High sensitivity CW-Cavity Ring Down Spectroscopy of N2O near 1.5 μm (II)

We present the second part of the investigation of the high sensitivity absorption spectrum of nitrous oxide by CW-Cavity Ring Down Spectroscopy near 1.5 μm. In a first paper [A.W. Liu, S. Kassi, P. Malara, D. Romanini, V.I. Perevalov, S.A. Tashkun, S.M. Hu, A. Campargue, J. Mol. Spectrosc. 244 (2007) 33-47] devoted to the 6000-6833 cm⁻¹ region, more than 6000 line positions of five isotopologues (¹⁴N₂¹⁶O, ¹⁵N¹⁴N¹⁶O, ¹⁴N¹⁵N¹⁶O, ¹⁴N₂¹⁷O, and ¹⁴N₂¹⁸O), were rovibrationally assigned to a total of 68 bands. The achieved noise equivalent absorption (α_min ∼ 2 × 10⁻¹⁰ cm⁻¹) allowed for the detection of lines with intensity weaker than 2 × 10⁻²⁹ cm/molecule. In this contribution, the investigated region was extended down to 5905 cm⁻¹ and additional recordings allowed accessing small spectral sections uncovered in our preceding recordings. A deeper analysis based on the predictions of the effective Hamiltonian model has allowed assigning a total of 3149 transitions and lowering the percentage of lines left unassigned from 51% to 28%. It led to the analysis of 35, 6, 7, and 6 bands for the ¹⁴N₂¹⁶O, ¹⁵N¹⁴N¹⁶O, ¹⁴N¹⁵N¹⁶O, and ¹⁴N₂¹⁸O isotopologues, respectively. Forty-two of these 54 bands are newly observed, while the rotational analysis of the twelve others is significantly extended and improved. Most of the bands were found unperturbed and their line positions could be reproduced within the experimental uncertainty (about 1 × 10⁻³ cm⁻¹). The corresponding spectroscopic parameters are reported. Local rovibrational perturbations induced by either intrapolyad or interpolyad couplings were found to affect five hot bands of ¹⁴N₂¹⁶O. Their detailed analysis is presented.     

Nonstatistical structures in the excitation functions of20Ne(16O,12C)24Mg and20Ne(16O,20Ne)16O reactions

The data on the excitation functions of²⁰Ne(¹⁶O,¹²C)²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(1.37, 2⁺),²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(4.12, 4⁺+4.24, 2⁺) +²⁰Ne(¹⁶O,¹²C^*(4.44, 2⁺))²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(6.01, 4⁺+6.43, 0⁺),²⁰Ne(¹⁶O,²⁰Ne)¹⁶O,²⁰Ne(¹⁶O,²⁰Ne^*(1.63, 2⁺))¹⁶O, and²⁰Ne(¹⁶O,²⁰Ne^*(4.25, 4⁺))¹⁶O reactions atθ _lab=13° fromE _c.m.=22.8 to 38.6 MeV have been subjected to a statistical analysis comprising of the calculations of the distribution of cross sections, deviation functions, cross-correlation functions, summed excitation functions, cross-channel correlation coefficients and coherence widths. The analysis confirms the existence of nonstatistical structures atE _c.m.=24.6, 27.8, 31.7 and 35.5 MeV, and identifies a new structure of the same nature atE _c.m. =25.6 MeV.     

Computer modeling of MWIR single heterojunction photodetector based on mercury cadmium telluride

In the present paper, an abrupt heterojunction photodetector based on Hg_1 − xCd_xTe (MCT) has been simulated theoretically for mid-infrared applications. A semi-analytical simulation of the device has been carried out in order to study the performance ratings of the photodetector for operation at room temperature. The energy band diagram, carrier concentration, electric field profile, dark current, resistance–area product, quantum efficiency and detectivity have been calculated and optimized as a function of different parameters such as device thickness, applied reverse voltage and operating wavelength. The effect of energy band offsets in conduction and valance band on the transportation of minority carriers has been studied. The influences of doping concentration, electron affinity gradient and the p–n junction position within heterostructure on potential barrier have been analyzed. The optical characterization has been carried out in respect of quantum efficiency, and detectivity of the heterojunction photodetector. In present model the Johnson–Nyquist and shot noise has been considered in calculation of detectivity. The simulated results has been compared and contrasted with the available experimental results. Results of our analytical-cum-simulation study reveal that under suitable biasing condition, the photodetector offers a dark current, I_D ≈ 6.5 × 10⁻¹² A, a zero-bias resistance–area product, R₀A ≈ 11.3 Ω m², quantum efficiency, η ≈ 78%, NEP = 2 × 10⁻¹² W Hz^1/2 and detectivity D^* ≈ 4.7 × 10¹⁰ mHz^1/2/W.     

