Temperature and solar zenith angle control of D-region positive ion chemistry     

Jeffrey M. Forbes 《Planetary and Space Science》1982,30(10):1065-1072

A numerical model is utilized to investigate the temperature (T) and solar zenith angle (χ) control of D-region positive ion chemistry between 75 and 90 km. It is assumed that NO^? is the precursor ion in a chain which involves three-body formation of the intermediary cluster ions NO⁺(H₂O)_m?1(X) (m = 1–3), where X can be N₂,O₂, H₂O, or CO₂, switching reactions which convert these weakly bound clusters to hydrates of NO⁺ and reaction of the third hydrate of NO⁺ with H₂O to initiate the chain to form H⁺(H₂O)_n (n = 1–7). Zonal mean and tidal temperatures from rocket observations and theory are synthesized to obtain the best available estimate of mean latitudinal, seasonal and local time variations of temperature in this height region. Relative compositions of NO⁺(H₂O)_m and H⁺(H₂O)_n are found to vary widely over the complete range of realistic conditions; however, the relative ion populations are entirely explicable in terms of the effects of χ and T on the relative life-times of the intermediary ion clusters with respect to recombination, switching and thermal decomposition. For instance, as χ increases (and electron production decreases) beyond 60° for a given temperature, the recombination times of the intermediate ion cluster species lengthen with respect to the formation time of the H⁺ water clusters, causing the relative H⁺ water cluster population to increase and thus raise the level where the cluster ion and NO⁺ concentrations are equal from about 85 km (normal midday) to 90 km. For a given χ the concentrations of NO⁺H₂O and H⁺(H₂O)₄ increase (decrease) for temperatures less than (greater than) 190 and 205 K, respectively. The transition occurs when the temperature becomes sufficiently high that the lifetimes of intermediary ion clusters with respect to thermal decomposition become less than their lifetimes with respect to H₂O switching (which ultimately leads to the third hydrate of NO⁺ and entry into the water chain). At this point, the formation time of H⁺(H₂O)₄ becomes long compared with its lifetime with respect to thermal decomposition and its relative concentration decreases also. Implications of these results with respect to studies of the D-region are discussed.  相似文献   

Measurements of positive ion conversion and removal reactions relating to the Jovian ionosphere     

Rainer Johnsen  Manfred A. Biondi 《Icarus》1974,23(2):139-143

Measured rates are presented for the reaction of He⁺ ions with H₂ (and D₂) molecules to form H⁺, H₂⁺, and HeH⁺ ions, as well as for the subsequent reactions of H⁺ and HeH⁺ ions with H₂ to form H₃⁺. The neutralization of H₃⁺ (and H₅⁺) ions by dissociative recombination with electrons is shown to be fast. The reaction He⁺ + H₂ is slow (k = 1.1 × 10^?13 cm³/sec at300°K) and produces principally H⁺ by the dissociative charge transfer branch. It is concluded that there may be a serious bottleneck in the conversion of two of the primary ions of the upper Jovian ionosphere, H⁺ and He⁺ (which recombine slowly), to the rapidly recombining H₃⁺ ion (α[H₃⁺]?3.4 × 10^?7 cm³/sec at 150°K).  相似文献   

Ion-ion mutual neutralization and ion-neutral switching reactions of some stratospheric ions     

D. Smith  N.G. Adams  E. Alge 《Planetary and Space Science》1981,29(4):449-454

Following the recent mass spectrometric observations of the ambient stratospheric positive and negative ions we have carried out co-ordinated laboratory experiments using a selected ion flow tube apparatus and a flowing afterglow apparatus for the following purposes: (i) to consider whether CH₃CN is a viable candidate molecule for the species X in the observed stratospheric ion series H⁺ (H₂O_n (X)_m and (ii) to determine the binary mutual neutralization rate coefficients α_i for the reactions ofH⁺ (H₂O₄ and H⁺(H₂O)(CH₃CN)₃ with several of the negative ion species observed in the stratosphere. We conclude from (i) that CH₃CN is indeed a viable candidate for X and from (ii) that the α_i for stratospheric ions are within the limited range (5–6) × 10^?8 cm³ s^?1.  相似文献   

