On G 2 Continuous Spline Interpolation of Curves in ℝ d

In this paper the problem of G ² continuous interpolation of curves in ^d by polynomial splines of degree n is studied. The interpolation of the data points and two tangent directions at the boundary is considered. The case n = r + 2 = d, where r is the number of interior points interpolated by each segment of the spline curve, is studied in detail. It is shown that the problem is uniquely solvable asymptotically, e., when the data points are sampled regularly and sufficiently dense, and lie on a regular, convex parametric curve in ^d . In this case the optimal approximation order is also determined.     

Structure of V(2)O(5)*nH(2)O xerogel solved by the atomic pair distribution function technique

A long-standing issue regarding the local and long-range structure of V(2)O(5)*nH(2)O xerogel has been successfully addressed. The full three-dimensional structure of the lamellar turbostratic V(2)O(5)*nH(2)O xerogel was determined by the atomic pair distribution function technique. We show that on the atomic scale the slabs of the xerogel can be described well as almost perfect pairs (i.e., bilayers) of single V(2)O(5) layers made of square pyramidal VO(5) units. These slabs are separated by water molecules and stack along the z-axis of a monoclinic unit cell (space group C2/m) with parameters a = 11.722(3) A, b = 3.570(3) A, c = 11.520(3) A, and beta = 88.65 degrees. The stacking sequence shows signatures of turbostratic disorder and a structural coherence limited to 50 A.     

The Bergman kernel function: Explicit formulas and zeroes

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in defined by the inequality , have zeroes.

     

Focal shift in focused truncated gaussian beams

It is known that under certain circumstances the point of maximum intensity in a focused aberration-free wave is not at the geometrical focus, but is closer to the focusing lens. In the present note such a focal shift is analyzed for the case of a gaussian beam, focused by a thin lens, which fills a circular aperture of any prescribed radius, the waist of the beam being assumed to be located in the aperture plane. Many previously known results follow as limiting cases of our analysis.     

Generalized stokes parameters of random electromagnetic beams

A generalization of the Stokes parameters of a random electromagnetic beam is introduced. Unlike the usual Stokes parameters, which depend on one spatial variable, the generalized Stokes parameters, depend on two spatial variables. They obey precise laws of propagation, both in free space and in any linear medium, whether deterministic or random. With the help of the generalized Stokes parameters, the changes in the ordinary Stokes parameters upon propagation can be determined. Numerical examples of such changes are presented. The generalized Stokes parameters contain information not only about the polarization properties of the beam but also about its coherence properties. We illustrate this fact by expressing the degree of coherence of the electromagnetic beam in terms of one of the generalized Stokes parameters.     

Intra-operative acoustic hemostasis of liver: production of a homogenate for effective treatment

Objective: We have shown that High-Intensity Focused Ultrasound (HIFU) can effectively control bleeding from injuries to solid organs such as liver, spleen, and lung. Achievement of hemostasis was augmented when a homogenate of tissue and blood was formed. The objective of this study was to investigate quantitatively the effect of homogenate production on HIFU application time for hemostasis. Possible mechanisms involved in homogenate production were also studied.Methods: Ten anesthetized rabbits had laparotomy and liver exposure. Liver incisions, 15-25 mm long and 3-4 mm deep, were made followed immediately by HIFU application. Two electrical powers of 80 and 100 W corresponding to focal acoustic intensities of 2264 and 2829 W/cm², respectively were used. Tissue and homogenate temperatures were measured. Smear and histological tissue sample analysis using light microscopy were performed.Results: In treatments with homogenate formation, hemostasis was achieved in 76 ± 1.3 s (Mean ± Standard Error Mean: SEM) at 80 W. In treatments without homogenate formation (at 80 W), hemostasis was achieved in 106 ± 0.87 s. At 100 W, hemostasis was achieved in 46 ± 0.3 s. The time required for homogenate formation, at 80 and 100 W were 60 ± 2.5 and 23 ± 0.3 s, respectively. The homogenate temperature was 83 °C (SEM 0.6 °C), and the non-homogenate tissue temperature at the treatment site was 60 °C (SEM 0.4 °C). The smear and histological analysis showed significant blood components and cellular debris in the homogenate, with some intact cells.Conclusion: The HIFU-induced homogenate of blood and tissue resulted in a statistically significant shorter HIFU application time for hemostasis. The incisions with homogenate had higher temperatures as compared to incisions without homogenate. Further studies of the correlation between homogenate formation and temperature must be done, as well as studies on the long-term effects of homogenate in achieving hemostasis.     

The Möbius Category of Some Combinatorial Inverse Semigroups

\noindent The purpose of this paper is to point out some aspects of the relationship between combinatorial inverse semigroups and their Möbius categories, and to explore combinatorial results arising from combinatorial Brandt semigroups, fundamental simple inverse -semigroups and from the free monogenic inverse semigroup.     

Interlaboratory evaluation of hydrophone sensitivity calibration from 0.1 to 2 MHz via time delay spectrometry

Knowing the low-frequency response of hydrophones, down to 100 kHz at least, is important for accurate biomedical ultrasound measurements. However, current international standards do not extend below 500 kHz. Furthermore, commercial hydrophone sources typically do not supply sensitivity data below 1-2 MHz. Therefore, to help identify and validate practical calibration methods below 2 MHz, the authors have extended their previous individual efforts in an interlaboratory evaluation of sensitivity calibration using the swept-frequency technique, time delay spectrometry (TDS). Calibrations were performed for needle and membrane PVDF hydrophones using each laboratory's TDS system. Each site employed the same purpose-built broadband source transducers, comprising both plano-concave and biconcave 1-3 piezocomposite elements 4 cm in diameter, with maximum and minimum thicknesses of approximately 1.5 and 0.1 cm. Agreement between laboratories was within the estimated measurement precision of +/-0.6 dB. The results demonstrated that a TDS system employing such transducers constitutes a viable method for hydrophone calibrations in this frequency range.