p-Adic Invariant Summation of Some p-Adic Functional Series

We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer argument. In this paper, we present rather large class of such p-adic functional series with integer coefficients which contain factorials. By recurrence relations, we constructed sequence of polynomials A_k(n;x) which are a generator for a few other sequences also relevant to some problems in number theory and combinatorics.Comment: 11 page

Optimization of Lithium Iron Phosphate Battery Charging and Performance

The goal of this project is to efficiently and safely charge a 5kWh battery pack in 15 minutes. Since the project is still in progress, this report describes experiments on a 56Wh battery. Experiments were performed to investigate various charging algorithms (Section 5.2.3), temperature effects (Sections 5.1.1-5.1.3 and 5.2.2) and long term health of the battery pack (Section 5.2.4). An introduction describing the motivation for the project is given in Section 1. Section 2 gives a detailed description of the equipment used including: cells, data acquisition devices, software, sensors, power sources and temperature control. Calculations performed on the data using Matlab are explained in Section 3. The methods for running experiments are described in Section 4. Section 5.1 gives the results for single cell experiments while Section 5.2 gives results for the battery pack. Some conclusions are drawn in Section 6. The report is followed by a few appendices which contain extra graphs.Award N00014-13-1-039

Bosnia and Herzegovina and the new Government Strategy

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A quality assurance phantom for electronic portal imaging devices

Electronic portal imaging device (EPID) plays an important role in radiation therapy portal imaging, geometric and dosimetric verification. Consistent image quality and stable radiation response is necessary for proper utilization that requires routine quality assurance (QA). A commercial ‘EPID QC’ phantom weighing 3.8 kg with a dimension of 25 × 25 × 4.8 cm3 is used for EPID QA. This device has five essential tools to measure the geometric accuracy, signal‐to‐noise ratio (SNR), dose linearity, and the low‐ and the high‐contrast resolutions. It is aligned with beam divergence to measure the imaging and geometric parameters in both X and Y directions, and can be used as a baseline check for routine QA. The low‐contrast tool consists of a series of holes with various diameters and depths in an aluminum slab, very similar to the Las Vegas phantom. The high‐resolution contrast tool provides the modulation transfer function (MTF) in both the x‐ and y‐dimensions to measure the focal spot of linear accelerator that is important for imaging and small field dosimetry. The device is tested in different institutions with various amorphous silicon imagers including Elekta, Siemens and Varian units. Images of the QA phantom were acquired at 95.2 cm source‐skin‐distance (SSD) in the range 1–15 MU for a 26 × 26 cm2 field and phantom surface is set normal to the beam direction when gantry is at 0° and 90°. The epidSoft is a software program provided with the EPID QA phantom for analysis of the data. The preliminary results using the phantom on the tested EPID showed very good low‐contrast resolution and high resolution, and an MTF (0.5) in the range of 0.3–0.4 lp/mm. All imagers also exhibit satisfactory geometric accuracy, dose linearity and SNR, and are independent of MU and spatial orientations. The epidSoft maintains an image analysis record and provides a graph of the temporal variations in imaging parameters. In conclusion, this device is simple to use and provides testing on basic and advanced imaging parameters for daily QA on any imager used in clinical practice

The Perils of Adapting to Dose Errors in Radiation Therapy

We consider adaptive robust methods for lung cancer that are also dose-reactive, wherein the treatment is modified after each treatment session to account for the dose delivered in prior treatment sessions. Such methods are of interest because they potentially allow for errors in the delivered dose to be corrected as the treatment progresses, thereby ensuring that the tumor receives a sufficient dose at the end of the treatment. We show through a computational study with real lung cancer patient data that while dose reaction is beneficial with respect to the final dose distribution, it may lead to exaggerated daily underdose and overdose relative to non-reactive methods that grows as the treatment progresses. However, by combining dose reaction with a mechanism for updating an estimate of the uncertainty, the magnitude of this growth can be mitigated substantially. The key finding of this paper is that reacting to dose errors – an adaptation strategy that is both simple and intuitively appealing – may backfire and lead to treatments that are clinically unacceptable.Natural Sciences and Engineering Research Council of Canada (Canadian Institutes of Health Research Collaborative Health Research Project Grant 398106-2011

Optical Properties of ZnP2 Nanoparticles in Zeolite

We report that for the first time the nanoparticles of II-V semiconductor (ZnP2) were prepared and studied. ZnP2 nanoparticles were prepared by incorporation into zeolite Na-X matrix. Absorption, diffuse reflection (DR) and photoluminescence (PL) spectra of the ZnP2 nanoclusters incorporated into the supercages of zeolite Na-X were measured at the temperature 77 K. Five bands B1-B5 are observed in both the DR and PL spectra demonstrating the blue shift from the line of free exciton in bulk crystal. We attribute the B1-B5 bands to some stable nanoclusters with size less than the size of zeolite Na-X supercage. We observed Stokes shift of the PL bands from the respective absorption bands. The nonmonotonic character of its dependence on the cluster size can be explained as the result of competition of the Frank-Condon shift and the shift due to electronic relaxation.Comment: Submitted to Microporous and Mesoporous Material

Data Lifetime Estimation in a Multicast-Based CoAP Proxy

In this work we consider kernel-based record lifetime estimation in a proactive Internet of Things (IoT) proxy with multicast based cache management. Multicast refreshment requests were based on lifetime expiration for a predefined number of records. To reduce the traffic volume in the IoT domain, we assume that only nodes where the observed physical variable has changed its value will respond to the multicast request. For estimating the data lifetime at the proxy, we use Gaussian kernels, assuming that the intrinsic data lifetime probability distribution was taken from Erlang-k family of sub-exponential distributions. In this setup, we consider that the proxy connects to the IoT domain using an IEEE 802.15.4-compatible wireless network. Results indicate that narrow and symmetrical lifetime probability distributions require more frequent multicasting refreshments compared to wider and asymmetric ones. This increases traffic intensity and energy consumption in IoT domain. We quantify finding with numerical results