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1.
Summary An explicit solution is obtained for the system of equations describing the spheroidal motion in a homogeneous, isotropic, gravitating, elastic medium possessing spherical symmetry. This solution is used to derive the Green's dyad for a homogeneous gravitating sphere. The Green's dyad is then employed to obtain the displacement field induced by tangential and tensile dislocations of arbitrary orientation and depth within the sphere.Notation G Gravitational constant - a Radius of the earth - A o =4/3 G - Perturbation of the gravitational potential - Circular frequency - V p ,V s Compressional and shear wave velocities - k p =/V p - k s =/V s - k p [(2.8)] - , [(2.17)] - f l + Spherical Bessel function of the first kind - f l – Spherical Hankel function of the second kind - x =r - y =r - x o =r o - y o =ro - x =r k s - y =r k p - x o =r o k s - y o =r o k p - =a - =a - [(5.17)] - m, l   相似文献   

2.
Equilibrium water uptake and the sizes of atmospheric aerosol particles have for the first time been determined for high relative humidities, i.e., for humidities above 95 percent, as a function of the particles chemical composition. For that purpose a new treatment of the osmotic coefficient has been developed and experimentally confirmed. It is shown that the equilibrium water uptake and the equilibrium sizes of atmospheric aerosol particles at large relative humidities are significantly dependent on their chemical composition.List of symbols A proportionality factor - a w activity of water in a solution - c p v specific heat of water vapour at constant pressure - c w specific heat of liquid water - f relative humidity - l w specific heat of evaporation of water - M i molar mass of solute speciesi - M s mean molar mass of all the solute species in a solution - M w molar mass of water - m 0 mass of an aerosol particle in dry state - m i mass of solute speciesi - m s mass of solute - m w mass of water taken up by an aerosol particle in equilibrium state - m total molality=number of mols of solute species in 1000 g of water - m i molality of solute speciesi - m k total molality of a pure electrolytek - O(m 2) remaining terms being of the second and of higher powers ofm - p + standard pressure - p total pressure of the gas phase - p pressure within a droplet - p 1,p 2,p 3 coefficients in the expansion of M - p 1i, p2i, p3i specific parameters of ioni - p s saturation vapour pressure - p w water vapour pressure - R w individual gas constant of water - r radius of a droplet - r 0 equivalent volume radius of an aerosol particle in dry state - T temperature - T 0 standard temperature - T 1 temperature of the pure water drop in the osmometer - v w specific volume of pure water - z i valence of ioni - i relativenumber concentration of ioni in a solution - correction term due to the adsorption of ions at liquid-solid interfaces - activity coefficient of solute speciesi in a solution, related to molalities - I bridge current - T temperature difference between solution and pure water drop in the osmometer - exponential mass increase coefficient - w specific chemical potential of water vapour - w specific chemical potential of water - 0 w specific chemical potential of pure water vapour - 0 w specific chemical potential of pure water - 0 density of an aerosol particle in dry state - w density of pure water - surface tension of a droplet - 0 surface tension of pure water, i.e., at infinite dilution of the solute - osmotic coefficient - k osmotic coefficient of a solution of a pure electrolytek - k osmotic coefficient of a solution of a mixed solute - M fugacity coefficient of water vapour - s i=1 i z 2 i This work is part of a Ph.D. thesis carried out at the Meteorological Institute of the Johannes Gutenberg-Universität, Mainz.  相似文献   

3.
The palaeo-intensities (F a) of the geomagnetic field in Egypt at some ages are determined by archaeomagnetic measurements and found to be:F a=36.2 T at 3100 B.C., Fa=46.8 T at 3000 B.C.,F a=36.5 T at 2780 B.C., 49.0 T at 2500 B.C., 36.4 T at 2200 B.C., 57.5 T at 1990 B.C., 62.1 T atca 1400 B.C., 61.5 T at 1400 B.C., 69.9 T at 600 B.C., 59.3 T at 550 B.C., 79.9 T at 460 B.C., 73.7 T at 450 B.C., 69.7 T at 320 B.C., 56.2 T at A.D. 50, 64.9 T, at A.D. 400, 54.4 T at A.D. 300, 57.5 T at A.D. 700 and 43.0 T at A.D. 1975.The palaeo-inclinations (I a) at some ages are found to be:I a=24.2° at 420 B.C., 44° at A.D. 50, 60.7° at A.D. 703 and 42° at A.D. 1795.The measured values ofF a are affected by the anisotropy of magnetic susceptibility of the samples by 13% to 20% of the expected correct value. The suitable correction of this effect is by multiplyingF by 1/((1+0.2(/90)) andF by 1/((1–0.13 (/90)), whereF andF are the resultant values ofF a if the laboratory field is perpendicular or parallel to the wall of the sample during the Thelliers' experiments, respectively, and is the angle between the direction of natural remnant magnetization of the sample and the direction of the laboratory field.The results of this paper, together with the previous results for Egypt and the neighbourhoods, lead to the production of the secular variation curve of the geomagnetic field in Egypt for the last 5000 years. The intensity of the field shows a periodicity of about 400 years with multiples.  相似文献   

