Viewing Ci(n,m) as entries of the Ni|Ni matrix Ci, we note that this matrix is symmetric because both the displacement vector D~d(m,n)D~D{~d(n,m)D~D~d(n,m)D and the track-segment length l(n,m)~l(m,n) are invariant under the time reversal operation n<m such that C(n,m)~C(m,n). Furthermore, the diagonal elements of Ci take values Ci(k,k)~1 because D~di(k,k)D~li(k,k) for all k. In general, 0ƒCi(n,...

The phenomenon of magnetization reversal in a hard magnet is studied analytically within a framework of a simplified energy minimization model for a two grain system. The transition region ~a domain wall-like moment structure! is found to play a crucial role in nucleating a reversed domain and in the subsequent formation of a domain wall near the grain boundary. This is shown to result in a con...

Transverse muon polarization in the K → μνγ decay is calculated in the model with scalar and pseudo scalar four-Fermi interactions. Combined with a similar calculation in theK → μνπ decay, a possible constraint on parameters in the three-Higgs model is obtained assuming sensitivity of the up-coming KEK experiment. It is pointed out that the predictions for the two polarizations are strongly cor...

The technique of in-situ associative permuting is introduced which is an association of in-situ permuting and in-situ inverting. It is suitable for associatively permutable permutations of {1, 2, . . . , n} where the elements that will be inverted are negative and stored in order relative to each other according to their absolute values. Let K[1 . . . n] be an array of n integer keys each in th...

Data from the muon g-2 experiment at Brookhaven National Lab has been analyzed to search for a muon electric dipole moment(EDM), which would violate parity and time reversal symmetries. An EDM would cause a tilt in the spin precession plane of the muons, resulting in a vertical oscillation in the position of electrons hitting the detectors. No signal has been observed. Based on this analysis, a...

We analyze the mathematical model of multiwave tomography with a variable speed with integrating measurements on planes tangent to a sphere surrounding the source. We prove sharp uniqueness and stability estimates with full and partial data and propose a time reversal algorithm which recovers the visible singularities.

We introduce time reversed absorbing conditions (TRAC) in time reversal methods. They enable one to “recreate the past” without knowing the source which has emitted the signals that are back-propagated. Two applications in inverse problems are presented. The method does not rely on any a priori knowledge of the physical properties of the inclusion. Numerical tests with the wave equation illustr...

In this paper we investigate the existence of permutation polynomials of the form F(x) = xd + L(x) over GF(2n), L being a linear polynomial. The results we derive have a certain impact on the long-term open problem on the nonexistence of APN permutations over GF(2n), when n is even. It is shown that certain choices of exponent d cannot yield APN permutations for even n. When n is odd, an infini...

Laboratory studies were performed in order to determine and enhance the possibility to localize microdamage based on a combination of classical time reversal techniques and nonlinear elastic wave response. The use of emitters having a more or less chaotic shape is investigated. Its benefit is clearly found in breaking the symmetry of the problem, leading to an unambiguous retrofocusing. Further...