The production of water-cluster positive ions in the quiet daytime D region     

George C. Reid 《Planetary and Space Science》1977,25(3):275-290

In the quiet daytime D region, the primary positive-ion species is thought to be NO⁺, produced by solar Lyman-alpha ionization of NO. Below the altitude of the mesopause, however, the dominant ambient species observed are water-cluster ions of the general type H⁺(H₂O)_n. No satisfactory reaction scheme for producing these cluster ions from NO⁺ has yet been proposed. Following earlier suggestions, a model calculation has been carried out in which successive hydrations of NO⁺ take place through clustering with N₂ and CO₂, followed by “switching” reactions with H₂O. The third hydrate of NO⁺ is then converted into the water-cluster species H⁺(H₂O)₃, and the other water-cluster species are produced by successive clustering and thermal breakup reactions. Many of the reactions involved have not been measured in the laboratory, but reasonable estimates of their rates can be made on the basis of existing measurements of other species. Since both temperature and water-vapor content are of major importance in the model, calculations were carried out for two temperature profiles and two water-vapor profiles. It is shown that the results are in reasonably good agreement with observations as far as the water-cluster species are concerned. Under low-temperature conditions, the model predicts relatively large concentrations of various clusters of NO⁺, in agreement with some observations but in disagreement with others. The importance of sampling breakup of these weakly bound clusters, and their relevance to the free electron concentrations are discussed.  相似文献   

Mass spectrometric measurements of fractional ion abundances in the stratosphere—Negative ions     

F. Arnold  R. Fabian  E.E. Ferguson  W. Joos 《Planetary and Space Science》1981,29(2):195-203

Fractional abundances of stratospheric negative ions are for the first time explicitly reported. The measurements made by balloon-borne ion mass spectrometers also rely on recent studies of electric field induced collisional dissociation of negative cluster ions conducted at our laboratory. These indicate that the negative ion composition measurements around 36 km conducted by our group do not suffer from any significant dissociation. The new composition data support ion identifications NO₃^?(HNO₃)_b and HSO₄^?(H₂SO₄)_c(HNO₃)_d and the underlying ion reactions propo previously. Moreover, it is found that HSO₄^?(H₂SO₄)_g-ions appear to be particularly stable and that H₂SO₄-association is very fast. Implications of the ion composition data for ion processes are discussed.  相似文献   

Ion-ion recombination rates in the earth's atmosphere     

D. Smith  M.J. Church 《Planetary and Space Science》1977,25(5):433-439

The temperature dependence of the binary recombination coefficient, α₂, for the reaction NO⁺+NO₂^? → products has been obtained over the range 185–530 K. It is found that the corresponding mean cross section $\text{σ}$ is described by the power law $\text{σ}\text{? A · T}{}^{\mathrm{?0.9}}$, and that α₂ ? B · T^?0.4. Data has also been obtained for two cluster ion recombination reactions which indicate that their recombination cross sections are only about 40% larger than for the parent ions at a given temperature, the cross sections for these reactions also apparently increasing with decreasing temperature. In the light of this data and by considering the most probable positive and negative ions existing at various altitudes up to 90km in the atmosphere, the most appropriate ionic recombination coefficients in various altitude ranges are deduced. Thus, between 30 and 90 km, where the recombination process is two-body, the coefficient varies over the narrow range 5–9 × 10^?8 cm³s^?1, while below 30 km the process is predominantly three-body with an effective two-body rate increasing rapidly to a maximum value ≈3 × 10^?6 cm³s^?1 in the troposphere, these deductions being based on published laboratory determinations of three-body recombination coefficients.  相似文献   

Measured ion-molecule reaction rates for modelling Titan's atmosphere     

Seksan Dheandhanoo  Rainer Johnsen  Manfred A. Biondi 《Planetary and Space Science》1984,32(10):1301-1305

Rate coefficients for several two- and three-body ion-molecule reactions involving hydrocarbons have been determined at thermal energies and above using drift tube-mass spectrometer techniques. The measured rates for clustering and breakup reactions involving CH₅⁺ and C₂H₅⁺ ions in methane are found to be strongly temperature dependent in the range from 80 to 240 K. The equilibrium constants determined for these reactions differ somewhat from those of Hiraoka and Kebarle. Rate coefficients for two-body reactions of CH₅⁺, C₂H₅⁺, N⁺, H⁺ and D⁺ ions with methane and/or ethane have been measured. The results indicate that the product yields of several of the fast ion-molecule reactions depend strongly on ion energy (temperature), and therefore previous room-temperature results may be of limited value for model calculations of Titan's atmosphere.  相似文献   