The evaluation of half-lives and other decay data used in nuclear astrophysics and cosmochronology

The current status of some decay data used in nuclear astrophysics and cosmochronology is presented. The half-life of ⁷⁹Se has been evaluated as 3.6(3) × 10⁵ yr. The total energy of non-neutrino radiation released in act of ³⁷Ar decay has been obtained being 2.709 (16) keV per disintegration. The recommended half-life values of the long-lived radionuclides (T _1/2 ≳ 10⁶ yr) of ²⁶Al, ⁴⁰K, ⁵³Mn, ⁶⁰Fe, ⁸⁷Rb, ⁹³Zr, ⁹⁸Tc, ¹⁰⁷Pd, ¹²⁹I, ¹³⁵Cs, ¹⁴⁶Sm, ¹⁷⁶Lu, ¹⁸²Hf, ¹⁸⁷Re, ²⁰⁵Pb, ²³²Th, ²³⁵U, ²³⁸U, ²⁴⁴Pu, and ²⁴⁷Cm are given based on the evaluations published until 2010.     

Spectroscopic nuclear quadrupole moments

A ‘year-2001’ set of nuclear quadrupole moments, Q, is presented. Compared to the previous, ‘year-1992’ set, a major revision of the value or a considerable improvement of the accuracy is reported for ⁶ ₃Li, ₇N, ¹⁹ ₉F (197 keV, I = 5/2), ₁₁Na, ₁₃Al, ₂₁Sc, ₂₂Ti, ₂₆Fe (14 keV, I = 3/2 Mössbauer state), ₃₁Ga, ₃₂Ge, ⁷⁷ ₃₄Se (250 keV, I = 5/2 state), ₃₅Br, ₃₆Kr, ₃₇Rb, ₃₉Y, ₄₀Zr, ¹⁰⁰ ₄₅Rh, ₅₀Sn (24 keV, I = Mössbauer state), ₅₃I, ₅₄Xe, ₅₅Cs and ₈₃Bi.     

Theoretical investigations of phases of AlAs by first-principles

Five potential novel phases of AlAs (Pmn2₁-AlAs, Pbam-AlAs, Pbca-AlAs, bct-AlAs and wz-AlAs) are proposed and the stabilities of them are verified by the enthalpy, independent elastic constants and phonon dispersion spectra. The mechanical, electronic and thermodynamic properties of ten AlAs phases are studied and the electronic properties are calculated by PBE0 hybrid functional. Pmn2₁-AlAs and Pbam-AlAs own direct band gaps, so they have electronic advantages over other phases of AlAs at 0?GPa. Our calculated band gaps are 3.02, 3.07, 3.21, 2.76, 3.12, 1.15, 1.88, 2.53, 2.75 and 2.53?eV for Pmn2₁-AlAs, Pbam-AlAs, Pbca-AlAs, bct-AlAs, wz-AlAs, oC12-AlAs, hP6-AlAs, cI24-AlAs, zb-AlAs and cmcm-AlAs, respectively. Additionally, these phases: Pmn2₁-AlAs, Pbam-AlAs, Pbca-AlAs, bct-AlAs, cI24-AlAs, and cmcm-AlAs behave in a ductile manner, and wz-AlAs, oC12-AlAs, hP6-AlAs and zb-AlAs behave in a brittle manner. Otherwise, cmcm-AlAs has the greatest anisotropy, and hP6-AlAs has the least anisotropy.     

Magnetic properties of RNi5−xCux intermetallics

The magnetic properties have been studied for the series of RNi_5−xCu_x intermetallics with R=Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu; x  ?2.5. Compositional dependences of magnetic susceptibility for the Pauli paramagnets (R=Y, La, Ce, Lu) and the Curie temperature for ferromagnets (R=Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm) have maximum at x=0.2–0.4$x=0.2–0.4$ and 1, respectively. The substitution of Cu for Ni is accompanied by decreasing spontaneous magnetic moment and increasing coercive force of all ferromagnetic RNi_5−xCu_x but GdNi_5−xCu_x. These results are explained in the frame of band magnetism, random local crystal field, and domain wall pinning theories.     