4.
Summary According to Newton's law of viscosity y = Dvy/dy. But experiments have shown that y is indeed proportional to –dv x/dy for all gases and for homogeneous nonpolymeric liquids. There are however, a few industrially important materials, e.g. plastics, asphalts, crystalline materials that are not described by the equation given by Newton's law of viscosity and they are referred to as non-Newtonian fluids. The steady state rheological behaviour of most fluids can be expressed by the generalised form, y = –(dvy/dy) where may be expressed as a function of eitherdv x/dy or y (where is independent of the rate of shear, the behaviour is Newtonian with =). Numerous empirical equations or models have been proposed to express the steady-state relation between y anddv x/dy. The flow of Newtonian fluids through circular tubes have been discussed before by many. Here we shall discuss the case of two such models of non-Newtonian fluids through circular tubes. The flow of fluids in circular tubes is encountered frequently in Physics, Chemistry, Biology and Engineering.  相似文献   

5.
Summary A forecast model to predict the fluctuations of level AT 500 hPa in a selected grid of points is derived. The solution of the compensation equation is sought in the form of a trigonometric polynomial in three idependent variables. It constitutes the basis of a numerical solution of the prediction problem with the use of a high-speed computer. A three-month forecast of the altitude fluctuation of level 500 hPa is evaluated by means of the daily values of the correlation coefficient. The results are satisfactory and the general evaluation shows the model to be prospective.
¶rt;um nmua ¶rt; ¶rt; na au m AT 500a a uum m m. u au nauu um u¶rt; mu mu nua m m auu n. m u u nmu a¶rt;au a . u¶rt;um a m na au m 500a nu nu m au uuma uu. mam m anumu, u nu ¶rt; n¶rt;mam nnmu.
List of symbols used * coupling coefficient between two conjugate atmospheric elements - * ageostrophicity coefficient of the atmospheric system - Coriolis' parameter (=2 sin) - , * geographic latitude, geographic longitude - *, geopotential reference and pressure levels - , * compensation and coupling frequencies - integration field over the entire atmospheric system - A** constant (A*=2 2(*+*)) - A r ,B r ,C r ,D r constants related to subsystem -r- - A s ,B s ,C s ,D s constants related to subsystem -s- - B** constant (B**= 4(*2+2**)) - C r constant (i=1, 2, 3, 4) - E k ,E v ,E p energies of the atmospheric system: kinetic, internal and potential - K transformation constant - m total number of generalized frequencies - R(T) frequency characteristics of the numerical band filter - r0(t),r1(t) daily values of the correlation coefficient - Q heat - x, y coordinates in the reference plane - t time - p 2 Laplace's differential operator in thep-system  相似文献   

6.
Summary Using the fromulae given byGutenberg andRichter, the writer has computed the magnitude and energy of 1804 earthquakes which occurred in Turkey during the period 1850–1960. For drawing the Isenerget, the formula =log10 S has been used in accordance with the definitions given byToperczer andTrapp, whereS=e i/F·p represents the energy in erg/m2 h corresponding to the surface element of 0.5° Lat. x 0.5° Long. Also the relationship between the seismicity and the tectonics of Turkey has been studied by drawing the maps of the epicenters, the focus-depths and the frequences of the earthquakes with various intensities.  相似文献   

