Ternary Matrix Research Articles

An input variable partitioning algorithm for functional decomposition of a system of Boolean functions based on the tabular method

Functional decomposition is a fundamental method for the optimization of multi-level logic circuits by breaking down a complex circuit into smaller and hopefully simpler sub-circuits. The problem of searching for an appropriate partition of input variables is the first step in the decomposition process, and it is a challenging task in the logic synthesis. The serial, two-block disjoint decomposition of a system of completely specified Boolean functions is investigated. An input variable partitioning algorithm is proposed, which is used for functional decomposition along with a tabular method. It is based on using the ternary matrix cover approach. A method for constructing the cover map that has the structure of the Karnaugh map is also presented. It is used in a step of the tabular method during the decomposition. There is a chance in a decomposable system, to choose such a solution of the task to reduce the circuit size exponentially. The paper emphasizes on obtaining the best possible partition in an efficient manner. A set of experiments has been carried out on the generated systems of Boolean functions and standard benchmarks. The results confirm the efficiency and effectiveness of the suggested algorithm along with the ternary matrix cover approach. The obtained solutions are optimal in the most cases, according to a certain criterion.

Improved Decomposition for a System of Completely Specified Boolean Functions

Functional decomposition is an important and powerful technique in the logic synthesis. The ternary matrix cover approach is one of the existing methods of this type. This method is also used in decomposition of a system of completely specified Boolean functions. Before constructing the desired superposition, it needs to encode a table. There is a trivial encoding method. But to find a better solution, it is important to use a special approach, because the result of the encoding has a direct influence on the obtained functions. In this paper, an efficient algorithm to encode this table is presented. It uses the approach connected with the assembling Boolean hyper cube method. The proposed algorithm is explained in details with an example. The benefits and impacts of the suggested technique are also discussed.

Propagation modeling of active P2P worms based on ternary matrix

Propagation modeling of worms has become an attractive research field in recent years since it facilitates worm prediction, detection, analysis and prevention etc. In this work, we propose a novel ternary-matrix-based model to describe the propagation trend of active P2P worms. Compared to existing logic-matrix-based models, our model takes the time lags into consideration by introducing new states and special matrix operations. Our model is easy of derivation and deployment because it confines derivation process to pure matrix operations. Moreover, two other advantages of our model are fully explored. One is expressiveness: (1) practical P2P topology can be modeled in the topology matrix; (2) the state of any node can be identified at any time; (3) and the attack path of any node can be backtracked in linear time. Flexibility is the other merit: our model can adapt to different scenes by changing the related parameters, particularly our model is general for different kinds of time lags and P2P topologies.

Effect of Feed Composition on the Gas Separation Performance of Binary and Ternary Mixed Matrix Membranes

Binary and ternary component mixed matrix membranes comprised of zeolite 4A and p-nitroaniline (pNA) in the polycarbonate (PC) matrix were prepared and appraised in gas separation. For comparison, homogenous membranes of PC and PC/pNA membranes were also investigated. The membranes were utilized to separate binary mixtures of CO2/CH4, H2/CH4, and CO2/N2. The effect of feed composition on the separation performance of membranes was investigated. Separation factors and ideal selectivities were similar for the PC membrane. A similar trend was also observed with the PC/pNA membrane. The separation factors of the PC/pNA membrane for CO2/CH4 were almost twice as high as those of the PC membrane regardless of the feed composition. The ideal selectivities were, however, higher than separation factors for PC/zeolite 4A and PC/pNA/zeolite 4A membranes. The PC/ pNA/zeolite 4A membrane has separation factors of 18 for 77% CO2/ 23% CH4 mixture, and 40 for 20% CO2/ 80% CH4 mixture, respectively. The separation factors of the mixed matrix membranes depended on the feed composition strongly. The PC/ pNA/zeolite 4A membrane had higher separation factors and lower permeabilities than the PC/zeolite 4A membrane. pNA assisted to eradicate partly the detrimental effects of interfacial voids and improved the molecular sieving effect of zeolite 4A dispersed in the PC.