Confrontation of nucleus deformation and multipole mixture parameters in (2+0 n ?2+01) transitions with rotational band structure for K π = 0 2+ and 0 3+

The difference of the energies of levels Δ _n = E _lev(2⁺0 _n ) − E _lev(0⁺0 _n ) at n = 1, 2, and 3 and the multipole-mixture parameter δ for (2⁺0₂−2⁺0₁) and (2⁺0₃−2⁺0₁) transitions are contrasted against the structure of the K ^π = 0₂⁺ and 0₃⁺ rotational bands that was calculated on the basis of the quasiparticle-phonon model. The values of (Δ₂ − Δ₁), (Δ₃ − Δ₁), and (Δ₂ − Δ₃) are found to correlate with the sign of the parameter δ and with the calculated structure of the K ^π = 0₂⁺ and 0₃⁺ bands. Original Russian Text ? A.M. Demidov, L.I. Govor, V.A. Kurkin, I.V. Mikhailov, 2009, published in Yadernaya Fizika, 2009, Vol. 72, No. 2, pp. 236–240.     

Very-high-order weno schemes

We study weno(2r − 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to weno17 (r=9)$(r=9)$. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent cfl limitation (cfl∈[0.8,1])$(\text{<small-caps>cfl</small-caps>}\in [0.8\text{,}1])$, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent p_β$p_{\beta }$ in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as p_β=r$p_{\beta }=r$, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of p_β=2$p_{\beta }=2$ (this is valid both for weno and wenom reconstructions), although the optimal value of the exponent is probably p_β(r)∈[2,r]$p_{\beta }(r)\in [2\text{,}r]$. Then, we apply the family of very-high-order wenom_pβ=r${\text{<small-caps>wenom</small-caps>}}_{p_{\beta }=r}$ reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding rorwenom_pβ=r${\text{<small-caps>rorwenom</small-caps>}}_{p_{\beta }=r}$ schemes are essentially nonoscillatory, as Δx→0$\mathrm{\Delta }x\to 0$, up to r=9$r=9$, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.     

Enhanced cyclability of triple-metal-doped LiMn2O4 spinel as the cathode material for rechargeable lithium batteries

To improve the cycle performance of spinel LiMn₂O₄ as the cathode of 4-V-class lithium secondary batteries, spinel phases LiM _x Mn_2 − x O₄ (M=Li, Fe, Co; x = 0, 0.05, 0.1, 0.15) and LiFe_0.05M _y Mn_{1.95 − y} O₄ (M=Li, Al, Ni, Co; y = 0.05, 0.1) were successfully prepared using the sol–gel method. The spinel materials were characterized by powder X-ray diffraction (XRD), elemental analysis, and scanning electron microscopy. All the samples exhibited a pure cubic spinel structure without any impurities in the XRD patterns. Electrochemical studies were carried out using the Li|LiM _x Mn_2 − x O₄ (M=Li, Fe, Co; x = 0, 0.05, 0.1, 0.15) and LiFe_0.05M _y Mn_{1.95 − y} O₄ (M=Li, Al, Ni, Co; y = 0.05, 0.1) cells. These cathodes were more tolerant to repeated lithium extraction and insertion than a standard LiMn₂O₄ spinel electrode in spite of a small reduction in the initial capacity. The improvement in cycling performance is attributed to the stabilization in the spinel structure by the doped metal cations.     

Structural and electrochemical properties of LiNi0.5Mn0.5 − xAlxO2 (x = 0, 0.02, 0.05, 0.08, and 0.1) cathode materials for lithium-ion batteries

Layered LiNi_0.5Mn_0.5 ? xAl_xO₂ (x = 0, 0.02, 0.05, 0.08, and 0.1) series cathode materials for lithium-ion batteries were synthesized by a combination technique of co-precipitation and solid-state reaction, and the structural, morphological, and electrochemical properties were examined by XRD, FT-IR, XPS, SEM, CV, EIS, and charge–discharge tests. It is proven that the aliovalent substitution of Al for Mn promoted the formation of LiNi_0.5Mn_0.5 ? xAl_xO₂ structures and induced an increase in the average oxidation number of Ni, thereby leading to the shrinkage of the lattice volume. Among the LiNi_0.5Mn_0.5 ? xAl_xO₂ materials, the material with x = 0.05 shows the best cyclability and rate ability, with discharge capacities of 219, 169, 155, and 129 mAh g^? 1 at 10, 100, 200, and 400 mA g^? 1 current density respectively. Cycled under 40 mA g^? 1 in 2.8–4.6 V, LiNi_{0. 5}Mn_0.45Al_0.05O₂ shows the highest discharge capacity of about 199 mAh g^? 1 for the first cycle, and 179 mAh g^? 1 after 40 cycles, with a capacity retention of 90%. EIS analyses of the electrode materials at pristine state and state after first charge to 4.6 V indicate that the observed higher current rate capability of LiNi_{0. 5}Mn_0.45Al_0.05O₂ can be understood due to the better charge transfer kinetics.     