Collisional vibrational quenching of O2+(v) and other molecular ions in planetary atmospheres     

H. Böhringer  M. Durup-Ferguson  E.E. Ferguson  D.W. Fahey 《Planetary and Space Science》1983,31(4):483-487

New experimental techniques have yielded several thermal energy vibrational quenching rate constants for O₂⁺(v). Rates for quenching of O₂⁺(v = 1) by O₂, N₂, Ar, CO₂, H₂, and CH₄ are 3(?10), 2(?12), 1(?12), 1(?10), 2.5(?12), and 6(?10) cm³s^?1 at 300 K. The quenching is somewhat faster for O₂⁺(v = 2). The triatomic ions CO₂⁺, NO₂⁺, N₂O⁺, SO₂⁺, and H₂O⁺ are all vibrationally deexcited with an efficiency greater than 10^?3 in Ar or Ne collisions. A theoretical rationalization of the experimental results leads to the prediction that vibrational quenching in planetary atmospheres will generally be efficient, k > 1(?12) cm³s^?1 for almost all ion and neutral gas pairs.  相似文献   

Flowing afterglow studies of temperature dependencies for electron dissociative recombination of HCNH, CH₃CNH and CH₃CH₂CNH and their symmetrical proton-bound dimers     

J.L. McLain 《Planetary and Space Science》2009,57(13):1642-39

A study has been made using a variable temperature flowing afterglow Langmuir probe technique (VT-FALP) to determine the equilibrium temperature dependencies of the dissociative electron-ion recombination of the protonated cyanide ions (RCNH⁺, where R=H, CH₃ and C₂H₅) and their symmetrical proton-bound dimers (RCNH⁺NCR). The power law temperature dependencies of the recombination coefficients, α_e, over the temperature range 180 to 600 K for the protonated ions are α_e(T)(cm³ s⁻¹)=3.5±0.5×10⁻⁷ (300/T)^1.38 for HCNH⁺, α_e(T)=3.4±0.5×10⁻⁷ (300/T)^1.03 for CH₃CNH⁺, and α_e(T)=4.6±0.7×10⁻⁷ (300/T)^0.81 for CH₃CH₂CNH⁺. The equivalent values for the proton-bound dimers are α_e(T)(cm³ s⁻¹)=2.4±0.4×10⁻⁶(300/T)^0.5 for (HCN)₂H⁺ to α_e(T)=2.8±0.4×10⁻⁶(300/T)^0.5 for (CH₃CN)₂H⁺, and α_e(T)=2.3±0.3×10⁻⁶(300/T)^0.5 for (CH₃CH₂CN)₂H⁺. The relevance of these data to molecular synthesis in the interstellar medium and the Titan ionosphere are discussed.  相似文献   

Stratospheric negative ions—detailed height profiles     

A.A. Viggiano  H. Schlager  F. Arnold 《Planetary and Space Science》1983,31(8):813-820

Balloon-borne mass spectrometers with extended mass range have been flown during controlled descents. This gave detailed height profiles of stratospheric negative ions between 15 and 34 km. The main ion families were HSO₄^?(H₂SO₄)_m(HNO₃)_n and NO₃^? (HNO₃)_n Information concerning trace gases is o well as an assessment of the problems of ion fragmentation and contamination. Finally, the data are used to derive information concerning the rate of H₂SO₄ clustering.  相似文献   

Silicon ion chemistry in the ionosphere     

E.E. Ferguson  D.W. Fahey  F.C. Fehsenfeld  D.L. Albritton 《Planetary and Space Science》1981,29(3):307-312

Loss processes which remove Si⁺ ions selectively relative to other meteor-derived atomic ions in the E- and D-regions of the ionosphere have been identified and measured in the laboratory. The major Si⁺ loss in the E-region is the reaction Si⁺ + H₂O → HSiO⁺ + H (1) with a rate constant 2.3 ± 0.9 × 10^?10 cm³s^?1 at 300 K. The corresponding reactions with Fe⁺, Mg⁺ and other metallic meteor ions are endothermic. Presumably (1) is followed by a fast dissociative-recombination with electrons to produce neutral SiO or Si. At lower altitudes Si⁺ ions associate in a three-body reaction with O₂ with a much larger rate constant than the corresponding associations of Fe⁺ and Mg⁺ with O₂.  相似文献   

