "riddle," of unknown origin. |
ridge ruk Fr.: faîte, dorsale A long, narrow elevation of the Earth's surface, generally sharp crested with steep sides, either independently or as part of a larger mountain or hill. See also: → submarine ridge, → wrinkle ridge, → mid-Atlantic ridge. M.E. rigge; O.E. hrycg "spine, back of a man or beast" (cf. O.Fris. hregg, Du. rug, O.H.G. hrukki, Ger. Rücken "the back"). Ruk, from dialectal Tabari ruk "mountain, ridge;" cf. (Dehxodâ) raš "hill." |
Riemann curvature tensor tânsor-e xamidegi-ye Riemann Fr.: tenseur de courbure de Riemann A 4th → rank tensor that characterizes the deviation of the geometry of space from the Euclidean type. The curvature tensor R^{λ}_{μνκ} is defined through the → Christoffel symbols Γ^{λ}_{μν} as follows: R^{λ}_{μνκ} = (∂Γ^{λ}_{μκ})/(∂x^{ν}) - (∂Γ^{λ}_{μν})/(∂x^{κ}) + Γ^{η}_{μκ}Γ^{λ}_{ην} - Γ^{η}_{μν}Γ^{λ}_{ηκ}. → Riemannian geometry; → curvature; → tensor. |
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°. |
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