Special Issue – Mathematical Imaging

The multidisciplinary subject of Imaging Science concerning the generation, collection, duplication, analysis, modification, restoration, enhancement, comparison, feature extraction, and visualisation of images is developing in a rapid speed. It is increasingly used in more and more application areas, especially in cutting edge technologies. Mathematical Imaging firmly establishes mathematics as a rigorous basis for imaging science, complementing the image processing methodologies, in the discrete setting, of computer science and information science

Minimal Production of Prompt Gravitational Waves during Reheating

The inflationary reheating phase begins when accelerated expansion ends. As all Standard Model particles are coupled to gravity, gravitational interactions will lead to particle production. This includes the thermal bath, dark matter and gravitational radiation. Here, we compute the spectrum of gravitational waves from the inflatoncondensate during the initial phase of reheating. As particular examples of inflation, we consider the Starobinsky model and T-models, all of which are in good phenomenological agreement with CMB anisotropy measurements. The T-models are distinguished by the shape of the potential about its minimum and can be approximated by $V \sim \phi^k$, where $\phi$ is the inflaton. Interestingly, the shape of the gravitational wave spectrum (when observed) can be used to distinguish among the models considered. As we show, the Starobinsky model and T-models with $k=2$, provide very different spectra when compared to models with $k=4$ or $k>4$. Observation of multiple harmonics in the spectrum can be interpreted as a direct measurement of the inflaton mass. Furthermore, the cutoff in frequency can be used to determine the reheating temperature.Comment: 11 pages, 4 figure

DETERMINATION OF THE 129I IN PRIMARY COOLANT OF PWR

Among the radioactive wastes generated from the nuclear power plant, a radioactive nuclide such as 129I is classified as a difficult-to-measure (DTM) nuclide, owing to its low specific activity. Therefore, the establishment of an analytical procedure, including a chemical separation for 129I as a representative DTM, becomes essential.In this report, the adsorption and recovery rate were measured by adding 125I as a radio-isotopic tracer (t1/2 = 60.14 d) to the simulation sample, in order to measure the activity concentration of 129I in a pressurized-water reactor primary coolant. The optimum condition for the maximum recovery yield of iodine on the anion exchange resins (AG1 x2, 50-100 mesh, Cl− form) was found to be at pH 7.In this report, the effect of the boron content in a pressurized-water reactor primary coolant on the separation process of 129I was examined, as was the effect of 3H on the measurement of the activity of iodine. As a result, no influence of the boron content and of the simultaneous 3H presence was found with activity concentrations of 3H lower than 50 Bq/mL, and with a boron concentration of less than 2,000 μg/mL

Vertex functions for d-wave mesons in the light-front approach

While the light-front quark model (LFQM) is employed to calculate hadronic transition matrix elements, the vertex functions must be pre-determined. In this work we derive the vertex functions for all d-wave states in this model. Especially, since both of $^3D_1$ and $^3S_1$ are $1^{--}$ mesons, the Lorentz structures of their vertex functions are the same. Thus when one needs to study the processes where $^3D_1$ is involved, all the corresponding formulas for $^3S_1$ states can be directly applied, only the coefficient of the vertex function should be replaced by that for $^3D_1$. The results would be useful for studying the newly observed resonances which are supposed to be d-wave mesons and furthermore the possible 2S-1D mixing in $\psi'$ with the LFQM.Comment: 12 pages, 2 figures, some typos corrected and more discussions added. Accepted by EPJ

Approximation Theory of Total Variation Minimization for Data Completion

Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in the framework of compressed sensing, there are few works on the restoration guarantee of the restoration from partial observations. This paper is to analyze the error of TV based restoration from random entrywise samples. In particular, we estimate the error between the underlying original data and the approximate solution that interpolates (or approximates with an error bound depending on the noise level) the given data that has the minimal TV seminorm among all possible solutions. Finally, we further connect the error estimate for the discrete model to the sparse gradient restoration problem and to the approximation to the underlying function from which the underlying true data comes

Superhydrophobic Waveguide: Liquid-core air-cladding waveguide platform for optofluidics

In this paper, we present an optofluidic waveguide platform consisting of liquid as a core material and air as cladding, enabled by using a superhydrophobic channel featured with hydrophobized high-aspect-ratio sharp-tip nanostructures. The contact of the liquid core with the superhydrophobic channel wall is minimized with an air layer retained between them so that the effective refractive index of the cladding layer is close to that of air. Thus, when light is introduced through the core liquid having a higher refractive index than that of the cladding air at the incident angle parallel to the channel direction less than a critical angle, it is reflected at the liquid-gas interface by the total internal reflection. When the cladding layer is filled with water (i.e., Wenzel state), the waveguide losses for the incident angles of 0 and 10° were ∼3.9 and ∼6.8 dB/cm, respectively. In contrast, when the cladding layer is retained with air (i.e., Cassie-Baxter state), the waveguide losses for the same incident angles were as low as ∼0.1 and ∼1.8 dB/cm, respectively. The significantly lowered waveguide losses at the Cassie-Baxter state indicate that superhydrophobic channels can provide the effective waveguide platform for optofluidics, exploiting the air layer as the cladding material