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Regulation of Fat Content in Triticale Based on Optimization of Technological Processing Modes 基于技术加工模式优化的大麦脂肪含量调控技术
Pub Date : 2024-05-08 DOI: 10.2174/0118741231264873231207105744
R. Kassymbek, A. Iztayev, Tahir Balevi, U. Chomanov, Muhtar Tultabayev, Gulzhan Zhumaliyeva, G. Aktokalova, Asiya Shoman
The aim of the study was to regulate the fat content based on the optimization of technological processing modes. A promising method of preparing grain for animal feeding is its preliminary germination. Sprouted grain is a dietary food product, as it increases the content of proteins, essential amino acids, and macro- and microelements in comparison with non-sprouted grain. The purpose of this study was to regulate the fat content based on the optimization of technological processing modes. Regression equations describing the dependences of the quality indicators of the triticale grain germination modes on the factors tw, τ, w and tg affecting them were investigated and obtained. During the study of triticale grains, it was found that the most significant parameter affecting the germination process is the fat content. The optimization of the germination modes of triticale Leather grain was carried out by the method of nonlinear programming. During the study, it was found that the maximum fat content during germination of triticale grain was observed with the following technological parameters of germination: grain temperature = 30°C; germination time = 24 h; grain moisture = 13%; and grain temperature = 26°C. When controlling the fat content in triticale based on the optimization of technological modes, the target function was 2.83%. The presented results and conclusion will allow to regulate the fat content in triticale grain during germination.
研究的目的是在优化技术加工模式的基础上调节脂肪含量。准备用于动物饲养的谷物的一种可行方法是初步发芽。发芽谷物是一种膳食食品,因为与未发芽谷物相比,它能增加蛋白质、必需氨基酸以及宏量和微量元素的含量。 本研究的目的是在优化技术加工模式的基础上调节脂肪含量。研究并获得了描述三棱麦谷物发芽模式质量指标与影响因素 tw、τ、w 和 tg 之间关系的回归方程。在对三粒谷物的研究中发现,影响发芽过程的最重要参数是脂肪含量。采用非线性编程方法对临界革谷物的发芽模式进行了优化。 研究发现,在下列发芽技术参数下,临界谷物发芽过程中脂肪含量最高:谷物温度 = 30°C;发芽时间 = 24 小时;谷物水分 = 13%;谷物温度 = 26°C。在优化技术模式的基础上控制三麦的脂肪含量时,目标函数为 2.83%。 上述结果和结论将有助于在发芽期间调节三粒谷物中的脂肪含量。
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引用次数: 0
Microrespirometric Validation of a Two-stage Process for Polyhydroxyalkanoates Production from Peanut Oil and Propionate with Cupriavidus necator 用花生油和丙酸盐生产聚羟基烷酸酯的两阶段工艺的微量吸气测定法验证
Pub Date : 2024-04-02 DOI: 10.2174/0118741231301420240306092952
Irazú Pérez-Camacho, N. Chavarría‐Hernández, Ma. del Rocío López-Cuellar, C. Guerrero-Barajas, A. Ordaz
Poly(3-hydroxyalkanoates) (PHA) is a biodegradable polyester synthesized by various bacteria, including Cupriavidus necator. The composition of PHA is influenced by the type of microorganism, cultivation conditions, and carbon substrate. The selection of a carbon source is critical for PHA production, significantly impacting process costs. Therefore, the common goal is scalability, with the design and optimization of PHA production relying on experimental determination of constitutive parameters. In this work, a two-stage process for PHA production was conducted in shaking flasks functioning as mini reactors with the bacteria Cupriavidus necator. During the first stage, fructose was used as the sole carbon source. Once fructose was exhausted, a second stage commenced with a new carbon source, either peanut oil or propionate, to enhance PHA production. Ex-situ pulse respirometry approach was employed during the two-stage process to follow the kinetics of substrate consumption. The results indicated that the use of peanut oil would be advantageous over propionate, resulting in 12.2% more biomass and 13.9% more PHA. Additionally, the growth rate was 88.9% higher with peanut oil. The characterization by pulse respirometry applied in microreactors, i.e., micro respirometry, allowed for the performance of up to 216 biological experiments to determine four important kinetic and stoichiometric parameters, namely maximum oxygen uptake (rO2max), substrate affinity constant (KS), growth yield (YX/S), and substrate oxidation yield (YO2/S). The values of these parameters indicated that peanut oil would be the best carbon source to promote PHA production during the second stage. The implementation of the microrespirometry technique during the screening of carbon sources for PHA production provided reliable information within a short period and with significantly less experimental effort.
