Symmetry at the Genotypic Level and the Simple Inversion Operator

Author(s):  
Cristian Munteanu ◽  
Agostinho Rosa
Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 925-933 ◽  
Author(s):  
C. T. Barnett

The eddy currents induced in a thin confined conductor by a fixed‐loop time‐domain EM system can be represented by a single equivalent current filament. The equivalent current filament stays in the plane of the conductor at all times during the decay of the secondary field, but tends to migrate from a position of maximum primary field coupling at early time toward the center of the conductor at late time. This filament approximation is used in the design of a least‐squares inversion procedure which fits circular or rectangular current filaments to an observed eddy current distribution. The inversion procedure provides a rapid but precise means of estimating the position, size, and attitude of a conductor which has been detected by a time‐domain EM survey.


2001 ◽  
Vol 6 (1) ◽  
pp. 138-146 ◽  
Author(s):  
P. Plaschinsky

Some results about inversion formula of functional operator with generalized dilation are given. By means of commutative Banach algebra theory the explicit form of inversion operator is expressed. Some commutative Banach algebras with countable generator systems are constructed, their maximal ideal spaces are investigated.


1981 ◽  
Vol 20 (9) ◽  
pp. 1511 ◽  
Author(s):  
Ting-i Wang ◽  
G. M. Lerfald ◽  
V. E. Derr

1991 ◽  
Vol 231 ◽  
pp. 575-598 ◽  
Author(s):  
D. W. Waugh ◽  
D. G. Dritschel

The linear stability of filaments or strips of ‘potential’ vorticity in a background shear flow is investigated for a class of two-dimensional, inviscid, non-divergent models having a linear inversion relation between stream function and potential vorticity. In general, the potential vorticity is not simply the Laplacian of the stream function – the case which has received the greatest attention historically. More general inversion relationships between stream function and potential vorticity are geophysically motivated and give an impression of how certain classic results, such as the stability of strips of vorticity, hold under more general circumstances.In all models, a strip of potential vorticity is unstable in the absence of a background shear flow. Imposing a shear flow that reverses the total shear across the strip, however, brings about stability, independent of the Green-function inversion operator that links the stream function to the potential vorticity. But, if the Green-function inversion operator has a sufficiently short interaction range, the strip can also be stabilized by shear having the same sense as the shear of the strip. Such stabilization by ‘co-operative’ shear does not occur when the inversion operator is the inverse Laplacian. Nonlinear calculations presented show that there is only slight disruption to the strip for substantially less adverse shear than necessary for linear stability, while for co-operative shear, there is major disruption to the strip. It is significant that the potential vorticity of the imposed flow necessary to create shear of a given value increases dramatically as the interaction range of the inversion operator decreases, making shear stabilization increasingly less likely. This implies an increased propensity for filaments to ‘roll-up’ into small vortices as the interaction range decreases, a finding consistent with many numerical calculations performed using the quasi-geostrophic model.


Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1091-1098 ◽  
Author(s):  
Andrew N. Norris ◽  
Bikash K. Sinha

Tube‐wave speed in the presence of a weakly anisotropic formation can be expressed in terms of an effective shear modulus for an equivalent isotropic formation. When combined with expressions for the speeds of the SH‐ and quasi‐SV‐waves along the borehole axis, a simple inversion procedure can be obtained to determine three of the five elasticities of a transversely isotropic (TI) formation tilted at some known angle with respect to the borehole axis. Subsequently, a fourth combination of elastic moduli can be estimated from the expression for the qP‐wave speed along the borehole axis. The possibility of determining all five elasticities of a TI formation based on an assumed correlation between two anisotropy parameters is discussed.


1825 ◽  
Vol 115 ◽  
pp. 317-327 ◽  

Dear Sir, It is more than two years since, in a conversation I had with you on subjects connected with magnetism, you enquired what effect I thought might result from giving to an iron ball a rapid rotation? The subject however dropped, and it did not occur to me again, till in some speculative views in which I was lately engaged, as to the cause of the rotation of the earth's magnetic poles, the apparent irregularity of the terrestrial directive powers, &c. I was led to consider that, probably, rotation might have a certain influence. We know that iron is rendered magnetic by various processes, as drilling, hammering, &c. and it was possible also by rotation; your query now occurred to my mind; and knowing at the same time that Mr. Christie had found a permanent change in the magnetic state of an iron plate by a mere change of position on its axis, it seemed highly probable this change, due only to a simple inversion, would be increased by a rapid rotation. In this respect, however, I was deceived; for I found afterwards, that all the effect that was produced was merely temporary; and if any permanent change did take place, it was too small in my cast iron shell to be observed with the small compass I employed in these experiments. Being however thus urged to the inquiry, as well by my own speculative views as by your query, and encouraged by Mr. Christie’s results, I resolved to put the idea to the test of experiment, and to attempt it at once upon a scale that should decide the question in the first instance.


1984 ◽  
Vol 7 (2) ◽  
pp. 371-396 ◽  
Author(s):  
R. P. Manandhar ◽  
L. Debnath

A study is made of the Post-Widder inversion operator to a class of generalized functions in the sense of distributional convergence. Necessary and sufficient conditions are proved for a given function to have the representation as therth operate of the Post-Widder inversion operator of generalized functions. Some representation theorems are also proved. Certain results concerning the testing function space and its dual are established. A fundamental theorem regarding the existence of the real inversion operator (1.6) withr=0is proved in section4. A classical inversion theory for the Post-Widder inversion operator with a few other theorems which are fundamental to the representation theory is also developed in this paper.


Author(s):  
Craig P. Lusk ◽  
Larry L. Howell

Change-point mechanisms are shown to be significant in the design of surface micromachined MEMS. The design space of change-point mechanisms is derived for an arbitrary single loop change-point mechanism using a global and local approach. A function on the design space, the mechanism’s length, is constructed for fourbars. An inversion operator, a mapping from the design space to the design space, is also constructed for fourbars. The method for constructing the function and the operator is shown to be capable of extension to single loop change-point mechanisms with five or more links. The results give insight into design possibilities and limitations of change-point mechanisms.


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