Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
4 sonuçtan 1-3 arası sonuçlar
Sayfa 10
... derive the following moments for ( 246 ) 11 12 • X2 X1 Su ( x , s ) x11.x2 ... λη dw , Xn u ( x , s ) : So , t = 0,1,2 , ... ) , ( 1 = 1,2 , ... , n ) 1 where So , t is a sphere of radius t with center at the origin . These moments ...
... derive the following moments for ( 246 ) 11 12 • X2 X1 Su ( x , s ) x11.x2 ... λη dw , Xn u ( x , s ) : So , t = 0,1,2 , ... ) , ( 1 = 1,2 , ... , n ) 1 where So , t is a sphere of radius t with center at the origin . These moments ...
Sayfa 12
... derive 1 an equation for v1 ( p , 0 ) . Apply L to ( 3 ) and use formula ( 7 ) for Lv . This results in Lv ( 8 ) = ∞ do d ( ε ) v ( p , ε ) + [ [ ¢ k - 1d ( e ) Vk ( P‚¤ ) + l ( ε ) O 。( e ) } } vo ( O ) 1 k = 1 dz + Ε مرد dz , V。( 2 ...
... derive 1 an equation for v1 ( p , 0 ) . Apply L to ( 3 ) and use formula ( 7 ) for Lv . This results in Lv ( 8 ) = ∞ do d ( ε ) v ( p , ε ) + [ [ ¢ k - 1d ( e ) Vk ( P‚¤ ) + l ( ε ) O 。( e ) } } vo ( O ) 1 k = 1 dz + Ε مرد dz , V。( 2 ...
Sayfa 16
... derive the formula ( 6 ) RK ( r , p ) = 2 Σ { ̧ √r - p + r2 [ 2vg ( r , p ) + ( r − p ) 31 , vg ( r , p ) ] 2 ° j = 1 • exp [ 1k ( -1 ) , ( r , p ) √r = p ] . · It is apparent from this that Ry D { O < p ≤r ≤ 1 } together with { k ...
... derive the formula ( 6 ) RK ( r , p ) = 2 Σ { ̧ √r - p + r2 [ 2vg ( r , p ) + ( r − p ) 31 , vg ( r , p ) ] 2 ° j = 1 • exp [ 1k ( -1 ) , ( r , p ) √r = p ] . · It is apparent from this that Ry D { O < p ≤r ≤ 1 } together with { k ...
İçindekiler
CHAPTER | 1 |
Problem of Determining a Function inside a Circle from | 13 |
On the Problem of Determining a Function from Its Mean | 19 |
Telif Hakkı | |
4 diğer bölüm gösterilmiyor
Diğer baskılar - Tümünü görüntüle
Multidimensional Inverse Problems for Differential Equations M. M. Lavrentiev,V. G. Romanov,V. G. Vasiliev Metin Parçacığı görünümü - 1970 |
Multidimensional Inverse Problems for Differential Equations M. M. Lavrentiev,V. G. Romanov,V. G. Vasiliev Metin Parçacığı görünümü - 1970 |
Sık kullanılan terimler ve kelime öbekleri
absolutely integrable functions analytic function arbitrary belong boundary conditions CAUCHY data chapter consider const continuous function corresponding Denote derive determining a function differential equation domain earth's ellipses ellipsoid of revolution exists expression family of curves following theorem function u(r fundamental solution given GREEN'S function half-plane half-space HOLDER condition hyperplane inequality 16 initial and boundary integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic inverse kinematic problem inverse problem inversion formula kernel L₁ linearized inverse problem M₁ mean values multidimensional inverse problems n₁ obtain operator L defined parameters polar problem for equation problem of determining Q₂ R₁ R₂ relations right-hand side second kind SM,t solution to equation take FOURIER transforms telegraph equation travel-times two-parameter family u₁ M,M,t unique solution uniqueness theorem unit circle values over spheres variables VOLTERRA equation waves wxxx θε ду эф