聚(3-羟基烷酸)(PHA)是一种可生物降解的聚酯,由各种细菌合成,其中包括坏死葡萄球菌(Cupriavidus necator)。PHA 的成分受微生物类型、培养条件和碳基质的影响。碳源的选择对 PHA 的生产至关重要,会对工艺成本产生重大影响。因此,共同的目标是可扩展性,PHA 生产的设计和优化依赖于构成参数的实验测定。 在这项工作中,我们在作为微型反应器的振荡烧瓶中,使用Cupriavidus necator细菌进行了两阶段的PHA生产过程。在第一阶段,果糖被用作唯一的碳源。果糖耗尽后,第二阶段开始使用新的碳源,即花生油或丙酸盐,以提高 PHA 产量。在两阶段过程中采用了原位脉冲呼吸测定法,以跟踪底物消耗的动力学过程。 结果表明,使用花生油比使用丙酸盐更有优势,生物量增加了 12.2%,PHA 增加了 13.9%。 此外,使用花生油后,生长速度提高了 88.9%。在微反应器中应用脉冲呼吸测定法(即微呼吸测定法)进行表征,可进行多达 216 次生物实验,以确定四个重要的动力学和化学计量学参数,即最大摄氧量(rO2max)、底物亲和常数(KS)、生长产量(YX/S)和底物氧化产量(YO2/S)。这些参数值表明,花生油是促进第二阶段 PHA 生产的最佳碳源。在 PHA 生产的碳源筛选过程中采用微呼吸测定法技术可在短时间内提供可靠的信息,而且大大减少了实验工作量。
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引用次数: 0
The Analytical Scheme on the Inertial Drag for Buoyancy-driven Nanofluid Flow Under Convective Thermal Surface with the Soret Effect 考虑Soret效应的对流热表面下浮力驱动纳米流体惯性阻力解析格式
Pub Date : 2023-10-13 DOI: 10.2174/0118741231267495230922112334
P.K. Pattnaik, Subhajit Panda, S.R. Mishra, Krushna K.P.N. Nayak
Introduction: The two-dimensional mixed convection of nanofluid over a vertical expanding surface is analysed in the current discussion. The expanding surface is embedded in a permeable medium. Methods: In advance, Darcy Forchheimer inertial drag is considered along with the influence of Brownian and thermophoresis, which enriches the study. The novelty of the study is due to the mass concentration along with the role of volume concentration in the flow phenomena. The proposed model is designed in association with a characterizing parameter, which is attained by the use of appropriate similarity conversion. Further, the system of first-order differential equations is resolved by employing a shooting-based numerical method, in particular, the Runge-Kutta fourth-order technique. Results: The simulated results for the said parameters and their behaviour are deployed through graphs and in tabular form. Conclusion: The physical description of each parameter is deliberated briefly. Finally, the important outcomes of the proposed study reported a remarkable hike in the temperature profile that is observed for the enhanced thermophoresis and Brownian motion. Further, the shear rate also increases for the enhanced mixed convection parameter.
