Quadric Polynomial Research Articles

Selenium nanoparticles coated with polysaccharide-protein complexes from abalone viscera improve growth and enhance resistance to diseases and hypoxic stress in juvenile Nile tilapia (Oreochromis niloticus)

The use of selenium nanoparticles (SeNPs) in aquaculture has been increasing gradually over the past few years. SeNPs enhance immunity, are highly effective against pathogens, and have low toxicity. In this study, SeNPs were prepared using polysaccharide-protein complexes (PSP) from abalone viscera. The acute toxicity of PSP-SeNPs to juvenile Nile tilapia and their effect on growth performance, intestinal tissue structure, antioxidation capacity, hypoxic stress, and Streptococcus agalactiae infection were investigated. The results showed that the spherical PSP-SeNPs were stable and safe, with an LC50 of 13.645 mg/L against tilapia, which was about 13-fold higher than that of sodium selenite (Na2SeO3). A basal diet supplemented with 0.1–1.5 mg/kg PSP-SeNPs improved the growth performance of tilapia juveniles to a certain extent, increased the intestinal villus length, and significantly enhanced the activities of liver antioxidant enzymes, including superoxide dismutase (SOD), glutathione peroxidase (GSH-PX), and catalase (CAT). PSP-SeNPs also enhanced the resistance of tilapia to hypoxic stress and Streptococcus agalactiae infection, with supplementation at 0.1–0.3 mg/kg exerting more obvious effects than 1.5 mg/kg. However, PSP-SeNPs at a concentration of 4.5 mg/kg and Na2SeO3 at 0.3 mg/kg negatively affected the growth, gut health, and the activity of the antioxidant enzymes of tilapia. Quadric polynomial regression analysis revealed that 0.1–1.2 mg/kg was the optimal PSP-SeNP supplementation concentration for tilapia feeds. The findings of this study lay a foundation for the application of PSP-SeNPs in aquaculture.

The Finite Element Method with High-Order Enrichment Functions for Elastodynamic Analysis

Elastodynamic problems are investigated in this work by employing the enriched finite element method (EFEM) with various enrichment functions. By performing the dispersion analysis, it is confirmed that for elastodynamic analysis, the amount of numerical dispersion, which is closely related to the numerical error from the space domain discretization, can be suppressed to a very low level when quadric polynomial bases are employed to construct the local enrichment functions, while the amount of numerical dispersion from the EFEM with other types of enrichment functions (linear polynomial bases or first order of trigonometric functions) is relatively large. Consequently, the present EFEM with a quadric polynomial enrichment function shows more powerful capacities in elastodynamic analysis than the other considered numerical techniques. More importantly, the attractive monotonic convergence property can be broadly realized by the present approach with the typical two-step Bathe temporal discretization technique. Three representative numerical experiments are conducted in this work to verify the abilities of the present approach in elastodynamic analysis.

Direct tensile test evaluation and characterization for mechanical and rheological properties of polymer modified hot mix asphalt concrete

AbstractUsing polymer to modify asphalt binder for better performance has become popular in pavement engineering, for which to evaluate the effect of polymer addition on the properties of the asphalt concrete is essential for mix design. Conventional mechanical test methods, primarily using bending of beams and indirect splitting, are not only materially and timely costly and labor intensive but also provide no direct information for the viscoelastic and rheological characteristics of the materials. This paper reports a study using direct tensile test (DTT) to evaluate the effect of polymer on both mechanical and rheological properties of modified asphalt concrete. Two types of polymers, which are styrene‐butadiene‐styrene (SBS), and a mixture of SBS and polyvinyl chloride (PVC), were investigated on two mixes using fine and coarse aggregates, respectively. It has been found that SBS generates improvement for both mechanical and rheological properties of hot mix asphalt concrete. However, using a hybrid mixture of SBS and PVC shows that PVC can further improve the mechanical properties, but deteriorate the toughness of the asphalt concrete. At the end, a simple quadric polynomial model has been proposed to characterize the combined SBS and PVC effects for the sake of the guidance for mix design.