7.
Zusammenfassung Die atmosphärische Aerosolstreuung wird im Bereich 0.52.1 m und 4°40° experimentell untersucht. Sie scheint im Infraroten weitgehend durch die Verhältnisse im Sichtbaren charakterisierbar zu sein, wenn auch die Streudispersion ein unerwartet gegensätzliches Verhalten zeigt. BeiA-ähnlichen, visuellen Streutypen (oder Typen nahe 1) verschwindet diese ab etwa 1.1 m fast vollständig. DieB-ähnlichen, visuellen Streutypen (oder Typen nahe 2) tritt in einem Zwischenbereich (etwa 0.8 bis 1.3 m) starke Streudispersion auf. Für den Gesamtstreutyp wird eine Klassifizierung in Anlehnung an die im Sichtbaren gebräuchliche [11–14]2) vorgeschlagen.
Summary The scattering by the atmospheric aerosol of radiation in the region 0.52.1 m and 4°40° is investigated experimentally. The features in the infrared can be characterized by that in the visible, but the scattering dispersion is found to be different to that expected. At scattering types nearA (or 1) in the visible there is almost no scattering dispersion for 1.1 m. At types nearB (or 2) in the visible a high scattering dispersion in the region between 0.8 m and 1.3 m was observed. For the whole region of wavelength including the infrared a classification similar to that used in the visible [11–14]2) is suggested.

Mitteilungen des Astronomischen Instituts der Universität Tübingen Nr. 77  相似文献   

8.
Multifractal measures,especially for the geophysicist   总被引：9，自引：0，他引：9  
This text is addressed to both the beginner and the seasoned professional, geology being used as the main but not the sole illustration. The goal is to present an alternative approach to multifractals, extending and streamlining the original approach inMandelbrot (1974). The generalization from fractalsets to multifractalmeasures involves the passage from geometric objects that are characterized primarily by one number, namely a fractal dimension, to geometric objects that are characterized primarily by a function. The best is to choose the function (), which is a limit probability distribution that has been plotted suitably, on double logarithmic scales. The quantity is called Hölder exponent. In terms of the alternative functionf() used in the approach of Frisch-Parisi and of Halseyet al., one has ()=f()–E for measures supported by the Euclidean space of dimensionE. Whenf()0,f() is a fractal dimension. However, one may havef()<0, in which case is called latent. One may even have <0, in which case is called virtual. These anomalies' implications are explored, and experiments are suggested. Of central concern in this paper is the study of low-dimensional cuts through high-dimensional multifractals. This introduces a quantityD q, which is shown forq>1 to be a critical dimension for the cuts. An enhanced multifractal diagram is drawn, includingf(), a function called (q) andD q.This text incorporatesand supersedes Mandelbrot (1988). A more detailed treatment, in preparation, will incorporateMandelbrot (1989).  相似文献   

9.
Summary The primary scattering of atmospheric haze is computed by modification of an approximative method evolved byde Bary, basing on skylight measurements carried out on the Musalla, a mountain of 3000 m height in Bulgaria, at various altitudes of the sun and in different horizontal circles at a wavelength of 450 nm. This measured total radiation is reduced by the radiation induced by the scattering at molecules as well as by secondary or multiple scattering at turbidity aerosol. The single scattering of the atmospheric haze thus computed is discussed for various assumed Linke turbidity factors.The concluding deductions relate to a comparison of haze scattering functions with theoretical scattering functions, the results attained agreeing closely with superimposed logarithmic Gaussian distributions and only partly with the scattering functions computed byBullrich. These deductions prove optically the increase of larger particles (r 00.64 m) during forenoon. The analysis of the scattering functions conductes to a shortage of particles withr 0=0.2 m in agreement with other investigations.
Zusammenfassung In Abwandlung einer vonde Bary angegebenen Approximationsmethode wird die Primärstreuung des atmosphärischen Dunstes berechnet. Zugrundegelegt werden Himmelsllichtmessungen, die auf dem etwa 3000 m hohen Mus Alla in Bulgarien bei verschiedenen Sonnenhöhen und in verschiedenen Horizontalkreisen bei einer Wellenlänge von 450 nm durchgeführt wurden. Von dieser gemessenen Gesamtstrahlung werden die Anteile substrahiert, die durch Streuung an Molekülen sowie durch zwei-oder mehrfache Streuung an Trübungsaerosol hervorgerufen werden. Die so berechnete Einfachstreuung des atmosphärischen Dunstes wird für verschiednee angenommene Linke'sche Trübungsfaktoren diskutiert.Abschließend werden die Dunststreufunktionen mit theoretischen Streufunktionen verglichen, wobei eine gute Übereinstimmung mit überlagerten logarithmischen Gauß-Verteilungen und nur teilweise mit vonBullrich berechneten Streufunktionen erzielt wurde. Es kann dabei optisch die Zunahme großer Teilchen (r 00,64 m) im Laufe des Vormittags gezeigt werden. Die Analyse der Streufunktionen führt zu einem Fehlen von Teilchen mitr 0=0,2 m in Übereinstimmung mit anderen Untersuchungen.
  相似文献   