Self-broadened widths and shifts of CO2: 4750-7000 cm

In the previous paper, we report line strength measurements for 58 bands of ¹²CO₂ between 4550 and 7000 cm⁻¹ [R.A. Toth, L.R. Brown, C.E. Miller, V. Malathy Devi, D. Chris Benner, J. Mol. Spectrosc., this issue, doi:10.1016/j.jms.2006.008.001.]. In the present study, self-broadenedwidth and self-induced pressure shift coefficients are determined in two intervals:

(a) between 4750 and 5400 cm⁻¹for bands of the Fermi triad (20011 ← 00001, 20012 ← 00001, 20013 ← 00001), three corresponding hot bands (21111 ← 01101, 21112 ← 01101, 21113 ← 01101) and the 01121← 00001 combination band;

(b) between 6100 and 7000 cm⁻¹ for the Fermi tetrad (30014 ← 00001, 30013 ← 00001, 30012 ← 00001, 30011 ← 00001), two associated hot bands (31113 ← 01101, 31112 ← 01101), as well as 00031 ← 00001 and its hot band 01131 ← 01101.

Least-squares fits of the experimental width and pressure shift coefficients are modeled using empirical expressions:

     

Activity study of graphite from the chernobyl NPP reactor

The content of the isotopes ³H, ¹⁴C, ³⁶Cl, ⁵⁵Fe, ⁵⁹Ni, ⁶³Ni, ⁶⁰Co, ⁹⁰Sr, ^93m Nb, ¹⁰⁸Ag, ¹³³Ba, ¹³⁴Cs, ¹³⁷Cs, ¹⁵⁴Eu, and ¹⁵⁵Eu in the GRP-2-125 graphite from the reactor of Power Unit 2 at the Chernobyl Nuclear Power Plant was measured. The results were compared with the calculations and literature data. Some regularities and correlations were revealed in the content of various radionuclides in graphite. Graphite porosity and desorption of radionuclides from graphite were studied. Original Russian Text ? M.D. Bondar’kov, D.M. Bondar’kov, A.M. Maksimenko, V.A. Zheltonozhskii, M.V. Zheltonozhskaya, V.V. Petrov, A.I. Savin, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 274–278.     

Investigation of double-beta decay with the NEMO-3 detector

The double-beta-decay experiment NEMO-3 has been taking data since February 2003. The aim of this experiment is to search for neutrinoless (0 νββ) decay and investigate two neutrino doublebeta decay in seven different isotopically enriched samples (¹⁰⁰Mo, ⁸²Se, ⁴⁸Ca, ⁹⁶Zr, ¹¹⁶Cd, ¹³⁰Te, and ¹⁵⁰Nd). After analysis of the data corresponding to 3.75 yr, no evidence for 0 νββ decay in the 100Mo and 82Se samples was found. The half-life limits at the 90% C.L. are 1.1 × 10²⁴ and 3.6 × 10²³ yr, respectively. Additionally for 0 νββ decay the following limits at the 90% C.L. were obtained, >1.3 × 10²² yr for ⁴⁸Ca, >9.2 × 10²¹ yr for ⁹⁶Zr, and >1.8 × 10²² yr for 150Nd. The 2 νββ decay half-life values were precisely measured for all investigated isotopes.     

Global Multi-isotopologue fit of measured rotation and vibration–rotation line positions of CO in X1Σ+ state and new set of mass-independent Dunham coefficients

A set of mass-independent U_mj and Δ_mj parameters globally describing vibration–rotation energy levels of the CO molecule in the X¹Σ⁺ ground electronic state was fitted to more than 19,000 transitions of ¹²C¹⁶O, ¹³C¹⁶O, ¹⁴C¹⁶O, ¹²C¹⁷O, ¹³C¹⁷O, ¹²C¹⁸O, and ¹³C¹⁸O isotopologues collected from the literature. The maximal values of the vibrational V and the rotational J quantum numbers included in the fit was 41 and 128, respectively. The weighted standard deviation of the fit is .66. Fitted parameters were used for calculation of Dunham coefficients Y_mj for nine isotopologues ¹²C¹⁶O, ¹³C¹⁶O, ¹⁴C¹⁶O, ¹²C¹⁷O, ¹³C¹⁷O, ¹⁴C¹⁷O, ¹²C¹⁸O, ¹³C¹⁸O, and ¹⁴C¹⁸O. Calculated transition frequencies based on the fitted parameters were compared with previously reported. A critical analysis of the CO HITRAN and HITEMP data is also presented.     