导言:本文分析了纳米流体在垂直膨胀表面上的二维混合对流。所述膨胀表面嵌入可渗透介质中。方法:提前考虑Darcy Forchheimer惯性阻力以及布朗和热泳运动的影响,丰富了研究内容。该研究的新颖之处在于质量浓度与体积浓度在流动现象中的作用。所提出的模型与特征参数相关联,通过使用适当的相似性转换来获得特征参数。此外,采用基于射击的数值方法,特别是龙格-库塔四阶技术,求解了一阶微分方程组。结果:上述参数及其行为的模拟结果通过图形和表格形式进行部署。结论:简要讨论了各参数的物理描述。最后,该研究的重要结果报告了由于热泳动和布朗运动的增强而观察到的温度分布的显著增加。此外,混合对流参数的增强也增加了剪切速率。
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引用次数: 0
Developing a CDY Model for Grapes and Experimentally Validating it with an Android App that Focuses on Agro-climatic and Disease Prevention Aspects 开发葡萄的CDY模型,并在侧重于农业气候和疾病预防方面的Android应用上进行实验验证
Pub Date : 2023-09-04 DOI: 10.2174/18741231-v17-230828-2023-4
A. Eswari, JG Manjunatha
Introduction: Crop development and yield are both influenced by the weather. This study has developed and analytically resolved a general agro-climatic model for grapes. Methods: In the field of mathematical biology, researchers, professors, and academics will find this model useful. To create the final version of the model for yield prediction, the CDY model and asymptotic analyses have been performed. Climate, disease, and grape production have been taken into consideration as dependent characteristics during the model construction process. The frequency of infection, the occurrence of disease, seasonality, and the elimination of grape output throughout each harvest cycle have been viewed as distinct qualities. Moreover, the model has been examined, and field-level data have been used to estimate the parameters collected between 2016-2021 from the nearby villages of GRS and Theni. Results: A description of this model’s stability analysis has also been provided. An association has been determined between the numerical validity and stability of the given analytical solution analyses. In addition, the developed Android mobile app for grapes has been validated using the proposed model under the climatic scenario. Conclusion: It is advised to apply the created model to estimate grape yield based on the findings obtained. A useful technique for forecasting crop yield has thus been proposed in this study.
作物的生长发育和产量都受天气的影响。本研究建立并解析解决了葡萄的一般农业气候模型。方法:在数学生物学领域,研究人员、教授和学者会发现这个模型很有用。为了创建产量预测模型的最终版本,进行了CDY模型和渐近分析。在模型构建过程中,气候、疾病和葡萄生产已被考虑为依赖特征。在每个收获周期中,感染的频率、疾病的发生、季节性和葡萄产量的消除被视为不同的品质。此外,还对该模型进行了检验,并使用现场数据来估计2016-2021年间从GRS和Theni附近村庄收集的参数。结果:给出了模型稳定性分析的描述。已经确定了给定解析解分析的数值有效性和稳定性之间的联系。此外,开发的Android手机葡萄应用程序已经在气候情景下使用所提出的模型进行了验证。结论:根据所得结果,建议应用所建立的模型对葡萄产量进行估算。因此,本研究提出了一种有用的作物产量预测技术。
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引用次数: 0
Mechanical and Structural Properties of Epoxy Resin-Allyl Guar Gum Composites 环氧树脂-烯丙基瓜尔胶复合材料的力学和结构性能
Pub Date : 2023-06-22 DOI: 10.2174/18741231-v17-e230505-2022-ht24-4379-1
Gopal Arora, A. Gupta
Guar gum is a non-ionic polysaccharide extracted from the endosperm of Cyamopsistetragonalobus. Guar gum and its derivatives are water-soluble hydrophilic polysaccharides, and hydrophobic modification is required to increase its compatibility in a polymer matrix. The present study investigates the synthesis of allyl-modified guar gum (AGG) and epoxy resin composites. The mechanical properties of the prepared composites with varying concentrations of filler (allyl guar gum) in the range of 0.5-4.5 wt% have been evaluated. The mechanical and structural properties of the prepared composites have been investigated using Universal Testing Machine (UTM) and Scanning Electron Microscope (SEM), respectively. The epoxy composites were prepared by casting technique using allyl guar gum as the filler. The polymer-filler interactions varied with the contents of the filler. The tensile strength was found to be enhanced up to 13% at 0.5% concentration of AGG. The % elongation at break values followed an opposite trend as compared to the tensile strength data of the composites. The observed mechanical properties have been correlated with the fracture morphology of the composites. A better dispersion, that is, polymer-filler interactions, improved the tensile strength of composites, while poor interactions declined the tensile strength. It is reported that max tensile strength can be obtained at 0.5% concentration of allyl guar gum (AGG1). The maximum increase in % elongation at break was 25% for AGG2-based epoxy composite at 3% of filler concentration.