Ionospheric composition in SAR-arcs     

W.J. Raitt  R.W. Schunk  P.M. Banks 《Planetary and Space Science》1976,24(2):105-114

The high electron temperatures existing within SAR-arcs can result in enhanced vibrational excitation of atmospheric N₂ molecules and, as a consequence, increase the rate coefficient of the reaction, O⁺ + N₂ → NO⁺ + N. This results in a change in the relative abundance of O⁺ and NO⁺+ in the SAR-arc region compared with that in the undisturbed ionosphere. Theoretical ion density profiles were computed by a triple ion analysis solving the mass, momentum and energy equations for O⁺, NO⁺ and O⁺₂ ions self-consistently. Although the electron temperature dependence of the recombination rate of NO⁺ is not well known, the results show that for a range of expected recombination rates NO⁺ still remains the dominant ion up to ca. 320 km at night within a bright SAR-arc. Studies were also made of the relative importance of a downward O⁺ flux and an upward ion drift in maintaining the F-region under SAR-arc conditions. It was found that the upward drift caused a marked increase in the NO⁺/O⁺ transition altitude as high as 460 km at night. However, for typical drift speeds up to 50 m sec^?1 the peak electron density was lower than experimental observations. The effect of a large, short-duration perpendicular electric field on the SAR-arc ion and electron density profiles was found to be small. In all cases considered the magnitude of the enhanced NO⁺ density as a result of vibrationally excited N₂ molecules was sufficient to prevent the electron density within the night-time SAR-arc from becoming vanishingly small.  相似文献   

Winter anomalous D-region over Sardinia (40°N)     

B.S.N. Prasad  S. Mohanty 《Planetary and Space Science》1979,27(11):1333-1342

A simplified D-region model consisting of O₂⁺, NO⁺ and their respective cluster ions grouped as Z_o2⁺ and Z_NO⁺ is used to reproduce the available rocket data on positive ion relative composition and effective clustering rates for the height range 70–90 km. The results of this analysis for a winter anomalous day (Sardinia, 40°N) are in good agreement with the presently known ideas on NO densities, O₂⁺ production rates, mesospheric temperature, negative ion to electron density ratio and effective loss coefficient for electrons. Mesospheric nitric oxide density and temperature profiles from this study are in excellent agreement with the findings of Zbinden et al. (1975) and Hidalgo (1977) for the anomalous day at Sardinia.  相似文献   

Mass spectrometer measurements of the positive ion composition in the D- and E-regions of the ionosphere     

