A review of research into the uses of low level ultrasound in cancer therapy

The use of low power ultrasound in therapeutic medicine is a developing field and this review will concentrate on the applications of this technology in cancer therapy. The effects of low power ultrasound have been evaluated in terms of the biological changes induced in the structure and function of tissue. The main fields of study have been in sonodynamic therapy, improving chemotherapy, gene therapy and apoptosis therapy. The range of ultrasonic power levels that can be effectively employed in therapy appears to be narrow and this may have hindered past research in the applications in cancer treatment.     

Layer Communities in Multiplex Networks

Journal of Statistical Physics - Multiplex networks are a type of multilayer network in which entities are connected to each other via multiple types of connections. We propose a method, based on...     

A novel editing technique for F MRI: Molecule-specific imaging

A novel technique is proposed to facilitate the selective imaging of specific molecules from a mixture. The application of the technique presented here demonstrates the ability to selectively produce ¹⁹F MR images of either trifluoroacetic acid or the perfluorocarbon emulsion Oxypherol-ET (perfluorotributylamine), when both molecules are present simultaneously. Selective detection is based on the presence of homonuclear J-modulation in one molecule and differential spin-spin relaxation time (T₂). Perfluorotributylamine, an A₃B₂ system, is subject to homonuclear J-modulation, which produces a null signal from the antiphase components of the triplet (A₃) when an echo time is used in a spin-echo image. At this echo time the second molecule, in this example trifluoroacetic acid, a non-coupled spin system, is selectively imaged. At longer echo times, e.g., TE = 1/J there is substantial recovery of the J-modulated signal, which may be solely observed due to T₂ decay of the trifluoroacetic acid signal. The method is demonstrated both using phantoms and in vivo.     

Pionic K X-rays in liquid He

Energies and lorentzian widths of pionic K X-ray transitions have been measured in liquid ³He with improved accuracy. The strong interaction on the π³He 1s level is found to be attractive and to produce an increase in the K transition energies of 34 ± 4 eV; the measured lorentzian width is 36 ±7 eV. Measured values are also presented for K X-ray energies in liquid π⁴He and μ⁴He, the lorentzian width of the 1s level in π⁴He, and relative intensities of K X-ray transitions in π³He, π⁴He and μ⁴He. The measurements are compared with those of others and with recent theoretical calculations.     

Group invariant solution for a pre-existing fluid-driven fracture in impermeable rock

The propagation of a two-dimensional fluid-driven fracture in impermeable rock is considered. The fluid flow in the fracture is laminar. By applying lubrication theory a partial differential equation relating the half-width of the fracture to the fluid pressure is derived. To close the model the PKN formulation is adopted in which the fluid pressure is proportional to the half-width of the fracture. By considering a linear combination of the Lie point symmetries of the resulting non-linear diffusion equation the boundary value problem is expressed in a form appropriate for a similarity solution. The boundary value problem is reformulated as two initial value problems which are readily solved numerically. The similarity solution describes a preexisting fracture since both the total volume and length of the fracture are initially finite and non-zero. Applications in which the rate of fluid injection into the fracture and the pressure at the fracture entry are independent of time are considered.     

Ultrasonic technology for enhanced oil recovery from failing oil wells and the equipment for its implemention

A new method for the ultrasonic enhancement of oil recovery from failing wells is described. The technology involves lowering a source of power ultrasound to the bottom of the well either for a short treatment before removal or as a permanent placement for intermittent use. In wells where the permeability is above 20 mD and the porosity is greater than 15% ultrasonic treatment can increase oil production by up to 50% and in some cases even more. For wells of lower permeability and porosity ultrasonic treatment alone is less successful but high production rates can be achieved when ultrasound is applied in conjunction with chemicals. An average productivity increase of nearly 3 fold can be achieved for this type of production well using the combined ultrasound with chemical treatment technology.     