瓜尔胶是从瓜尔豆胚乳中提取的一种非离子型多糖。瓜尔胶及其衍生物是水溶性亲水性多糖,需要进行疏水改性以增加其在聚合物基质中的相容性。本文研究了烯丙基改性瓜尔胶(AGG)及其环氧树脂复合材料的合成。在0.5-4.5 wt%范围内,对所制备的复合材料的力学性能进行了评价。利用万能试验机(UTM)和扫描电子显微镜(SEM)对复合材料的力学性能和结构性能进行了研究。以烯丙基瓜尔胶为填料,采用铸造工艺制备了环氧复合材料。聚合物与填料的相互作用随填料含量的变化而变化。当AGG浓度为0.5%时,拉伸强度可提高13%。断裂伸长率与复合材料的抗拉强度数据相反。观察到的力学性能与复合材料的断裂形貌相关。良好的分散性,即聚合物与填料的相互作用,提高了复合材料的抗拉强度,而不良的相互作用则降低了复合材料的抗拉强度。据报道,0.5%浓度的烯丙基瓜尔胶(AGG1)可获得最大拉伸强度。当填料浓度为3%时,agg2基环氧复合材料断裂伸长率的最大增幅为25%。
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引用次数: 0
Experimental Study and Modeling of Solid – Liquid Equilibrium for Binary and Ternary Pharmaceutical and Food Systems 二元和三元药物和食品系统固液平衡的实验研究和建模
Pub Date : 2023-01-11 DOI: 10.2174/18741231-v17-e230111-2022-9
Bitchikh Karima, Smakghi Nabil, M. Abdeslam-Hassen
The experimental measurement of the solubility of a solute in a given solvent is a difficult task, hence the need of reliable thermodynamic models for its prediction. However, these models require either molecular or group interaction parameters which are not always available. The objective of the present study is to measure experimentally the solubility of different solutes in solvents selected from pharmaceutical or food fields, on the basis that not all the required model interaction parameters are available to use the obtained experimental data for their determination. The experimental study of solid-liquid equilibrium for chosen binary and ternary systems at different temperatures was carried out using the Differential Scanning Calorimetry to determine the essential thermo physical properties like melting temperature and enthalpy. The modeling of these phase equilibrium data was performed by means of thermodynamic models like Random Two Liquids (NRTL) and Universal Functional Activity Coefficient (UNIFAC). The required NRTL interaction parameters were determined by minimizing a well-defined objective function, using the simplex method. The solubilities of the solutes in the different considered solvents at different temperatures obtained experimentally provided the required NRTL molecular interaction parameters. Solute solubilities were obtained by means of NRTL, UNIFAC, and ideal models. The comparisons showed an excellent agreement between the experimental values and the NRTL results, contrary to UNIFAC and ideal case models. This study shows the importance of thermodynamic modeling to predict solubility data that may be difficult, time consuming, and costly to obtain experimentally.