10.
Summary Measuring, with the aid of two filters, the instantaneous intensity of the solar radiation in two wave lengths ( B = 0.44 , R = 0.64 ) by means of a sun photometer designed byVolz, we carried out determinations of the decadic turbidity coefficientB (=0.5 ) and the wave length exponent of the haze extinction for Mexico City. Observations were made for almost two and a half years (1960 to 1962 period). A seasonal size distribution in both parameters was found. Although the data thus obtained are provenient of a contaminated atmosphere, comparison of our data is made with those found for higher latitudes ofÅngström, Schüepp andVolz. The height of the homogeneous haze layerH D was calculated showing pronounced variations for a given wind direction. The maximum and minimum values ofB enable us to get, by the first approximation, the aerosol size distribution ofJunge for our latitudes. However, for exceptional very clear days having maximum actinometric intensity of the solar radiation the sensitivity of the microamperimeter in theVolz sun photometer fails.  相似文献   

11.
Summary Discussion of Pellinen-Ostach's concept of the gravity anomaly for geodetic purposes[3] from the point of view of theoretical exactness and the possibility of unifying gravity maps.

6.2. .  相似文献   

12.
Numerous studies of magnetic fluctuations with a zero mean-field for small magnetic Prandtl numbers (Pr m 1) show that magnetic fluctuations cannot be generated by turbulent fluid flow with the Kolmogorov energy spectrum. In addition, the generation of magnetic fluctuations with a zero mean-field for Pr m 1 were not observed in numerical simulations. However, in astrophysical plasmas the magnetic Prandtl numbers are small and magnetic fluctuations are observed. Thus a mechanism of generation of magnetic fluctuations for Pr m 1 still remains poorly understood. On the other hand, in astrophysical applications (e.g., solar and stellar convection zones, galaxies, accretion disks) the turbulent velocity field cannot be considered as a divergence-free. The generation of magnetic fluctuations by turbulent flow of conducting fluid with a zero mean magnetic field for Pr m 1 is studied by means of linear and nonlinear analysis. The turbulent fluid velocity field is assumed to be homogeneous and isotropic with a power law energy spectrum ( k –p ) and with a very short scale-dependent correlation time. It is found that magnetic fluctuations can be generated when the exponent p > 3/2. It is shown also that the growth rates of the higher moments of the magnetic field are larger than those of the lower moments, i.e., the spatial distribution of the magnetic field is intermittent. In addition, the effect of compressibility (i.e., u 0) of the low-Mach-number turbulent fluid flow u is studied. It is demonstrated that the threshold for the generation of magnetic fluctuations by turbulent fluid flow with u 0 is higher than that for incompressible fluid. This implies that the compressibility impairs the generation of magnetic fluctuations. Nonlinear effects result in saturation of growth of the magnetic fluctuations. Asymptotic properties of the steady state solution for the second moment of the magnetic field in the case of the Hall nonlinearity for the low-Mach-number compressible flow are studied.  相似文献   

13.
The Drude law (molecular refraction) for the temperature radiation in a monoatomic model of the Earth's mantle is derived. The considerations are based on the Lorentz electron theory of solids. The characteristic frequency (or eigenfrequency) of independent electron oscillators (in energy units, ) is identified with the band gapE G of a solid. The only assumption is that solid material related to the Earth's mantle has the mean atomic weight A21 g/mole, and its energy gap (E G) is about 9 eV. In this case the value of molecular refraction (in cm3/g) is (n 2–1)/=0.5160.52, where andn are the density and the refractive index at wavelength D=0.5893 m (sodium light), respectively. The average molecular refraction of important silicate and oxide minerals with A21, obtained byAnderson andSchreiber (1965) from laboratory data, is , where denotes the mean arithmetic value calculated from three principal refractive indices of crystal. For the rock-forming minerals with 19A<24 g/mole the new relation was found byAnderson (1975).  相似文献   