Physical states and BRST operators for higher-spin <Emphasis Type="Italic">W</Emphasis> strings

In this paper, we mainly investigate the W _2,s ^M ⊗ W _2,s ^L system, in which the matter and the Liouville subsystems generate the W _2,s ^M and W _2,s ^L algebras, respectively. We first give a brief discussion of the physical states for the corresponding W strings. The lower states are given by freezing the spin-2 and spin-s currents. Then, introducing two pairs of ghost-like fields, we give the realizations of the W _1,2,s algebras. Based on these linear realizations, the BRST operators for the W _2,s algebras are obtained. Finally, we construct new BRST charges of the Liouville system for the W _2,s ^L strings at the specific values of the central charges c: for the W _2,3^L algebra, c=−24 for the W _2,4^L algebra and for the W _2,6^L algebra, at which the corresponding W _2,s ^L algebras are singular.     

Calculation of the spectroscopic constants for the electronic states A1Σ u+ , B1Πu, C1Πu, D1Σ u+ , and E1Σ u+ of the cesium dimer

The vibrational, rotational, and centrifugal distortion constants have been calculated for the electronic states A ¹Σ _u ⁺ , B ¹Π_u, C ¹Π_u, D ¹Σ _u ⁺ , and E ¹Σ _u ⁺ of the Cs₂ molecule. The calculation was performed on the basis of the semiempirical potential energy curves constructed in this paper. The calculated spectroscopic constants are compared with the experimental data. Original Russian Text ? A.D. Smirnov, 2007, published in Optika i Spektroskopiya, 2007, Vol. 102, No. 1, pp. 23–27.     

Thermal stability and electrical conductivity of multiferroics BiFeO<Subscript>3</Subscript>/REEs

Ceramic samples of bismuth ferrite and solid solutions of Bi_{1 − x} A _x FeO₃ type (where A = Lu, Yb, Tm, Er, Ho, Dy, Tb, Gb, Eu, Sm, Nd, Pr, La; 0.05 ≤ x ≤ 0.20; Δx = 0.05) were prepared. Spectra of the real part of electrical conductivity were studied within the range 10⁻⁴–10⁻⁶ Hz. The dependence of the samples’ thermal stability and electrical conductivity on the size of the substituting ions was established.     

Gamma-ray spectroscopy of 64Zn and 65Zn and the role of the g92 orbital

Measurements of γ-ray excitation functions, γ-γ coincidence spectra and γ-ray angular distributions have been made. following the reactions ⁶¹Ni(α, n)⁶⁴Zn, ⁶²Ni(α, n)⁶⁵Zn, ⁵⁶Fe(¹⁴N, αnp)⁶⁴Zn, ⁵⁶Fe(¹²C, 2pn)⁶⁵Zn, and ⁵⁴Fe(¹²C, 2p)⁶⁴Zn. Among the new levels observed in ⁶⁴Zn are those at 5624 keV, 6765 keV, 6940 keV, and 6124 keV, the last one with a suggested assignment of (9^?). In ⁶⁵Zn. ten new levels probably in the positive-parity chain, with spin up to ($\text{21}\text{2}$), and a few others, have been found. Comparison of the ⁶⁵Zn positive-parity levels with the ⁶⁴Zn ground-state band supports the concept of a single neutron in the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ orbital weakly coupled to a core essentially identical to ⁶⁴Zn. Many high-spin states in ⁶⁴Zn itself can be aggregated into bands whose band heads are suggestive of two-quasiparticle states involving one $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ excitation.     

Low-field magnetization of ludwigites Co3O2BO3 and Co3 ? xFexO2BO3 (x ≈ 0.14)

Ludwigite single crystals of compositions Co₃O₂BO₃ and Co_{3 − x} Fe _x O₂BO₃ (x ≈ 0.14) have been synthesized. The crystal structure is investigated at room temperature, and the magnetization is studied in the temperature range T = 4.2–100 K in magnetic fields of up to 600 Oe. The orthorhombic symmetry is revealed, and the unit cell parameters are determined. A number of features are established for the temperature dependence of the magnetization. In unsubstituted Co₃O₂BO₃, two magnetic transitions are found at T _C1 = 43 K and T _C2 = 15 K. At temperatures below 40 K, spin-glass state is revealed. Substitution of iron ions for cobalt ions leads to a noticeable shift in the magnetic transitions toward the high-temperature range: T _C1 = 83 K and T _C2 = 74 K. A ferromagnetic ordering of the P type is found in the Co_{3 − x} Fe _x O₂BO₃ (x ≈ 0.14) compound. Original Russian Text ? N.V. Kazak, N.B. Ivanova, V.V. Rudenko, A.D. Vasil’ev, D.A. Velikanov, S.G. Ovchinnikov, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 5, pp. 916–919.