Microporous network-assisted formation of copper-in-polymer gradient composite film

In this article, a copper-in-polymer-gradient composite film (CPGCF) was synthesized by electrochemical strategy via reducing a solvent-swollen cathode film (SCF). The latex nanoparticles of a ternary copolymer including styrene, butyl acrylate, and acrylic acid structural units play the key role to form well-graded copper distribution in this ternary copolymer matrix through the porous morphological structure developed by latex nanoparticle semimelt joining. The morphological structure along cross-section of CPGCF includes three layers: (1) a dense copper layer in ternary copolymer matrix whose most outside was originally attached to cathode in electrochemical reactor, (2) a shrublike layer that grew from dense copper layer, and (3) a clear layer in which there is no obvious reduced copper phase whose most outside was originally contacted with liquid electrolyte medium in electrochemical reactor. As experimental aspects, the influences of emulsion polymerization conditions of ternary copolymer, predrying time and temperature of SCF, dc voltage in electrochemical reduction on CPGCF structure were investigated. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

An Algorithm for Excluding Redundant Assessments in a Multiattribute Utility Problem

The construction of a multiattribute utility function (MUF) is a fundamental step in decision analysis and can be a difficult task to perform unless some decomposition of the utility function is performed. When partial utility independence conditions exist, the functional form is decomposed into a number of lower-order utility assessments. Often the functional form, resulting from such independence conditions, includes duplicate and redundant assessments. This paper introduces a twos-complement exclusion algorithm for determining the minimal set of utility assessments required for a MUF with partial utility independence. The algorithm uses a ternary matrix representation of utility assessments. A comparison with a “brute-force” approach is also provided.

A Study on Embedding Efficiency of Matrix Encoding

In this paper, the authors examine embedding efficiency, which influences the most concerned performance of steganography, security, directly. Embedding efficiency is defined as the number of random message bits embedded per embedding change. Recently, matrix embedding has gained extensive attention because of its outstanding performance in boosting steganographic schemes’ embedding efficiency. Firstly, the authors evaluate embedding change not only on the number of changed coefficients but also on the varying magnitude of changed coefficients. Secondly, embedding efficiency of matrix embedding with different radixes is formularized and investigated. A conclusion is drawn that ternary matrix embedding can achieve the highest embedding efficiency.

Application of albumin-grafted scaffolds to promote neocartilage formation

This study investigates the capacity of albumin-grafted biomaterials as tissue engineering scaffolds to regenerate cartilaginous components. Porcine knee chondrocytes were seeded and cultivated in porous ternary matrix consisting of polyethylene oxide, chitin, and chitosan with surface albumin. The results revealed that the quantity of albumin did not affect the viability of porcine knee chondrocytes in the constructs. However, a high grafting concentration of albumin favored the adhesion of porcine knee chondrocytes on the scaffolding pore surface. After cultivation over 4 weeks, an increase in the concentration of albumin enhanced the quantities of porcine knee chondrocytes, glycosaminoglycans, and collagen in the constructs. The histological staining of porcine knee chondrocytes showed an active chondrocytic growth in the albumin-grafted constructs. In addition, the safranin-O staining indicated that the surface albumin could stabilize the secretion of glycosaminoglycans. Moreover, the immunochemical staining against type II collagen exhibited a regular production of collagen by phenotypic porcine knee chondrocytes in the constructs. Albumin-grafted polyethylene oxide/chitin/chitosan scaffolds can be a promising biomimetic substrate in neocartilage formation.

Ternary Matrix for the Matrix-Assisted Laser Desorption Ionization Time-of-Flight Mass Spectrometry (MALDI–TOF MS) Analysis of Non-fuel Lipid Components in Biodiesel

Trace components present in biodiesel have been shown to contribute to the precipitation of solids at temperatures above the cloud point. These precipitates represent an operability problem for use of biodiesel in cold climates. Separation methods for analysis of trace lipid impurities, such as gas and liquid chromatography, have been problematic, and chromatographic signals for these compounds are often eclipsed by the signals for the fatty acid methyl esters (FAMEs), the major components of biodiesel. The method described herein has been developed as a rapid procedure for analyzing non-FAME lipid biodiesel components, which have been postulated to contribute to cold-weather operability problems. Representative standards of the non-FAME lipids present in biodiesel were analyzed with matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI–TOF MS) using pure and mixed matrix systems. An optimized ternary matrix system consisting of dithranol, 2,5-dihydroxybenzoic acid, and α-cyano-4-hydroxycinnamic acid doped with sodium iodide was developed for analysis of the widest range of trace components possible by capitalizing on the positives of each matrix in ionizing compounds with differing functional groups. Mixtures of matrix compounds produced smaller, more homogeneous crystals, which resulted in increased reproducibility and sensitivity. This increase in reproducibility allowed quantitative relationships to be established with standards and between fuel samples. Spectral peak identification was based on molecular weight and tandem mass spectrometry collision-induced dissociation. Two palm oil-derived biodiesels, one of which was distilled, were analyzed to determine their non-FAME components and to quantitatively compare the number and relative concentration of trace species detected. Trace lipid species in precipitates from canola-oil-derived biodiesel were also isolated via refrigerated centrifugation, followed by analysis with the ternary matrix.