14.
Summary The conditions are studied under which ballistic effects of transmission of waves through opacity barriers can be observed in magnetospheric experiments on board satellites. The mechanism of this effect consists of the regeneration of the radiation beyond the barrier by resonance electrons, modulated by a quasimonochromatic wave incident and reflected from the barrier. Ballistic processes in continuously inhomogeneous plasma are studied. Detailed analysis has been carried out for a barrier with a parabolic density profile. Recommendations are presented as to experimental procedures in circumterrestrial space and data processing. The possibilities are studied of observing ballistic effects in the course of active space experiments with sources of intensive broadband turbulence such as beam of charged particles, injected into the magnetosphere.
¶rt;a u, nu m ¶rt; nmu num aum na m a¶rt;am aumuu m n¶rt;u a namu, au m mum auu uu a a au mau, n¶rt;uau auamu , na¶rt;a a a u maa m . am aumuu n na¶rt;¶rt; na. ma u n¶rt; ¶rt; aa naauu nu nmmu. a ¶rt;auu n n¶rt;u numa nmam u n am ¶rt;a. ¶rt;am m a¶rt;u aumuu m ¶rt; amu uu num umuau umu un mmmu, mauu, a nu a amu umu aum.
  相似文献   

15.
Summary The influence of the velocity of the movement of the centre of the cycloneV c.c. on the rate of amplitudes' change A/t and periods' change T/t of storm microseisms is investigated. The dependence A/t=k V c.c. and T/t=k 1 V c.c. is obtained. Unmovable depression (V c.c. =0) does not stipulate the change of A/t and T/t.
u V c.c. A/t T/t . A/t=k V c.c. T/t=1 V c.c. . (V c.c. =0) A/t T/t.

Presented as a scientific communication to the IASPEI Assembly in Madrid, Sept. 1969.  相似文献   

16.
Summary The paper deals with a comparison of two models used in determining the heat flow qM at the lower boundary of two-dimensional geothermal models of the Earth's crust. Method I is based on a linear relationship between the component of the surface heat flow, which is not generated by heat sources inside the model, and the heat flow qM. This method uses a regularization process, in which the variation of the sought function qM is limited from above. Method II is the most frequently used iterative method, in which the (i + 1)-th approximation of qM is determined from the surface heat flow, corresponding to the i-th approximation of qM used as a boundary condition in solving the direct problem. The comparison of both methods has revealed that the solution obtained by method I satisfies the supposed reality better than the solution obtained by method II. Method II is attractive especially for its simplicity. To eliminate the local variations of the estimated heat flow qM, which are due to automatic transmission from the surface heat flow, a combination of method II with some smoothing procedure could be applied.
¶rt;am ¶rt;a m¶rt;a uu mn nma qM a uau ¶rt; muu ¶rt; . m¶rt; unm u ¶rt; ma nm nma, ma uaa umuau mna mu ¶rt;u, u nm qM. m m¶rt; nu n uauu, auuau auau u uu qM . m m¶rt;, mu nm ¶rt; u n a , umau: (i + 1)-a annuau nma qM um n auma nm nma, ma i- annuauu qM. au ¶rt;m, m nm qM, a¶rt; n m¶rt;, mam n¶rt;naa ¶rt;mummu , u, n m m¶rt;. m m¶rt; nuam nmm. ¶rt; mau a auau a¶rt; nma qM, uu ¶rt;mu amamu na u auau nm nma, ¶rt;a uuam au-u¶rt; m¶rt; auau.
  相似文献   

