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Mathematical Notes - We obtain the uniform stability of recovering entire functions of special form from their zeros. To such a form, we can reduce the characteristic determinants of strongly... 相似文献
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S.A. Buterin 《Journal of Mathematical Analysis and Applications》2007,335(1):739-749
An inverse spectral problem is studied for a non-selfadjoint Sturm-Liouville operator on a finite interval with an arbitrary behavior of the spectrum. The spectral data introduced generalize the classical discrete spectral data corresponding to the specification of the spectral function in the selfadjoint case. The connection with other types of spectral characteristics is investigated and a uniqueness theorem is proved. A constructive procedure for solving the inverse problem is given. 相似文献
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An inverse nodal problem is studied for the diffusion operator with real-valued coefficients on a finite interval with Dirichlet boundary conditions. The oscillation of the eigenfunctions corresponding to large modulus eigenvalues is established and an asymptotic of the nodal points is obtained. The uniqueness theorem is proved and a constructive procedure for solving the inverse problem is given. 相似文献
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S. A. Buterin 《Mathematical Notes》2006,80(5-6):631-644
We consider a one-dimensional perturbation of the convolution operator. We study the inverse reconstruction problem for the convolution component using the characteristic numbers under the assumption that the perturbation summand is known a priori. The problem is reduced to the solution of the so-called basic nonlinear integral equation with singularity. We prove the global solvability of this nonlinear equation. On the basis of these results, we prove a uniqueness theorem and obtain necessary and sufficient conditions for the solvability of the inverse problem. 相似文献
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Sergey Alexandrovich Buterin 《Results in Mathematics》2007,50(3-4):173-181
The operator of double differentiation perturbed by the composition of a Volterra convolution operator and the differentiation
one on a finite interval with Dirichlet boundary conditions is considered. It is proved that the standard asymptotics is necessary
and sufficient for an arbitrary sequence of complex numbers to be the spectrum of such an operator, which is determined uniquely.
A constructive procedure for solving the inverse problem is given.
Received: March 5, 2007. 相似文献
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S. A. Buterin 《Differential Equations》2010,46(1):150-154
We consider the sum of the Sturm-Liouville operator and a convolution operator. We study the inverse problem of reconstructing
the convolution operator from the spectrum. This problem is reduced to a nonlinear integral equation with a singularity. We
prove the global solvability of this nonlinear equation, which permits one to show that the asymptotics of the spectrum is
a necessary and sufficient condition for the solvability of the inverse problem. The proof is constructive. 相似文献
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We prove uniqueness theorems for so-called half inverse spectral problem (and also for some its modification) for second order differential pencils on a finite interval with Robin boundary conditions. Using the obtained result we show that for unique determination of the pencil it is sufficient to specify the nodal points only on a part of the interval slightly exceeding its half. 相似文献
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Synthetic DNA probes were incubated in human cell extracts to dissect the early step of bulky lesion recognition in the nucleotide excision repair pathway. Excision was induced upon combination of the target adduct with either a two-sided bulge, involving both the damaged sequence and its undamaged partner strand, or a one-sided bulge, affecting exclusively the undamaged complementary sequence. Surprisingly, the same adduct became refractory to repair when only the modified strand was bulged out of the double helix. Adduct removal was further dependent on an intact opposing strand and, at carcinogen-DNA adducts, the assembly of excision complexes was triggered by a single flipped-out deoxyribonucleotide in the complementary sequence. These findings describe a mechanism of molecular readout in DNA repair that, unexpectedly, is entirely confined to the undamaged side of the double helix. 相似文献
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