IMAGE ENCRYPTION BASED ON TWO-DIMENSIONAL FRACTIONAL QUADRIC POLYNOMIAL MAP

A new fractional two-dimensional quadric polynomial discrete chaotic map (2D-QPDM) with the discrete fractional difference is proposed. Afterwards, the new dynamical behaviors are observed, so that the bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits of the proposed map are given, respectively. The new discrete fractional map is exploited into color image encryption algorithm and it is illustrated with several examples. The proposed image encryption algorithm is analyzed in six aspects which indicates that the proposed algorithm is superior to other known algorithms as a conclusion.

Image Magnification Based on Bicubic Approximation with Edge as Constraint

Image magnification can be reduced to construct an approximation surface with data points in the image while keeping image details and edge features. In this paper, a new image magnification method is proposed by constructing piecewise bicubic polynomial surfaces constrained by edge features. The main innovation includes three parts. First, on the small adjacent area of each pixel, the new method constructs a quadratic polynomial sampling patch to approximate pixels on the small neighborhood with edge features as constraints. All quadric polynomial sampling patches are weighted to generate piecewise whole bicubic polynomial sampling surface. Second, a technique for calculating the error image is proposed: the error image is used to construct a correction surface to improve the accuracy and visual effect of the magnified image. Finally, in order to improve the accuracy of the approximation surface, a technology of balancing polynomial coefficients is put forward. Experimental results show that, compared with other methods, the proposed method makes better use of the local feature information of the image, which not only improves the PSNR/SSIM numerical accuracy of the magnified image but also improves the visual effect of the magnified image.

Application of mathematical model methods for optimization tasks in construction materials technology

In this paper, the regression equations method for design of construction material was studied. Regression and polynomial equations representing the correlation between the studied parameters were proposed. The logic design and software interface of the regression equations method focused on parameter optimization to provide the energy saving effect at the stage of autoclave aerated concrete design considering the replacement of traditionally used quartz sand by coal mining by-product such as argillite. The mathematical model represented by a quadric polynomial for the design of experiment was obtained using calculated and experimental data. This allowed the estimation of relationship between the composition and final properties of the aerated concrete. The surface response graphically presented in a nomogram allowed the estimation of concrete properties in response to variation of composition within the x-space. The optimal range of argillite content was obtained leading to a reduction of raw materials demand, development of target plastic strength of aerated concrete as well as a reduction of curing time before autoclave treatment. Generally, this method allows the design of autoclave aerated concrete with required performance without additional resource and time costs.

Effect of Dietary Energy to Protein Ratio on Growth, Biological Indices, Proximate Composition, and Amino Acid Profiles in the Muscle of Varicorhinus macrolepis

AbstractA 150‐d feeding experiment was conducted to assess the effect of the dietary energy to protein ratio (E/P ratio) on growth, biological indices, proximate composition, and amino acid profiles in the muscle of Varicorhinus macrolepis. Six experimental diets were formulated with different E/P ratios (30.51, 33.90, 37.82, 42.34, 47.70, and 54.09 kJ/g). In the experiment, 360 fish with a mean weight of 8.75 g (SD, 0.59) were randomly divided into six groups (three replicates per group, 20 fish per replicate) and fed three times daily with the experimental diet. Results showed that when the dietary E/P ratio was 37.82 kJ/g, Varicorhinus macrolepis tended to gain the highest specific growth rate. With a change in the increment of dietary E/P ratio, the condition factor, intestosomatic index, hepatosomatic index, and viscerosomatic index all changed in the quadric polynomial regression model. Muscle crude lipid content showed a tendency of leveling‐off first and then increased with increasing dietary E/P ratio. Varicorhinus macrolepis gained the highest concentration of total amino acids and essential amino acids when the dietary E/P ratio was 37.82 kJ/g. Except for methionine + cysteine, phenylalanine + tyrosine, and the amino acid score of lysine, the amino acid scores and chemical scores of the other essential amino acids were highest when the dietary E/P ratio was 37.82 kJ/g. These results suggest that Varicorhinus macrolepis obtained optimal growth and muscle amino acid composition when the dietary E/P ratio was 37.82 kJ/g.

