Trkalian fields: ray transforms and mini-twistors

We study X-ray and Divergent beam transforms of Trkalian fields and their relation with Radon transform. We make use of four basic mathematical methods of tomography due to Grangeat, Smith, Tuy and Gelfand-Goncharov for an integral geometric view on them. We also make use of direct approaches which provide a faster but restricted view of the geometry of these transforms. These reduce to well known geometric integral transforms on a sphere of the Radon or the spherical Curl transform in Moses eigenbasis, which are members of an analytic family of integral operators. We also discuss their inversion. The X-ray (also Divergent beam) transform of a Trkalian field is Trkalian. Also the Trkalian subclass of X-ray transforms yields Trkalian fields in the physical space. The Riesz potential of a Trkalian field is proportional to the field. Hence, the spherical mean of the X-ray (also Divergent beam) transform of a Trkalian field over all lines passing through a point yields the field at this point. The pivotal point is the simplification of an intricate quantity: Hilbert transform of the derivative of Radon transform for a Trkalian field in the Moses basis. We also define the X-ray transform of the Riesz potential (of order 2) and Biot-Savart integrals. Then, we discuss a mini-twistor respresentation, presenting a mini-twistor solution for the Trkalian fields equation. This is based on a time-harmonic reduction of wave equation to Helmholtz equation. A Trkalian field is given in terms of a null vector in C3 with an arbitrary function and an exponential factor resulting from this reduction.Comment: 37 pages, http://dx.doi.org/10.1063/1.482610

Cancer cure with organ preservation using radiation therapy

In 1987, the American Cancer Society has anticipated that 965,000 new cases of invasive cancer will be diagnosed in the United States. About 40% of those patients can be treated for cure with organ preservation using radiation therapy. The basic biologic background for such an approach to the problem has become well established. The clinical data to substantiate the validity of the concept date from 1902 until the present. Organ preservation has become a major and important concept in the management of the patient with invasive cancer. New and innovative techniques for treatment are enabling the organ to be preserved, the cancer to be cured, and appropriate cosmesis and function to be preserved. Many tumor sites are appropriate for this treatment technique, including breast, eye, larynx, prostate, soft tissue sarcomas, etc

Increased splenic transplantable colony-forming units related to increased radioresistance after rauscher leukemia virus infection of the sjl/j mouse.

Using the exogenous colony-forming unit (CFU) assay of Till and McCulloch, we studied changes in splenic CFU content as a function of time after Rauscher leukemia virus (RLV) infection of the SJL/J mouse, and we related splenic CFU content to previously reported changes in radiosensitivity after infection. Total splenic CFU content [colony-forming potential (CFP)/spleen] first increased after the 6th day of infection, correlating with the appearance of splenomegaly and of radioresistance. CFP/spleen continued to increase until day 22 after infection, reaching 16 times normal levels. This increase was positively correlated with greater radioresistance. Beyond the 22d day of infection, CFP/spleen fell somewhat but was never <9 times normal values. However, calculations based on existing information regarding spleen cell radiation survival and turnover indicated that this level of splenic CFU was sufficient to provide radioprotection at the level of X-ray exposure used. We conclude, from these studies, that RLV infection increased the number of splenic hematopoietic stem cells of the SJL/J mouse and this increase resulted in the greater radio-resistance