Constrained near-minimax approximation by weighted expansion and interpolation using Chebyshev polynomials of the second,third, and fourth kinds

Well known results on near-minimax approximation using Chebyshev polynomials of the first kind are here extended to Chebyshev polynomials of the second, third, and fourth kinds. Specifically, polynomial approximations of degreen weighted by (1–x ²)^1/2, (1+x)^1/2 or (1–x)^1/2 are obtained as partial sums of weighted expansions in Chebyshev polynomials of the second, third, or fourth kinds, respectively, to a functionf continuous on [–1, 1] and constrained to vanish, respectively, at ±1, –1 or +1. In each case a formula for the norm of the resulting projection is determined and shown to be asymptotic to 4^–2logn +A +o(1), and this provides in each case and explicit bound on the relative closeness of a minimax approximation. The constantA that occurs for the second kind polynomial is markedly smaller, by about 0.27, than that for the third and fourth kind, while the latterA is identical to that for the first kind, where the projection norm is the classical Lebesgue constant _n . The results on the third and fourth kind polynomials are shown to relate very closely to previous work of P.V. Galkin and of L. Brutman.Analogous approximations are also obtained by interpolation at zeros of second, third, or fourth kind polynomials of degreen+1, and the norms of resulting projections are obtained explicitly. These are all observed to be asymptotic to 2^–1logn +B +o(1), and so near-minimax approximations are again obtained. The norms for first, third, and fourth kind projections appear to be converging to each other. However, for the second kind projection, we prove that the constantB is smaller by a quantity asymptotic to 2^–1log2, based on a conjecture about the point of attainment of the supremum defining the projection norm, and we demonstrate that the projection itself is remarkably close to a minimal (weighted) interpolation projection.All four kinds of Chebyshev polynomials possess a weighted minimax property, and, in consequence, all the eight approximations discussed here coincide with minimax approximations when the functionf is a suitably weighted polynomial of degreen+1.     

The Minimality Properties of Chebyshev Polynomials and Their Lacunary Series

By considering four kinds of Chebyshev polynomials, an extended set of (real) results are given for Chebyshev polynomial minimality in suitably weighted Hölder norms on [–1,1], as well as (L ) minimax properties, and best L ₁ sufficiency requirements based on Chebyshev interpolation. Finally we establish best L _p , L and L ₁ approximation by partial sums of lacunary Chebyshev series of the form _i=0 a ⁱ _b ⁱ(x) where _n (x) is a Chebyshev polynomial and b is an odd integer 3. A complete set of proofs is provided.     

Laurent-Padé approximants to four kinds of Chebyshev polynomial expansions. Part II: Clenshaw-Lord type approximants

Laurent-Padé (Chebyshev) rational approximantsP _m (w, w ⁻¹)/Q _n (w, w ⁻¹) of Clenshaw-Lord type [2,1] are defined, such that the Laurent series ofP _m /Q _n matches that of a given functionf(w, w ⁻¹) up to terms of orderw ^±(m+n) , based only on knowledge of the Laurent series coefficients off up to terms inw ^±(m+n) . This contrasts with the Maehly-type approximants [4,5] defined and computed in part I of this paper [6], where the Laurent series ofP _m matches that ofQ _n f up to terms of orderw ^±(m+n ), but based on knowledge of the series coefficients off up to terms inw ^±(m+2n). The Clenshaw-Lord method is here extended to be applicable to Chebyshev polynomials of the 1st, 2nd, 3rd and 4th kinds and corresponding rational approximants and Laurent series, and efficient systems of linear equations for the determination of the Padé-Chebyshev coefficients are obtained in each case. Using the Laurent approach of Gragg and Johnson [4], approximations are obtainable for allm≥0,n≥0. Numerical results are obtained for all four kinds of Chebyshev polynomials and Padé-Chebyshev approximants. Remarkably similar results of formidable accuracy are obtained by both Maehly-type and Clenshaw-Lord type methods, thus validating the use of either.