A Recommendation Model Based on Deep Neural Network

In recent years, recommendation systems have been widely used in various commercial platforms to provide recommendations for users. Collaborative filtering algorithms are one of the main algorithms used in recommendation systems. Such algorithms are simple and efficient; however, the sparsity of the data and the scalability of the method limit the performance of these algorithms, and it is difficult to further improve the quality of the recommendation results. Therefore, a model combining a collaborative filtering recommendation algorithm with deep learning technology is proposed, therein consisting of two parts. First, the model uses a feature representation method based on a quadric polynomial regression model, which obtains the latent features more accurately by improving upon the traditional matrix factorization algorithm. Then, these latent features are regarded as the input data of the deep neural network model, which is the second part of the proposed model and is used to predict the rating scores. Finally, by comparing with other recommendation algorithms on three public datasets, it is verified that the recommendation performance can be effectively improved by our model.

Numerical modeling of tidal notch sequences on rocky coasts of the Mediterranean Basin

AbstractTidal notches have had the potential to form at sea level from ~6.5 kyr B.P. in the Mediterranean Basin and preserve a symmetrical shape comparable to a quadric polynomial. Continuous erosion, predominantly by biological agents, affects a limestone cliff face from low‐ to high‐tide level at <1 mm/yr. Statically determined, the roots of a quadric polynomial are defined by the tidal range representing the limits of effective erosion. However, gradual variations of eustatic sea level rise (slow) and coseismic uplift/subsidence (fast) in tectonically active regions contribute to vertical shifts in the erosional base at coastlines. As a consequence, the cliff morphology gets modified through time resulting in widening, deepening, and separation of notches and possible overprinting of older features. In order to investigate successive modifications of coastal cliff morphology, we developed a numerical model that considers the erosion rate, the erosion zone relative to sea level, the regional sea level curve, and tectonic motion. The results show how slow and rapid sea level changes bias the modern cliff face and highlight that the present‐day notch sequence from top descending to sea level is not inevitably of decreasing age. Furthermore, the initiation of notch formation is not necessarily linked to the date of a certain seismic event. Especially in extensional tectonic settings where coseismic uplift is low and coastal morphological marks are not as distinct, knowledge about coastal evolution is beneficial for paleoseismological research.

Optimization of extraction process for polyphenols from pineapple leaves fiber by response surface methodology

The extraction technology of total polyphenols from pineapple leaf fiber were investigated by using ethanol reflux method.Based on the single factor experimental analysis,through the response surfac,extraction conditions was optimized by investigating the effect of ethanol concentration,solid-to-solvent ratio,extraction temperature,extraction time and their interaction on thepolyphenols extracts and the process of quadric polynomial mathematics model was established. Experiment results showed that regression equation fit well with experimental data and the interaction effect of ethanol concentration and extraction temperature was significant. The optimal of extraction conditions including ethanol concentration,solid-to-solvent ratio,extraction temperature,extraction time were 59%,1 ∶23( g/m L),71 ℃ and 118 min respectively. The content of polyphenols extracted from pineapple leaf fiber under the conditions was( 1.67±0.02) mg/g closing to predicted extraction rate1.6978 mg/g.

Lorenz Wind Disturbance Model Based on Grey Generated Components

In order to meet the needs of wind speed prediction in wind farms, we consider the influence of random atmospheric disturbances on wind variations. Considering a simplified fluid convection mode, a Lorenz system can be employed as an atmospheric disturbance model. Here Lorenz disturbance is defined as the European norm of the solutions of the Lorenz equation. Grey generating and accumulated generating models are employed to explore the relationship between wind speed and its related disturbance series. We conclude that a linear or quadric polynomial generating model are optimal through the verification of short-term wind speed prediction in the Sotavento wind farm. The new proposed model not only greatly improves the precision of short-term wind speed prediction, but also has great significance for the maintenance and stability of wind power system operation.