实验测量溶质在给定溶剂中的溶解度是一项困难的任务,因此需要可靠的热力学模型来预测溶质的溶解度。然而,这些模型需要分子或基团相互作用参数,而这些参数并不总是可用的。本研究的目的是通过实验测量不同溶质在选定的制药或食品领域溶剂中的溶解度,在此基础上,并非所有所需的模型相互作用参数都可用来使用获得的实验数据进行测定。采用差示扫描量热法对选定的二元和三元体系在不同温度下的固液平衡进行了实验研究,确定了其熔融温度和焓等基本热物性。采用随机两液(Random Two fluids, NRTL)和通用功能活度系数(Universal Functional Activity Coefficient, UNIFAC)等热力学模型对相平衡数据进行了建模。使用单纯形法,通过最小化定义良好的目标函数来确定所需的NRTL相互作用参数。实验得到的溶质在不同温度下在不同溶剂中的溶解度提供了所需的NRTL分子相互作用参数。溶质溶解度通过NRTL、UNIFAC和理想模型得到。比较表明,实验值与NRTL结果非常吻合,与UNIFAC和理想情况模型相反。这项研究表明,热力学建模的重要性,以预测溶解度数据,可能是困难的,耗时的,和昂贵的实验获得。
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引用次数: 0
Trends of Dye Removal and Heavy Metal Removal of Different Hydrogel-Based Materials and Their Mixtures 不同水凝胶基材料及其混合物对染料和重金属的去除趋势
Pub Date : 2022-12-07 DOI: 10.2174/18741231-v16-e221207-2022-11
Mahy M. Abdelhamid, Shaza H. Saleh, M. Radwan, M. A. Sadek, Sohair A. Darwish
Hydrogels are relatively newly developed materials that has piqued the curiosity of scientists in various fields, particularly for wastewater treatment applications. Heavy metal ions and dye removal hydrogels is becoming more popular due to its ease of use, low cost, increased effectiveness, biodegradability, and reusability. Evaluate and study the adsorption behaviour of different hydrogel materials towards heavy metal ions and dyes. The hydrogels investigated are Poly(2-Acrylamido-2-Methylpropane Sulphonic Acid) (PAMPS) hydrogels, commercial sodium polyacrylates (Na-PA), chitosan (CH), along with their binary and ternary mixtures. A semi-interpenetrating network (IPN) based on PAMPS and Na-PA was also investigated. The performance of each hydrogel towards six different heavy metals (Co+2, Cu+2, Ni+2, Cd+2, Zn+2, and Mn+2), cationic Methylene Blue (MB) dye, and anionic Methyl Orange (MO) dye, was studied and analysed. It was found that the Na-PA/CH hydrogel was the best performing hydrogel for heavy metal removal, removing more than 84% of all metals, followed by PAMPS/Na-PA which removed up to 70%. The best hydrogel mixture with both cationic and anionic dyes is PAMPS/CH, removing 90.1% and 85%, respectively. The proposed dye removal mechanism is electrostatic attraction between the dyes and the charged functional groups on the hydrogel’s surface. It is concluded that the use of Na-PA with CH for heavy metal removal yields better results than when using each hydrogel separately. For dye removal, it was found that combining PAMPS with CH creates a very promising hydrogel suitable for removing both anionic and cationic dyes, which is critical for industrial applications.
水凝胶是一种相对较新开发的材料,它引起了各个领域科学家的好奇心,特别是在废水处理应用方面。重金属离子和染料去除水凝胶因其易于使用、成本低、效率高、可生物降解和可重复使用而越来越受欢迎。评价和研究不同水凝胶材料对重金属离子和染料的吸附行为。所研究的水凝胶是聚2-丙烯酰胺-2-甲基丙烷磺酸(PAMPS)水凝胶、商品聚丙烯酸钠(Na-PA)、壳聚糖(CH)及其二元和三元混合物。研究了基于PAMPS和Na-PA的半互穿网络(IPN)。研究并分析了每种水凝胶对6种不同重金属(Co+2、Cu+2、Ni+2、Cd+2、Zn+2和Mn+2)、阳离子亚甲基蓝(MB)染料和阴离子甲基橙(MO)染料的吸附性能。结果表明,Na-PA/CH水凝胶对重金属的去除率最高,达84%以上;PAMPS/Na-PA水凝胶次之,去除率达70%。阳离子和阴离子染料的最佳水凝胶混合物为PAMPS/CH,去除率分别为90.1%和85%。提出的染料去除机制是染料与水凝胶表面带电官能团之间的静电吸引。综上所述,Na-PA与CH混合使用对重金属的去除效果优于单独使用两种水凝胶。在染料去除方面,研究人员发现PAMPS与CH的结合产生了一种非常有前途的水凝胶,适用于去除阴离子和阳离子染料,这对工业应用至关重要。
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引用次数: 0
A Comparative Study on Heavy Metal Removal Capacity of Different Hydrogels through Electrostatic Interactions and Ion-Exchange Mechanisms 不同水凝胶通过静电相互作用和离子交换机制去除重金属能力的比较研究
Pub Date : 2022-11-28 DOI: 10.2174/18741231-v16-e221128-2022-10
