Malmheden's theorem revisited

In 1934 H. Malmheden discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin 23 years later, it still does not seem to be widely known. In this paper we return to Malmheden's theorem, give an alternative proof of the result that allows generalization to polyharmonic functions and, also, discuss applications of his theorem to geometric properties of harmonic measures in balls in Euclidean spaces

Range descriptions for the spherical mean Radon transform

The transform considered in the paper averages a function supported in a ball in \RR^n over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic tomography and sonar and radar imaging. Range descriptions for such transforms are important in all these areas, for instance when dealing with incomplete data, error correction, and other issues. Four different types of complete range descriptions are provided, some of which also suggest inversion procedures. Necessity of three of these (appropriately formulated) conditions holds also in general domains, while the complete discussion of the case of general domains would require another publication.Comment: LATEX file, 55 pages, two EPS figure

Friend murine leukemia virus-immortalized myeloid cells are converted into tumorigenic cell lines by Abelson leukemia virus

Friend murine leukemia virus (Fr-MuLV) is a replication-competent murine retrovirus that induces acute nonlymphocytic leukemias in NFS/n mice. Fr-MuLV disease is divided into two stages based on the ability of the leukemia cells to grow in culture and transplant into syngeneic mice. Hematopoietic cells taken from the early stage of disease after Fr-MuLV infection grow as immortal myeloid cell lines in the presence of WEHI-3 cell-conditioned medium (CM) or interleukin 3. These growth factor-dependent cell lines do not grow in culture in the absence of CM and do not form tumors in syngeneic animals. If these Fr-MuLV-infected cells are superinfected with Abelson murine leukemia virus (Ab-MuLV), they lose their dependence on WEHI-3 CM and proliferate in culture in the absence of exogenous growth factors. Concomitant with the loss of growth factor dependence in culture, the Ab-MuLV-infected cell lines become tumorigenic in syngeneic mice. This secondary level of transformation is Ab-MuLV specific. Fr-MuLV-immortalized myeloid cell lines superinfected with Harvey murine sarcoma virus (Ha-MuSV) or amphotropic virus remain dependent on WEHI-3 CM for growth in vitro and are not tumorigenic in vivo. Neither Ab-MuLV- nor Ha-MuSV-infected normal mouse myeloid cell cultures produce growth factor-independent or tumorigenic cell lines. We conclude that at least two genetic events are needed to convert a murine myeloid precursor into a tumorigenic cell line. The first event occurs in Fr-MuLV-infected mice, generating cells that are growth factor dependent but immortal in vitro. The second event, which can be accomplished by Ab-MuLV infection, converts these immortal myeloid precursors into growth factor-independent and tumorigenic cells

Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography

The paper contains a simple approach to reconstruction in Thermoacoustic and Photoacoustic Tomography. The technique works for any geometry of point detectors placement and for variable sound speed satisfying a non-trapping condition. A uniqueness of reconstruction result is also obtained

Thermoacoustic tomography with variable sound speed

We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval, greater than the diameter of the domain. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary

A series solution and a fast algorithm for the inversion of the spherical mean Radon transform

An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centers of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our approach results in an explicit series solution for any closed measuring surface surrounding a region for which the eigenfunctions of the Dirichlet Laplacian are explicitly known - such as, for example, cube, finite cylinder, half-sphere etc. In addition, we present a fast reconstruction algorithm applicable in the case when the detectors (the centers of the integration spheres) lie on a surface of a cube. This algorithm reconsrtucts 3-D images thousands times faster than backprojection-type methods

On the injectivity of the circular Radon transform arising in thermoacoustic tomography

The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation theory to integral geometry, to inverse problems for PDEs, and recently to newly developing types of tomography. The article discusses known and provides new results that one can obtain by methods that essentially involve only the finite speed of propagation and domain dependence for the wave equation.Comment: To appear in Inverse Problem

Extremal discs and the holomorphic extension from convex hypersurfaces

Let D be a convex domain with smooth boundary in complex space and let f be a continuous function on the boundary of D. Suppose that f holomorphically extends to the extremal discs tangent to a convex subdomain of D. We prove that f holomorphically extends to D. The result partially answers a conjecture by Globevnik and Stout of 1991

Time reversal in thermoacoustic tomography - an error estimate

The time reversal method in thermoacoustic tomography is used for approximating the initial pressure inside a biological object using measurements of the pressure wave made on a surface surrounding the object. This article presents error estimates for the time reversal method in the cases of variable, non-trapping sound speeds.Comment: 16 pages, 6 figures, expanded "Remarks and Conclusions" section, added one figure, added reference