ISSN:0025-5793    

DOI:10.1112/S0025579300008846

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S002557930000886X

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300008871

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY

摘要:

AbstractAn internal wave motion, below a layer of uniform fluid, induces a weak current on the free surface in the form of a long wave with phase velocity cI. A uniform progressive train of surface waves, whose wave‐length is much shorter than that of the current is incident on it from infinity and undergoes modification. In particular, when the group velocity cgof the progressive wave is equal to cI, the resonance takes place and then, even though the amplitude of the current is small, the interaction builds up near a number of its wavelengths until the train of surface waves is significantly modified. The equations governing the modifications are derived, using the method of multiple scales, and the roles of the Döppler shift and the radiation stress in resonant situations are elucidated. Three‐dimensional interactions are discussed and an analogy is drawn between the fundamental equation describing the interactions and Schrödinger's equation.

ISSN:0025-5793    

DOI:10.1112/S0025579300008883

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300008895

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300008901

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY

摘要:

SummaryIt is proved that, ifRis a set ofrvertices of ann–dimensional cube, then the number of distinct mid‐points of line‐segments joining pairs of points ofR(including the points ofRthemselves as mid‐points) is at leastrx, where∝ = log 3/log 2.This result is (in a sense) best possible.

ISSN:0025-5793    

DOI:10.1112/S0025579300008913

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY

摘要:

abstractIn finding the resistance to the motion of a closely fitting plug along a tube filled with fluid, allowance must be made for the leakage of fluid through the gap between the plug and the tube. If there is no leakage, theoresistance is theoretically infinite. For a plug of lengthdin a tube of radius a and with a gap b between the plug and tube, the dominant term in the resistance comes from the flow in the gap, and is proportional toda/b. If, however, the plug is very short, so that it may be considered as a disk, the calculation of the flow near the disk shows that the resistance is now proportional to aln (a/b) and the presence of the disk increases the force on the tube by an amount equivalent to an increase in length of the tube by only a few radii.

ISSN:0025-5793    

DOI:10.1112/S0025579300008925

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300008937

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300008949

出版商:London Mathematical Society    

年代:1977

数据来源: WILEY