I. Ibrahim, M. Radwan, M. A. Sadek, Sohair A. Darwish, N. Mostafa
The use of hydrogel materials as adsorbents for heavy metal ions removal has grabbed the attention of several researchers due to its high removal capacity and generatability, thus providing both operational and economic efficiency. The design phase of fabricating the hydrogel material is a very critical step. A full knowledge of the effect of different potential functional groups and their interactions together can surely save resources and time. This study evaluates the removal capacity of different hydrogels whose functional groups remove via ion-exchange versus electrostatic interactions. The removal of Poly(2-Acrylamido-2-Methylpropane Sulphonic Acid) (PAMPS) was compared to that of sodium polyacrylate (NA-PA) hydrogels, which remove metals through electrostatic attraction and ion exchange respectively. It was found that the removal capacity of PAMPS, which has two anionic functional groups, is almost as good as one salt group available for ion exchange, reaching up to 92% and 87% respectively. A semi-interpenetrating network (IPN) based on both hydrogels showed slightly decreased removal capacity, almost to 80%, which was interpreted due to the loss of some active sites due to the inevitable attraction between PAMPS’s anionic functional groups and Na-PA’s salt group. The obtained results encourage the use of hydrogel materials with salt groups employing ion-exchange mechanism.
利用水凝胶材料作为吸附剂去除重金属离子,由于其高的去除能力和可再生性,从而提供了操作和经济效益,已经引起了许多研究者的关注。制备水凝胶材料的设计阶段是非常关键的一步。充分了解不同潜在官能团的作用及其相互作用,无疑可以节省资源和时间。本研究评估了通过离子交换和静电相互作用去除官能团的不同水凝胶的去除能力。对聚2-丙烯酰胺-2-甲基丙烷磺酸(PAMPS)和聚丙烯酸钠(NA-PA)水凝胶对金属的去除效果进行了比较,这两种水凝胶分别通过静电吸引和离子交换去除金属。结果表明,具有两个阴离子官能团的PAMPS的去除率可达92%和87%,几乎与用于离子交换的一个盐基相当。基于两种水凝胶的半互穿网络(IPN)的去除率略有下降,接近80%,这是由于PAMPS的阴离子官能团与Na-PA的盐基之间不可避免的吸引力导致一些活性位点的损失。所得结果鼓励采用离子交换机制的盐基水凝胶材料。
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引用次数: 0
Impact of Newtonian Heating on MHD Micropolar Fluid for the Influence of Heat Source 牛顿加热对MHD微极流体热源影响的研究
Pub Date : 2022-11-16 DOI: 10.2174/18741231-v16-e2208220
K. K. Prusty, S. Sahoo, S. Mishra
The current analysis deals with the flow of time-independent conducting micropolar fluid past a stretching sheet. Furthermore, the influences of magnetic field strength and heat sources are also discussed in this study. The current study is important for the growing applications of magnetism in various chemical systems like pumping, transportation, trapping, sorting, separation, etc. In addition, the objective of the present exploration is the consideration of Newtonian heating conditions. Transformation of nonlinear PDEs of the flow phenomena into nonlinear coupled ODEs is done using suitable similarity variables, and these are handled by employing the “Runge-Kutta fourth-order” scheme in association with the “shooting technique”. The influence of flow characteristics proposed in this study is analyzed via graphs. The engineering coefficients for various parameters are simulated numerically and deployed through the table. Finally, it was found that the rotational viscosity dominates over the fluid viscosity and enhances the momentum profile. An augmentation in the Prandtl number retards the fluid temperature and the application of applied magnetic field built up the resistance that retards fluid momentum.