Construction of Point Set Surfaces through Quadric Polynomials

This paper constructs PSSs (Point Set Surfaces) by combining locally fitted quadric polynomials. First, an energy function is defined as the weighted sum of distances from a point to these quadric polynomials. Then, a vector field is constructed by the weighted sum of normal vectors at input points. Finally, points on a PSS are obtained by finding local minima of the energy function along the vector field. Experiments demonstrate that high quality PSSs can be obtained from the method presented for input point clouds sampled from various shapes.

Optimization of Separation Process of Waste Polyester-Cotton Fiber by Using Response Surface Analysis

In this study, the response surface methodology was used to optimize parameters of the diluted hydrochloric acid hydrolysis method, which was adopted to separate the polyester-cotton blend fiber. The four parameters reaction time, mass fraction of hydrochloric acid, reaction temperature and solid-liquid ratio were determined by the single factor experiment as they are significant for the process of separation. By introducing the experiment of four factors on three levels designed by Box-Benhnken central composite method, a quadric polynomial regression model for the fiber weight loss rate was established. And the response surface graphs were plotted to illustrate the optimizing process. The response surface analysis determined that the optimized value of the four parameters were 98 minutes, 10.7%, 96.5 °C and 4.3 g/100ml respectively. Under these conditions, polyester-cotton blend fiber was completely separated.

Response Surface Methodology, an effective strategy in the optimization of the generation of curcumin‐loaded micelles

ABSTRACTCurcumin, a yellow pigment extracted from the dried rhizome of Curcuma longa, found to have significant pharmaceutical activities. However, the bioavailability of curcumin after administration is always low because of its extremely poor solubility in water. To improve the absorption rate of curcumin in vivo, curcumin‐loaded micelles have been developed by using GRAS surfactants, namely Brij 56 and Span 20, and by the application of ultrasonic cavitation. To investigate the interaction between different factors and to optimize the formulation conditions, Response Surface Methodology has been adopted. Both Central Composite Design and Box–Behnken Design (BBD) have been attempted in this study, and a better fitted quadric polynomial equation has been obtained from BBD that resulted into the coefficient of determination (R2) of 0.9894 and 0.9574 for the zeta‐average and polydispersity index of the formulation, respectively. In contrast, Analysis of Variance suggested a coefficient of determination (R2) for Central Composite Design plots that is 0.9172 for particle size response surface and 0.8246 for the polydispersity response surface. Optimization based on BBD model suggested 28 possible solutions, for which the generated solution with the highest desirability (0.764) predicted the curcumin‐loaded micelle formulation with 19.99 nm particle size and with 0.267 polydispersity index, when the formulation hydrophilic–lipophilic balance number is 9.46, curcumin‐to‐water weight ratio is 0.7 and surfactant‐to‐water weight ratio is 0.11. The whole investigation clearly supports the potential of ultrasonic cavitation in the generation of curcumin‐loaded micelles. © 2012 Curtin University of Technology and John Wiley & Sons, Ltd.

Optimization of Fermentation Conditions of Marine Algicidal Bacterium Microbulbifer sp. BS03 by Uniform Design

The optimal parameters of fermentation conditions of marine bacterium Microbulbifer sp.BS03 producing algicidal substances against Alexandrium tamarense were obtained by using Uniform Design and quadric polynomial regression methods.Five main factors were achieved through single factor experiments,that is,carbon source,nitrogen source,pH,incubation time and inoculum size.The U15(155) design result showed the optimum conditions of experiment were as follows: sugar 8 g/L,peptone 10.5 g/L,initial pH 7.5,incubation time 32 h,and inoculum size of 3.00%.According to the verification experiment,under the optimal conditions,the dry biomass was 4.725 g/L which was increased by 31.35% and LD50was 0.768% which was decreased by 25.14% compared with those of the basic fermentation conditions.This outcome will help us to separate active substances from complex components in medium and thus to reveal the mechanism of algicidal activity in the future.

