Capacity-achieving sequences for the erasure channel

This paper starts a systematic study of capacity-achieving (c.a.) sequences of low-density parity-check codes for the erasure channel. We introduce a class A of analytic functions and develop a procedure to obtain degree distributions for the codes. We show various properties of this class which help us to construct new distributions from old ones. We then study certain types of capacity-achieving sequences and introduce new measures for their optimality. For instance, it turns out that the right-regular sequence is c.a. in a much stronger sense than, e.g., the Tornado sequence. This also explains why numerical optimization techniques tend to favor graphs with only one degree of check nodes.     

Gel-casting of transparent magnesium aluminate spinel ceramics fabricated by spark plasma sintering (SPS)

In this paper, a transparent magnesium aluminate spinel ceramic was fabricated through the newest colloidal gel casting method, using a synthetic powder with the average particle size of 90 nm and Isobutylene-Maleic Anhydride (ISOBAM) additive. ISOBAM served as both a dispersant and a gelation agent to achieve a dense body. Also, the suspension rheological behavior was optimized by the solid loading of 85 wt%, the additive content of 0.7 wt%, and the gelation time of 350 s. This led to a green body with a density equal to 65% of theoretical density and the green strength of 14.48 MPa. The results revealed that the reduction of porosity and the uniform distribution of pores in the green body (smaller than half of the initial powder particle size, 35 nm), as accompanied by spark plasma sintering (SPS), resulted in the final body density of 99.97%, as well as the high in-line transmittance of 86.7% at the wavelength of 1100 nm.     

Effect of self-complementary motifs on phase compatibility and material properties in blends of supramolecular polymers

Applicability of supramolecular polymers blending in preparation of materials with tunable properties is reported. The effect of strongly dimerising 2-ureido-4[1H]-pyrimidinone (UPy) end groups on phase compatibility in binary polymer blends was studied. A low molecular weight poly(tetrahydrofuran) diol was functionalized with UPy moieties (PTHF(UPy)₂, a soft material) and mixed with varying amounts of low molecular weight UPy functionalized polycaprolactone di- and triol (PCL(UPy)₂ and PCL(UPy)₃, both relatively strong and stiff materials). Thermal studies showed that T_g of the homopolymers shifted to intermediate temperatures. AFM observation suggested that the phase domain decreased significantly after UPy functionalization of diols. Also the mechanical properties improved at a higher rate than those predicted by the rule of mixtures. These findings indicate that blend components are placed in intimate contact as a result of the UPy-UPy interactions. The reversible crosslinking by PCL(UPy)₃ gave better control still over the mechanical properties of the supramolecular polymer blends.     

Fast and precise Fourier transforms

Many applications of fast Fourier transforms (FFTs), such as computer tomography, geophysical signal processing, high-resolution imaging radars, and prediction filters, require high-precision output. An error analysis reveals that the usual method of fixed-point computation of FFTs of vectors of length 2^l leads to an average loss of l/2 bits of precision. This phenomenon, often referred to as computational noise, causes major problems for arithmetic units with limited precision which are often used for real-time applications. Several researchers have noted that calculation of FFTs with algebraic integers avoids computational noise entirely. We combine a new algorithm for approximating complex numbers by cyclotomic integers with Chinese remaindering strategies to give an efficient algorithm to compute b-bit precision FFTs of length L. More precisely, we approximate complex numbers by cyclotomic integers in Z[e(2πi/2ⁿ)] whose coefficients, when expressed as polynomials in e(2πi/2ⁿ), are bounded in absolute value by some integer M. For fixed n our algorithm runs in time O(log(M)), and produces an approximation with worst case error of O(1/M(2^n-2-1)). We prove that this algorithm has optimal worst case error by proving a corresponding lower bound on the worst case error of any approximation algorithm for this task. The main tool for designing the algorithms is the use of the cyclotomic units, a subgroup of finite index in the unit group of the cyclotomic field. First implementations of our algorithms indicate that they are fast enough to be used for the design of low-cost high-speed/high-precision FFT chips     

Effect of interface on mechanical properties and biodegradation of PCL HAp supramolecular nano-composites

This research explores the correlation between the structural properties of supramolecular biocomposites and their mechanical strength. Hybrid biocomposites composed of surface-modified hydroxyapatite nano-particles and supramolecular polycaprolactone (SP PCL), were prepared at different compositions, and their mechanical, thermal and viscoelastic properties as well as biodegradability, biocompatibility and cytotoxicity were evaluated in vitro. The results were compared with those for SP PCL/naked hydroxyapatite nano-composites. We show that surface modification of hydroxyapatite nanoparticles resulted in outstanding improvement of tensile strength and modulus up to 3.6 and 2.2-fold, respectively. At above 10 wt% HAp and 20 wt% HApUPy, heterogeneous nano-composites with inferior mechanical properties were obtained. Based on rheological (in steady shear mode) and small/wide angle X-ray scattering measurements, unusual improved mechanical properties were ascribed to the formation of supramolecular clusters around nanoparticles. In-vitro degradation of the supramolecular nano-composites was also studied to investigate the overall product biodegradation as well as toxicity of the degradation product(s).     

