Abstract:
A double-base representation of an integer n is an expression n = n_1 + ... + n_r, where the n_i are (positive or negative) integers that are divisible by no primes other than 2 or 3; the length of the representation is the number r of terms. It is known that there is a constant a > 0 such that every integer n has a double-base representation of length at most a log n / log log n. We show that there is a constant c > 0 such that there are infinitely many integers n whose shortest double-base representations have length greater than c log n / (log log n log log log n). Our methods allow us to find the smallest positive integers with no double-base representations of several lengths. In particular, we show that 103 is the smallest positive integer with no double-base representation of length 2, that 4985 is the smallest positive integer with no double-base representation of length 3, that 641687 is the smallest positive integer with no double-base representation of length 4, and that 326552783 is the smallest positive integer with no double-base representation of length 5.

Abstract:
A low complexity digital VLSI architecture for the computation of an algebraic integer (AI) based 8-point Arai DCT algorithm is proposed. AI encoding schemes for exact representation of the Arai DCT transform based on a particularly sparse 2-D AI representation is reviewed, leading to the proposed novel architecture based on a new final reconstruction step (FRS) having lower complexity and higher accuracy compared to the state-of-the-art. This FRS is based on an optimization derived from expansion factors that leads to small integer constant-coefficient multiplications, which are realized with common sub-expression elimination (CSE) and Booth encoding. The reference circuit [1] as well as the proposed architectures for two expansion factors α？ = 4.5958 and α′ = 167.2309 are implemented. The proposed circuits show 150% and 300% improvements in the number of DCT coefficients having error ≤ 0:1% compared to [1]. The three designs were realized using both 40 nm CMOS Xilinx Virtex-6 FPGAs and synthesized using 65 nm CMOS general purpose standard cells from TSMC. Post synthesis timing analysis of 65 nm CMOS realizations at 900 mV for all three designs of the 8-point DCT core for 8-bit inputs show potential real-time operation at 2.083 GHz clock frequency leading to a combined throughput of 2.083 billion 8-point Arai DCTs per second. The expansion-factor designs show a 43% reduction in area (A) and 29% reduction in dynamic power (PD) for FPGA realizations. An 11% reduction in area is observed for the ASIC design for α？ = 4.5958 for an 8% reduction in total power ( PT ). Our second ASIC design having α′ = 167.2309 shows marginal improvements in area and power compared to our reference design but at significantly better accuracy.

Abstract:
Transformation and quantization play a critical role in video codecs. Recently proposed algebraic-integer-(AI-) based discrete cosine transform (DCT) algorithms are analyzed in the presence of quantization, using the High Efficiency Video Coding (HEVC) standard. AI DCT is implemented and tested on asynchronous quasi delay-insensitive logic, using Achronix SPD60 field programmable gate array (FPGA), which leads to lower complexity, higher speed of operation, and insensitivity to process-voltage-temperature variations. Performance of AI DCT with HEVC is measured in terms of the accuracy of the transform coefficients and the overall rate-distortion (R-D) characteristics, using HM 7.1 reference software. Results indicate a 31% improvement over the integer DCT in the number of transform coefficients having error within 1%. The performance of the 65？nm asynchronous hardware in terms of speed of operation is investigated and compared with the 65？nm synchronous Xilinx FPGA. Considering word lengths of 5 and 6 bits, a speed increase of 230% and 199% is observed, respectively. These results indicate that AI DCT can be potentially utilized in HEVC for applications demanding high accuracy as well as high throughput. However, novel quantization schemes are required to allow the accuracy improvements obtained. 1. Introduction High dynamic range (HDR) video and image transmission over digital communication channels is undergoing exponential growth [1]. With the increasing demand for high-definition programming, there exists a strong need for efficient digital video coding (DVC) that provides high data compression ratios which in turn leads to better utilization of network resources [2]. The H.264/AVC standard [3] does not provide the required compression ratios for emerging capture and display technologies such as ultra high definition (UHD) [4], multiview [5], and autostereoscopy [6]. To address such emerging needs, the Joint Collaborative Team on Video Coding (JCT-VC) has developed the successor for H.264/AVC, called High Efficiency Video Coding (HEVC) [4]. The HEVC standard aims at achieving a 50% reduction in data rate compared with its predecessors while maintaining low complexity computation. Video compression systems operating at high frequencies and resolutions require hardware capable of significant throughput with tolerable area and power requirements. Real-time video compression circuits having high numerical accuracy are needed for next-generation video [1], coding systems [2, 3, 7], and retina displays [8]. The two-dimensional (2D) 8 8 discrete cosine

Abstract:
This paper addresses the implementation of a filterbank for digital hearing aids using a multi-dimensional logarithmic number system (MDLNS). The MDLNS, which has similar properties to the classical logarithmic number system (LNS), provides more degrees of freedom than the LNS by virtue of having two, or more, orthogonal bases and the ability to use multiple MDLNS components or digits. The logarithmic properties of the MDLNS also allow for reduced complexity multiplication and large dynamic range, and a multiple-digit MDLNS provides a considerable reduction in hardware complexity compared to a conventional LNS approach. We discuss an improved design for a two-digit 2D MDLNS filterbank implementation which reduces power and area by over two times compared to the original design.