Drug release from extruded solid lipid matrices: Theoretical predictions and independent experiments

The aim of this study was to use a mechanistically realistic mathematical model based on Fick‘s second law to quantitatively predict the release profiles from solid lipid extrudates consisting of a ternary matrix. Diprophylline was studied as a freely water-soluble model drug, glycerol tristearate as a matrix former and polyethylene glycol or crospovidone as a pore former (blend ratio: 50:45:5% w/w/w). The choice of these ratios is based on former studies. Strains with a diameter of 0.6, 1, 1.5, 2.7 and 3.5 mm were prepared using a twin-screw extruder at 65 °C and cut into cylinders of varying lengths. Drug release in demineralised water was measured using the USP 32 basket apparatus. Based on SEM pictures of extrudates before and after exposure to the release medium as well as on DSC measurements and visual observations, an analytical solution of Fick’s second law of diffusion was identified in order to quantify the resulting diprophylline release kinetics from the systems. Fitting the model to one set of experimentally determined diprophylline release kinetics from PEG containing extrudates allowed determining the apparent diffusion coefficient of this drug (or water) in this lipid matrix. Knowing this value, the impact of the dimensions of the cylinders on drug release could be quantitatively predicted. Importantly, these theoretical predictions could be confirmed by independent experimental results. Thus, diffusion is the dominant mass transport mechanism controlling drug release in this type of advanced drug delivery systems. In contrast, theoretical predictions of the impact of the device dimensions in the case of crospovidone containing extrudates significantly underestimated the real diprophylline release rates. This could be attributed to the disintegration of this type of dosage forms when exceeding a specific minimal device diameter. Thus, mathematical modelling can potentially significantly speed up the development of solid lipid extrudates, but care has to be taken that none of the assumptions the mathematical theory is based on is violated.

Design and microstructural analysis of magnesium alloys for dynamical applications

A microanalytical characterization of cast magnesium alloys of eutectic origin based on the Mg–Al–Ca ternary matrix system has been carried out in order to investigate the influence of alloying elements on their microstructure as well as microchemistry-processing-microstructural relations using structure-sensitive techniques of electron microscopy, mechanical spectroscopy (internal friction), X-ray diffractometry, and advanced microanalytical methods including electron probe compositional analysis. Following the data obtained here there is direct correlation of microstructure with creep properties of the new experimental magnesium alloys. The creep and heat-induced properties of the multicomponent magnesium alloys containing low range of inexpensive additions of titanium (0.07–0.2%) or strontium (of about 1.8%) are defined by resulting structure dynamically formed during creep strain (up to 200 h). It is noteworthy that Ti as novel alloying element competes for creep resistance and cost with Sr and attracts as-cast desirable properties minimizing solute effects at ambient temperatures because of the pinning of slowly moving dislocations with the binding energy no more then 0.3 eV as well as because of stress-induced strengthening. The Ti and Sr solute atmosphere dragging is believed to be the rate-controlling mechanism responsible for radical improvement of creep resistance and long-term strength in the newly developed magnesium alloys at elevated temperatures. The new experimental alloys are superior to commercial alloys AZ91D, AE42, and AS21 following their creep resistance, long-term strength, heat resistance, and castability because of their novel microstructure having desirable engineering properties for structural applications (creep strain ec less than 0.3–0.4% at 423 K and 70 MPa for 200 h; έc ~ 10−9 s−1). The newly developed magnesium alloys with improved castability could be used in die-casting technology and automobile (powertrain) industry for manufacturing of components and parts which are difficult to cast with more desirable microstructure.

Microstructure and magnetoresistance of heterogeneous gold-rich Ag 3Au 1.1Te 2

Dispersions of very small non-magnetic metal particles or inclusions in a non-magnetic semiconductor matrix are well known to produce unusually large and linear magnetoresistance effects. So far these materials were limited to the binary silver-rich chalcogenides Ag 2Se and Ag 2Te. In this contribution Ag 3AuTe 2 was selected as a first candidate for a ternary matrix material, thus offering enhanced capabilities for the generation of heterogeneous microstructure and spatially varying composition on the nanoscale. In gold-rich Ag 3Au 1.1Te 2 two kinds of inhomogeneities are present, namely Au deposits with a size on the micron scale and an inhomogeneous distribution of Au and Ag within the matrix. The matrix consists of micron-sized grains with the structure type of Ag 3AuTe 2 as studied by electron microscopy. Like the binary silver chalcogenide phases, the material also shows a large and linear magnetoresistance effect. The transversal magnetoresistance effect was measured between 20 K and 270 K in magnetic fields up to B = 5 T. The results are discussed on the basis of existing models for a large and linear positive MR effect.

