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10 Feb 2004: In this case, Eq. (24) becomes..

10 Feb 2004: 24). where we have used the relations.. ... 27). (28). Eq. (24) becomes..

10 Feb 2004: Next: Principles Up: Preconditioned iterative minimization Previous: Introduction.. Formulation of the problem. A system of noninteracting particles in a potential. is described by.. (1). where. is the single-particle Hamiltonian of the system, with

10 Feb 2004: Phys. Rev. 140 (4A), A1133 (1965). 24.

5 Mar 2004: illation, isg() = g(; S1) = vuut 14Æ1T exp 24( Æ1)24Æ1T 35 : (21)5. ... 0: (24)We an redu e its order to get the equationT dfd f = J: (25)6.

29 Sep 2004: Therefore, two hermitian opera-tors âx;y = Ax;yp2Hare well dened. As a result the ommutation relations ould be rewritten as[ax;ay = iL (24)[L;ax = iay (25)[L;ay = ... Indeed, we see that the ommutationrelations in the form of Eqs (24,25,26) forms the su

1 Aug 2004: Tale 3Supersymmetri Quantum Me hani s1. let us begin from well-known example of a linear os illator,whi h has the Hamiltonian:Ĥ = E ; Ĥ = p̂22m m!2x22 [p̂; x̂ = ih (1)Or, in dimensionless variables:P = vuut 1mh!p; q = sm!h x; (2)H = h! H; H =

13 Jan 2004: 0. ux1du. 1 u= 2πi (24). Identifying the sin πx and dividing through, the required result is obtained.

12 Nov 2004: 24.) At this point, the Test Proctor will interpret the results of the test.

10 Mar 2004: really sick?”. (c) “Have you not bathed or showered in the last 24 hours?”. ... Q̄s = “Have you bathed in the last 24 hours?”. With some (known) probability θ a subject answers Qs,.

19 Nov 2004: We refer thereader to [24], p.214 for a definition and basic properties of sub-gradients of convex functions. ... Performance Evaluation (2002) 49, 451–469. [24] Rockafellar (T.), Convex Analysis. (1970) Princeton University Press.

10 May 2004: 7 The calculations underlying this chart are based on a peak rate of 64 kb/s and a mean rate of 24.8 kb/s for each voice connection.

5 Jul 2004: Wα = AM1Mα,(24)whereM = diag(µ), A is theJ I matrix obtained fromA by eliminating thoserows ofA that are not indexed by elements ofJ, and.

17 Dec 2004: 001, andthe younger adults, G2(1) 172.3, p. 001. Specific-sourcediscrimination of the older adults (d 0.24) was significantlybetter as a result of multiple study exposures, G2(1) ... Journal of Ex-perimental Psychology: Learning, Memory, and Cognition, 24

3 Aug 2004: Test formats changesource-monitoring decision processes. Journal ofExperimental Psychology: Learning, Memory, & Cognition,24, 1137–1151. ... Journal of Neuroscience, 24,3917–3925. Ranganath, C., Johnson, M. K., & D’Esposito, M.

3 Aug 2004: MFG 9 45 25 29 50 4.24. MFG 10 45 47 11 29 3.91. ... SOG 19 39 83 24 19 4.06. MOG 19 33 75 18 11 3.34.

26 Apr 2004: 0005. The three-way interaction was notsignificant, F(10, 315) 1.24, MSE 0.721, p. ... 05. 03. 03. Total. 24 1.00. 68 1.00. 81 1.00Factual recognition.

10 Feb 2004: 24 February. Steve Roper. (ITG). Magma fracture in tough materials. 2 March.

10 Jun 2004: a. r – riri. sandsaltricecouscoussugar slope 1.24. Figure 9. The non-dimensional radial excursion, (r ri )/ri , as a function of the aspect ratioa with a < 1.7 for sand, salt, ... A straight line through the origin atslope 1.24 has a regression

9 Mar 2004: J. Fluid Mech. (2003), vol. 497, pp. 167–199. c 2003 Cambridge University PressDOI: 10.1017/S002211200300661X Printed in the United Kingdom. 167. Solidification and compositional convectionof a ternary alloy. By ANDREW F. THOMPSON†, HERBERT E.

9 Mar 2004: 6.3 6.3 24.3 5.89 1.00 3.86 9.6 6.1 3.8 0.7417 6.3 6.3 24.3 10.71 1.00 ... 86 9.6 8.2 5.2 0.8118 6.3 6.3 24.3 20.37 1.00 3.86 9.6 11.3 7.1 0.8919 13.2

9 Mar 2004: are captured by Figure 4.[24] The calculations in Figure 4 illustrate that volcanic.

9 Mar 2004: 6 1.9 1.7ID 20 26.5 1.4 1.3IE 23 20 3.9 10.5IF 12 18 4.0 11.25IG 24 20 4.1 11.5. ... IIA 23 26 5.22 2.62 29 48IIB 17.5 24 5.36 2.68 30 48IIC 15 21 5.94 2.01 25 24IID 28 15 7.02

9 Mar 2004: H.) 3–24 (Springer, Berlin, 1990). 5. Nakada, S., Shimizu, H. & Ohta, K.

9 Mar 2004: Sm =. 0. (ni=1. ψi(0) exp (2Viy))1/2. dy. (2.24). Recall thatn. ... 1 = 2/H0. (3.24)Hence from (3.16), by forming an expansion for ϕi, we find that.