P. A. Zbinden  M. A. Hidalgo  P. Eberhahdt  J. Geiss 《Planetary and Space Science》1975,23(12):1621-1642

On 14 December 1971, during the maximum of the Geminid Meteor Shower, the positive ion composition was measured in the D- and E-regions above Sardinia. The payload was launched at 12:11 UT, and measurements were made between 68.5 and 152 km altitude. A magnetic sector type mass spectrometer with dual collector and a liquid helium cryopump was used. The instrument covered the mass range from 11 to 73 AMU and had a resolution at the 1 % level of M/ΔM = 60.In the E-region two distinct metal ion layers were observed, centred at 95 and 119 km, respectively. In the lower layer Fe⁺ and Mg⁺ were the most abundant metal ions, and in the upper layer Si⁺ was dominant. Si⁺ ions were conspicuously absent in the lower layer (Si⁺/Mg⁺ < 2 × 10⁻³). This particular behaviour of Si could be due to the inability of atomic oxygen to reduce SiO, whereas in the upper layer Si⁺ions might be formed directly by the charge rearrangement reaction SiO + O⁺ → Si⁺+ O₂. In addition, Na⁺, Al⁺, K⁺, Ca⁺, Ti⁺, Cr⁺, Ni⁺ and Co⁺ were also identified. The metal oxide ions AlO⁺ and SiO⁺ were detected, and probably also MgO⁺ and SiOH⁺. The concentrations of NO⁺ and O₂⁺ show a deep minimum at the maximum of the lower metal ion layer. A very high neutral metal density of 6 × 10⁷ cm⁻³ would be required to explain this feature as resulting from charge transfer reactions between the molecular and metal ions Such a high metal density is in contradiction to direct measurements and to cosmic dust influx rates. The isotopic ratios of Mg⁺, Si⁺, and of the major isotopes of Fe⁺ and Ni⁺ were measured, some of them with an accuracy of a few per cent (²⁵Mg⁺/²⁴Mg⁺ = 0.124 ± 0.006; ²⁶Mg⁺/²⁴Mg⁺ = 0.139 ± 0.008; ²⁹Si⁺/²⁸Si⁺ = 0.050 ± 0.004; ⁵⁴Fe⁺/⁵⁶Fe⁺ = 0.069 ± 0.005; ⁵⁷Fe⁺/⁵⁶Fe⁺ = 0.029 ± 0.004; ⁶⁰Ni⁺/⁵⁸Ni⁺ = 0.31 ± 0.12). The isotopic ratios agree within the experimental errors with the corresponding terrestrial ratios, thus giving evidence that these elements have the same isotopic composition in the Geminid meteors as in the Earth's crust, in chrondrites, and in lunar material.In the D-region the ions Na⁺H₂O, Na⁺(H₂O)₂, NaO⁺ and NaOH⁺ were tentatively identified. Below 95 km altitude the relative abundances of the ions 32⁺, 33⁺ and 34⁺ deviate from the values expected for molecular oxygen isotopes. Their abundances can not be explained by the presence of S-ions only, and we conclude that HO₂⁺ and H₂O₂⁺ are present.The ion density profiles of the major D-region constituents show some remarkable deviations from typical D-region conditions. These deviations are related to the winter anomaly in ionospheric absorption observed over Spain during the launch day, and our data represent the first ion composition measurements during such conditions. In particular, H⁺(H₂O)₂ is the major ion only up to 77 km, and at 80 km altitude the NO⁺ concentration exceeds the total water cluster ion density by almost two orders of magnitude. An increase of the mesospheric NO, O₃ and O concentrations as well as of the O/H₂O ratio could explain the observed ion profiles. The low NO⁺/O₂⁺ ratios of approximately unity measured in the E-region are in agreement with a strong downward transport of NO and/or O into the mesosphere during the launch day. A simple four-ion model was used to interpret our D-region data. The calculated neutral NO concentration increases from about 2 × 10⁷ cm⁻³ at 85 km to 5 × 10⁷ cm⁻³ at 80 km. In addition, evidence for an increased O₂⁺ production rate above 83 km was found, probably due to an enhanced O₃ concentration. We conclude that our data strongly support vertical transport of minor neutral consituents as cause of the winter anomaly.  相似文献   

Evidence for excited states of CO₃⁻¹ and NO₃⁻¹ from collisional dissociation processes     

Richard L.C. Wu  Thomas O. Tiernan 《Planetary and Space Science》1981,29(7):735-739

Excitation functions for collision-induced dissociation reactions of CO ₃^? and NO₃^? to give O^? and the corresponding neutral species have been studied using an in-line tandem mass spectrometer. When these ions were prepared from certain gaseous mixtures, larger cross-sections and lower thresholds were observed for the dissociation processes than those found for the same ions in their apparent ground states. These observations suggest the existence of long-lived excited states of CO₃^?1 and NO₃^?1. The heats of formation of these excited ionic states were determined to be ?4.8 ± 0.1 and ?0.3 ± 0.2 eV for CO₃^?1 and NO₃^?1, respectively. Possible implications of these findings with respect to the D -region negative ion reaction scheme are discussed.  相似文献   

Cosmic ray ionization of the Jovian atmosphere     

Louis A. Capone  John Dubach  Robert C. Whitten  Sheo S. Prasad 《Icarus》1979,39(3):433-449

An approximate form of the Boltzmann equation has been used to obtain local ionization rates due to the absorption of galactic cosmic rays in the Jovian atmosphere. It is shown that the muon flux component of the cosmic ray-induced cascade may be especially importannt in ionizing the atmosphere at levels where the total number density exceeds 10¹⁹ cm^?3 (well below the ionospheric layers produced by solar euv). A model containing both positive and negative ion reactions has been employed to compute equilibrium electron and ion number densities. Peak electron number densities on the order of 10³ cm^?3 may be expected even at relatively low magnetic latitudes. The dominant positive ions are NH₄⁺ and C_nH_m⁺ cluster ions, with n ? 2; it is suggested that the absorption of galactic cosmic ray energy at such relatively high pressures in the Jovian atmosphere $\text{(M ? 10}{}^{18}\text{to}\text{10}{}^{20}\text{cm}{}^{\mathrm{?3}}\text{)}$ and the subsequent chemical reactions may be instrumental in the local formation of complex hydrocarbons.  相似文献   