Characterisation of detonation sprayed Mo–Co–Cr–B alloy coatings

A novel thermal spray material of Mo–Co–Cr–B with high durability in molten alloys has been developed to utilise for die casting parts and for galvanising bath parts. In the present paper, detonation gun (D gun) spray technique was used to deposit a Mo–Co–Cr–B alloy coating onto 316L stainless steel substrate, and the microstructures and mechanical properties of the coating system were studied using XRD, SEM, tensile test and Vickers microhardness. The results show that the microstructures of the coating consisted of ternary transition metal borides matrix CoMo2B2, CoMoB, as well as a little amount of binary borides, MoB and CrB. The ternary borides matrix contained both amorphous phase and nanocrystalline grains with a size of 60±35 nm. The bond strength of the coating decreases with increasing thickness of the as sprayed coatings. The anisotropy in the mechanical properties between the cross-section and plan section of the coatings is examined. Comparing the microhardness and bond strength of detonation sprayed Mo–Co–Cr–B coating with those of HVOF sprayed Mo–Co–Cr–B coating, it can be concluded that the detonation spray process has a better performance than HVOF spray process.

Modifications in stability and structure of whey protein-coated o/w emulsions by interacting chitosan and gum arabic mixed dispersions

The influence of chitosan and gum arabic mixtures on the behaviour of o/w emulsions has been investigated at pH = 3.0. The emulsion behaviour, properties and microstructure were found to be greatly dependent on the precise gum arabic to chitosan ratio. Mixing of gum arabic with chitosan leads to the formation of coacervates of a size dependent on their ratio. Incorporation of low gum arabic to chitosan weight ratios into whey protein-coated emulsions causes depletion flocculation and gravity-induced phase separation. Increasing the polysaccharide weight ratio further, a droplet network with a rather high viscosity (at low shear stress) is generated, which prevents or even inhibits phase separation. At even higher gum arabic to chitosan ratios, the emulsion droplets were immobilised into clusters of an insoluble ternary matrix. Although the emulsion droplet charge had the same sign as that of the coacervates, clusters of oil droplets in a ternary matrix were generated. A mechanism to explain the behaviour of the whey protein-stabilised o/w emulsions is described on the basis of confocal and phase contrast microscopic observations, rheological data, zeta potential measurements, particle size analysis and visual assessment of the macroscopic phase separation events.

Bismaleimide Modified Epoxy-Diallylbisphenol System – Effect of Bismaleimide Nature on Properties

The properties of the ternary matrix system (EPB), obtained by the reactive blending of epoxy resin - diallyl bisphenol and a bismaleimide, depend on the structure and properties of its components. The influence of the structural variations of bismaleimide on the thermal, physical and mechanical properties of the ternary blend was examined. EPB compositions were prepared using novolac epoxy, diallyl phenol A and three different bismaleimide systems viz. 2, 2-bis 4-(4 maleimidophenoxy) phenyl propane-BMIP, bis (4-maleimidophenyl) methane-BMIM and bis (4-maleimido phenyl) ether-BMIE. The EPB systems with different types of bismaleimides were processed and characterized for their thermal, physical and rheological properties. EPB-glass composites processed using these matrix systems were characterized for their thermo-physical and mechanical properties. High temperature properties of these systems were assessed by their adhesive strength retention at different temperatures. The EPB system formed by the reactive blending of epoxy- phenol system with BMIP was found to yield the blend with improved mechanical performance at ambient conditions, while that with BMIM proved to be the best for high temperature application.

Influence of Epoxy Nature on the Properties of an Epoxy– Diallylbisphenol A–Bismaleimide Matrix System

The ternary matrix system comprising a reactive blend of epoxy, diallylbisphenol A, and bisphenol A bismaleimide (EPB) was found to be comparable with the epoxy–phenol (EP) system in terms of its mechanical properties, and superior to it in terms of its high-temperature performance. The influence of structural variations of the epoxy resin on the thermal, physical, and mechanical properties of the ternary blend was examined. EPB compositions were prepared using a combination of bisphenol A bismaleimide and diallylbisphenol A with three different epoxy resin systems, namely novolac epoxy (E1), bisphenol A diglycidyl ether (E2), and tris(4-glycidyloxyphenyl)methane (E3). Cure characterisation of these reactive blends (EPB–E1, EPB–E2 and EPB–E3) was carried out using IR spectroscopy, differential scanning calorimetry, and rheological analysis. The trend in their thermal stability, based on the temperature of the onset of decomposition, is EPB–E3 > EPB–E1 > EPB–E2. The mechanical properties – compressive, flexural, and interlaminar shear strength – of the glass composites of these matrices were found to depend on the epoxy structure. The higher crosslink density of the trifunctional epoxy improved the high-temperature properties of the system. The ternary system served as a very good adhesive, where its strength as well as its retention at high temperature increased in proportion to the functionality of the resin. In general, the maximum strength values were observed for the system containing the novolac epoxy.