9 Mar 2004: These substitutions transform (2.24) into. uN = I(hN) = Fr(hN) h1/2N. ... Appendix. The functions I and χA.1. The function I(hN). From the definitions (2.19), (2.24) and (2.25) we obtain.

9 Feb 2004: H 0 1!5 2F P12 f P1 1! 4.24! FIG. 2. ... On applicationthe boundary conditions4.23! and 4.24!, we find that. a 5 4.523 102 3, F P15 2 8.42 for Fr5 11.9.

9 Mar 2004: 0.9993 4.81 0 1.52 – –S3 0 45.8 79.80 0.574 1.375 1.0192 0.9996 19.24 0 1.36 – –S7 0 45.2 ... 19.24 0.0282 1.37 550 0.100R10 0.0500 46.3 79.97 0.579 1.390 1.0107 1.0007 9.80 0.0551 0.99 450

9 Mar 2004: Received 24 April 2000 and in revised form 7 December 2000).

9 Mar 2004: 15 P 24.2 P25.2 L25.2 P25.2 P30.2 L. T (C) T (C).

9 Mar 2004: Indeed, for most of the experimentsdiscussed by TML λ was in the range 0.02–0.24. ... tr dr rN. drNdthN. (2.24). We eliminate h/t with the aid of (2.12) and, after some rearrangement, we againobtain the result (2.22).

9 Mar 2004: which indicates that, at least initially,. s = (ΓT 4/3/L)t. (2.24). ... 24 H. E. Huppert. surface. The magma flows in conduits or dykes in a manner controlled by elastic, fluid.

9 Feb 2004: 5H1 2(H0U1)′=0, (24)3U1 H ′1 H ′0ϕ1. 1. 2H0ϕ. ′1=0, (25)ϕ1=2720. ... 4y2)], (38). and then subsequent substitution into (24) yields a second-order differential equation forH1(y), namely(1.

9 Mar 2004: salinity of the ice) is very small; k #1 0 24 [Gross et al., 1987].

9 Mar 2004: rNt 0 rN0 24. M. Ungarish, H.E. Huppert / International Journal of Multiphase Flow 25 (1999) 715737 725. ... For this case. the box model yields [rN/rN(0)]max=[8Fr/(3 b)]1/4. (This is by about 24% smaller than for.

9 Feb 2004: The volume fration of particles in suspension evolves as23,24. df. dt5. ... X5 x/l , 24! T5 t/ v sl /q!1/ a 2 1!, 25!

12 Mar 2004: requires. P q02pd. : 24. Equation (24) thus links the dendrite tip radius to. ... This solution has a scaled tip radius P = 10.8. and a scaled tip position Z 2:24.

9 Feb 2004: 870.0 461.1A25 9 3.0 8.0 24.0 500.0 0.432 1.957 939.0 479.8. ... 675.6 0.350 1.776 761.2 428.A13 53 3.0 8.0 24.0 500.0 0.432 1.957 939.0 479.

9 Mar 2004: Consequently, the relationships between the variables on the characteristics with. 24 M. ... v = r[1. (rinitr. )2]. (2.24). In particular, at the nose.

9 Mar 2004: J. Fluid Mech. (1998), vol. 359, pp. 109–142. Printed in the United Kingdom. c 1998 Cambridge University Press109. Effects of external flow on compositional andparticle gravity currents. By M A R K A. H A L L W O R T H, A N D R E W J. H O G GA N D

9 Feb 2004: r = (F/πV )1/2. (2.24)In contrast to the instantaneous, fixed volume release of the last section, there is not a finite radius at whichthe mass of particulate matter ... Applying these concepts to the relationship for the density of deposit for a single

9 Mar 2004: e-mail: grae@esc.cam.ac.uk; heh1@esc.cam.ac.uk. (Received 24 July and in revised form 27 March 1997). ... 24/3λRa1/3 (3.1). between the Nusselt number Nu for thermal convection in the liquid region and theRayleigh number.

9 Mar 2004: J. Fluid Mech. (2003), vol. 497, pp. 167–199. c 2003 Cambridge University PressDOI: 10.1017/S002211200300661X Printed in the United Kingdom. 167. Solidification and compositional convectionof a ternary alloy. By ANDREW F. THOMPSON†, HERBERT E.

9 Mar 2004: 15 P 24.2 P25.2 L25.2 P25.2 P30.2 L. T (C) T (C).

8 Mar 2004: 24 R. E. Hunt, 2002. and both sides must be constant, λ say.

25 Jun 2004: 2 ( a 2 1 ),where the parameters a and l were determined by numericalanalysis as a' 1.24 @17# and l' 1.2 @6#. ... JETP Lett. 67, 521 1998!#.@23# B.V. Svistunov, Phys. Lett. A 287, 169 2001!@24# M.J.

19 Jan 2004: 2iUψ. z= 2ψ (1 |ψ|2)ψ (24). subject to the boundary condition ψ 1 as |x|. ... The expansion of equation (24) about zero to O(2) gives four equations on seven unknownsU, m, a00, b00, c20, c10, c01.

19 Nov 2004: VpLp dV = 2iσ. V. p[ψ 20 p. 2iσp] dV. (24)Re-arranging this equation and using (15) again, we find that. ... S′ = 12zR. ′ v00 R′, (B.24). or, after simplification,. 2.

8 Oct 2004: EP/Uk. 2 =(κ. 2πh. )2k2. [lnh. 2aδ+. 1. 2. ](24). which differs from (18) by 12.

25 Jun 2004: 1.24 for U = 0.63 andh , dy1.62 for U. = 0.69.