当前的分析处理的是不依赖于时间的导电微极流体通过拉伸片的流动。此外,本文还讨论了磁场强度和热源的影响。目前的研究对于磁性在泵送、输送、捕获、分选、分离等各种化学系统中的日益广泛的应用具有重要意义。此外,本研究的目的是考虑牛顿加热条件。利用合适的相似变量将流动现象的非线性偏微分方程转化为非线性耦合偏微分方程,并结合“射击技术”采用“龙格-库塔四阶”格式进行处理。通过图形分析了本研究提出的流动特性的影响。对各参数下的工程系数进行了数值模拟,并通过表格展开。最后,发现旋转粘度比流体粘度占主导地位,并增强了动量分布。普朗特数的增大延缓了流体温度,外加磁场的施加形成了阻碍流体动量的阻力。
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引用次数: 1
On Orthogonal Polynomials and Finite Moment Problem 正交多项式与有限矩问题
Pub Date : 2022-11-01 DOI: 10.2174/18741231-v16-e2209260
F. Hjouj, M. Jouini
This paper is an improvement of a previous work on the problem recovering a function or probability density function from a finite number of its geometric moments, [1]. The previous worked solved the problem with the help of the B-Spline theory which is a great approach as long as the resulting linear system is not very large. In this work, two solution algorithms based on the approximate representation of the target probability distribution function via an orthogonal expansion are provided. One primary application of this theory is the reconstruction of the Particle Size Distribution (PSD), occurring in chemical engineering applications. Another application of this theory is the reconstruction of the Radon transform of an image at an unknown angle using the moments of the transform at known angles which leads to the reconstruction of the image form limited data. The aim is to recover a probability density function from a finite number of its geometric moments. The tool is the orthogonal expansion approach. The Shifted-Legendre Polynomials and the Chebyshev Polynomials as bases for the orthogonal expansion are used in this study. A high degree of accuracy has been obtained in recovering a function without facing a possible ill-conditioned linear system, which is the case with many typical approaches of solving the problem. In fact, for a normalized template function f on the interval [0, 1], and a reconstructed function ; the reconstruction accuracy is measured in two domains. One is the moment domain, in which the error (difference between the moments of f and the moments of ) is zero. The other measure is the standard difference in the norm -space ||f- || which can be ≈ 10-6 or less. This paper discusses the problem of recovering a function from a finite number of its geometric moments for the PSD application. Linear transformations were used, as needed, so that the function is supported on the unit interval [0, 1], or on [0, α] for some choice of α. This transformation forces the sequence of moments to vanish. Then, an orthogonal expansion of the Scaled Shifted Legendre Polynomials, as well as the Chebyshev Polynomials, are developed. The result shows good accuracy in recovering different types of synthetic functions. It is believed that up to fifteen moments, this approach is safe and reliable.
本文改进了先前关于从有限个数的几何矩中恢复函数或概率密度函数问题的工作。以前的工作是借助b样条理论来解决这个问题的,这是一个很好的方法,只要得到的线性系统不是很大。本文给出了两种基于目标概率分布函数的正交展开式近似表示的求解算法。该理论的一个主要应用是粒度分布(PSD)的重建,发生在化学工程应用中。该理论的另一个应用是利用已知角度变换的矩重建未知角度图像的拉东变换,从而从有限的数据中重建图像。目的是从有限数量的几何矩中恢复概率密度函数。该工具是正交展开法。本文采用平移勒让德多项式和切比雪夫多项式作为正交展开的基。在不面对可能的病态线性系统的情况下恢复函数获得了很高的精度,这是许多典型的解决问题的方法的情况。实际上,对于区间[0,1]上的归一化模板函数f,和重构函数;重构精度在两个域中测量。一个是矩域,其中误差(f的矩与的矩之差)为零。另一个测度是范数空间||f- ||的标准差分,它可以≈10-6或更小。本文讨论了PSD应用中从有限个数的几何矩中恢复函数的问题。根据需要使用线性变换,以便在单位区间[0,1]上支持函数,或者在[0,α]上支持函数(对于α的某些选择)。这种转换迫使时刻序列消失。然后,给出了缩放移位勒让德多项式和切比雪夫多项式的正交展开式。结果表明,该方法能较好地恢复不同类型的合成函数。相信在15分钟内,这种方法是安全可靠的。
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引用次数: 11
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The Open Chemical Engineering Journal
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