17.
Summary The complete two-dimensional theory of stresses and displacements in the loaded elastic floating lithosphere is presented. Analytical expressions are derived describing these quantittes as functions of the physical and geometrical parameters of the model. It is shown that horizontal stresses xx may considerably exceed the surface load and that values of xx200 MPa can be generated under certain conditions. Numerical calculations are carried out for geophysically acceptable input parameters.
am na ¶rt;a mu anu u u a n naa um. ¶rt; aaumuu au, nuau mu uu a uu m uuu umuu naam ¶rt;u. aa, muma anu m aum num anu nm au u m¶rt; a m m n¶rt;a 200 a. n u am ¶rt;uuu ¶rt;nmu ¶rt; naam.
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18.
From the events synthesized from the one-dimensional dynamical mass-spring model proposed byBurridge andKnopoff (1967), the relation between rupture length and earthquake momentM is studied for various model parameters. The earthquake moment is defined to be the total displacement of a connected set of mass elements which slide during an event. A parameter stiffness ratios is defined as the ratio of the spring constant between the two mass elements to that between one mass element and the moving plate. The velocity-dependent friction law (including weakening and hardening processes) is taken to control the sliding of a mass element. The distribution of the breaking strengths over the system is considered to be a fractal function. The cases for severals values and different velocity-dependent friction laws with different decreasing ratesr w of the frictional force with sliding velocity are studied numerically. The weakening process of the frictional force from the static one to the dynamic one obviously affects theM– relation. Meanwhile, a rapid weakening process rather than a slow weakening process can result in aM– relation, which is comparable to the observed one. Although an increase in thes value can yield an increase in the upper bound of the value and the number of events with largeM and values, the scaling of theM– relation is not affected by the change of thes value. For the cases in this study, the theoretical –M relations for small events withM<1 are almost in the form: M 1/2, while those for large events withM>1 have a scaling exponent less than but close to 1. In addition, the fractal dimension, the friction drop ratio and the roughness of the distribution of the breaking strengths over the fault surface are the minor parameters influencing the –M relation. A comparison between the theoreticalM– relation and the observed one for strike-slip earthquakes shows that for large events the theoreticalM– relation is quite consistent with the observed one, while for small events there is a one-order difference in the two relations. For the one-dimensional model, the decreasing rate of the dynamic frictional force with velocity is the main factor in affecting the characteristic value of the earthquake moment, at which the scaling of theM– relation changes.  相似文献   

19.
Summary The paper presents, in a condensed form, the fundamentals of global atmospheric energetics that have a bearing on the linear theory of compensation of non-equilibrium states in the Earth's atmosphere. The author introduces a new coordinate system with the vertical coordinate *=Z*/T*, which suits global atmospheric energetice.The relation between the energetics of the atmospheric system as a whole and the mean energetics level (MEL) is shown. Contrary to what has been assumed so far, it is proved that this level is neither an isopycnic level nor a physical surface, where */t=0 applies everywhere.List of Symbols Used x, y, z space coordinates in thez-system - x, y, space coordinates in the -system - t time - p, T, pressure, thermodynamic temperature and air density - p*, T*, pressure, temperature, density and geopotential on the mean energy level - g acceleration of the Earth's gravity - c p ,c v ,R specific temperature under constant pressure, volume and specific gas constant - = c p /c v Poisson's constant - E k ,E v ,E p kinetic, internal and potential energies of the atmospheric system - r'(x,y) correction function to inhomogeneous atmosphere - v, v n magnitude of motion velocity, magnitude of the normal component of velocity - O, S, S 0 volume of the whole atmospheric system, surface limiting volumeO and the Earth's surface - Z S height of surfaceS - arbitrary scalar quantity - H , horizontal differential operators in thez- andp-systems Dedicated to Corresponding Member Vojtch Vítek, Director of the Institute of Physics of the Atmosphere of the Czechoslovak Academy of Sciences, at the occasion of his sixtieth birthday.  相似文献   

20.
The vertical velocity, , and the diabatic heating were computed at 800, 600, 400 and 200 mb surfaces using the Omega equation. The highest contribution to is from the diabatic heating produced by condensation associated with the precipitations appearing to be the main source of diabatic heating. The net radiative cooling and the thermal advection in the upper troposphere over the warm anticyclone result in diabatic cooling over the eastern part of the Bay of Bengal and adjoining northern and eastern regions.List of Symbols Used C p Heat capacity at constant pressure - f Coriolis parameter - g Acceleration due to gravity - P Atmospheric pressure - Q Diabatic heating rate per unit mass - R Gas constant of air - S Static stability parameter - t Time - U, V Zonal and meridional wind components - Specific volume - Relative vorticity - Absolute vorticity - Potential temperature - Geopotential - Vertical velocity (dP/dt) - 1 Adiabatic vertical velocity - 2 Vertical velocity due to certain forcing - 3 Diabatic vertical velocity - Isobaric gradient operator - 2 Laplacian operator - J(A, B) Jacobian operator  相似文献   

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