摘要:

AbstractA basic notion in the classical theory of differentiation is that of a differentiation base. However, some differentiation type theorems only require the less restricted notion of a contraction. We demonstrate that the classical criteria, such as the covering criteria of de Possel, continue to hold in the new setting.

ISSN:0025-5793    

DOI:10.1112/S0025579300010883

出版商:London Mathematical Society    

年代:1985

数据来源: WILEY

摘要:

AbstractWhen a displacement front meets a heterogeneity in a porous medium, its shape will be altered. The amount of distortion depends on the size and shape of the heterogeneity, the amount of variation of the heterogeneous properties, and the mobility ratio between the displaced and displacing fluids. The solution for a circular permeability discontinuity is known when the capillary pressure is uniform and the mobility ratioMis unity [4]. Here, we extend the theory to the case where there is a small changeεin capillary pressure as well as a nearly unit mobility ratio M = 1 + εγ. Corrections can then be found, in closed form, to first order in ε, to the shape of the front and the pressure field. Computations using these expressions are simpler than the full free‐boundary problem, and some analytical estimates are possible in further limits. Finally, the theory is extended to the case of a front passing a number of such heterogeneous patches which are widely spaced.

ISSN:0025-5793    

DOI:10.1112/S0025579300010895

出版商:London Mathematical Society    

年代:1985

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300010901

出版商:London Mathematical Society    

年代:1985

数据来源: WILEY

摘要:

AbstractThe asymptotic behaviour of a sequence of polynomialscm= cm(v)satisfyingcm+2=12[(m+3)cm+1−∑k=0mcm−kck]is established. These polynomials occur in Hawkins' formula for the residues of a Bessel‐zeta function at its possible poles in the left half plane. The results imply thatcm(v)/cm(0)converges uniformly to cosπVon compact sets. This in turn implies that, forvnot a half odd integer, all but finitely many of the possible poles are actual poles.

ISSN:0025-5793    

DOI:10.1112/S0025579300010913

出版商:London Mathematical Society    

年代:1985

数据来源: WILEY

摘要:

SummarySome interlacing properties of the zeros of the generalized Airy functionsA1(z, p)are given for non‐positive integral values ofp. The result thatA1(z,p)has no real zero forp>12is extended to show that all the zeros ofA1(z,p)are real and simple ifp<12. It is also shown that all the zeros of the functionsBk(z,p, 1) fork= 1, 2, 3 are simple for non‐positive integralp.

ISSN:0025-5793    

DOI:10.1112/S0025579300010925

出版商:London Mathematical Society    

年代:1985

数据来源: WILEY

摘要:

AbstractConsider apoint transformationof the biharmonic equation(∂2∂x2+∂2∂y2)2χ(x, y)=0,namely a coordinate transformationξ=ξ(x, y), η=η(x, y),together with a change of dependent variable given byχ(x, y)=F(ξ, η)φ(ξ, η),for some multiplier F(ξ, η).

ISSN:0025-5793    

DOI:10.1112/S0025579300010937

出版商:London Mathematical Society    

年代:1985

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300010949

出版商:London Mathematical Society    

年代:1985

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300010950

出版商:London Mathematical Society    

年代:1985

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300010962

出版商:London Mathematical Society    

年代:1985

数据来源: WILEY