Abstract:
Recently we have reported the observation of colossal magnetostriction effect in HoMn2O5 single crystals. Besides we have made the supposition for possible correlation between the peculiarities, observed in the field depended polarization measurements, and the colossal magnetostriction effect at a 4.2 K temperature. In this article we present our results received by polarization and magnetostriction measurements on HoMn2O5 and TbMn2O5 single crystals and the strong correlation between magnetostriction and polarization phase transition for these two compounds. The origin of this correlation is discussed.

Abstract:
Purpose: To determine the normal sonographic features of rabbit kidneys with regard to their use in diagnostic imaging of renal lesions in this species. Materials: Twelve sexually mature clinically healthy New Zealand White rabbits weighing 2.8 kg to 3.2 kg were examined after anaesthesia. Methods: A diagnostic ultrasound system with microconvex multifrequency 6.5 MHz probe was used. The animals were positioned in dorsal recumbency. The transabdominal paravertebral imaging approach was used. Longitudinal and transverse scans of the kidneys were obtained. Six rabbits were sacrificed, their kidneys removed and studied in isotonic liquid medium. Results: The shape of kidneys was elliptical. The fibrous capsule was visualized as a straight hyperechoic band. The fatty capsule was hyperechoic and with irregular borders. The cortex exhibited a heterogeneous echogenicity. The acoustic density of the cortex was lower than that of the liver. The echoicity of the medulla was lower as compared to the cortex and the structures of the kidney pelvis. The latter appeared as a centrally located hyperechoic structure. The post mortem examination showed that kidneys were oval and hyperechoic. The kidney pelvis was seen as a centrally located longitudinal finding, and the renal hilum as a centrally located hyperechoic finding. Conclusions: The transabdominal paravertebral approach was a good method for visualization of rabbit kidneys. The dorsal recumbency of the subjects allowed the visualization. The in vivo results corresponded to those from the post mortem study. The rabbit kidney was oval in shape. The hypoechoic peripheral zone is occupied by the cortex and the medulla, while the hyperechoic central zone by the kidney pelvis. The cortex was less echoic than the liver parenchyma. The kidney pelvic cavity had a lower acoustic density than its walls, due to the presence of peripelvic adipose tissue. The present results could be used in the interpretation of normal and pathological renal findings in the rabbit. [Vet. World 2012; 5(5.000): 274-278]

Abstract:
The article evaluates the application of the precautionary principle at the international level. It employs a comparative study of four cases in global environmental politics: ozone depletion, acid rain,deforestation and coral reef degradation. Contrary to widespread academic notions, the precautionary principle is not widely applied in international environmental policy. The empirical record shows thatgovernments abstain from regulatory policy when they face uncertainty about key aspects of ecological problems. The key question that the literature has ignored is: what kind of uncertainty? Indeed, statesdo take action when the extent of ecological problems is unknown. However, uncertainty about the transboundary consequences of alleged problems prevents international policy. Existing scholarship has misappraised the status of PP in international law, by underspecifying when PP is applied and under what kind of scientific uncertainty.

Abstract:
Conditions for the existence of shear-free and expansion-free non-null vector fields in spaces with affine connections and metrics are found. On their basis Weyl's spaces with shear-free and expansion-free conformal Killing vectors are considered. The necessary and sufficient conditions are found under which a free spinless test particle could move in spaces with affine connections and metrics on a curve described by means of an auto-parallel equation. In Weyl's spaces with Weyl's covector, constructed by the use of a dilaton field, the dilaton field appears as a scaling factor for the rest mass density of the test particle. PACS numbers: 02.40.Ky, 04.20.Cv, 04.50.+h, 04.90.+e

Abstract:
Conditions for the existence of a gyroscope in spaces with affine connections and metrics are found. They appear as special types of Fermi-Walker transports for vector fields, lying in a subspace, orthogonal to the velocity vector field of an observer. PACS numbers: 04.20Cv, 04.90.+e, 04.50.+h, 02.40.Ky

Abstract:
We explore the shadow of certain class of rotating traversable wormholes within classical general relativity. The images depend on the angular momentum of the wormhole, and the inclination angle of the observer. We compare the results with the case of the Kerr black hole. For small angular momenta the shadows for the two solutions are nearly identical, however with the increasing of the angular momentum they start to deviate considerably.