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81.
82.
A method is proposed which uses a lower-frequency transmit to create a known harmonic acoustical source in tissue suitable for wavefront correction without a priori assumptions of the target or requiring a transponder. The measurement and imaging steps of this method were implemented on the Duke phased array system with a two-dimensional (2-D) array. The method was tested with multiple electronic aberrators [0.39π to 1.16π radians root-mean-square (rms) at 4.17 MHz] and with a physical aberrator 0.17π radians rms at 4.17 MHz) in a variety of imaging situations. Corrections were quantified in terms of peak beam amplitude compared to the unaberrated case, with restoration between 0.6 and 36.6 dB of peak amplitude with a single correction. Standard phantom images before and after correction were obtained and showed both visible improvement and 14 dB contrast improvement after correction. This method, when combined with previous phase correction methods, may be an important step that leads to improved clinical images. 相似文献
83.
Alexander G. Ramm 《Applicable analysis》2013,92(4):833-836
A counterexample is given to the uniqueness result given in the article by Cox and Thompson (1970), "Note on the uniqueness of the solution of an equation of interest in inverse scattering problem." J. Math. Phys ., 11 , N3, 815-817. 相似文献
84.
A. G. Ramm 《Proceedings of the American Mathematical Society》2006,134(4):1059-1063
Let be an unbounded linear operator in a real Hilbert space , a generator of a semigroup, and let be a nonlinear map. The DSM (dynamical systems method) for solving equation consists of solving the Cauchy problem , , where is a suitable operator, and proving that i) 0$">, ii) , and iii) .
Conditions on and are given which allow one to choose such that i), ii), and iii) hold.
85.
A.G. Ramm 《Journal of Mathematical Analysis and Applications》2010,363(2):729-732
A class of infinite-dimensional dissipative dynamical systems is defined for which the slow invariant manifolds can be calculated. Large-time behavior of the evolution of such systems is studied. 相似文献
86.
A.G. Ramm 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1916-1921
Sufficient conditions are given for an implicit function theorem to hold. The result is established by an application of the Dynamical Systems Method (DSM). It allows one to solve a class of nonlinear operator equations in the case when the Fréchet derivative of the nonlinear operator is a smoothing operator, so that its inverse is an unbounded operator. 相似文献
87.
A.G. Ramm 《Physics letters. A》2009,373(33):2988-2991
Let A(β,α,k) be the scattering amplitude corresponding to a real-valued potential which vanishes outside of a bounded domain D⊂R3. The unit vector α is the direction of the incident plane wave, the unit vector β is the direction of the scattered wave, k>0 is the wave number. The governing equation for the waves is [∇2+k2−q(x)]u=0 in R3. For a suitable class M of potentials it is proved that if Aq1(−β,β,k)=Aq2(−β,β,k),∀β∈S2, ∀k∈(k0,k1), and q1, q2∈M, then q1=q2. This is a uniqueness theorem for the solution to the inverse scattering problem with backscattering data. It is also proved for this class of potentials that if , ∀k∈(k0,k1), and q1, q2∈M, then q1=q2. Here is an arbitrarily small open subset of S2, and |k0−k1|>0 is arbitrarily small. 相似文献
88.
89.
90.
A.G Ramm 《Journal of Mathematical Analysis and Applications》1981,80(1):57-66
When does the root system of a nonselfadjoint operator form a Riesz basis of a Hilbert space? This question is discussed in the paper. 相似文献