Morphology and properties of cyanate ester/liquid polyurethane/silica nanocomposites

The high-speed homogeneous shearing method was applied to prepare nanocomposites of cyanate ester (CE) with liquid polyurethane elastomer (PUR) and silica. To investigate the influence of various components on the morphology and properties of the ternary composites, the binary composites of CE/PUR and CE/silica were also involved in this article. The morphology of the cured materials of binary and ternary systems was investigated by transmission electron microscopy (TEM), and the results show that silica nanoparticles were uniformly distributed in the ternary and binary matrix. Phase separation of elastomer in composites was not observed by TEM. FTIR test and dynamic mechanical analysis (DMA) proved that chemical linking was existent between PUR and CE. Scanning electron microscopy examinations and mechanical properties tests were carried out. The results show that ternary composites displayed higher fracture toughness and impact strength compared with most of the binary systems. This suggests that the addition of PUR and nanosilica can synergistically improve the toughness of CE. DMA studies confirmed that the incorporation of silica can increase the storage modulus and Tg for CE and CE/PUR system, since there are a good adhesion and a strong hydrogen bonding between silica and polymers. The thermal property of ternary composites increases with the increase of silica nanoparticle loading. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1243–1251, 2008

Ternary Thiol−Ene/Acrylate Photopolymers: Effect of Acrylate Structure on Mechanical Properties

Model ternary thiol−ene/acrylate photopolymerization involving acrylate homopolymerization and copolymerization of thiol−ene and thiol−acrylate monomers were monitored by real-time FTIR. In all ternary mixtures, including those prepared with different acrylate concentrations, acrylate conversion was 100%. However, thiol−ene conversions were found to be controlled by their initial concentrations. The influence of acrylate monomer chemical structure on the thermophysical properties of ternary thiol−ene/acrylate systems was studied with DMA, DSC, and the absorbance of a nondestructive impact energy. The addition of acrylate to the thiol−ene system increased the rubbery modulus while the tan δmax shifted to higher temperatures. Densely cross-linked, heterogeneous matrix formation was observed with the broadening of tan δ peaks at high acrylate concentrations. The high impact absorption of these ternary thermoset photopolymers was correlated with the dynamic mechanical damping ability of the networks. Acrylates with higher functionality and low molecular weight per double bond are more effective at increasing the glass transition temperature of the thiol−ene polymer network. Fracture behavior of ternary thiol−ene/acrylate networks under impact shows a dependence on the chemical structure of the acrylate, component concentrations, and low-temperature relaxation processes. The ternary matrix formed with a bisphenol A based difunctional acrylate monomer exhibited improved impact energy absorption at room temperature. Finally, tensile properties of polymer networks formed with thiol−ene/acrylate and thiol−acrylate mixtures are given for comparison purposes.

GENERALIZED COMPACT TABLE IN DECOMPOSITION OF A BOOLEAN FUNCTION

The concept of generalized compact table as a form of specification of a Boolean function is introduced. This form is a further generalization of the decomposition chart and uses the concept of ternary matrix cover. A method for decomposition of a Boolean function using its representation in the form of generalized compact table is given.

D-Optimal Mixture Design: Optimization of Ternary Matrix Blends for Controlled Zero-Order Drug Release From Oral Dosage Forms

ABSTRACTThe objective of the present study was to develop a tablet formulation with a zero-order drug release profile based on a balanced blend of three matrix ingredients. To accomplish this goal, a 17-run, three-factor, two-level D-Optimal mixture design was employed to evaluate the effect of Polyox™ (X1), Carbopol® (X2), and lactose (X3) concentrations on the release rate of theophylline from the matrices. Tablets were prepared by direct compression and were subjected to an in vitro dissolution study in phosphate buffer at pH 7.2. Polynomial models were generated for the responses Y4 (percent released in 8 h) and Y6 (similarity factor or f2). Fitted models were used to predict the composition of a formulation that would have a similar dissolution profile to an ideal zero-order release at a rate of 8.33% per hour. When tested, dissolution profile of the optimized formulation was comparable to the reference profile (f2 was 74.2, and n [release exponent] was 0.9). This study demonstrated that a balanced blend of matrix ingredients could be used to attain a zero-order release profile. Optimization was feasible by the application of response surface methodology, which proved efficient in designing controlled-release dosage forms.