Determination of performance of non-ideal aluminized explosives

Non-ideal explosives can have Chapman-Jouguet (C-J) detonation pressure significantly different from those expected from existing thermodynamic computer codes, which usually allows finding the parameters of ideal detonation of individual high explosives with good accuracy. A simple method is introduced by which detonation pressure of non-ideal aluminized explosives with general formula C(a)H(b)N(c)O(d)Al(e) can be predicted only from a, b, c, d and e at any loading density without using any assumed detonation products and experimental data. Calculated detonation pressures show good agreement with experimental values with respect to computed results obtained by complicated computer code. It is shown here how loading density and atomic composition can be integrated into an empirical formula for predicting detonation pressure of proposed aluminized explosives.     

Offline Robust Model Predictive Control for Lipschitz Non‐Linear Systems Using Polyhedral Invariant Sets

In this paper the concept of maximal admissible set (MAS) for linear systems with polytopic uncertainty is extended to non‐linear systems composed of a linear constant part followed by a non‐linear term. We characterize the maximal admissible set for the non‐linear system with unstructured uncertainty in the form of polyhedral invariant sets. A computationally efficient state‐feedback RMPC law is derived off‐line for Lipschitz non‐linear systems. The state‐feedback control law is calculated by solving a convex optimization problem within the framework of linear matrix inequalities (LMIs), which leads to guaranteeing closed‐loop robust stability. Most of the computational burdens are moved off‐line. A linear optimization problem is performed to characterize the maximal admissible set, and it is shown that an ellipsoidal invariant set is only an approximation of the true stabilizable region. This method not only remarkably extends the size of the admissible set of initial conditions but also greatly reduces the on‐line computational time. The usefulness and effectiveness of the method proposed here is verified via two simulation examples.     

Flame atomic absorption spectrometric (FAAS) determination of copper,iron and zinc in food samples after solid-phase extraction on Schiff base-modified duolite XAD 761

The present study involves the development of solid-phase extraction (SPE) procedure for the preconcentration of trace amounts of copper (Cu^2 +), iron (Fe^3 +) and zinc (Zn^2 +) ions on duolite XAD 761 modified by bis(2-hydroxyacetophenone)-2,2-dimethyl-1,3-propanediimine(BHAPDMPDI). The complexation between the metal ions and the proposed ligand was investigated potentiometrically. The metal ions retained on the sorbent were quantitatively determined via complexation with BHAPDMPDI. The complexed metal ions were efficiently eluted using 6 mL of 4 mol L^? 1 nitric acid in acetone. The influences of the analytical parameters, including pH, amounts of the ligand and the solid phase, eluent conditions and sample volume, on the recoveries of the metal ions were optimized. Using the optimized parameters, the linear response of the SPE method for Cu^2 +, Zn^2 + and Fe^3 + ions were in the ranges of 0.01–0.34, 0.01–0.28 and 0.02–0.31 μg mL^? 1, respectively, and the detection limits for Cu^2 +, Zn^2 + and Fe^3 + ions were 1.8, 1.6 and 2.4 μg mL^? 1, respectively. The proposed method exhibits a preconcentration factor of 208 for all of the ions studied and an enhancement factor for Cu^2 +, Fe^3 + and Zn^2 + ions of 34, 28 and 38, respectively. The presented results demonstrate the successful application of the proposed method for the determination of these metal ions in some real samples with high recoveries (> 95%) and reasonable relative standard deviation (RDS < 5%).     

Fifth‐order Π‐type load resonant converters analysis based‐on immittance property for constant output current applications

Passive resonant tanks (PRTs) with immittance property are suitable candidates to achieve constant output current in load resonant converters (LRCs). In this paper, fifth‐order Π‐type LC networks are investigated to accede this target. At the first step, fifth‐order Π‐type passive LC networks that can be applied as a PRT are specified based on source and sink natures. Also, their structural advantages are described in detail to give a suitable perspective for the topology selection. At the second step, immittance property is verified for the proposed topologies and immittance PRTs (IPRTs), with their immittance operation conditions, are derived. To confirm the effectiveness, a 150‐W LRC is implemented leveraging new Π‐type IPRTs. A deep investigation is devoted to analyze the current/voltage stress in the components of the designed LRC. Moreover, kVA/kW ratio is considered as a key parameter for the reactive component size minimization. The proposed constant current LRC presents high load regulation capability in addition to the minimum reactive power and zero‐voltage switching (ZVS) on the inverter MOSFETs under the various loads. A significant robustness against load variations, less sensitivity versus parameters variation, and relatively higher efficiency are the main superiorities of the fifth‐order IPRTs to the lower order counterparts.