The reaction of O+2 with atomic nitrogen and NO+· H2O and NO+2 with atomic oxygen     

F.C. Fehsenfeld 《Planetary and Space Science》1977,25(2):195-196

The reactions of atomic nitrogen with O⁺₂ and atomic oxygen and atomic nitrogen with NO⁺· H₂O and NO⁺₂ have been measured at 296 K. The rate constants are reported and the implication of the measurements to atmospheric ion chemistry is discussed.  相似文献   

Mass spectrometric measurements of fractional ion abundances in the stratosphere—Positive ions     

F. Arnold  G. Henschen  E.E. Ferguson 《Planetary and Space Science》1981,29(2):185-193

Measured fractional abundances for stratospheric positive ions are reported for the first time. The measurements which were obtained from balloon-borne ion mass spectrometer experiments relied on recent simulation studies of electric field induced cluster ion dissociation conducted at our laboratory.The ion abundance data provide strong support for identifications of the observed ions as H⁺(H₂O)_n and Hx⁺x_L(H₂O)_m proposed previously. Moreover, it is found that x most likely cannot be identified as NaOH or MgOH which implies that gaseous metal compounds do not exist in the middle stratosphere in significant abundances.Implications of the present findings for the composition and chemistry of stratospheric ions as well as for stratospheric aerosols are discussed.  相似文献   

Recombination of electrons with H₃⁺ and H₅⁺ ions     

Jeffrey A. Macdonald  Manfred A. Biondi  Rainer Johnsen 《Planetary and Space Science》1984,32(5):651-654

The dissociative recombination coefficients α for capture of electrons by H₃⁺ and H₅⁺ ions have been determined as a function of electron temperature T_e using a microwave afterglow-mass spectrometer apparatus. At ion and neutral temperatures T_u+ = T_n = 240 K, the coefficient α (H₃⁺) is found to vary slowly with T_e at first, decreasing from 1.6 × 10^?7 cm³/s at T_e = 240 K to 1.2 × 10^?7 cm³/s at T_e = 500 K, thereafter falling as T_e^?1 over the range 500 K ? T_e, ? 3000 K. These results, which have a ± 20% uncertainty, agree satisfactorily over the common energy range (0.03–0.36 eV) with the recombination cross sections determined in merged beam measurements by Auerbach et al. At T₊ = T_n = 128 K, the coefficient α(H₅⁺) is found to be (1.8 ± 0.3) × 10^?6 [T_e(K)/300]^?0.69 cm³/s over the range 128 K ? T_e ? 3000 K, with a more rapid decrease, as T_e^?1, between 3000 K and 5500 K. The implications of these results for modelling planetary atmospheres and interstellar clouds are briefly touched on.  相似文献   

A self-consistent evaluation of the rate constants for the production of the OI 6300 Å airglow     

R. Link  J.C. McConnell  G.G. Shepherd 《Planetary and Space Science》1981,29(6):589-594

The quenching rate k_N2 of $\text{O(}{}^1\text{D)}$ by N₂ and the specific recombination rate α_1D of O₂⁺ leading to $\text{O(}{}^1\text{D)}$ are re-examined in light of available laboratory and satellite data. Use of recent experimental values for the $\text{O(}{}^1\text{D)}$ transition probabilities in a re-analysis of AE-C satellite 6300 Å airglow data results in a value for k_N2 of 2.3 × 10^?11 cm³s^?1 at thermospheric temperatures, in excellent agreement with the laboratory measurements. This implies a value of J_O2 = 1.5 × 10^?6s^?1 for the O₂ photodissociation rate in the Schumann-Runge continuum. The specific recombination coefficient α_1D = 2.1 × 10^?7cm³s^?1 is also in agreement with the laboratory value. Implications for the suggested $\text{N}\text{(}{}^2\text{D) + O}{}_2\text{→ O(}{}^1\text{D) + NO}$ reaction are discussed.  相似文献