Gasification of two and three-components mixture in supercritical water: Influence of NaOH and initial reactants of acetic acid and phenol

Acetic acid (HAc) and phenol are the most common and refractory compounds during supercritical water gasification (SCWG) of organic waste water for hydrogen production. Here we report SCWG of HAc and the two and three-components mixture containing HAc and phenol with and without sodium hydroxide catalyst, which was conducted in a tubular flow reactor. Sodium hydroxide had a catalytic effect on the steam reforming reaction of methane during SCWG of HAc. For SCWG of HAc (0.5wt%) and phenol (1.0wt%) mixture, yield of hydrogen and carbon dioxide reached a maximum at 0.2wt% of sodium hydroxide. The hydrogenation of phenol to form benzene and further to cyclohexane can be reinforced by the acceleration of NaOH on hydrogen production. The amount of undesired long-chain alkyl esters were also found in the liquid products. Large amount of sodium acetate and sodium phenolate formed at high NaOH concentrations, which can lead to lower reaction efficiency and more serious deposition and coking problem. For SCWG of the three-components (methanol, HAc and phenol) mixture, TOC (Total Organic Carbon) removal efficiency, H and C gasification efficiency can be strongly retarded by both HAc and phenol. Decarboxylation of HAc leaded to relatively higher C gasification efficiency. Besides, their empirical quadric polynomial regression models were provided via response surface method.

Optimization of cordycepin extraction from cultured Cordyceps militaris by HPLC‐DAD coupled with uniform design

AbstractBACKGROUND: Uniform design was used to optimize the ultrasonic‐assisted extraction of cordycepin from cultured Cordyceps militaris. The peak area of cordycepin identified using high performance liquid chromatography (HPLC) at a detection wavelength of 260 nm was considered the detection index. Three factors, ethanol concentration, extraction time and volume ratio of solvent to sample were studied. Optimal quadric polynomial step by step regression was applied to process the experimental results.RESULTS: Results show that the main factors affecting cordycepin extraction yield were the volume ratio of solvent to sample, extraction time and ethanol concentration, in that order. Cordycepin extraction yield reached a peak with ethanol concentration 20.21%, extraction time 101.88 min, and volume ratio of solvent to sample 33.13 mL g−1. An extraction model was developed based on the findings.CONCLUSION: A direct, reliable and accurate assay has been developed for the quantification of cordycepin in cultured Cordyceps militaris by a HPLC‐DAD method. The validation procedure confirmed that this method is appropriate for the quality control of cordycepin. Results show that the uniform experimental design approach is useful for finding polynomial functions describing the relationships between variables and responses and to find the best experimental conditions for the extraction of cordycepin in the experimental domain considered. Copyright © 2007 Society of Chemical Industry

General pure multipartite entangled states and the Segre variety

In this paper, we construct a measure of entanglement by generalizing the quadric polynomial of the Segre variety for general multipartite states. We give explicit expressions for general pure three-partite and four-partite states. Moreover, we will discuss and compare this measure of entanglement with the generalized concurrence.

Extraction optimization of coumarins from radix angelicae pubescentis by HPLC-DAD coupled with uniform design

Uniform design was used to optimize extraction condition of direct refluence extraction of coumarins from the Chinese traditional medicine of radix angelicae pubescentis(Duhuo); the sum peak area of coumarins separated with high performance liquid chromatography (HPLC) at detection wavelength of 320 nm was considered as detection index, two factors of solvent concentration and extraction time were mainly studied at extraction temperature of 85°C and a volume ratio of solvent to sample of 10 : 1. Optimal subclass, quadric polynomial step by step aggression and neural network method were applied to process the experimental results. The results show that the first and second methods give the same factors combination (concentration of ethanol: 95%, extraction time: 3.6 h) and the second method is much better than the first one. The extraction model is consequently developed.

A polynomial scattering radiation technique in X-ray fluorescence spectrometry

This work shows that there is a quadric polynomial instead of a linear relationship between mass attenuation coefficients and inverse incoherent scattering radiation in a wide range of atomic number. With this in mind a new absorption correction method, ‘polynomial scattering radiation technique', is recommended for matrix absorption correction in X-ray fluorescence spectrometry.