The paley-wiener theorem for the radon transform

We prove that the support of a complex-valued function f in ?^k is contained in a convex set K if and only if the support of its Radon transform k(s, ω) is, for each ω, contained in s ≦ S_K (ω); here S_K is the support function of the set K. This theorem is used to determine the propagation speeds of hyperbolic differential equations with constant coefficients, to prove the nonexistence of point spectrum for a certain class of partial differential operators, and to give a simple reduction of Lions' convolution theorem to the one-dimensional convolution theorem of Titchmarsh.     

Number fluctuation analysis of random locomotion. Statistics of a Smoluchowski process

We analyze a scheme, originally suggested by Smoluchowski, by which a diffusion coefficientD can be estimated by measuring the number of particles occupying a fixed region of a surface at various times. An expression is derived relating the variance of the estimated valueD to several experimental parameters. This expression is evaluated numerically to determine how statistical uncertainty depends on adjustable variables. Particular attention is given to experiments involving locomotion of migrating leukocytes.     

Assessment of pulmonary air trapping and obstruction in expiration: an experimental MRI study

PURPOSE: The aim of this experimental study was to evaluate the potential of a simple expiration technique by means of magnetic resonance imaging (MRI) in an animal model to detect pulmonary air-trapping areas after artificial bronchial obstruction. MATERIAL AND METHODS: Sixteen pigs were evaluated by means of a modified T1-weighted FLASH with fat saturation in respiratory arrest (TR=4.6 ms, TE=1.8 ms, alpha=10 degrees, S.D.=3-5 mm). A measurement of the signal intensity (SI) in the peripheral lung tissue was made in both inspiration and expiration before and after inhalation of 2 ml of 0.5% acetylcholine to simulate a bronchial obstruction. A final measurement of the lung SI was also made after bronchospasmolytic induction through salbutamol (beta2-mimetic bronchodilator). RESULTS: In expiration, a mean SI increase in peripheral lung tissue of about 183% was seen in comparison to inspiration (mean SI increase of 11-32). After inhalation of 0.5% acetylcholine, the expirational signal increase in peripheral lung tissue was only 114% of the original SI. The expirational signal homogeneity decreased after inhalation of acetylcholine. After inhalation of salbutamol, the lung tissue signal elevation in expiration was 193%. CONCLUSION: We interpret the low expiratory signal elevation after acetylcholine inhalation as a result of an air-trapped bronchial constriction in certain areas. The simple expiratory technique in an animal model showed that it is suitable to demonstrate obstructive air trapping using MRI.     

Viscoelastic shear properties of in vivo breast lesions measured by MR elastography

Elastography is a technique to assess the viscoelastic properties of tissue by measuring an acoustic wave propagating though the object. Here, the technique is applied in the course of standard MR mammography to 15 patients with different pathologies (six breast cancer cases, six fibroadenoma cases and three mastopathy cases). Low-frequency mechanical waves are coupled longitudinally into the tissue in order to obtain sufficient wave amplitude throughout the entire breast. This leads to the presence of a substantial fraction of compressional waves, which contribute to the total displacement field. It is shown theoretically that the correct evaluation of these contributions from the compressional wave is rather difficult due to the almost incompressible nature of tissue. To overcome this problem, it is proposed to apply the curl-operator to the measured displacement field in order to completely remove contributions from the compressional wave. Results from simulations and a breast phantom demonstrate the feasibility of the technique. The in vivo results show a good separation between breast cancer and benign fibroadenoma utilizing the shear modulus. Breast cancer appears on average 2.2 (P<.001) times stiffer. All breast cancer cases showed a good delineation to the surrounding breast tissue with an average elevation of a factor of 3.3 (P< 1.4 x 10(-6)). The results as obtained for the shear viscosity do not indicate to be useful for separating benign from malignant lesions.     

Measurement of quantum weak values of photon polarization

We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S1 Stokes parameter more than an order of magnitude outside of the operator's spectrum for the smallest measurement strengths.     

A novel and highly efficient synthetic route to unsymmetrical organoselenides using cesium bases

A new and convenient one-pot method for the preparation of unsymmetrical selenides has been developed. In the presence of cesium hydroxide, molecular sieves, and DMF, benzeneselenol undergoes direct alkylation with various alkyl halides for the synthesis of alkyl phenyl selenides in moderate to excellent yields. Another method to prepare unsymmetrical organoselenides was also completed by coupling terminal alkynes with benzeneselenyl bromide. As an application, the synthesis of a selenopeptide was also accomplished. Furthermore, this methodology was extended to the synthesis of an organoselenide on solid support.     

A comparative study of myo-inositol quantification using LCmodel at 1.5 T and 3.0 T with 3 D 1H proton spectroscopic imaging of the human brain

Myo-inositol is a strongly coupled system and resonates at four chemical shift positions. At 1.5 T, only the singlet component at 3.57 ppm is detected. However, at 3 T this resonance is resolved into its components at 3.55 ppm and 3.61 ppm. Due to the increased spectral resolution and signal-to-noise ratio, it is anticipated that the quantification of myo-inositol should improve at 3 T. Using data from normal controls and the LCmodel quantification procedure, we found that the quantification precision, reproducibility and detection sensitivity of myo-inositol is significantly better at 3 T relative to 1.5 T.     

Oxidation of alkylsilane-based monolayers on gold

The oxidation of alkylsilane monolayers on Au has been studied by X-ray photoelectron spectroscopy, reflection-absorption infrared spectroscopy, contact-angle measurements, and scanning tunneling microscopy. Exposure of the monolayers at 298 K to pure O(2) or H(2)O (>5 x 10(-5) Torr and >150 000 L) does not cause oxidation. Ambient atmosphere only causes oxidation if direct sight lines are maintained to the sample. Ozone exposure results in rapid monolayer oxidation. Oxidation initially occurs only at the Si atom, resulting in formation of a cross-linked siloxane monolayer that retains alkyl surface termination. Prolonged ozone exposures result in the oxidation and subsequent loss of the alkyl chain.